What element of art is being described by roughness and smoothness of the visual impact of an earthquake?

Match the proper term to its definition.

1. Protestant Reformation-The 16th century schism within Western Christianity initiated by Martin Luther, John Calvin, and other early Protestants; characterized by the objection to the doctrines, rituals, and ecclesiastical structure of the Roman Catholic Church and led to the creation of Protestant churches, which were outside of the control of the Vatican.

2. Iconoclasm-The belief in, participation in, or sanction of destroying religious icons and other symbols or monuments, usually with religious or political motives.

3. Mannerism-Style of art in Europe from c. 1520-1600. Mannerism came after the High Renaissance and before the Baroque. Not every artist painting during this period is considered a Mannerist artist.

4. Sack of Rome-A military event carried out on May 6, 1527, by the mutinous troops of Charles V, Holy Roman Emperor in Rome.

5. Refectory-A dining-hall especially in an institution such as a college or monastery.

6. Counter-Reformation-The period of Catholic revival beginning with the Council of Trent (1545-1563) and ending at the close of the Thirty Years' War (1648).

• Home
• About
• STEM Opportunities
• Sign In

Sample records for earthquakes suggests fractal

1. Fractal dynamics of earthquakes

   SciTech Connect

   Bak, P.; Chen, K.

   1995-05-01

   Many objects in nature, from mountain landscapes to electrical breakdown and turbulence, have a self-similar fractal spatial structure. It seems obvious that to understand the origin of self-similar structures, one must understand the nature of the dynamical processes that created them: temporal and spatial properties must necessarily be completely interwoven. This is particularly true for earthquakes, which have a variety of fractal aspects. The distribution of energy released during earthquakes is given by the Gutenberg-Richter power law. The distribution of epicenters appears to be fractal with dimension D {approx} 1--1.3. The number of after shocks decay as a function ofmore » time according to the Omori power law. There have been several attempts to explain the Gutenberg-Richter law by starting from a fractal distribution of faults or stresses. But this is a hen-and-egg approach: to explain the Gutenberg-Richter law, one assumes the existence of another power-law--the fractal distribution. The authors present results of a simple stick slip model of earthquakes, which evolves to a self-organized critical state. Emphasis is on demonstrating that empirical power laws for earthquakes indicate that the Earth`s crust is at the critical state, with no typical time, space, or energy scale. Of course the model is tremendously oversimplified; however in analogy with equilibrium phenomena they do not expect criticality to depend on details of the model (universality).« less

2. Fractals and Forecasting in Earthquakes and Finance

   NASA Astrophysics Data System (ADS)

   Rundle, J. B.; Holliday, J. R.; Turcotte, D. L.

   2011-12-01

   It is now recognized that Benoit Mandelbrot's fractals play a critical role in describing a vast range of physical and social phenomena. Here we focus on two systems, earthquakes and finance. Since 1942, earthquakes have been characterized by the Gutenberg-Richter magnitude-frequency relation, which in more recent times is often written as a moment-frequency power law. A similar relation can be shown to hold for financial markets. Moreover, a recent New York Times article, titled "A Richter Scale for the Markets" [1] summarized the emerging viewpoint that stock market crashes can be described with similar ideas as large and great earthquakes. The idea that stock market crashes can be related in any way to earthquake phenomena has its roots in Mandelbrot's 1963 work on speculative prices in commodities markets such as cotton [2]. He pointed out that Gaussian statistics did not account for the excessive number of booms and busts that characterize such markets. Here we show that both earthquakes and financial crashes can both be described by a common Landau-Ginzburg-type free energy model, involving the presence of a classical limit of stability, or spinodal. These metastable systems are characterized by fractal statistics near the spinodal. For earthquakes, the independent ("order") parameter is the slip deficit along a fault, whereas for the financial markets, it is financial leverage in place. For financial markets, asset values play the role of a free energy. In both systems, a common set of techniques can be used to compute the probabilities of future earthquakes or crashes. In the case of financial models, the probabilities are closely related to implied volatility, an important component of Black-Scholes models for stock valuations. [2] B. Mandelbrot, The variation of certain speculative prices, J. Business, 36, 294 (1963)

3. Characterizing spatial heterogeneity based on the b-value and fractal analyses of the 2015 Nepal earthquake sequence

   NASA Astrophysics Data System (ADS)

   Nampally, Subhadra; Padhy, Simanchal; Dimri, Vijay P.

   2018-01-01

   The nature of spatial distribution of heterogeneities in the source area of the 2015 Nepal earthquake is characterized based on the seismic b-value and fractal analysis of its aftershocks. The earthquake size distribution of aftershocks gives a b-value of 1.11 ± 0.08, possibly representing the highly heterogeneous and low stress state of the region. The aftershocks exhibit a fractal structure characterized by a spectrum of generalized dimensions, Dq varying from D2 = 1.66 to D22 = 0.11. The existence of a fractal structure suggests that the spatial distribution of aftershocks is not a random phenomenon, but it self-organizes into a critical state, exhibiting a scale-independent structure governed by a power-law scaling, where a small perturbation in stress is sufficient enough to trigger aftershocks. In order to obtain the bias in fractal dimensions resulting from finite data size, we compared the multifractal spectrum for the real data and random simulations. On comparison, we found that the lower limit of bias in D2 is 0.44. The similarity in their multifractal spectra suggests the lack of long-range correlation in the data, with an only weakly multifractal or a monofractal with a single correlation dimension D2 characterizing the data. The minimum number of events required for a multifractal process with an acceptable error is discussed. We also tested for a possible correlation between changes in D2 and energy released during the earthquakes. The values of D2 rise during the two largest earthquakes (M > 7.0) in the sequence. The b- and D2 values are related by D2 = 1.45 b that corresponds to the intermediate to large earthquakes. Our results provide useful constraints on the spatial distribution of b- and D2-values, which are useful for seismic hazard assessment in the aftershock area of a large earthquake.

4. Fractal analysis of earthquake swarms of Vogtland/NW-Bohemia intraplate seismicity

   NASA Astrophysics Data System (ADS)

   Mittag, Reinhard J.

   2003-03-01

   The special type of intraplate microseismicity with swarm-like occurrence of earthquakes within the Vogtland/NW-Bohemian Region is analysed to reveal the nature and the origin of the seismogenic regime. The long-term data set of continuous seismic monitoring since 1962, including more than 26000 events within a range of about 5 units of local magnitude, provides an unique database for statistical investigations. Most earthquakes occur in narrow hypocentral volumes (clusters) within the lower part of the upper crust, but also single event occurrence outside of spatial clusters is observed. Temporal distribution of events is concentrated in clusters (swarms), which last some days until few month in dependence of intensity. Since 1962 three strong swarms occurred (1962, 1985/86, 2000), including two seismic cycles. Spatial clusters are distributed along a fault system of regional extension (Leipzig-Regensburger Störung), which is supposed to act as the joint tectonic fracture zone for the whole seismogenic region. Seismicity is analysed by fractal analysis, suggesting a unifractal behaviour of seismicity and uniform character of seismotectonic regime for the whole region. A tendency of decreasing fractal dimension values is observed for temporal distribution of earthquakes, indicating an increasing degree of temporal clustering from swarm to swarm. Following the idea of earthquake triggering by magma intrusions and related fluid and gas release into the tectonically pre-stressed parts of the crust, a steady increased intensity of intrusion and/or fluid and gas release might account for that observation. Additionally, seismic parameters for Vogtland/NW-Bohemia intraplate seismicity are compared with an adequate data set of mining-induced seismicity in a nearby mine of Lubin/Poland and with synthetic data sets to evaluate parameter estimation. Due to different seismogenic regime of tectonic and induced seismicity, significant differences between b-values and temporal

5. Fractal analysis of the spatial distribution of earthquakes along the Hellenic Subduction Zone

   NASA Astrophysics Data System (ADS)

   Papadakis, Giorgos; Vallianatos, Filippos; Sammonds, Peter

   2014-05-01

   The Hellenic Subduction Zone (HSZ) is the most seismically active region in Europe. Many destructive earthquakes have taken place along the HSZ in the past. The evolution of such active regions is expressed through seismicity and is characterized by complex phenomenology. The understanding of the tectonic evolution process and the physical state of subducting regimes is crucial in earthquake prediction. In recent years, there is a growing interest concerning an approach to seismicity based on the science of complex systems (Papadakis et al., 2013; Vallianatos et al., 2012). In this study we calculate the fractal dimension of the spatial distribution of earthquakes along the HSZ and we aim to understand the significance of the obtained values to the tectonic and geodynamic evolution of this area. We use the external seismic sources provided by Papaioannou and Papazachos (2000) to create a dataset regarding the subduction zone. According to the aforementioned authors, we define five seismic zones. Then, we structure an earthquake dataset which is based on the updated and extended earthquake catalogue for Greece and the adjacent areas by Makropoulos et al. (2012), covering the period 1976-2009. The fractal dimension of the spatial distribution of earthquakes is calculated for each seismic zone and for the HSZ as a unified system using the box-counting method (Turcotte, 1997; Robertson et al., 1995; Caneva and Smirnov, 2004). Moreover, the variation of the fractal dimension is demonstrated in different time windows. These spatiotemporal variations could be used as an additional index to inform us about the physical state of each seismic zone. As a precursor in earthquake forecasting, the use of the fractal dimension appears to be a very interesting future work. Acknowledgements Giorgos Papadakis wish to acknowledge the Greek State Scholarships Foundation (IKY). References Caneva, A., Smirnov, V., 2004. Using the fractal dimension of earthquake distributions and the

6. Verifying the Dependence of Fractal Coefficients on Different Spatial Distributions

   NASA Astrophysics Data System (ADS)

   Gospodinov, Dragomir; Marekova, Elisaveta; Marinov, Alexander

   2010-01-01

   A fractal distribution requires that the number of objects larger than a specific size r has a power-law dependence on the size N(r) = C/rD∝r-D where D is the fractal dimension. Usually the correlation integral is calculated to estimate the correlation fractal dimension of epicentres. A `box-counting' procedure could also be applied giving the `capacity' fractal dimension. The fractal dimension can be an integer and then it is equivalent to a Euclidean dimension (it is zero of a point, one of a segment, of a square is two and of a cube is three). In general the fractal dimension is not an integer but a fractional dimension and there comes the origin of the term `fractal'. The use of a power-law to statistically describe a set of events or phenomena reveals the lack of a characteristic length scale, that is fractal objects are scale invariant. Scaling invariance and chaotic behavior constitute the base of a lot of natural hazards phenomena. Many studies of earthquakes reveal that their occurrence exhibits scale-invariant properties, so the fractal dimension can characterize them. It has first been confirmed that both aftershock rate decay in time and earthquake size distribution follow a power law. Recently many other earthquake distributions have been found to be scale-invariant. The spatial distribution of both regional seismicity and aftershocks show some fractal features. Earthquake spatial distributions are considered fractal, but indirectly. There are two possible models, which result in fractal earthquake distributions. The first model considers that a fractal distribution of faults leads to a fractal distribution of earthquakes, because each earthquake is characteristic of the fault on which it occurs. The second assumes that each fault has a fractal distribution of earthquakes. Observations strongly favour the first hypothesis. The fractal coefficients analysis provides some important advantages in examining earthquake spatial distribution, which are

7. (Multi)fractality of Earthquakes by use of Wavelet Analysis

   NASA Astrophysics Data System (ADS)

   Enescu, B.; Ito, K.; Struzik, Z. R.

   2002-12-01

   The fractal character of earthquakes' occurrence, in time, space or energy, has by now been established beyond doubt and is in agreement with modern models of seismicity. Moreover, the cascade-like generation process of earthquakes -with one "main" shock followed by many aftershocks, having their own aftershocks- may well be described through multifractal analysis, well suited for dealing with such multiplicative processes. The (multi)fractal character of seismicity has been analysed so far by using traditional techniques, like the box-counting and correlation function algorithms. This work introduces a new approach for characterising the multifractal patterns of seismicity. The use of wavelet analysis, in particular of the wavelet transform modulus maxima, to multifractal analysis was pioneered by Arneodo et al. (1991, 1995) and applied successfully in diverse fields, such as the study of turbulence, the DNA sequences or the heart rate dynamics. The wavelets act like a microscope, revealing details about the analysed data at different times and scales. We introduce and perform such an analysis on the occurrence time of earthquakes and show its advantages. In particular, we analyse shallow seismicity, characterised by a high aftershock "productivity", as well as intermediate and deep seismic activity, known for its scarcity of aftershocks. We examine as well declustered (aftershocks removed) versions of seismic catalogues. Our preliminary results show some degree of multifractality for the undeclustered, shallow seismicity. On the other hand, at large scales, we detect a monofractal scaling behaviour, clearly put in evidence for the declustered, shallow seismic activity. Moreover, some of the declustered sequences show a long-range dependent (LRD) behaviour, characterised by a Hurst exponent, H > 0.5, in contrast with the memory-less, Poissonian model. We demonstrate that the LRD is a genuine characteristic and is not an effect of the time series probability

8. Fractals in geology and geophysics

   NASA Technical Reports Server (NTRS)

   Turcotte, Donald L.

   1989-01-01

   The definition of a fractal distribution is that the number of objects N with a characteristic size greater than r scales with the relation N of about r exp -D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photograhs of many geological features is one indication of the wide applicability of scale invariance to geological problems; scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.

9. Is the co-seismic slip distribution fractal?

   NASA Astrophysics Data System (ADS)

   Milliner, Christopher; Sammis, Charles; Allam, Amir; Dolan, James

   2015-04-01

   Co-seismic along-strike slip heterogeneity is widely observed for many surface-rupturing earthquakes as revealed by field and high-resolution geodetic methods. However, this co-seismic slip variability is currently a poorly understood phenomenon. Key unanswered questions include: What are the characteristics and underlying causes of along-strike slip variability? Do the properties of slip variability change from fault-to-fault, along-strike or at different scales? We cross-correlate optical, pre- and post-event air photos using the program COSI-Corr to measure the near-field, surface deformation pattern of the 1992 Mw 7.3 Landers and 1999 Mw 7.1 Hector Mine earthquakes in high-resolution. We produce the co-seismic slip profiles of both events from over 1,000 displacement measurements and observe consistent along-strike slip variability. Although the observed slip heterogeneity seems apparently complex and disordered, a spectral analysis reveals that the slip distributions are indeed self-affine fractal i.e., slip exhibits a consistent degree of irregularity at all observable length scales, with a 'short-memory' and is not random. We find a fractal dimension of 1.58 and 1.75 for the Landers and Hector Mine earthquakes, respectively, indicating that slip is more heterogeneous for the Hector Mine event. Fractal slip is consistent with both dynamic and quasi-static numerical simulations that use non-planar faults, which in turn causes heterogeneous along-strike stress, and we attribute the observed fractal slip to fault surfaces of fractal roughness. As fault surfaces are known to smooth over geologic time due to abrasional wear and fracturing, we also test whether the fractal properties of slip distributions alters between earthquakes from immature to mature fault systems. We will present results that test this hypothesis by using the optical image correlation technique to measure historic, co-seismic slip distributions of earthquakes from structurally mature, large

10. Is volcanic phenomena of fractal nature?

    NASA Astrophysics Data System (ADS)

    Quevedo, R.; Lopez, D. A. L.; Alparone, S.; Hernandez Perez, P. A.; Sagiya, T.; Barrancos, J.; Rodriguez-Santana, A. A.; Ramos, A.; Calvari, S.; Perez, N. M.

    2016-12-01

    A particular resonance waveform pattern has been detected beneath different physical volcano manifestations from recent 2011-2012 period of volcanic unrest at El Hierro Island, Canary Islands, and also from other worldwide volcanoes with different volcanic typology. This mentioned pattern appears to be a fractal time dependent waveform repeated in different time scales (periods of time). This time dependent feature suggests this resonance as a new approach to volcano phenomena for predicting such interesting matters as earthquakes, gas emission, deformation etc. as this fractal signal has been discovered hidden in a wide typical volcanic parameters measurements. It is known that the resonance phenomenon occurring in nature usually denote a structure, symmetry or a subjacent law (Fermi et al., 1952; and later -about enhanced cross-sections symmetry in protons collisions), which, in this particular case, may be indicative of some physical interactions showing a sequence not completely chaotic but cyclic provided with symmetries. The resonance and fractal model mentioned allowed the authors to make predictions in cycles from a few weeks to months. In this work an equation for this waveform has been described and also correlations with volcanic parameters and fractal behavior demonstration have been performed, including also some suggestive possible explanations of this signal origin.

11. The cyclic and fractal seismic series preceding an mb 4.8 earthquake on 1980 February 14 near the Virgin Islands

    USGS Publications Warehouse

    Varnes, D.J.; Bufe, C.G.

    1996-01-01

    Seismic activity in the 10 months preceding the 1980 February 14, mb 4.8 earthquake in the Virgin Islands, reported on by Frankel in 1982, consisted of four principal cycles. Each cycle began with a relatively large event or series of closely spaced events, and the duration of the cycles progressively shortened by a factor of about 3/4. Had this regular shortening of the cycles been recognized prior to the earthquake, the time of the next episode of setsmicity (the main shock) might have been closely estimated 41 days in advance. That this event could be much larger than the previous events is indicated from time-to-failure analysis of the accelerating rise in released seismic energy, using a non-linear time- and slip-predictable foreshock model. Examination of the timing of all events in the sequence shows an even higher degree of order. Rates of seismicity, measured by consecutive interevent times, when plotted on an iteration diagram of a rate versus the succeeding rate, form a triangular circulating trajectory. The trajectory becomes an ascending helix if extended in a third dimension, time. This construction reveals additional and precise relations among the time intervals between times of relatively high or relatively low rates of seismic activity, including period halving and doubling. The set of 666 time intervals between all possible pairs of the 37 recorded events appears to be a fractal; the set of time points that define the intervals has a finite, non-integer correlation dimension of 0.70. In contrast, the average correlation dimension of 50 random sequences of 37 events is significantly higher, dose to 1.0. In a similar analysis, the set of distances between pairs of epicentres has a fractal correlation dimension of 1.52. Well-defined cycles, numerous precise ratios among time intervals, and a non-random temporal fractal dimension suggest that the seismic series is not a random process, but rather the product of a deterministic dynamic system.

12. Fractal 1/f Dynamics Suggest Entanglement of Measurement and Human Performance

    ERIC Educational Resources Information Center

    Holden, John G.; Choi, Inhyun; Amazeen, Polemnia G.; Van Orden, Guy

    2011-01-01

    Variability of repeated measurements in human performances exhibits fractal 1/f noise. Yet the relative strength of this fractal pattern varies widely across conditions, tasks, and individuals. Four experiments illustrate how subtle details of the conditions of measurement change the fractal patterns observed across task conditions. The results…

13. Fractal Dimension and b-VALUE Mapping in the NW Himalaya and Adjoining Regions, India

    NASA Astrophysics Data System (ADS)

    Kumar, Sushil; Sushil, Rama; Joshi, Deepika

    2011-07-01

    The northwest Himalayan region and the adjoining regions fall in the intense seismic zone. Earthquakes of varying intensities have hit the region in the past and similar threats remain imminent. In the last 105 years, the main earthquakes occurred in the North-Western (NW) Himalaya are as follows: the Kangra earthquake of 1905 (Ms = 8.0), the Kinnaur earthquake of 1975 (M = 6.8), Dharchula earthquake of 1980 (Mw = 6.5), Uttarkashi earthquake of 1991 (Mb = 6.6), Chamoli earthquake of 1999 (Mb = 6.8), and the Kashmir earthquake of 2005 (Mw = 7.6), which resulted in tremendous loss of life and property. The earthquake occurrence possesses non-linear relationship with respect to space and size. Fractal dimension and b-value are determined from 1221 well-located earthquakes, recorded at 10-19 WIHG seismic stations in NW Himalaya during 2004-2010 and at USGS stations during 1995-2003. A detailed study of the frequency-magnitude distribution and fractal dimension has been carried out and discussed in this paper.

14. Temporal and spatial variations of Gutenberg-Richter parameter and fractal dimension in Western Anatolia, Turkey

    NASA Astrophysics Data System (ADS)

    Bayrak, Erdem; Yılmaz, Şeyda; Bayrak, Yusuf

    2017-05-01

    The temporal and spatial variations of Gutenberg-Richter parameter (b-value) and fractal dimension (DC) during the period 1900-2010 in Western Anatolia was investigated. The study area is divided into 15 different source zones based on their tectonic and seismotectonic regimes. We calculated the temporal variation of b and DC values in each region using Zmap. The temporal variation of these parameters for the prediction of major earthquakes was calculated. The spatial distribution of these parameters is related to the stress levels of the faults. We observed that b and DC values change before the major earthquakes in the 15 seismic regions. To evaluate the spatial distribution of b and DC values, 0.50° × 0.50° grid interval were used. The b-values smaller than 0.70 are related to the Aegean Arc and Eskisehir Fault. The highest values are related to Sultandağı and Sandıklı Faults. Fractal correlation dimension varies from 1.65 to 2.60, which shows that the study area has a higher DC value. The lowest DC values are related to the joining area between Aegean and Cyprus arcs, Burdur-Fethiye fault zone. Some have concluded that b-values drop instantly before large shocks. Others suggested that temporally stable low b value zones identify future large earthquake locations. The results reveal that large earthquakes occur when b decreases and DC increases, suggesting that variation of b and DC can be used as an earthquake precursor. Mapping of b and DC values provide information about the state of stress in the region, i.e. lower b and higher DC values associated with epicentral areas of large earthquakes.

15. H-fractal seismic metamaterial with broadband low-frequency bandgaps

    NASA Astrophysics Data System (ADS)

    Du, Qiujiao; Zeng, Yi; Xu, Yang; Yang, Hongwu; Zeng, Zuoxun

    2018-03-01

    The application of metamaterial in civil engineering to achieve isolation of a building by controlling the propagation of seismic waves is a substantial challenge because seismic waves, a superposition of longitudinal and shear waves, are more complex than electromagnetic and acoustic waves. In this paper, we design a broadband seismic metamaterial based on H-shaped fractal pillars and report numerical simulation of band structures for seismic surface waves propagating. Comparative study on the band structures of H-fractal seismic metamaterials with different levels shows that a new level of fractal structure creates new band gap, widens the total band gaps and shifts the same band gap towards lower frequencies. Moreover, the vibration modes for H-fractal seismic metamaterials are computed and analyzed to clarify the mechanism of widening band gaps. A numerical investigation of seismic surface waves propagation on a 2D array of fractal unit cells on the surface of semi-infinite substrate is proposed to show the efficiency of earthquake shielding in multiple complete band gaps.

16. Fractals: To Know, to Do, to Simulate.

    ERIC Educational Resources Information Center

    Talanquer, Vicente; Irazoque, Glinda

    1993-01-01

    Discusses the development of fractal theory and suggests fractal aggregates as an attractive alternative for introducing fractal concepts. Describes methods for producing metallic fractals and a computer simulation for drawing fractals. (MVL)

17. Fractal analysis of INSAR and correlation with graph-cut based image registration for coastline deformation analysis: post seismic hazard assessment of the 2011 Tohoku earthquake region

    NASA Astrophysics Data System (ADS)

    Dutta, P. K.; Mishra, O. P.

    2012-04-01

    Satellite imagery for 2011 earthquake off the Pacific coast of Tohoku has provided an opportunity to conduct image transformation analyses by employing multi-temporal images retrieval techniques. In this study, we used a new image segmentation algorithm to image coastline deformation by adopting graph cut energy minimization framework. Comprehensive analysis of available INSAR images using coastline deformation analysis helped extract disaster information of the affected region of the 2011 Tohoku tsunamigenic earthquake source zone. We attempted to correlate fractal analysis of seismic clustering behavior with image processing analogies and our observations suggest that increase in fractal dimension distribution is associated with clustering of events that may determine the level of devastation of the region. The implementation of graph cut based image registration technique helps us to detect the devastation across the coastline of Tohoku through change of intensity of pixels that carries out regional segmentation for the change in coastal boundary after the tsunami. The study applies transformation parameters on remotely sensed images by manually segmenting the image to recovering translation parameter from two images that differ by rotation. Based on the satellite image analysis through image segmentation, it is found that the area of 0.997 sq km for the Honshu region was a maximum damage zone localized in the coastal belt of NE Japan forearc region. The analysis helps infer using matlab that the proposed graph cut algorithm is robust and more accurate than other image registration methods. The analysis shows that the method can give a realistic estimate for recovered deformation fields in pixels corresponding to coastline change which may help formulate the strategy for assessment during post disaster need assessment scenario for the coastal belts associated with damages due to strong shaking and tsunamis in the world under disaster risk mitigation programs.

18. Fractal electrodynamics via non-integer dimensional space approach

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2015-09-01

    Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.

19. High-frequency spectral falloff of earthquakes, fractal dimension of complex rupture, b value, and the scaling of strength on faults

    USGS Publications Warehouse

    Frankel, A.

    1991-01-01

    The high-frequency falloff ??-y of earthquake displacement spectra and the b value of aftershock sequences are attributed to the character of spatially varying strength along fault zones. I assume that the high frequency energy of a main shock is produced by a self-similar distribution of subevents, where the number of subevents with radii greater than R is proportional to R-D, D being the fractal dimension. In the model, an earthquake is composed of a hierarchical set of smaller earthquakes. The static stress drop is parameterized to be proportional to R??, and strength is assumed to be proportional to static stress drop. I find that a distribution of subevents with D = 2 and stress drop independent of seismic moment (?? = 0) produces a main shock with an ??-2 falloff, if the subevent areas fill the rupture area of the main shock. By equating subevents to "islands' of high stress of a random, self-similar stress field on a fault, I relate D to the scaling of strength on a fault, such that D = 2 - ??. Thus D = 2 corresponds to constant stress drop scaling (?? = 0) and scale-invariant fault strength. A self-similar model of aftershock rupture zones on a fault is used to determine the relationship between the b value, the size distribution of aftershock rupture zones, and the scaling of strength on a fault. -from Author

20. A Brief Historical Introduction to Fractals and Fractal Geometry

    ERIC Educational Resources Information Center

    Debnath, Lokenath

    2006-01-01

    This paper deals with a brief historical introduction to fractals, fractal dimension and fractal geometry. Many fractals including the Cantor fractal, the Koch fractal, the Minkowski fractal, the Mandelbrot and Given fractal are described to illustrate self-similar geometrical figures. This is followed by the discovery of dynamical systems and…

1. Order-fractal transitions in abstract paintings

   SciTech Connect

   Calleja, E.M. de la, E-mail: ; Cervantes, F.; Calleja, J. de la

   2016-08-15

   In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-ordermore » transition via the dark paint strokes in Pollock’s paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri’s Find. We obtained similar spectra for Teri’s Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition from Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.« less

2. Fractals, Coherence and Brain Dynamics

   NASA Astrophysics Data System (ADS)

   Vitiello, Giuseppe

   2010-11-01

   I show that the self-similarity property of deterministic fractals provides a direct connection with the space of the entire analytical functions. Fractals are thus described in terms of coherent states in the Fock-Bargmann representation. Conversely, my discussion also provides insights on the geometrical properties of coherent states: it allows to recognize, in some specific sense, fractal properties of coherent states. In particular, the relation is exhibited between fractals and q-deformed coherent states. The connection with the squeezed coherent states is also displayed. In this connection, the non-commutative geometry arising from the fractal relation with squeezed coherent states is discussed and the fractal spectral properties are identified. I also briefly discuss the description of neuro-phenomenological data in terms of squeezed coherent states provided by the dissipative model of brain and consider the fact that laboratory observations have shown evidence that self-similarity characterizes the brain background activity. This suggests that a connection can be established between brain dynamics and the fractal self-similarity properties on the basis of the relation discussed in this report between fractals and squeezed coherent states. Finally, I do not consider in this paper the so-called random fractals, namely those fractals obtained by randomization processes introduced in their iterative generation. Since self-similarity is still a characterizing property in many of such random fractals, my conjecture is that also in such cases there must exist a connection with the coherent state algebraic structure. In condensed matter physics, in many cases the generation by the microscopic dynamics of some kind of coherent states is involved in the process of the emergence of mesoscopic/macroscopic patterns. The discussion presented in this paper suggests that also fractal generation may provide an example of emergence of global features, namely long range

3. Some problems in fractal differential equations

   NASA Astrophysics Data System (ADS)

   Su, Weiyi

   2016-06-01

   Based upon the fractal calculus on local fields, or p-type calculus, or Gibbs-Butzer calculus ([1],[2]), we suggest a constructive idea for "fractal differential equations", beginning from some special examples to a general theory. However, this is just an original idea, it needs lots of later work to support. In [3], we show example "two dimension wave equations with fractal boundaries", and in this note, other examples, as well as an idea to construct fractal differential equations are shown.

4. Scaling in geology: landforms and earthquakes.

   PubMed Central

   Turcotte, D L

   1995-01-01

   Landforms and earthquakes appear to be extremely complex; yet, there is order in the complexity. Both satisfy fractal statistics in a variety of ways. A basic question is whether the fractal behavior is due to scale invariance or is the signature of a broadly applicable class of physical processes. Both landscape evolution and regional seismicity appear to be examples of self-organized critical phenomena. A variety of statistical models have been proposed to model landforms, including diffusion-limited aggregation, self-avoiding percolation, and cellular automata. Many authors have studied the behavior of multiple slider-block models, both in terms of the rupture of a fault to generate an earthquake and in terms of the interactions between faults associated with regional seismicity. The slider-block models exhibit a remarkably rich spectrum of behavior; two slider blocks can exhibit low-order chaotic behavior. Large numbers of slider blocks clearly exhibit self-organized critical behavior. Images Fig. 6 PMID:11607562

5. Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

   NASA Astrophysics Data System (ADS)

   Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

   2016-02-01

   One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

6. Detecting Blind Fault with Fractal and Roughness Factors from High Resolution LiDAR DEM at Taiwan

   NASA Astrophysics Data System (ADS)

   Cheng, Y. S.; Yu, T. T.

   2014-12-01

   There is no obvious fault scarp associated with blind fault. The traditional method of mapping this unrevealed geological structure is the cluster of seismicity. Neither the seismic event nor the completeness of cluster could be captured by network to chart the location of the entire possible active blind fault within short period of time. High resolution DEM gathered by LiDAR could denote actual terrain information despite the existence of plantation. 1-meter interval DEM of mountain region at Taiwan is utilized by fractal, entropy and roughness calculating with MATLAB code. By jointing these handing, the regions of non-sediment deposit are charted automatically. Possible blind fault associated with Chia-Sen earthquake at southern Taiwan is served as testing ground. GIS layer help in removing the difference from various geological formation, then multi-resolution fractal index is computed around the target region. The type of fault movement controls distribution of fractal index number. The scale of blind fault governs degree of change in fractal index. Landslide induced by rainfall and/or earthquake possesses larger degree of geomorphology alteration than blind fault; special treatment in removing these phenomena is required. Highly weathered condition at Taiwan should erase the possible trace remained upon DEM from the ruptured of blind fault while reoccurrence interval is higher than hundreds of years. This is one of the obstacle in finding possible blind fault at Taiwan.

7. Thermodynamics of photons on fractals.

   PubMed

   Akkermans, Eric; Dunne, Gerald V; Teplyaev, Alexander

   2010-12-03

   A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV(s) = U/d(s), where d(s) is the spectral dimension and V(s) defines the "spectral volume." For regular manifolds, V(s) coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.

8. Variability of fractal dimension of solar radio flux

   NASA Astrophysics Data System (ADS)

   Bhatt, Hitaishi; Sharma, Som Kumar; Trivedi, Rupal; Vats, Hari Om

   2018-04-01

   In the present communication, the variation of the fractal dimension of solar radio flux is reported. Solar radio flux observations on a day to day basis at 410, 1415, 2695, 4995, and 8800 MHz are used in this study. The data were recorded at Learmonth Solar Observatory, Australia from 1988 to 2009 covering an epoch of two solar activity cycles (22 yr). The fractal dimension is calculated for the listed frequencies for this period. The fractal dimension, being a measure of randomness, represents variability of solar radio flux at shorter time-scales. The contour plot of fractal dimension on a grid of years versus radio frequency suggests high correlation with solar activity. Fractal dimension increases with increasing frequency suggests randomness increases towards the inner corona. This study also shows that the low frequency is more affected by solar activity (at low frequency fractal dimension difference between solar maximum and solar minimum is 0.42) whereas, the higher frequency is less affected by solar activity (here fractal dimension difference between solar maximum and solar minimum is 0.07). A good positive correlation is found between fractal dimension averaged over all frequencies and yearly averaged sunspot number (Pearson's coefficient is 0.87).

9. Tectonic implications and seismicity triggering during the 2008 Baluchistan, Pakistan earthquake sequence

   NASA Astrophysics Data System (ADS)

   Yadav, R. B. S.; Gahalaut, V. K.; Chopra, Sumer; Shan, Bin

   2012-02-01

   A damaging and widely felt moderate earthquake (Mw 6.4) hit the rural, mountainous region of southwestern Pakistan on October 28, 2008. The main shock was followed by another earthquake of identical magnitude (Mw 6.4) on the next day. The spatial distribution of aftershocks and focal mechanism revealed a NW-SE striking rupture with right-lateral strike-slip motion which is sympathetic to the NNW-SSE striking active mapped Urghargai Fault. The occurrence of strike-slip earthquakes suggests that along with the thrust faults, strike slip faults too are present beneath the fold-and-thrust belt of Sulaiman-Kirthar ranges and accommodates some of the relative motion of the Indian and Eurasian plates. To assess the characteristics of this sequence, the statistical parameters like aftershocks temporal decay, b-value of G-R relationship, partitioning of radiated seismic energy due to aftershocks, and spatial fractal dimension (D-value) have been examined. The b-value is estimated as 1.03 ± 0.42 and suggests the tectonic genesis of the sequence and crustal heterogeneity within rock mass. The low p-value of 0.89 ± 0.07 implies slow decay of aftershocks activity which is probably an evidence for low surface heat flow. A value of spatial fractal dimension of 2.08 ± 0.02 indicates random spatial distribution and that the source is a two-dimensional plane filled-up by fractures. The static coseismic Coulomb stress changes due to the foreshock (Mw 5.3) were found to increase stress by more than 0.04 bars at the hypocenter of the main shock, thus promoting the failure. The cumulative coseismic Coulomb stress changes due to the foreshock and mainshocks suggest that most of the aftershocks occurred in the region of increased Coulomb stress, and to the SE to the mainshock rupture.

10. Music and fractals

    NASA Astrophysics Data System (ADS)

    Wuorinen, Charles

    2015-03-01

    Any of the arts may produce exemplars that have fractal characteristics. There may be fractal painting, fractal poetry, and the like. But these will always be specific instances, not necessarily displaying intrinsic properties of the art-medium itself. Only music, I believe, of all the arts possesses an intrinsically fractal character, so that its very nature is fractally determined. Thus, it is reasonable to assert that any instance of music is fractal...

11. Fractal Bread.

    ERIC Educational Resources Information Center

    Esbenshade, Donald H., Jr.

    1991-01-01

    Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)

12. Fractal Interrelationships in Field and Seismic Data

    SciTech Connect

    Wilson, T.H.; Dominic, Jovita; Halverson, Joel

    1997-10-01

    Size scaling interrelationships are evaluated in this study using a fractal model. Fractal models of several geologic variables are examined and include fracture patterns, reflection travel times, structural relief, drainage, topographic relief and active fault patterns. The fractal properties of structural relief inferred from seismic data and structural cross sections provide a quantitative means to characterize and compare complex structural patterns. Studies were conducted using seismic data from the Granny Creek oil field in the Appalachian Plateau. Previous studies of the field reveal that subtle detached structures present on the limb of a larger structure are associated with enhanced productionmore » from the field. Vertical increases of fractal dimension across the zone of detachment provide a measure of the extent to which detachment has occurred. The increases of fractal dimension are greatest in the more productive areas of the field. A result with equally important ramifications is that fracture systems do not appear to be intrinsically fractal as is often suggested in the literature. While examples of nearly identical patterns can be found at different scales supporting the idea of self-similarity, these examples are often taken from different areas and from different lithologies. Examination of fracture systems at different scales in the Valley and Ridge Province suggest that their distribution become increasingly sparse with scale reduction, and therefore are dissimilar or non-fractal. Box counting data in all cases failed to yield a fractal regime. The results obtained from this analysis bring into question the general applicability of reservoir simulations employing fractal models of fracture distribution. The same conclusions were obtained from the analysis of 1D fracture patterns such as those that might appear in a horizontal well.« less

13. Multifractal analysis of 2001 Mw 7 . 7 Bhuj earthquake sequence in Gujarat, Western India

    NASA Astrophysics Data System (ADS)

    Aggarwal, Sandeep Kumar; Pastén, Denisse; Khan, Prosanta Kumar

    2017-12-01

    The 2001 Mw 7 . 7 Bhuj mainshock seismic sequence in the Kachchh area, occurring during 2001 to 2012, has been analyzed using mono-fractal and multi-fractal dimension spectrum analysis technique. This region was characterized by frequent moderate shocks of Mw ≥ 5 . 0 for more than a decade since the occurrence of 2001 Bhuj earthquake. The present study is therefore important for precursory analysis using this sequence. The selected long-sequence has been investigated first time for completeness magnitude Mc 3.0 using the maximum curvature method. Multi-fractal Dq spectrum (Dq ∼ q) analysis was carried out using effective window-length of 200 earthquakes with a moving window of 20 events overlapped by 180 events. The robustness of the analysis has been tested by considering the magnitude completeness correction term of 0.2 to Mc 3.0 as Mc 3.2 and we have tested the error in the calculus of Dq for each magnitude threshold. On the other hand, the stability of the analysis has been investigated down to the minimum magnitude of Mw ≥ 2 . 6 in the sequence. The analysis shows the multi-fractal dimension spectrum Dq decreases with increasing of clustering of events with time before a moderate magnitude earthquake in the sequence, which alternatively accounts for non-randomness in the spatial distribution of epicenters and its self-organized criticality. Similar behavior is ubiquitous elsewhere around the globe, and warns for proximity of a damaging seismic event in an area. OS: Please confirm math roman or italics in abs.

14. Fractal nematic colloids

    NASA Astrophysics Data System (ADS)

    Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.

    2017-01-01

    Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.

15. Fractal nematic colloids

    PubMed Central

    Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.

    2017-01-01

    Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325

16. Geoethical suggestions for reducing risk of next (not only strong) earthquakes

    NASA Astrophysics Data System (ADS)

    Nemec, Vaclav

    2013-04-01

    Three relatively recent examples of earthquakes can be used as a background for suggesting geoethical views into any prediction accompanied by a risk analysis. ĹAquila earthquake (Italy - 2009): ĹAquila was largely destroyed by earthquakes in 1315, 1319, 1452, 1461, 1501, 1646, 1703 (until that time altogether about 3000 victims) and 1786 (about 6000 victims of this event only). The city was rebuilt and remained stable until October 2008, when tremors began again. From January 1 through April 5, 2009, additional 304 tremors were reported. When after measuring increased levels of radon emitted from the ground a local citizen (for many years working for the Italian National Institute of Astrophysics) predicted a major earthquake on Italian television, he was accused of being alarmist. Italy's National Commission for Prediction and Prevention of Major Risks met in L'Aquila for one hour on March 31, 2009, without really evaluating and characterising the risks that were present. On April 6 a 6.3 magnitude earthquake struck Aquila and nearby towns, killing 309 people and injuring more than 1,500. The quake also destroyed roughly 20,000 buildings, temporarily displacing another 65,000 people. In July 2010, prosecutor Fabio Picuti charged the Commission members with manslaughter and negligence for failing to warn the public of the impending risk. Many international organizations joined the chorus of criticism wrongly interpreting the accusation and sentence at the first stage as a problem of impossibility to predict earthquakes. - The Eyjafjallajokull volcano eruption (Iceland - 2010) is a reminder that in our globalized, interconnected world because of the increased sensibility of the new technology even a relatively small natural disaster may cause unexpected range of problems. - Earthquake and tsunami (Japan - 2011) - the most powerful known earthquake ever to have hit Japan on March 11. Whereas the proper earthquake with the magnitude of 9.0 has caused minimum of

17. Anisotropic fractal media by vector calculus in non-integer dimensional space

    SciTech Connect

    Tarasov, Vasily E., E-mail:

    2014-08-15

    A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensionalmore » space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.« less

18. Anisotropic fractal media by vector calculus in non-integer dimensional space

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2014-08-01

    A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

19. Long-range dependence in earthquake-moment release and implications for earthquake occurrence probability.

    PubMed

    Barani, Simone; Mascandola, Claudia; Riccomagno, Eva; Spallarossa, Daniele; Albarello, Dario; Ferretti, Gabriele; Scafidi, Davide; Augliera, Paolo; Massa, Marco

    2018-03-28

    Since the beginning of the 1980s, when Mandelbrot observed that earthquakes occur on 'fractal' self-similar sets, many studies have investigated the dynamical mechanisms that lead to self-similarities in the earthquake process. Interpreting seismicity as a self-similar process is undoubtedly convenient to bypass the physical complexities related to the actual process. Self-similar processes are indeed invariant under suitable scaling of space and time. In this study, we show that long-range dependence is an inherent feature of the seismic process, and is universal. Examination of series of cumulative seismic moment both in Italy and worldwide through Hurst's rescaled range analysis shows that seismicity is a memory process with a Hurst exponent H ≈ 0.87. We observe that H is substantially space- and time-invariant, except in cases of catalog incompleteness. This has implications for earthquake forecasting. Hence, we have developed a probability model for earthquake occurrence that allows for long-range dependence in the seismic process. Unlike the Poisson model, dependent events are allowed. This model can be easily transferred to other disciplines that deal with self-similar processes.

20. Fractal vector optical fields.

    PubMed

    Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

    2016-07-15

    We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.

1. A Fractal Dimension Survey of Active Region Complexity

   NASA Technical Reports Server (NTRS)

   McAteer, R. T. James; Gallagher, Peter; Ireland, Jack

   2005-01-01

   A new approach to quantifying the magnetic complexity of active regions using a fractal dimension measure is presented. This fully-automated approach uses full disc MDI magnetograms of active regions from a large data set (2742 days of the SoHO mission; 9342 active regions) to compare the calculated fractal dimension to both Mount Wilson classification and flare rate. The main Mount Wilson classes exhibit no distinct fractal dimension distribution, suggesting a self-similar nature of all active regions. Solar flare productivity exhibits an increase in both the frequency and GOES X-ray magnitude of flares from regions with higher fractal dimensions. Specifically a lower threshold fractal dimension of 1.2 and 1.25 exists as a necessary, but not sufficient, requirement for an active region to produce M- and X-class flares respectively .

2. Unification of two fractal families

   NASA Astrophysics Data System (ADS)

   Liu, Ying

   1995-06-01

   Barnsley and Hurd classify the fractal images into two families: iterated function system fractals (IFS fractals) and fractal transform fractals, or local iterated function system fractals (LIFS fractals). We will call IFS fractals, class 2 fractals and LIFS fractals, class 3 fractals. In this paper, we will unify these two approaches plus another family of fractals, the class 5 fractals. The basic idea is given as follows: a dynamical system can be represented by a digraph, the nodes in a digraph can be divided into two parts: transient states and persistent states. For bilevel images, a persistent node is a black pixel. A transient node is a white pixel. For images with more than two gray levels, a stochastic digraph is used. A transient node is a pixel with the intensity of 0. The intensity of a persistent node is determined by a relative frequency. In this way, the two families of fractals can be generated in a similar way. In this paper, we will first present a classification of dynamical systems and introduce the transformation based on digraphs, then we will unify the two approaches for fractal binary images. We will compare the decoding algorithms of the two families. Finally, we will generalize the discussion to continuous-tone images.

3. The fractal forest: fractal geometry and applications in forest science.

   Treesearch

   Nancy D. Lorimer; Robert G. Haight; Rolfe A. Leary

   1994-01-01

   Fractal geometry is a tool for describing and analyzing irregularity. Because most of what we measure in the forest is discontinuous, jagged, and fragmented, fractal geometry has potential for improving the precision of measurement and description. This study reviews the literature on fractal geometry and its applications to forest measurements.

4. Elasticity of fractal materials using the continuum model with non-integer dimensional space

   NASA Astrophysics Data System (ADS)

   Tarasov, Vasily E.

   2015-01-01

   Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

5. Fractal dimension and nonlinear dynamical processes

   NASA Astrophysics Data System (ADS)

   McCarty, Robert C.; Lindley, John P.

   1993-11-01

   Mandelbrot, Falconer and others have demonstrated the existence of dimensionally invariant geometrical properties of non-linear dynamical processes known as fractals. Barnsley defines fractal geometry as an extension of classical geometry. Such an extension, however, is not mathematically trivial Of specific interest to those engaged in signal processing is the potential use of fractal geometry to facilitate the analysis of non-linear signal processes often referred to as non-linear time series. Fractal geometry has been used in the modeling of non- linear time series represented by radar signals in the presence of ground clutter or interference generated by spatially distributed reflections around the target or a radar system. It was recognized by Mandelbrot that the fractal geometries represented by man-made objects had different dimensions than the geometries of the familiar objects that abound in nature such as leaves, clouds, ferns, trees, etc. The invariant dimensional property of non-linear processes suggests that in the case of acoustic signals (active or passive) generated within a dispersive medium such as the ocean environment, there exists much rich structure that will aid in the detection and classification of various objects, man-made or natural, within the medium.

6. Pond fractals in a tidal flat.

   PubMed

   Cael, B B; Lambert, Bennett; Bisson, Kelsey

   2015-11-01

   Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.

7. Pond fractals in a tidal flat

   NASA Astrophysics Data System (ADS)

   Cael, B. B.; Lambert, Bennett; Bisson, Kelsey

   2015-11-01

   Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.

8. Fractal astronomy.

   NASA Astrophysics Data System (ADS)

   Beech, M.

   1989-02-01

   The author discusses some of the more recent research on fractal astronomy and results presented in several astronomical studies. First, the large-scale structure of the universe is considered, while in another section one drops in scale to examine some of the smallest bodies in our solar system; the comets and meteoroids. The final section presents some thoughts on what influence the fractal ideology might have on astronomy, focusing particularly on the question recently raised by Kadanoff, "Fractals: where's the physics?"

9. Aesthetic Responses to Exact Fractals Driven by Physical Complexity

   PubMed Central

   Bies, Alexander J.; Blanc-Goldhammer, Daryn R.; Boydston, Cooper R.; Taylor, Richard P.; Sereno, Margaret E.

   2016-01-01

   Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality, symmetry, recursion, and the number of segments in the generator. Across two studies, a variety of fractal patterns were visually presented to human participants to determine the typical response to exact fractals. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as fractal dimension increases. For the majority of individuals, preference increased with dimension. We replicated these results for other exact fractal patterns in a second study. In the second study, we also tested the effects of symmetry and recursion by presenting asymmetric dragon fractals, symmetric dragon fractals, and Sierpinski carpets and Koch snowflakes, which have radial and mirror symmetry. We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in a pattern that lacked mirror or radial symmetry, while others were less discriminating. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a

10. Exploring fractal behaviour of blood oxygen saturation in preterm babies

    NASA Astrophysics Data System (ADS)

    Zahari, Marina; Hui, Tan Xin; Zainuri, Nuryazmin Ahmat; Darlow, Brian A.

    2017-04-01

    Recent evidence has been emerging that oxygenation instability in preterm babies could lead to an increased risk of retinal injury such as retinopathy of prematurity. There is a potential that disease severity could be better understood using nonlinear methods for time series data such as fractal theories [1]. Theories on fractal behaviours have been employed by researchers in various disciplines who were motivated to look into the behaviour or structure of irregular fluctuations in temporal data. In this study, an investigation was carried out to examine whether fractal behaviour could be detected in blood oxygen time series. Detection for the presence of fractals in oxygen data of preterm infants was performed using the methods of power spectrum, empirical probability distribution function and autocorrelation function. The results from these fractal identification methods indicate the possibility that these data exhibit fractal nature. Subsequently, a fractal framework for future research was suggested for oxygen time series.

11. Fractals for Geoengineering

    NASA Astrophysics Data System (ADS)

    Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga

    2016-04-01

    The effectiveness of fractal toolbox to capture the scaling or fractal probability distribution, and simply fractal statistics of main hydrocarbon reservoir attributes, was highlighted by Mandelbrot (1995) and confirmed by several researchers (Zhao et al., 2015). Notwithstanding, after more than twenty years, it's still common the opinion that fractals are not useful for the petroleum engineers and especially for Geoengineering (Corbett, 2012). In spite of this negative background, we have successfully applied the fractal and multifractal techniques to our project entitled "Petroleum Reservoir as a Fractal Reactor" (2013 up to now). The distinguishable feature of Fractal Reservoir is the irregular shapes and rough pore/solid distributions (Siler, 2007), observed across a broad range of scales (from SEM to seismic). At the beginning, we have accomplished the detailed analysis of Nelson and Kibler (2003) Catalog of Porosity and Permeability, created for the core plugs of siliciclastic rocks (around ten thousand data were compared). We enriched this Catalog by more than two thousand data extracted from the last ten years publications on PoroPerm (Corbett, 2012) in carbonates deposits, as well as by our own data from one of the PEMEX, Mexico, oil fields. The strong power law scaling behavior was documented for the major part of these data from the geological deposits of contrasting genesis. Based on these results and taking into account the basic principles and models of the Physics of Fractals, introduced by Per Back and Kan Chen (1989), we have developed new software (Muukíl Kaab), useful to process the multiscale geological and geophysical information and to integrate the static geological and petrophysical reservoir models to dynamic ones. The new type of fractal numerical model with dynamical power law relations among the shapes and sizes of mesh' cells was designed and calibrated in the studied area. The statistically sound power law relations were established

12. Vector calculus in non-integer dimensional space and its applications to fractal media

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2015-02-01

    We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

13. The role of the circadian system in fractal neurophysiological control

    PubMed Central

    Pittman-Polletta, Benjamin R.; Scheer, Frank A.J.L.; Butler, Matthew P.; Shea, Steven A.; Hu, Kun

    2013-01-01

    Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations - similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system’s role in fractal regulation. PMID:23573942

14. Fractal analysis of narwhal space use patterns.

    PubMed

    Laidre, Kristin L; Heide-Jørgensen, Mads P; Logsdon, Miles L; Hobbs, Roderick C; Dietz, Rune; VanBlaricom, Glenn R

    2004-01-01

    Quantifying animal movement in response to a spatially and temporally heterogeneous environment is critical to understanding the structural and functional landscape influences on population viability. Generalities of landscape structure can easily be extended to the marine environment, as marine predators inhabit a patchy, dynamic system, which influences animal choice and behavior. An innovative use of the fractal measure of complexity, indexing the linearity of movement paths over replicate temporal scales, was applied to satellite tracking data collected from narwhals (Monodon monoceros) (n = 20) in West Greenland and the eastern Canadian high Arctic. Daily movements of individuals were obtained using polar orbiting satellites via the ARGOS data location and collection system. Geographic positions were filtered to obtain a daily good quality position for each whale. The length of total pathway was measured over seven different temporal length scales (step lengths), ranging from one day to one week, and a seasonal mean was calculated. Fractal dimension (D) was significantly different between seasons, highest during summer (D = 1.61, SE 0.04) and winter (D = 1.69, SE 0.06) when whales made convoluted movements in focal areas. Fractal dimension was lowest during fall (D = 1.34, SE 0.03) when whales were migrating south ahead of the forming sea ice. There were no significant effects of size category or sex on fractal dimension by season. The greater linearity of movement during the migration period suggests individuals do not intensively forage on patchy resources until they arrive at summer or winter sites. The highly convoluted movements observed during summer and winter suggest foraging or searching efforts in localized areas. Significant differences between the fractal dimensions on two separate wintering grounds in Baffin Bay suggest differential movement patterns in response to the dynamics of sea ice.

15. Fractal pharmacokinetics.

    PubMed

    Pereira, Luis M

    2010-06-01

    Pharmacokinetics (PK) has been traditionally dealt with under the homogeneity assumption. However, biological systems are nowadays comprehensively understood as being inherently fractal. Specifically, the microenvironments where drug molecules interact with membrane interfaces, metabolic enzymes or pharmacological receptors, are unanimously recognized as unstirred, space-restricted, heterogeneous and geometrically fractal. Therefore, classical Fickean diffusion and the notion of the compartment as a homogeneous kinetic space must be revisited. Diffusion in fractal spaces has been studied for a long time making use of fractional calculus and expanding on the notion of dimension. Combining this new paradigm with the need to describe and explain experimental data results in defining time-dependent rate constants with a characteristic fractal exponent. Under the one-compartment simplification this strategy is straightforward. However, precisely due to the heterogeneity of the underlying biology, often at least a two-compartment model is required to address macroscopic data such as drug concentrations. This simple modelling step-up implies significant analytical and numerical complications. However, a few methods are available that make possible the original desideratum. In fact, exploring the full range of parametric possibilities and looking at different drugs and respective biological concentrations, it may be concluded that all PK modelling approaches are indeed particular cases of the fractal PK theory.

16. Reply to "Comment on 'Hydrodynamics of fractal continuum flow' and 'Map of fluid flow in fractal porous medium into fractal continuum flow'".

    PubMed

    Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

    2013-11-01

    The aim of this Reply is to elucidate the difference between the fractal continuum models used in the preceding Comment and the models of fractal continuum flow which were put forward in our previous articles [Phys. Rev. E 85, 025302(R) (2012); 85, 056314 (2012)]. In this way, some drawbacks of the former models are highlighted. Specifically, inconsistencies in the definitions of the fractal derivative, the Jacobian of transformation, the displacement vector, and angular momentum are revealed. The proper forms of the Reynolds' transport theorem and angular momentum principle for the fractal continuum are reaffirmed in a more illustrative manner. Consequently, we emphasize that in the absence of any internal angular momentum, body couples, and couple stresses, the Cauchy stress tensor in the fractal continuum should be symmetric. Furthermore, we stress that the approach based on the Cartesian product measured and used in the preceding Comment cannot be employed to study the path-connected fractals, such as a flow in a fractally permeable medium. Thus, all statements of our previous works remain unchallenged.

17. Scattering from fractals

    NASA Astrophysics Data System (ADS)

    Hurd, Alan J.

    The realization that structures in Nature often can be described by Mandelbrot's fractals has led to a revolution in many areas of physics. The interaction of waves with fractal systems has, understandably, become intensely studied since scattering is the method of choice to probe delicate fractal structures such as chainlike particle aggregates. Not all of these waves are electromagnetic. Neutron scattering, for example, is an important complementary tool to structural studies by X-ray and light scattering. Since the phenomenology of small-angle neutron scattering (SANS), as it is applied to fractal systems, is identical to that of small-angle X-ray scattering (SAXS), it falls within the scope of this paper.

18. Spatiotemporal distribution of Oklahoma earthquakes: Exploring relationships using a nearest-neighbor approach

    NASA Astrophysics Data System (ADS)

    Vasylkivska, Veronika S.; Huerta, Nicolas J.

    2017-07-01

    Determining the spatiotemporal characteristics of natural and induced seismic events holds the opportunity to gain new insights into why these events occur. Linking the seismicity characteristics with other geologic, geographic, natural, or anthropogenic factors could help to identify the causes and suggest mitigation strategies that reduce the risk associated with such events. The nearest-neighbor approach utilized in this work represents a practical first step toward identifying statistically correlated clusters of recorded earthquake events. Detailed study of the Oklahoma earthquake catalog's inherent errors, empirical model parameters, and model assumptions is presented. We found that the cluster analysis results are stable with respect to empirical parameters (e.g., fractal dimension) but were sensitive to epicenter location errors and seismicity rates. Most critically, we show that the patterns in the distribution of earthquake clusters in Oklahoma are primarily defined by spatial relationships between events. This observation is a stark contrast to California (also known for induced seismicity) where a comparable cluster distribution is defined by both spatial and temporal interactions between events. These results highlight the difficulty in understanding the mechanisms and behavior of induced seismicity but provide insights for future work.

19. Fractal and chaotic laws on seismic dissipated energy in an energy system of engineering structures

    NASA Astrophysics Data System (ADS)

    Cui, Yu-Hong; Nie, Yong-An; Yan, Zong-Da; Wu, Guo-You

    1998-09-01

    Fractal and chaotic laws of engineering structures are discussed in this paper, it means that the intrinsic essences and laws on dynamic systems which are made from seismic dissipated energy intensity E d and intensity of seismic dissipated energy moment I e are analyzed. Based on the intrinsic characters of chaotic and fractal dynamic system of E d and I e, three kinds of approximate dynamic models are rebuilt one by one: index autoregressive model, threshold autoregressive model and local-approximate autoregressive model. The innate laws, essences and systematic error of evolutional behavior I e are explained over all, the short-term behavior predictability and long-term behavior probability of which are analyzed in the end. That may be valuable for earthquake-resistant theory and analysis method in practical engineering structures.

20. Fractal Electronic Circuits Assembled From Nanoclusters

    NASA Astrophysics Data System (ADS)

    Fairbanks, M. S.; McCarthy, D.; Taylor, R. P.; Brown, S. A.

    2009-07-01

    Many patterns in nature can be described using fractal geometry. The effect of this fractal character is an array of properties that can include high internal connectivity, high dispersivity, and enhanced surface area to volume ratios. These properties are often desirable in applications and, consequently, fractal geometry is increasingly employed in technologies ranging from antenna to storm barriers. In this paper, we explore the application of fractal geometry to electrical circuits, inspired by the pervasive fractal structure of neurons in the brain. We show that, under appropriate growth conditions, nanoclusters of Sb form into islands on atomically flat substrates via a process close to diffusion-limited aggregation (DLA), establishing fractal islands that will form the basis of our fractal circuits. We perform fractal analysis of the islands to determine the spatial scaling properties (characterized by the fractal dimension, D) of the proposed circuits and demonstrate how varying growth conditions can affect D. We discuss fabrication approaches for establishing electrical contact to the fractal islands. Finally, we present fractal circuit simulations, which show that the fractal character of the circuit translates into novel, non-linear conduction properties determined by the circuit's D value.

1. Tidal triggering of earthquakes suggests poroelastic behavior on the San Andreas Fault

   DOE PAGES

   Delorey, Andrew A.; van der Elst, Nicholas J.; Johnson, Paul Allan

   2016-12-28

   Tidal triggering of earthquakes is hypothesized to provide quantitative information regarding the fault's stress state, poroelastic properties, and may be significant for our understanding of seismic hazard. To date, studies of regional or global earthquake catalogs have had only modest successes in identifying tidal triggering. We posit that the smallest events that may provide additional evidence of triggering go unidentified and thus we developed a technique to improve the identification of very small magnitude events. We identify events applying a method known as inter-station seismic coherence where we prioritize detection and discrimination over characterization. Here we show tidal triggering ofmore » earthquakes on the San Andreas Fault. We find the complex interaction of semi-diurnal and fortnightly tidal periods exposes both stress threshold and critical state behavior. Lastly, our findings reveal earthquake nucleation processes and pore pressure conditions – properties of faults that are difficult to measure, yet extremely important for characterizing earthquake physics and seismic hazards.« less

2. Tidal triggering of earthquakes suggests poroelastic behavior on the San Andreas Fault

   SciTech Connect

   Delorey, Andrew A.; van der Elst, Nicholas J.; Johnson, Paul Allan

   Tidal triggering of earthquakes is hypothesized to provide quantitative information regarding the fault's stress state, poroelastic properties, and may be significant for our understanding of seismic hazard. To date, studies of regional or global earthquake catalogs have had only modest successes in identifying tidal triggering. We posit that the smallest events that may provide additional evidence of triggering go unidentified and thus we developed a technique to improve the identification of very small magnitude events. We identify events applying a method known as inter-station seismic coherence where we prioritize detection and discrimination over characterization. Here we show tidal triggering ofmore » earthquakes on the San Andreas Fault. We find the complex interaction of semi-diurnal and fortnightly tidal periods exposes both stress threshold and critical state behavior. Lastly, our findings reveal earthquake nucleation processes and pore pressure conditions – properties of faults that are difficult to measure, yet extremely important for characterizing earthquake physics and seismic hazards.« less

3. Tidal triggering of earthquakes suggests poroelastic behavior on the San Andreas Fault

   USGS Publications Warehouse

   Delorey, Andrew; Van Der Elst, Nicholas; Johnson, Paul

   2017-01-01

   Tidal triggering of earthquakes is hypothesized to provide quantitative information regarding the fault's stress state, poroelastic properties, and may be significant for our understanding of seismic hazard. To date, studies of regional or global earthquake catalogs have had only modest successes in identifying tidal triggering. We posit that the smallest events that may provide additional evidence of triggering go unidentified and thus we developed a technique to improve the identification of very small magnitude events. We identify events applying a method known as inter-station seismic coherence where we prioritize detection and discrimination over characterization. Here we show tidal triggering of earthquakes on the San Andreas Fault. We find the complex interaction of semi-diurnal and fortnightly tidal periods exposes both stress threshold and critical state behavior. Our findings reveal earthquake nucleation processes and pore pressure conditions – properties of faults that are difficult to measure, yet extremely important for characterizing earthquake physics and seismic hazards.

4. Generalized statistical mechanics approaches to earthquakes and tectonics.

   PubMed

   Vallianatos, Filippos; Papadakis, Giorgos; Michas, Georgios

   2016-12-01

   Despite the extreme complexity that characterizes the mechanism of the earthquake generation process, simple empirical scaling relations apply to the collective properties of earthquakes and faults in a variety of tectonic environments and scales. The physical characterization of those properties and the scaling relations that describe them attract a wide scientific interest and are incorporated in the probabilistic forecasting of seismicity in local, regional and planetary scales. Considerable progress has been made in the analysis of the statistical mechanics of earthquakes, which, based on the principle of entropy, can provide a physical rationale to the macroscopic properties frequently observed. The scale-invariant properties, the (multi) fractal structures and the long-range interactions that have been found to characterize fault and earthquake populations have recently led to the consideration of non-extensive statistical mechanics (NESM) as a consistent statistical mechanics framework for the description of seismicity. The consistency between NESM and observations has been demonstrated in a series of publications on seismicity, faulting, rock physics and other fields of geosciences. The aim of this review is to present in a concise manner the fundamental macroscopic properties of earthquakes and faulting and how these can be derived by using the notions of statistical mechanics and NESM, providing further insights into earthquake physics and fault growth processes.

5. Fractals and foods.

   PubMed

   Peleg, M

   1993-01-01

   Fractal geometry and related concepts have had only a very minor impact on food research. The very few reported food applications deal mainly with the characterization of the contours of agglomerated instant coffee particles, the surface morphology of treated starch particles, the microstructure of casein gels viewed as a product limited diffusion aggregation, and the jagged mechanical signatures of crunchy dry foods. Fractal geometry describes objects having morphological features that are scale invariant. A demonstration of the self-similarity of fractal objects can be found in the familiar morphology of cauliflower and broccoli, both foods. Processes regulated by nonlinear dynamics can exhibit a chaotic behavior that has fractal characteristics. Examples are mixing of viscous fluids, turbulence, crystallization, agglomeration, diffusion, and possibly food spoilage.

6. Fractals in the Classroom

   ERIC Educational Resources Information Center

   Fraboni, Michael; Moller, Trisha

   2008-01-01

   Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…

7. Changes in Dimensionality and Fractal Scaling Suggest Soft-Assembled Dynamics in Human EEG

   PubMed Central

   Wiltshire, Travis J.; Euler, Matthew J.; McKinney, Ty L.; Butner, Jonathan E.

   2017-01-01

   Humans are high-dimensional, complex systems consisting of many components that must coordinate in order to perform even the simplest of activities. Many behavioral studies, especially in the movement sciences, have advanced the notion of soft-assembly to describe how systems with many components coordinate to perform specific functions while also exhibiting the potential to re-structure and then perform other functions as task demands change. Consistent with this notion, within cognitive neuroscience it is increasingly accepted that the brain flexibly coordinates the networks needed to cope with changing task demands. However, evaluation of various indices of soft-assembly has so far been absent from neurophysiological research. To begin addressing this gap, we investigated task-related changes in two distinct indices of soft-assembly using the established phenomenon of EEG repetition suppression. In a repetition priming task, we assessed evidence for changes in the correlation dimension and fractal scaling exponents during stimulus-locked event-related potentials, as a function of stimulus onset and familiarity, and relative to spontaneous non-task-related activity. Consistent with predictions derived from soft-assembly, results indicated decreases in dimensionality and increases in fractal scaling exponents from resting to pre-stimulus states and following stimulus onset. However, contrary to predictions, familiarity tended to increase dimensionality estimates. Overall, the findings support the view from soft-assembly that neural dynamics should become increasingly ordered as external task demands increase, and support the broader application of soft-assembly logic in understanding human behavior and electrophysiology. PMID:28919862

8. Fractal analysis of Xylella fastidiosa biofilm formation

   NASA Astrophysics Data System (ADS)

   Moreau, A. L. D.; Lorite, G. S.; Rodrigues, C. M.; Souza, A. A.; Cotta, M. A.

   2009-07-01

   We have investigated the growth process of Xylella fastidiosa biofilms inoculated on a glass. The size and the distance between biofilms were analyzed by optical images; a fractal analysis was carried out using scaling concepts and atomic force microscopy images. We observed that different biofilms show similar fractal characteristics, although morphological variations can be identified for different biofilm stages. Two types of structural patterns are suggested from the observed fractal dimensions Df. In the initial and final stages of biofilm formation, Df is 2.73±0.06 and 2.68±0.06, respectively, while in the maturation stage, Df=2.57±0.08. These values suggest that the biofilm growth can be understood as an Eden model in the former case, while diffusion-limited aggregation (DLA) seems to dominate the maturation stage. Changes in the correlation length parallel to the surface were also observed; these results were correlated with the biofilm matrix formation, which can hinder nutrient diffusion and thus create conditions to drive DLA growth.

9. Clusters of Earthquakes In The Southern of Iberian Peninsula

   NASA Astrophysics Data System (ADS)

   Posadas, A. M.; Luzón, F.; Vidal, F.

   The southern part of the Iberian Peninsula forms part of the western border of Eurasia- Africa plate boundary. This area is characterized by the occurrence of earthquakes of moderate magnitude (the maximum magnitude ranging from 4.5 to 5.5). From the point of view of seismic activity, this region is the most active one in he Iberian Penin- sula. Until earlier 80, only the National Seismic Network belonging to the National Geographic Institute monitores the activity in the south of Iberian Peninsula. From 1983 to the actuality, the Andalusian Seismic Network belonging to the Andalusian Geophysics Institute and Seismic Disaster Prevention, records the microseismicity of the area. Nowadays, the earthquakes catalogue used belongs to the Andalusian Insti- tute of Geophysics and Seismic Disaster Prevention and it counts on more than 20000 events registered from 1985 to 2001. Today, after 20 years of recording seismic ac- tivity, statistics analysis of the catalogue have sense. In this paper we present a first approach to the clustering properties of the seismicity in the south of the Iberian Penin- sula. The analysis carried out starts with the study of clustering properties (temporal and spatial properties) in the Southern of Iberian Peninsula seismicity to demonstrate, by using the Fractal Dimension of the temporal earthquake distribution and the Mor- ishita Index of the spatial distribution of earthquakes, that this seismicity is charac- terized by a tendency to form earthquake clusters, both spatial and temporal clusters. As an example, five seismogenetic areas of the zone are analyzed (Adra-Berja, Agron, Alboran, Antequera and Loja). This particular study of the series find out the b param- eter from the Gutenberg-Richter's Law (which characterizes the energetic relaxation of events), the p parameter from Omori's Law (that characterizes the temporal relax- ation of aftershocks) and the Fractal Dimension of the spatial distribution of earth- quakes (to find the

10. Fundamental Fractal Antenna Design Process

    NASA Astrophysics Data System (ADS)

    Zhu, L. P.; Kim, T. C.; Kakas, G. D.

    2017-12-01

    Antenna designers are always looking to come up with new ideas to push the envelope for new antennas, using a smaller volume while striving for higher bandwidth, wider bandwidth, and antenna gain. One proposed method of increasing bandwidth or shrinking antenna size is via the use of fractal geometry, which gives rise to fractal antennas. Fractals are those fun shapes that if one zooms in or zoom out, the structure is always the same. Design a new type of antenna based on fractal antenna design by utilize the Design of Experiment (DOE) will be shown in fractal antenna design process. Investigate conformal fractal antenna design for patterns, dimensions, and size, of the antenna but maintaining or improving the antenna performance. Research shows an antenna designer how to create basic requirements of the fractal antenna through a step by step process, and provides how to optimize the antenna design with the model prediction, lab measurement, and actual results from the compact range measurement on the antenna patterns.

11. Fractal Physiology and the Fractional Calculus: A Perspective

    PubMed Central

    West, Bruce J.

    2010-01-01

    This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a

12. Quantitative Earthquake Prediction on Global and Regional Scales

    NASA Astrophysics Data System (ADS)

    Kossobokov, Vladimir G.

    2006-03-01

    The Earth is a hierarchy of volumes of different size. Driven by planetary convection these volumes are involved into joint and relative movement. The movement is controlled by a wide variety of processes on and around the fractal mesh of boundary zones, and does produce earthquakes. This hierarchy of movable volumes composes a large non-linear dynamical system. Prediction of such a system in a sense of extrapolation of trajectory into the future is futile. However, upon coarse-graining the integral empirical regularities emerge opening possibilities of prediction in a sense of the commonly accepted consensus definition worked out in 1976 by the US National Research Council. Implications of the understanding hierarchical nature of lithosphere and its dynamics based on systematic monitoring and evidence of its unified space-energy similarity at different scales help avoiding basic errors in earthquake prediction claims. They suggest rules and recipes of adequate earthquake prediction classification, comparison and optimization. The approach has already led to the design of reproducible intermediate-term middle-range earthquake prediction technique. Its real-time testing aimed at prediction of the largest earthquakes worldwide has proved beyond any reasonable doubt the effectiveness of practical earthquake forecasting. In the first approximation, the accuracy is about 1-5 years and 5-10 times the anticipated source dimension. Further analysis allows reducing spatial uncertainty down to 1-3 source dimensions, although at a cost of additional failures-to-predict. Despite of limited accuracy a considerable damage could be prevented by timely knowledgeable use of the existing predictions and earthquake prediction strategies. The December 26, 2004 Indian Ocean Disaster seems to be the first indication that the methodology, designed for prediction of M8.0+ earthquakes can be rescaled for prediction of both smaller magnitude earthquakes (e.g., down to M5.5+ in Italy) and

13. The fractal heart — embracing mathematics in the cardiology clinic

    PubMed Central

    Captur, Gabriella; Karperien, Audrey L.; Hughes, Alun D.; Francis, Darrel P.; Moon, James C.

    2017-01-01

    For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care. PMID:27708281

14. Fractal design concepts for stretchable electronics.

    PubMed

    Fan, Jonathan A; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J; Huang, Yonggang; Rogers, John A

    2014-01-01

    Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

15. Fractal design concepts for stretchable electronics

    NASA Astrophysics Data System (ADS)

    Fan, Jonathan A.; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J.; Huang, Yonggang; Rogers, John A.

    2014-02-01

    Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

16. Non-extensivity and complexity in the earthquake activity at the West Corinth rift (Greece)

    NASA Astrophysics Data System (ADS)

    Michas, Georgios; Vallianatos, Filippos; Sammonds, Peter

    2013-04-01

    Earthquakes exhibit complex phenomenology that is revealed from the fractal structure in space, time and magnitude. For that reason other tools rather than the simple Poissonian statistics seem more appropriate to describe the statistical properties of the phenomenon. Here we use Non-Extensive Statistical Physics [NESP] to investigate the inter-event time distribution of the earthquake activity at the west Corinth rift (central Greece). This area is one of the most seismotectonically active areas in Europe, with an important continental N-S extension and high seismicity rates. NESP concept refers to the non-additive Tsallis entropy Sq that includes Boltzmann-Gibbs entropy as a particular case. This concept has been successfully used for the analysis of a variety of complex dynamic systems including earthquakes, where fractality and long-range interactions are important. The analysis indicates that the cumulative inter-event time distribution can be successfully described with NESP, implying the complexity that characterizes the temporal occurrences of earthquakes. Further on, we use the Tsallis entropy (Sq) and the Fischer Information Measure (FIM) to investigate the complexity that characterizes the inter-event time distribution through different time windows along the evolution of the seismic activity at the West Corinth rift. The results of this analysis reveal a different level of organization and clusterization of the seismic activity in time. Acknowledgments. GM wish to acknowledge the partial support of the Greek State Scholarships Foundation (IKY).

17. Electromagnetism on anisotropic fractal media

    NASA Astrophysics Data System (ADS)

    Ostoja-Starzewski, Martin

    2013-04-01

    Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.

18. Fractal geometry of music.

    PubMed Central

    Hsü, K J; Hsü, A J

    1990-01-01

    Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot. PMID:11607061

19. Generalized statistical mechanics approaches to earthquakes and tectonics

    PubMed Central

    Papadakis, Giorgos; Michas, Georgios

    2016-01-01

    Despite the extreme complexity that characterizes the mechanism of the earthquake generation process, simple empirical scaling relations apply to the collective properties of earthquakes and faults in a variety of tectonic environments and scales. The physical characterization of those properties and the scaling relations that describe them attract a wide scientific interest and are incorporated in the probabilistic forecasting of seismicity in local, regional and planetary scales. Considerable progress has been made in the analysis of the statistical mechanics of earthquakes, which, based on the principle of entropy, can provide a physical rationale to the macroscopic properties frequently observed. The scale-invariant properties, the (multi) fractal structures and the long-range interactions that have been found to characterize fault and earthquake populations have recently led to the consideration of non-extensive statistical mechanics (NESM) as a consistent statistical mechanics framework for the description of seismicity. The consistency between NESM and observations has been demonstrated in a series of publications on seismicity, faulting, rock physics and other fields of geosciences. The aim of this review is to present in a concise manner the fundamental macroscopic properties of earthquakes and faulting and how these can be derived by using the notions of statistical mechanics and NESM, providing further insights into earthquake physics and fault growth processes. PMID:28119548

20. The fractal geometry of life.

    PubMed

    Losa, Gabriele A

    2009-01-01

    The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".

1. Human physiological benefits of viewing nature: EEG responses to exact and statistical fractal patterns.

   PubMed

   Hagerhall, C M; Laike, T; Küller, M; Marcheschi, E; Boydston, C; Taylor, R P

   2015-01-01

   Psychological and physiological benefits of viewing nature have been extensively studied for some time. More recently it has been suggested that some of these positive effects can be explained by nature's fractal properties. Virtually all studies on human responses to fractals have used stimuli that represent the specific form of fractal geometry found in nature, i.e. statistical fractals, as opposed to fractal patterns which repeat exactly at different scales. This raises the question of whether human responses like preference and relaxation are being driven by fractal geometry in general or by the specific form of fractal geometry found in nature. In this study we consider both types of fractals (statistical and exact) and morph one type into the other. Based on the Koch curve, nine visual stimuli were produced in which curves of three different fractal dimensions evolve gradually from an exact to a statistical fractal. The patterns were shown for one minute each to thirty-five subjects while qEEG was continuously recorded. The results showed that the responses to statistical and exact fractals differ, and that the natural form of the fractal is important for inducing alpha responses, an indicator of a wakefully relaxed state and internalized attention.

2. Fractals in physiology and medicine

   NASA Technical Reports Server (NTRS)

   Goldberger, Ary L.; West, Bruce J.

   1987-01-01

   The paper demonstrates how the nonlinear concepts of fractals, as applied in physiology and medicine, can provide an insight into the organization of such complex structures as the tracheobronchial tree and heart, as well as into the dynamics of healthy physiological variability. Particular attention is given to the characteristics of computer-generated fractal lungs and heart and to fractal pathologies in these organs. It is shown that alterations in fractal scaling may underlie a number of pathophysiological disturbances, including sudden cardiac death syndromes.

3. Comparison of two fractal interpolation methods

   NASA Astrophysics Data System (ADS)

   Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo

   2017-03-01

   As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has

4. Noninvasive fractal biomarker of clock neurotransmitter disturbance in humans with dementia

   PubMed Central

   Hu, Kun; Harper, David G.; Shea, Steven A.; Stopa, Edward G.; Scheer, Frank A. J. L.

   2013-01-01

   Human motor activity has a robust, intrinsic fractal structure with similar patterns from minutes to hours. The fractal activity patterns appear to be physiologically important because the patterns persist under different environmental conditions but are significantly altered/reduced with aging and Alzheimer's disease (AD). Here, we report that dementia patients, known to have disrupted circadian rhythmicity, also have disrupted fractal activity patterns and that the disruption is more pronounced in patients with more amyloid plaques (a marker of AD severity). Moreover, the degree of fractal activity disruption is strongly associated with vasopressinergic and neurotensinergic neurons (two major circadian neurotransmitters) in postmortem suprachiasmatic nucleus (SCN), and can better predict changes of the two neurotransmitters than traditional circadian measures. These findings suggest that the SCN impacts human activity regulation at multiple time scales and that disrupted fractal activity may serve as a non-invasive biomarker of SCN neurodegeneration in dementia. PMID:23863985

5. Statistical validation of earthquake related observations

   NASA Astrophysics Data System (ADS)

   Kossobokov, V. G.

   2011-12-01

   The confirmed fractal nature of earthquakes and their distribution in space and time implies that many traditional estimations of seismic hazard (from term-less to short-term ones) are usually based on erroneous assumptions of easy tractable or, conversely, delicately-designed models. The widespread practice of deceptive modeling considered as a "reasonable proxy" of the natural seismic process leads to seismic hazard assessment of unknown quality, which errors propagate non-linearly into inflicted estimates of risk and, eventually, into unexpected societal losses of unacceptable level. The studies aimed at forecast/prediction of earthquakes must include validation in the retro- (at least) and, eventually, in prospective tests. In the absence of such control a suggested "precursor/signal" remains a "candidate", which link to target seismic event is a model assumption. Predicting in advance is the only decisive test of forecast/predictions and, therefore, the score-card of any "established precursor/signal" represented by the empirical probabilities of alarms and failures-to-predict achieved in prospective testing must prove statistical significance rejecting the null-hypothesis of random coincidental occurrence in advance target earthquakes. We reiterate suggesting so-called "Seismic Roulette" null-hypothesis as the most adequate undisturbed random alternative accounting for the empirical spatial distribution of earthquakes: (i) Consider a roulette wheel with as many sectors as the number of earthquake locations from a sample catalog representing seismic locus, a sector per each location and (ii) make your bet according to prediction (i.e., determine, which locations are inside area of alarm, and put one chip in each of the corresponding sectors); (iii) Nature turns the wheel; (iv) accumulate statistics of wins and losses along with the number of chips spent. If a precursor in charge of prediction exposes an imperfection of Seismic Roulette then, having in mind

6. About Schrödinger Equation on Fractals Curves Imbedding in R 3

   NASA Astrophysics Data System (ADS)

   Golmankhaneh, Alireza Khalili; Golmankhaneh, Ali Khalili; Baleanu, Dumitru

   2015-04-01

   In this paper we introduced the quantum mechanics on fractal time-space. In a suggested formalism the time and space vary on Cantor-set and Von-Koch curve, respectively. Using Feynman path method in quantum mechanics and F α -calculus we find Schrëdinger equation on on fractal time-space. The Hamiltonian and momentum fractal operator has been indicated. More, the continuity equation and the probability density is given in view of F α -calculus.

7. Earthquake hazard and risk assessment based on Unified Scaling Law for Earthquakes: Greater Caucasus and Crimea

   NASA Astrophysics Data System (ADS)

   Kossobokov, Vladimir G.; Nekrasova, Anastasia K.

   2018-05-01

   We continue applying the general concept of seismic risk analysis in a number of seismic regions worldwide by constructing regional seismic hazard maps based on morphostructural analysis, pattern recognition, and the Unified Scaling Law for Earthquakes (USLE), which generalizes the Gutenberg-Richter relationship making use of naturally fractal distribution of earthquake sources of different size in a seismic region. The USLE stands for an empirical relationship log10 N(M, L) = A + B·(5 - M) + C·log10 L, where N(M, L) is the expected annual number of earthquakes of a certain magnitude M within a seismically prone area of linear dimension L. We use parameters A, B, and C of USLE to estimate, first, the expected maximum magnitude in a time interval at seismically prone nodes of the morphostructural scheme of the region under study, then map the corresponding expected ground shaking parameters (e.g., peak ground acceleration, PGA, or macro-seismic intensity). After a rigorous verification against the available seismic evidences in the past (usually, the observed instrumental PGA or the historically reported macro-seismic intensity), such a seismic hazard map is used to generate maps of specific earthquake risks for population, cities, and infrastructures (e.g., those based on census of population, buildings inventory). The methodology of seismic hazard and risk assessment is illustrated by application to the territory of Greater Caucasus and Crimea.

8. Turbulence Enhancement by Fractal Square Grids: Effects of the Number of Fractal Scales

   NASA Astrophysics Data System (ADS)

   Omilion, Alexis; Ibrahim, Mounir; Zhang, Wei

   2017-11-01

   Fractal square grids offer a unique solution for passive flow control as they can produce wakes with a distinct turbulence intensity peak and a prolonged turbulence decay region at the expense of only minimal pressure drop. While previous studies have solidified this characteristic of fractal square grids, how the number of scales (or fractal iterations N) affect turbulence production and decay of the induced wake is still not well understood. The focus of this research is to determine the relationship between the fractal iteration N and the turbulence produced in the wake flow using well-controlled water-tunnel experiments. Particle Image Velocimetry (PIV) is used to measure the instantaneous velocity fields downstream of four different fractal grids with increasing number of scales (N = 1, 2, 3, and 4) and a conventional single-scale grid. By comparing the turbulent scales and statistics of the wake, we are able to determine how each iteration affects the peak turbulence intensity and the production/decay of turbulence from the grid. In light of the ability of these fractal grids to increase turbulence intensity with low pressure drop, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.

9. Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics.

   PubMed

   Rhea, Christopher K; Kiefer, Adam W; D'Andrea, Susan E; Warren, William H; Aaron, Roy K

   2014-08-01

   Fractal patterns characterize healthy biological systems and are considered to reflect the ability of the system to adapt to varying environmental conditions. Previous research has shown that fractal patterns in gait are altered following natural aging or disease, and this has potential negative consequences for gait adaptability that can lead to increased risk of injury. However, the flexibility of a healthy neurological system to exhibit different fractal patterns in gait has yet to be explored, and this is a necessary step toward understanding human locomotor control. Fifteen participants walked for 15min on a treadmill, either in the absence of a visual stimulus or while they attempted to couple the timing of their gait with a visual metronome that exhibited a persistent fractal pattern (contained long-range correlations) or a random pattern (contained no long-range correlations). The stride-to-stride intervals of the participants were recorded via analog foot pressure switches and submitted to detrended fluctuation analysis (DFA) to determine if the fractal patterns during the visual metronome conditions differed from the baseline (no metronome) condition. DFA α in the baseline condition was 0.77±0.09. The fractal patterns in the stride-to-stride intervals were significantly altered when walking to the fractal metronome (DFA α=0.87±0.06) and to the random metronome (DFA α=0.61±0.10) (both p<.05 when compared to the baseline condition), indicating that a global change in gait dynamics was observed. A variety of strategies were identified at the local level with a cross-correlation analysis, indicating that local behavior did not account for the consistent global changes. Collectively, the results show that a gait dynamics can be shifted in a prescribed manner using a visual stimulus and the shift appears to be a global phenomenon. Copyright © 2014 Elsevier B.V. All rights reserved.

10. Evolution of fractality in space plasmas of interest to geomagnetic activity

    NASA Astrophysics Data System (ADS)

    Muñoz, Víctor; Domínguez, Macarena; Alejandro Valdivia, Juan; Good, Simon; Nigro, Giuseppina; Carbone, Vincenzo

    2018-03-01

    We studied the temporal evolution of fractality for geomagnetic activity, by calculating fractal dimensions from the Dst data and from a magnetohydrodynamic shell model for turbulent magnetized plasma, which may be a useful model to study geomagnetic activity under solar wind forcing. We show that the shell model is able to reproduce the relationship between the fractal dimension and the occurrence of dissipative events, but only in a certain region of viscosity and resistivity values. We also present preliminary results of the application of these ideas to the study of the magnetic field time series in the solar wind during magnetic clouds, which suggest that it is possible, by means of the fractal dimension, to characterize the complexity of the magnetic cloud structure.

11. Contour fractal analysis of grains

    NASA Astrophysics Data System (ADS)

    Guida, Giulia; Casini, Francesca; Viggiani, Giulia MB

    2017-06-01

    Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]). Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.

12. Fractal density modeling of crustal heterogeneity from the KTB deep hole

    NASA Astrophysics Data System (ADS)

    Chen, Guoxiong; Cheng, Qiuming

    2017-03-01

    Fractal or multifractal concepts have significantly enlightened our understanding of crustal heterogeneity. Much attention has focused on 1/f scaling natures of physicochemical heterogeneity of Earth crust from fractal increment perspective. In this study, fractal density model from fractal clustering point of view is used to characterize the scaling behaviors of heterogeneous sources recorded at German Continental Deep Drilling Program (KTB) main hole, and of special contribution is the local and global multifractal analysis revisited by using Haar wavelet transform (HWT). Fractal density modeling of mass accumulation generalizes the unit of rock density from integer (e.g., g/cm3) to real numbers (e.g., g/cmα), so that crustal heterogeneities with respect to source accumulation are quantified by singularity strength of fractal density in α-dimensional space. From that perspective, we found that the bulk densities of metamorphic rocks exhibit fractal properties but have a weak multifractality, decreasing with the depth. The multiscaling natures of chemical logs also have been evidenced, and the observed distinct fractal laws for mineral contents are related to their different geochemical behaviors within complex lithological context. Accordingly, scaling distributions of mineral contents have been recognized as a main contributor to the multifractal natures of heterogeneous density for low-porosity crystalline rocks. This finally allows us to use de Wijs cascade process to explain the mechanism of fractal density. In practice, the proposed local singularity analysis based on HWT is suggested as an attractive high-pass filtering to amplify weak signatures of well logs as well as to delineate microlithological changes.

13. Fractal scaling in bottlenose dolphin (Tursiops truncatus) echolocation: A case study

    NASA Astrophysics Data System (ADS)

    Perisho, Shaun T.; Kelty-Stephen, Damian G.; Hajnal, Alen; Houser, Dorian; Kuczaj, Stan A., II

    2016-02-01

    Fractal scaling patterns, which entail a power-law relationship between magnitude of fluctuations in a variable and the scale at which the variable is measured, have been found in many aspects of human behavior. These findings have led to advances in behavioral models (e.g. providing empirical support for cascade-driven theories of cognition) and have had practical medical applications (e.g. providing new methods for early diagnosis of medical conditions). In the present paper, fractal analysis is used to investigate whether similar fractal scaling patterns exist in inter-click interval and peak-peak amplitude measurements of bottlenose dolphin click trains. Several echolocation recordings taken from two male bottlenose dolphins were analyzed using Detrended Fluctuation Analysis and Higuchi's (1988) method for determination of fractal dimension. Both animals were found to exhibit fractal scaling patterns near what is consistent with persistent long range correlations. These findings suggest that recent advances in human cognition and medicine may have important parallel applications to echolocation as well.

14. A fractal analysis of quaternary, Cenozoic-Mesozoic, and Late Pennsylvanian sea level changes

    NASA Technical Reports Server (NTRS)

    Hsui, Albert T.; Rust, Kelly A.; Klein, George D.

    1993-01-01

    Sea level changes are related to both climatic variations and tectonic movements. The fractal dimensions of several sea level curves were compared to a modern climatic fractal dimension of 1.26 established for annual precipitation records. A similar fractal dimension (1.22) based on delta(O-18/O-16) in deep-sea sediments has been suggested to characterize climatic change during the past 2 m.y. Our analysis indicates that sea level changes over the past 150,000 to 250,000 years also exhibit comparable fractal dimensions. Sea level changes for periods longer than about 30 m.y. are found to produce fractal dimensions closer to unity and Missourian (Late Pennsylvanian) sea level changes yield a fractal dimension of 1.41. The fact that these sea level curves all possess fractal dimensions less than 1.5 indicates that sea level changes exhibit nonperiodic, long-run persistence. The different fractal dimensions calculated for the various time periods could be the result of a characteristic overprinting of the sediment recored by prevailing processes during deposition. For example, during the Quaternary, glacio-eustatic sea level changes correlate well with the present climatic signature. During the Missourian, however, mechanisms such as plate reorganization may have dominated, resulting in a significantly different fractal dimension.

15. Fractal Analyses of High-Resolution Cloud Droplet Measurements.

    NASA Astrophysics Data System (ADS)

    Malinowski, Szymon P.; Leclerc, Monique Y.; Baumgardner, Darrel G.

    1994-02-01

    Fractal analyses of individual cloud droplet distributions using aircraft measurements along one-dimensional horizontal cross sections through clouds are performed. Box counting and cluster analyses are used to determine spatial scales of inhomogeneity of cloud droplet spacing. These analyses reveal that droplet spatial distributions do not exhibit a fractal behavior. A high variability in local droplet concentration in cloud volumes undergoing mixing was found. In these regions, thin filaments of cloudy air with droplet concentration close to those observed in cloud cores were found. Results suggest that these filaments may be anisotropic. Additional box counting analyses performed for various classes of cloud droplet diameters indicate that large and small droplets are similarly distributed, except for the larger characteristic spacing of large droplets.A cloud-clear air interface defined by a certain threshold of total droplet count (TDC) was investigated. There are indications that this interface is a convoluted surface of a fractal nature, at least in actively developing cumuliform clouds. In contrast, TDC in the cloud interior does not have fractal or multifractal properties. Finally a random Cantor set (RCS) was introduced as a model of a fractal process with an ill-defined internal scale. A uniform measure associated with the RCS after several generations was introduced to simulate the TDC records. Comparison of the model with real TDC records indicates similar properties of both types of data series.

16. Fractal reaction kinetics.

    PubMed

    Kopelman, R

    1988-09-23

    Classical reaction kinetics has been found to be unsatisfactory when the reactants are spatially constrained on the microscopic level by either walls, phase boundaries, or force fields. Recently discovered theories of heterogeneous reaction kinetics have dramatic consequences, such as fractal orders for elementary reactions, self-ordering and self-unmixing of reactants, and rate coefficients with temporal "memories." The new theories were needed to explain the results of experiments and supercomputer simulations of reactions that were confined to low dimensions or fractal dimensions or both. Among the practical examples of "fractal-like kinetics" are chemical reactions in pores of membranes, excitation trapping in molecular aggregates, exciton fusion in composite materials, and charge recombination in colloids and clouds.

17. Earthquake Hazard and Risk Assessment based on Unified Scaling Law for Earthquakes: Altai-Sayan Region

    NASA Astrophysics Data System (ADS)

    Kossobokov, V. G.; Nekrasova, A.

    2017-12-01

    We continue applying the general concept of seismic risk analysis in a number of seismic regions worldwide by constructing regional seismic hazard maps based on morphostructural analysis, pattern recognition, and the Unified Scaling Law for Earthquakes, USLE, which generalizes the Gutenberg-Richter relationship making use of naturally fractal distribution of earthquake sources of different size in a seismic region. The USLE stands for an empirical relationship log10N(M, L) = A + B·(5 - M) + C·log10L, where N(M, L) is the expected annual number of earthquakes of a certain magnitude M within an seismically prone area of linear dimension L. We use parameters A, B, and C of USLE to estimate, first, the expected maximum credible magnitude in a time interval at seismically prone nodes of the morphostructural scheme of the region under study, then map the corresponding expected ground shaking parameters (e.g. peak ground acceleration, PGA, or macro-seismic intensity etc.). After a rigorous testing against the available seismic evidences in the past (usually, the observed instrumental PGA or the historically reported macro-seismic intensity), such a seismic hazard map is used to generate maps of specific earthquake risks for population, cities, and infrastructures (e.g., those based on census of population, buildings inventory, etc.). This, USLE based, methodology of seismic hazard and risks assessment is applied to the territory of Altai-Sayan Region, of Russia. The study supported by the Russian Science Foundation Grant No. 15-17-30020.

18. Chaos, Fractals, and Polynomials.

    ERIC Educational Resources Information Center

    Tylee, J. Louis; Tylee, Thomas B.

    1996-01-01

    Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

19. Fractals in biology and medicine

    NASA Technical Reports Server (NTRS)

    Havlin, S.; Buldyrev, S. V.; Goldberger, A. L.; Mantegna, R. N.; Ossadnik, S. M.; Peng, C. K.; Simons, M.; Stanley, H. E.

    1995-01-01

    Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent alpha quantifying these long-range correlations ("fractal complexity") is smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the normal heart is characterized by long-range "anticorrelations" which are absent in the diseased heart.

20. Fractal-Based Image Analysis In Radiological Applications

    NASA Astrophysics Data System (ADS)

    Dellepiane, S.; Serpico, S. B.; Vernazza, G.; Viviani, R.

    1987-10-01

    We present some preliminary results of a study aimed to assess the actual effectiveness of fractal theory and to define its limitations in the area of medical image analysis for texture description, in particular, in radiological applications. A general analysis to select appropriate parameters (mask size, tolerance on fractal dimension estimation, etc.) has been performed on synthetically generated images of known fractal dimensions. Moreover, we analyzed some radiological images of human organs in which pathological areas can be observed. Input images were subdivided into blocks of 6x6 pixels; then, for each block, the fractal dimension was computed in order to create fractal images whose intensity was related to the D value, i.e., texture behaviour. Results revealed that the fractal images could point out the differences between normal and pathological tissues. By applying histogram-splitting segmentation to the fractal images, pathological areas were isolated. Two different techniques (i.e., the method developed by Pentland and the "blanket" method) were employed to obtain fractal dimension values, and the results were compared; in both cases, the appropriateness of the fractal description of the original images was verified.

1. Langevin Equation on Fractal Curves

   NASA Astrophysics Data System (ADS)

   Satin, Seema; Gangal, A. D.

   2016-07-01

   We analyze random motion of a particle on a fractal curve, using Langevin approach. This involves defining a new velocity in terms of mass of the fractal curve, as defined in recent work. The geometry of the fractal curve, plays an important role in this analysis. A Langevin equation with a particular model of noise is proposed and solved using techniques of the Fα-Calculus.

2. Emergence of fractal scaling in complex networks

   NASA Astrophysics Data System (ADS)

   Wei, Zong-Wen; Wang, Bing-Hong

   2016-09-01

   Some real-world networks are shown to be fractal or self-similar. It is widespread that such a phenomenon originates from the repulsion between hubs or disassortativity. Here we show that this common belief fails to capture the causality. Our key insight to address it is to pinpoint links critical to fractality. Those links with small edge betweenness centrality (BC) constitute a special architecture called fractal reference system, which gives birth to the fractal structure of those reported networks. In contrast, a small amount of links with high BC enable small-world effects, hiding the intrinsic fractality. With enough of such links removed, fractal scaling spontaneously arises from nonfractal networks. Our results provide a multiple-scale view on the structure and dynamics and place fractality as a generic organizing principle of complex networks on a firmer ground.

3. On the fractal morphology of combustion-generated soot aggregates

   SciTech Connect

   Koylu, U.O.

   1995-12-31

   The fractal properties of soot aggregates were investigated using ex-situ and in-situ experimental methods as well as computer simulations. Ex-situ experiments involved thermophoretic sampling and analysis by transmission electron microscopy (TEM), while in-situ measurements employed angular static light scattering and data inversion based on Rayleigh-Debye-Gans (RDG) approximation. Computer simulations used a sequential algorithm which mimics mass fractal-like structures. So from a variety of hydrocarbon-fueled laminar and turbulent nonpremixed flame environments were considered in the present study. The TEM analysis of projected soot images sampled from fuel-rich conditions of buoyant and weakly-buoyant laminar flames indicated that the fractal dimension of sootmore » was relatively independent of position in flames, fuel type and flame condition. These measurements yielded an average fractal dimension of 1.8, although other structure parameters such as the primary particle diameters and number of primary particles in aggregates had wide range of values. Fractal prefactor (lacunarity) was also measured for soot sampled from the fuel-lean conditions of turbulent flames, considering the actual morphology by tilting the samples during TEM analysis. These measurements yielded a fractal dimension of 1.65 and a lacunarity of 8.5, with experimental uncertainties (95% confidence) of 0.08 and 0.5, respectively. Relationships between the actual and projected structure properties of soot were also developed by combining TEM observations with numerical simulations. Practical approximate formulae were suggested to find radius of gyration of an aggregate from its maximum dimension, and number of primary particles in an aggregate from projected area. Finally, the fractal dimension and lacunarity of soot were obtained using light scattering for the same conditions of the above TEM measurements.« less

4. Fractality and the law of the wall

   NASA Astrophysics Data System (ADS)

   Xu, Haosen H. A.; Yang, X. I. A.

   2018-05-01

   Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the D =2.33 fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.

5. Nonlinear dynamics, fractals, cardiac physiology and sudden death

   NASA Technical Reports Server (NTRS)

   Goldberger, Ary L.

   1987-01-01

   The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

6. Fractal structures and fractal functions as disease indicators

   USGS Publications Warehouse

   Escos, J.M; Alados, C.L.; Emlen, J.M.

   1995-01-01

   Developmental instability is an early indicator of stress, and has been used to monitor the impacts of human disturbance on natural ecosystems. Here we investigate the use of different measures of developmental instability on two species, green peppers (Capsicum annuum), a plant, and Spanish ibex (Capra pyrenaica), an animal. For green peppers we compared the variance in allometric relationship between control plants, and a treatment group infected with the tomato spotted wilt virus. The results show that infected plants have a greater variance about the allometric regression line than the control plants. We also observed a reduction in complexity of branch structure in green pepper with a viral infection. Box-counting fractal dimension of branch architecture declined under stress infection. We also tested the reduction in complexity of behavioral patterns under stress situations in Spanish ibex (Capra pyrenaica). Fractal dimension of head-lift frequency distribution measures predator detection efficiency. This dimension decreased under stressful conditions, such as advanced pregnancy and parasitic infection. Feeding distribution activities reflect food searching efficiency. Power spectral analysis proves to be the most powerful tool for character- izing fractal behavior, revealing a reduction in complexity of time distribution activity under parasitic infection.

7. Holographic Characterization of Colloidal Fractal Aggregates

   NASA Astrophysics Data System (ADS)

   Wang, Chen; Cheong, Fook Chiong; Ruffner, David B.; Zhong, Xiao; Ward, Michael D.; Grier, David G.

   In-line holographic microscopy images of micrometer-scale fractal aggregates can be interpreted with the Lorenz-Mie theory of light scattering and an effective-sphere model to obtain each aggregate's size and the population-averaged fractal dimension. We demonstrate this technique experimentally using model fractal clusters of polystyrene nanoparticles and fractal protein aggregates composed of bovine serum albumin and bovine pancreas insulin. This technique can characterize several thousand aggregates in ten minutes and naturally distinguishes aggregates from contaminants such as silicone oil droplets. Work supported by the SBIR program of the NSF.

8. On fractal properties of arterial trees.

   PubMed

   Zamir, M

   1999-04-21

   The question of fractal properties of arterial trees is considered in light of data from the extensive tree structure of the right coronary artery of a human heart. Because of the highly non-uniform structure of this tree, the study focuses on the purely geometrical rather than statistical aspects of fractal properties. The large number of arterial bifurcations comprising the tree were found to have a mixed degree of asymmetry at all levels of the tree, including the depth of the tree where it has been generally supposed that they would be symmetrical. Cross-sectional area ratios of daughter to parent vessels were also found to be highly mixed at all levels, having values both above and below 1.0, rather than consistently above as has been generally supposed in the past. Calculated values of the power law index which describes the theoretical relation between the diameters of the three vessel segments at an arterial bifurcation were found to range far beyond the two values associated with the cube and square laws, and not clearly favoring one or the other. On the whole the tree structure was found to have what we have termed "pseudo-fractal" properties, in the sense that vessels of different calibers displayed the same branching pattern but with a range of values of the branching parameters. The results suggest that a higher degree of fractal character, one in which the branching parameters are constant throughout the tree structure, is unlikely to be attained in non-uniform vascular structures. Copyright 1999 Academic Press.

9. Fractal analysis of time varying data

   DOEpatents

   Vo-Dinh, Tuan; Sadana, Ajit

   2002-01-01

   Characteristics of time varying data, such as an electrical signal, are analyzed by converting the data from a temporal domain into a spatial domain pattern. Fractal analysis is performed on the spatial domain pattern, thereby producing a fractal dimension D.sub.F. The fractal dimension indicates the regularity of the time varying data.

10. [Features of fractal dynamics EEG of alpha-rhythm in patients with neurotic and neurosis-like disorders].

    PubMed

    Shul'ts, E V; Baburin, I N; Karavaeva, T A; Karvasarskiĭ, B D; Slezin, V B

    2011-01-01

    Fifty-five patients with neurotic and neurosis-like disorders and 20 healthy controls, aged 17-64 years, have been examined. The basic research method was electroencephalography (EEG) with the fractal analysis of alpha power fluctuations. In patients, the changes in the fractal structure were of the same direction: the decrease of fractal indexes of low-frequency fluctuations and the increase of fractal indexes of mid-frequency fluctuations. Patients with neurosis-like disorders, in comparison to those with neurotic disorders, were characterized by more expressed (quantitative) changes in fractal structures of more extended character. It suggests the presence of deeper pathological changes in patients with neurosis-like disorders.

11. Roughness Perception of Haptically Displayed Fractal Surfaces

    NASA Technical Reports Server (NTRS)

    Costa, Michael A.; Cutkosky, Mark R.; Lau, Sonie (Technical Monitor)

    2000-01-01

    Surface profiles were generated by a fractal algorithm and haptically rendered on a force feedback joystick, Subjects were asked to use the joystick to explore pairs of surfaces and report to the experimenter which of the surfaces they felt was rougher. Surfaces were characterized by their root mean square (RMS) amplitude and their fractal dimension. The most important factor affecting the perceived roughness of the fractal surfaces was the RMS amplitude of the surface. When comparing surfaces of fractal dimension 1.2-1.35 it was found that the fractal dimension was negatively correlated with perceived roughness.

12. A Double-Minded Fractal

    ERIC Educational Resources Information Center

    Simoson, Andrew J.

    2009-01-01

    This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)

13. Seismic dynamics in advance and after the recent strong earthquakes in Italy and New Zealand

    NASA Astrophysics Data System (ADS)

    Nekrasova, A.; Kossobokov, V. G.

    2017-12-01

    We consider seismic events as a sequence of avalanches in self-organized system of blocks-and-faults of the Earth lithosphere and characterize earthquake series with the distribution of the control parameter, η = τ × 10B × (5-M) × L C of the Unified Scaling Law for Earthquakes, USLE (where τ is inter-event time, B is analogous to the Gutenberg-Richter b-value, and C is fractal dimension of seismic locus). A systematic analysis of earthquake series in Central Italy and New Zealand, 1993-2017, suggests the existence, in a long-term, of different rather steady levels of seismic activity characterized with near constant values of η, which, in mid-term, intermittently switch at times of transitions associated with the strong catastrophic events. On such a transition, seismic activity, in short-term, may follow different scenarios with inter-event time scaling of different kind, including constant, logarithmic, power law, exponential rise/decay or a mixture of those. The results do not support the presence of universality in seismic energy release. The observed variability of seismic activity in advance and after strong (M6.0+) earthquakes in Italy and significant (M7.0+) earthquakes in New Zealand provides important constraints on modelling realistic earthquake sequences by geophysicists and can be used to improve local seismic hazard assessments including earthquake forecast/prediction methodologies. The transitions of seismic regime in Central Italy and New Zealand started in 2016 are still in progress and require special attention and geotechnical monitoring. It would be premature to make any kind of definitive conclusions on the level of seismic hazard which is evidently high at this particular moment of time in both regions. The study supported by the Russian Science Foundation Grant No.16-17-00093.

14. Evolving random fractal Cantor superlattices for the infrared using a genetic algorithm

    PubMed Central

    Bossard, Jeremy A.; Lin, Lan; Werner, Douglas H.

    2016-01-01

    Ordered and chaotic superlattices have been identified in Nature that give rise to a variety of colours reflected by the skin of various organisms. In particular, organisms such as silvery fish possess superlattices that reflect a broad range of light from the visible to the UV. Such superlattices have previously been identified as ‘chaotic’, but we propose that apparent ‘chaotic’ natural structures, which have been previously modelled as completely random structures, should have an underlying fractal geometry. Fractal geometry, often described as the geometry of Nature, can be used to mimic structures found in Nature, but deterministic fractals produce structures that are too ‘perfect’ to appear natural. Introducing variability into fractals produces structures that appear more natural. We suggest that the ‘chaotic’ (purely random) superlattices identified in Nature are more accurately modelled by multi-generator fractals. Furthermore, we introduce fractal random Cantor bars as a candidate for generating both ordered and ‘chaotic’ superlattices, such as the ones found in silvery fish. A genetic algorithm is used to evolve optimal fractal random Cantor bars with multiple generators targeting several desired optical functions in the mid-infrared and the near-infrared. We present optimized superlattices demonstrating broadband reflection as well as single and multiple pass bands in the near-infrared regime. PMID:26763335

15. Spatio-temporal distribution of Oklahoma earthquakes: Exploring relationships using a nearest-neighbor approach: Nearest-neighbor analysis of Oklahoma

    DOE PAGES

    Vasylkivska, Veronika S.; Huerta, Nicolas J.

    2017-06-24

    Determining the spatiotemporal characteristics of natural and induced seismic events holds the opportunity to gain new insights into why these events occur. Linking the seismicity characteristics with other geologic, geographic, natural, or anthropogenic factors could help to identify the causes and suggest mitigation strategies that reduce the risk associated with such events. The nearest-neighbor approach utilized in this work represents a practical first step toward identifying statistically correlated clusters of recorded earthquake events. Detailed study of the Oklahoma earthquake catalog’s inherent errors, empirical model parameters, and model assumptions is presented. We found that the cluster analysis results are stable withmore » respect to empirical parameters (e.g., fractal dimension) but were sensitive to epicenter location errors and seismicity rates. Most critically, we show that the patterns in the distribution of earthquake clusters in Oklahoma are primarily defined by spatial relationships between events. This observation is a stark contrast to California (also known for induced seismicity) where a comparable cluster distribution is defined by both spatial and temporal interactions between events. These results highlight the difficulty in understanding the mechanisms and behavior of induced seismicity but provide insights for future work.« less

16. Spatio-temporal distribution of Oklahoma earthquakes: Exploring relationships using a nearest-neighbor approach: Nearest-neighbor analysis of Oklahoma

    SciTech Connect

    Vasylkivska, Veronika S.; Huerta, Nicolas J.

    Determining the spatiotemporal characteristics of natural and induced seismic events holds the opportunity to gain new insights into why these events occur. Linking the seismicity characteristics with other geologic, geographic, natural, or anthropogenic factors could help to identify the causes and suggest mitigation strategies that reduce the risk associated with such events. The nearest-neighbor approach utilized in this work represents a practical first step toward identifying statistically correlated clusters of recorded earthquake events. Detailed study of the Oklahoma earthquake catalog’s inherent errors, empirical model parameters, and model assumptions is presented. We found that the cluster analysis results are stable withmore » respect to empirical parameters (e.g., fractal dimension) but were sensitive to epicenter location errors and seismicity rates. Most critically, we show that the patterns in the distribution of earthquake clusters in Oklahoma are primarily defined by spatial relationships between events. This observation is a stark contrast to California (also known for induced seismicity) where a comparable cluster distribution is defined by both spatial and temporal interactions between events. These results highlight the difficulty in understanding the mechanisms and behavior of induced seismicity but provide insights for future work.« less

17. Paradigms of Complexity: Fractals and Structures in the Sciences

    NASA Astrophysics Data System (ADS)

    Novak, Miroslav M.

    The Table of Contents for the book is as follows: * Preface * The Origin of Complexity (invited talk) * On the Existence of Spatially Uniform Scaling Laws in the Climate System * Multispectral Backscattering: A Fractal-Structure Probe * Small-Angle Multiple Scattering on a Fractal System of Point Scatterers * Symmetric Fractals Generated by Cellular Automata * Bispectra and Phase Correlations for Chaotic Dynamical Systems * Self-Organized Criticality Models of Neural Development * Altered Fractal and Irregular Heart Rate Behavior in Sick Fetuses * Extract Multiple Scaling in Long-Term Heart Rate Variability * A Semi-Continous Box Counting Method for Fractal Dimension Measurement of Short Single Dimension Temporal Signals - Preliminary Study * A Fractional Brownian Motion Model of Cracking * Self-Affine Scaling Studies on Fractography * Coarsening of Fractal Interfaces * A Fractal Model of Ocean Surface Superdiffusion * Stochastic Subsurface Flow and Transport in Fractal Fractal Conductivity Fields * Rendering Through Iterated Function Systems * The σ-Hull - The Hull Where Fractals Live - Calculating a Hull Bounded by Log Spirals to Solve the Inverse IFS-Problem by the Detected Orbits * On the Multifractal Properties of Passively Convected Scalar Fields * New Statistical Textural Transforms for Non-Stationary Signals: Application to Generalized Mutlifractal Analysis * Laplacian Growth of Parallel Needles: Their Mullins-Sekerka Instability * Entropy Dynamics Associated with Self-Organization * Fractal Properties in Economics (invited talk) * Fractal Approach to the Regional Seismic Event Discrimination Problem * Fractal and Topological Complexity of Radioactive Contamination * Pattern Selection: Nonsingular Saffman-Taylor Finger and Its Dynamic Evolution with Zero Surface Tension * A Family of Complex Wavelets for the Characterization of Singularities * Stabilization of Chaotic Amplitude Fluctuations in Multimode, Intracavity-Doubled Solid-State Lasers * Chaotic

18. Definition of fractal topography to essential understanding of scale-invariance

    NASA Astrophysics Data System (ADS)

    Jin, Yi; Wu, Ying; Li, Hui; Zhao, Mengyu; Pan, Jienan

    2017-04-01

    Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hurst exponent, which is analytically expressed by Hxy = log Px/log Py where Px and Py are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which . Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.

19. An Approach to Study Elastic Vibrations of Fractal Cylinders

    NASA Astrophysics Data System (ADS)

    Steinberg, Lev; Zepeda, Mario

    2016-11-01

    This paper presents our study of dynamics of fractal solids. Concepts of fractal continuum and time had been used in definitions of a fractal body deformation and motion, formulation of conservation of mass, balance of momentum, and constitutive relationships. A linearized model, which was written in terms of fractal time and spatial derivatives, has been employed to study the elastic vibrations of fractal circular cylinders. Fractal differential equations of torsional, longitudinal and transverse fractal wave equations have been obtained and solution properties such as size and time dependence have been revealed.

20. Fractal dimension of turbulent black holes

    NASA Astrophysics Data System (ADS)

    Westernacher-Schneider, John Ryan

    2017-11-01

    We present measurements of the fractal dimension of a turbulent asymptotically anti-de Sitter black brane reconstructed from simulated boundary fluid data at the perfect fluid order using the fluid-gravity duality. We argue that the boundary fluid energy spectrum scaling as E (k )˜k-2 is a more natural setting for the fluid-gravity duality than the Kraichnan-Kolmogorov scaling of E (k )˜k-5 /3, but we obtain fractal dimensions D for spatial sections of the horizon H ∩Σ in both cases: D =2.584 (1 ) and D =2.645 (4 ), respectively. These results are consistent with the upper bound of D =3 , thereby resolving the tension with the recent claim in Adams et al. [Phys. Rev. Lett. 112, 151602 (2014), 10.1103/PhysRevLett.112.151602] that D =3 +1 /3 . We offer a critical examination of the calculation which led to their result, and show that their proposed definition of the fractal dimension performs poorly as a fractal dimension estimator on one-dimensional curves with known fractal dimension. Finally, we describe how to define and in principle calculate the fractal dimension of spatial sections of the horizon H ∩Σ in a covariant manner, and we speculate on assigning a "bootstrapped" value of fractal dimension to the entire horizon H when it is in a statistically quasisteady turbulent state.

1. Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.

   PubMed

   Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

   2018-01-22

   We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

2. Pre-Service Teachers' Concept Images on Fractal Dimension

   ERIC Educational Resources Information Center

   Karakus, Fatih

   2016-01-01

   The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…

3. Fractal Analysis of Rock Joint Profiles

   NASA Astrophysics Data System (ADS)

   Audy, Ondřej; Ficker, Tomáš

   2017-10-01

   Surface reliefs of rock joints are analyzed in geotechnics when shear strength of rocky slopes is estimated. The rock joint profiles actually are self-affine fractal curves and computations of their fractal dimensions require special methods. Many papers devoted to the fractal properties of these profiles were published in the past but only a few of those papers employed a convenient computational method that would have guaranteed a sound value of that dimension. As a consequence, anomalously low dimensions were presented. This contribution deals with two computational modifications that lead to sound fractal dimensions of the self-affine rock joint profiles. These are the modified box-counting method and the modified yard-stick method sometimes called the compass method. Both these methods are frequently applied to self-similar fractal curves but the self-affine profile curves due to their self-affine nature require modified computational procedures implemented in computer programs.

4. Static friction between rigid fractal surfaces

   NASA Astrophysics Data System (ADS)

   Alonso-Marroquin, Fernando; Huang, Pengyu; Hanaor, Dorian A. H.; Flores-Johnson, E. A.; Proust, Gwénaëlle; Gan, Yixiang; Shen, Luming

   2015-09-01

   Using spheropolygon-based simulations and contact slope analysis, we investigate the effects of surface topography and atomic scale friction on the macroscopically observed friction between rigid blocks with fractal surface structures. From our mathematical derivation, the angle of macroscopic friction is the result of the sum of the angle of atomic friction and the slope angle between the contact surfaces. The latter is obtained from the determination of all possible contact slopes between the two surface profiles through an alternative signature function. Our theory is validated through numerical simulations of spheropolygons with fractal Koch surfaces and is applied to the description of frictional properties of Weierstrass-Mandelbrot surfaces. The agreement between simulations and theory suggests that for interpreting macroscopic frictional behavior, the descriptors of surface morphology should be defined from the signature function rather than from the slopes of the contacting surfaces.

5. Fractal Properties of Some Machined Surfaces

   NASA Astrophysics Data System (ADS)

   Thomas, T. R.; Rosén, B.-G.

   Many surface profiles are self-affine fractals defined by fractal dimension D and topothesy Λ. Traditionally these parameters are derived laboriously from the slope and intercept of the profile's structure function. Recently a quicker and more convenient derivation from standard roughness parameters has been suggested. Based on this derivation, it is shown that D and Λ depend on two dimensionless numbers: the ratio of the mean peak spacing to the rms roughness, and the ratio of the mean local peak spacing to the sampling interval. Using this approach, values of D and Λ are calculated for 125 profiles produced by polishing, plateau honing and various single-point machining processes. Different processes are shown to occupy different regions in D-Λ space, and polished surfaces show a relationship between D and Λ which is independent of the surface material.

6. Fractal Patterns and Chaos Games

   ERIC Educational Resources Information Center

   Devaney, Robert L.

   2004-01-01

   Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.

7. Band structures in fractal grading porous phononic crystals

   NASA Astrophysics Data System (ADS)

   Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin

   2018-05-01

   In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.

8. Statistical physics approach to earthquake occurrence and forecasting

   NASA Astrophysics Data System (ADS)

   de Arcangelis, Lucilla; Godano, Cataldo; Grasso, Jean Robert; Lippiello, Eugenio

   2016-04-01

   There is striking evidence that the dynamics of the Earth crust is controlled by a wide variety of mutually dependent mechanisms acting at different spatial and temporal scales. The interplay of these mechanisms produces instabilities in the stress field, leading to abrupt energy releases, i.e., earthquakes. As a consequence, the evolution towards instability before a single event is very difficult to monitor. On the other hand, collective behavior in stress transfer and relaxation within the Earth crust leads to emergent properties described by stable phenomenological laws for a population of many earthquakes in size, time and space domains. This observation has stimulated a statistical mechanics approach to earthquake occurrence, applying ideas and methods as scaling laws, universality, fractal dimension, renormalization group, to characterize the physics of earthquakes. In this review we first present a description of the phenomenological laws of earthquake occurrence which represent the frame of reference for a variety of statistical mechanical models, ranging from the spring-block to more complex fault models. Next, we discuss the problem of seismic forecasting in the general framework of stochastic processes, where seismic occurrence can be described as a branching process implementing space-time-energy correlations between earthquakes. In this context we show how correlations originate from dynamical scaling relations between time and energy, able to account for universality and provide a unifying description for the phenomenological power laws. Then we discuss how branching models can be implemented to forecast the temporal evolution of the earthquake occurrence probability and allow to discriminate among different physical mechanisms responsible for earthquake triggering. In particular, the forecasting problem will be presented in a rigorous mathematical framework, discussing the relevance of the processes acting at different temporal scales for different

9. Fractal Signals & Space-Time Cartoons

   NASA Astrophysics Data System (ADS)

   Oetama, H. C. Jakob; Maksoed, W. H.

   2016-03-01

   In ``Theory of Scale Relativity'', 1991- L. Nottale states whereas ``scale relativity is a geometrical & fractal space-time theory''. It took in comparisons to ``a unified, wavelet based framework for efficiently synthetizing, analyzing ∖7 processing several broad classes of fractal signals''-Gregory W. Wornell:``Signal Processing with Fractals'', 1995. Furthers, in Fig 1.1. a simple waveform from statistically scale-invariant random process [ibid.,h 3 ]. Accompanying RLE Technical Report 566 ``Synthesis, Analysis & Processing of Fractal Signals'' as well as from Wornell, Oct 1991 herewith intended to deducts =a Δt + (1 - β Δ t) ...in Petersen, et.al: ``Scale invariant properties of public debt growth'',2010 h. 38006p2 to [1/{1- (2 α (λ) /3 π) ln (λ/r)}depicts in Laurent Nottale,1991, h 24. Acknowledgment devotes to theLates HE. Mr. BrigadierGeneral-TNI[rtd].Prof. Ir. HANDOJO.

10. The Calculation of Fractal Dimension in the Presence of Non-Fractal Clutter

    NASA Technical Reports Server (NTRS)

    Herren, Kenneth A.; Gregory, Don A.

    1999-01-01

    The area of information processing has grown dramatically over the last 50 years. In the areas of image processing and information storage the technology requirements have far outpaced the ability of the community to meet demands. The need for faster recognition algorithms and more efficient storage of large quantities of data has forced the user to accept less than lossless retrieval of that data for analysis. In addition to clutter that is not the object of interest in the data set, often the throughput requirements forces the user to accept "noisy" data and to tolerate the clutter inherent in that data. It has been shown that some of this clutter, both the intentional clutter (clouds, trees, etc) as well as the noise introduced on the data by processing requirements can be modeled as fractal or fractal-like. Traditional methods using Fourier deconvolution on these sources of noise in frequency space leads to loss of signal and can, in many cases, completely eliminate the target of interest. The parameters that characterize fractal-like noise (predominately the fractal dimension) have been investigated and a technique to reduce or eliminate noise from real scenes has been developed. Examples of clutter reduced images are presented.

11. Fractal characteristic in the wearing of cutting tool

    NASA Astrophysics Data System (ADS)

    Mei, Anhua; Wang, Jinghui

    1995-11-01

    This paper studies the cutting tool wear with fractal geometry. The wearing image of the flank has been collected by machine vision which consists of CCD camera and personal computer. After being processed by means of preserving smoothing, binary making and edge extracting, the clear boundary enclosing the worn area has been obtained. The fractal dimension of the worn surface is calculated by the methods called `Slit Island' and `Profile'. The experiments and calciating give the conclusion that the worn surface is enclosed by a irregular boundary curve with some fractal dimension and characteristics of self-similarity. Furthermore, the relation between the cutting velocity and the fractal dimension of the worn region has been submitted. This paper presents a series of methods for processing and analyzing the fractal information in the blank wear, which can be applied to research the projective relation between the fractal structure and the wear state, and establish the fractal model of the cutting tool wear.

12. Fractal-based wideband invisibility cloak

    NASA Astrophysics Data System (ADS)

    Cohen, Nathan; Okoro, Obinna; Earle, Dan; Salkind, Phil; Unger, Barry; Yen, Sean; McHugh, Daniel; Polterzycki, Stefan; Shelman-Cohen, A. J.

    2015-03-01

    A wideband invisibility cloak (IC) at microwave frequencies is described. Using fractal resonators in closely spaced (sub wavelength) arrays as a minimal number of cylindrical layers (rings), the IC demonstrates that it is physically possible to attain a `see through' cloaking device with: (a) wideband coverage; (b) simple and attainable fabrication; (c) high fidelity emulation of the free path; (d) minimal side scattering; (d) a near absence of shadowing in the scattering. Although not a practical device, this fractal-enabled technology demonstrator opens up new opportunities for diverted-image (DI) technology and use of fractals in wideband optical, infrared, and microwave applications.

13. Exterior dimension of fat fractals

    NASA Technical Reports Server (NTRS)

    Grebogi, C.; Mcdonald, S. W.; Ott, E.; Yorke, J. A.

    1985-01-01

    Geometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which is called the exterior dimension. In addition, it is shown that the exterior dimension is related to the 'uncertainty exponent' previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted.

14. Power dissipation in fractal AC circuits

    NASA Astrophysics Data System (ADS)

    Chen, Joe P.; Rogers, Luke G.; Anderson, Loren; Andrews, Ulysses; Brzoska, Antoni; Coffey, Aubrey; Davis, Hannah; Fisher, Lee; Hansalik, Madeline; Loew, Stephen; Teplyaev, Alexander

    2017-08-01

    We extend Feynman’s analysis of an infinite ladder circuit to fractal circuits, providing examples in which fractal circuits constructed with purely imaginary impedances can have characteristic impedances with positive real part. Using (weak) self-similarity of our fractal structures, we provide algorithms for studying the equilibrium distribution of energy on these circuits. This extends the analysis of self-similar resistance networks introduced by Fukushima, Kigami, Kusuoka, and more recently studied by Strichartz et al.

15. The fractal dimension of cell membrane correlates with its capacitance: A new fractal single-shell model

    PubMed Central

    Wang, Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.

    2010-01-01

    The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski–Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM. PMID:21198103

16. Poiseuille equation for steady flow of fractal fluid

    NASA Astrophysics Data System (ADS)

    Tarasov, Vasily E.

    2016-07-01

    Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

17. Archaeon and archaeal virus diversity classification via sequence entropy and fractal dimension

    NASA Astrophysics Data System (ADS)

    Tremberger, George, Jr.; Gallardo, Victor; Espinoza, Carola; Holden, Todd; Gadura, N.; Cheung, E.; Schneider, P.; Lieberman, D.; Cheung, T.

    2010-09-01

    Archaea are important potential candidates in astrobiology as their metabolism includes solar, inorganic and organic energy sources. Archaeal viruses would also be expected to be present in a sustainable archaeal exobiological community. Genetic sequence Shannon entropy and fractal dimension can be used to establish a two-dimensional measure for classification and phylogenetic study of these organisms. A sequence fractal dimension can be calculated from a numerical series consisting of the atomic numbers of each nucleotide. Archaeal 16S and 23S ribosomal RNA sequences were studied. Outliers in the 16S rRNA fractal dimension and entropy plot were found to be halophilic archaea. Positive correlation (R-square ~ 0.75, N = 18) was observed between fractal dimension and entropy across the studied species. The 16S ribosomal RNA sequence entropy correlates with the 23S ribosomal RNA sequence entropy across species with R-square 0.93, N = 18. Entropy values correspond positively with branch lengths of a published phylogeny. The studied archaeal virus sequences have high fractal dimensions of 2.02 or more. A comparison of selected extremophile sequences with archaeal sequences from the Humboldt Marine Ecosystem database (Wood-Hull Oceanography Institute, MIT) suggests the presence of continuous sequence expression as inferred from distributions of entropy and fractal dimension, consistent with the diversity expected in an exobiological archaeal community.

18. Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

    NASA Astrophysics Data System (ADS)

    Besselink, R.; Stawski, T. M.; Van Driessche, A. E. S.; Benning, L. G.

    2016-12-01

    Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4 ṡ 2H2O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals.

19. Micro and MACRO Fractals Generated by Multi-Valued Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Banakh, T.; Novosad, N.

    2014-08-01

    Given a multi-valued function Φ : X \\mumap X on a topological space X we study the properties of its fixed fractal \\malteseΦ, which is defined as the closure of the orbit Φω(*Φ) = ⋃n∈ωΦn(*Φ) of the set *Φ = {x ∈ X : x ∈ Φ(x)} of fixed points of Φ. A special attention is paid to the duality between micro-fractals and macro-fractals, which are fixed fractals \\maltese Φ and \\maltese {Φ -1} for a contracting compact-valued function Φ : X \\mumap X on a complete metric space X. With help of algorithms (described in this paper) we generate various images of macro-fractals which are dual to some well-known micro-fractals like the fractal cross, the Sierpiński triangle, Sierpiński carpet, the Koch curve, or the fractal snowflakes. The obtained images show that macro-fractals have a large-scale fractal structure, which becomes clearly visible after a suitable zooming.

20. Self-organized criticality in complex systems: Applicability to the interoccurrent and recurrent statistical behavior of earthquakes

    NASA Astrophysics Data System (ADS)

    Abaimov, Sergey G.

    The concept of self-organized criticality is associated with scale-invariant, fractal behavior; this concept is also applicable to earthquake systems. It is known that the interoccurrent frequency-size distribution of earthquakes in a region is scale-invariant and obeys the Gutenberg-Richter power-law dependence. Also, the interoccurrent time-interval distribution is known to obey Poissonian statistics excluding aftershocks. However, to estimate the hazard risk for a region it is necessary to know also the recurrent behavior of earthquakes at a given point on a fault. This behavior has been investigated in the literature, however, major questions remain unresolved. The reason is the small number of earthquakes in observed sequences. To overcome this difficulty this research utilizes numerical simulations of a slider-block model and a sand-pile model. Also, experimental observations of creep events on the creeping section of the San Andreas fault are processed and sequences up to 100 events are studied. Then the recurrent behavior of earthquakes at a given point on a fault or at a given fault is investigated. It is shown that both the recurrent frequency-size and the time-interval behaviors of earthquakes obey the Weibull distribution.

1. Application to recognition of ferrography image with fractal neural network

   NASA Astrophysics Data System (ADS)

   Tian, Xianzhong; Hu, Tongsen; Zhang, Jian

   2005-10-01

   Because wear particles have fractal characteristics, it is necessary that adding fractal parameters to studying wear particles and diagnosing machine troubles. This paper discusses fractal parameters of wear particles, presents arithmetic calculating fractal dimension, and constructs a fractal neural network which can recognize wear particles image. It is proved by experiments that this fractal neural network can recognize some characteristics of wear particles image, and can also classify wear types.

2. Fractal characterization of fracture surfaces in concrete

   USGS Publications Warehouse

   Saouma, V.E.; Barton, C.C.; Gamaleldin, N.A.

   1990-01-01

   Fractal geometry is used to characterize the roughness of cracked concrete surfaces through a specially built profilometer, and the fractal dimension is subsequently correlated to the fracture toughness and direction of crack propagation. Preliminary results indicate that the fracture surface is indeed fractal over two orders of magnitudes with a dimension of approximately 1.20. ?? 1990.

3. Fractal Theory and Field Cover Experiments: Implications for the Fractal Characteristics and Radon Diffusion Behavior of Soils and Rocks.

   PubMed

   Tan, Wanyu; Li, Yongmei; Tan, Kaixuan; Duan, Xianzhe; Liu, Dong; Liu, Zehua

   2016-12-01

   Radon diffusion and transport through different media is a complex process affected by many factors. In this study, the fractal theories and field covering experiments were used to study the fractal characteristics of particle size distribution (PSD) of six kinds of geotechnical materials (e.g., waste rock, sand, laterite, kaolin, mixture of sand and laterite, and mixture of waste rock and laterite) and their effects on radon diffusion. In addition, the radon diffusion coefficient and diffusion length were calculated. Moreover, new formulas for estimating diffusion coefficient and diffusion length functional of fractal dimension d of PSD were proposed. These results demonstrate the following points: (1) the fractal dimension d of the PSD can be used to characterize the property of soils and rocks in the studies of radon diffusion behavior; (2) the diffusion coefficient and diffusion length decrease with increasing fractal dimension of PSD; and (3) the effectiveness of final covers in reducing radon exhalation of uranium tailings impoundments can be evaluated on the basis of the fractal dimension of PSD of materials.

4. Fractal fluctuations in gaze speed visual search.

   PubMed

   Stephen, Damian G; Anastas, Jason

   2011-04-01

   Visual search involves a subtle coordination of visual memory and lower-order perceptual mechanisms. Specifically, the fluctuations in gaze may provide support for visual search above and beyond what may be attributed to memory. Prior research indicates that gaze during search exhibits fractal fluctuations, which allow for a wide sampling of the field of view. Fractal fluctuations constitute a case of fast diffusion that may provide an advantage in exploration. We present reanalyses of eye-tracking data collected by Stephen and Mirman (Cognition, 115, 154-165, 2010) for single-feature and conjunction search tasks. Fluctuations in gaze during these search tasks were indeed fractal. Furthermore, the degree of fractality predicted decreases in reaction time on a trial-by-trial basis. We propose that fractality may play a key role in explaining the efficacy of perceptual exploration.

5. Emerging of fractal geometry on surface of human cervical epithelial cells during progression towards cancer

   PubMed Central

   Dokukin, M. E.; Guz, N. V.; Woodworth, C.D.; Sokolov, I.

   2015-01-01

   Despite considerable advances in understanding the molecular nature of cancer, many biophysical aspects of malignant development are still unclear. Here we study physical alterations of the surface of human cervical epithelial cells during stepwise in vitro development of cancer (from normal to immortal (premalignant), to malignant). We use atomic force microscopy to demonstrate that development of cancer is associated with emergence of simple fractal geometry on the cell surface. Contrary to the previously expected correlation between cancer and fractals, we find that fractal geometry occurs only at a limited period of development when immortal cells become cancerous; further cancer progression demonstrates deviation from fractal. Because of the connection between fractal behaviour and chaos (or far from equilibrium behaviour), these results suggest that chaotic behaviour coincides with the cancer transformation of the immortalization stage of cancer development, whereas further cancer progression recovers determinism of processes responsible for cell surface formation. PMID:25844044

6. Selective modulation of cell response on engineered fractal silicon substrates

   PubMed Central

   Gentile, Francesco; Medda, Rebecca; Cheng, Ling; Battista, Edmondo; Scopelliti, Pasquale E.; Milani, Paolo; Cavalcanti-Adam, Elisabetta A.; Decuzzi, Paolo

   2013-01-01

   A plethora of work has been dedicated to the analysis of cell behavior on substrates with ordered topographical features. However, the natural cell microenvironment is characterized by biomechanical cues organized over multiple scales. Here, randomly rough, self-affinefractal surfaces are generated out of silicon,where roughness Ra and fractal dimension Df are independently controlled. The proliferation rates, the formation of adhesion structures, and the morphology of 3T3 murine fibroblasts are monitored over six different substrates. The proliferation rate is maximized on surfaces with moderate roughness (Ra ~ 40 nm) and large fractal dimension (Df ~ 2.4); whereas adhesion structures are wider and more stable on substrates with higher roughness (Ra ~ 50 nm) and lower fractal dimension (Df ~ 2.2). Higher proliferation occurson substrates exhibiting densely packed and sharp peaks, whereas more regular ridges favor adhesion. These results suggest that randomly roughtopographies can selectively modulate cell behavior. PMID:23492898

7. a Fractal Network Model for Fractured Porous Media

   NASA Astrophysics Data System (ADS)

   Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung

   2016-04-01

   The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.

8. The fractal nature of vacuum arc cathode spots

   SciTech Connect

   Anders, Andre

   2005-05-27

   Cathode spot phenomena show many features of fractals, for example self-similar patterns in the emitted light and arc erosion traces. Although there have been hints on the fractal nature of cathode spots in the literature, the fractal approach to spot interpretation is underutilized. In this work, a brief review of spot properties is given, touching the differences between spot type 1 (on cathodes surfaces with dielectric layers) and spot type 2 (on metallic, clean surfaces) as well as the known spot fragment or cell structure. The basic properties of self-similarity, power laws, random colored noise, and fractals are introduced. Severalmore » points of evidence for the fractal nature of spots are provided. Specifically power laws are identified as signature of fractal properties, such as spectral power of noisy arc parameters (ion current, arc voltage, etc) obtained by fast Fourier transform. It is shown that fractal properties can be observed down to the cutoff by measurement resolution or occurrence of elementary steps in physical processes. Random walk models of cathode spot motion are well established: they go asymptotically to Brownian motion for infinitesimal step width. The power spectrum of the arc voltage noise falls as 1/f {sup 2}, where f is frequency, supporting a fractal spot model associated with Brownian motion.« less

9. Fractal dimension analysis of weight-bearing bones of rats during skeletal unloading

   NASA Technical Reports Server (NTRS)

   Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Sanhueza, A. I.; Yamauchi, M.

   2001-01-01

   Fractal analysis was used to quantify changes in trabecular bone induced through the use of a rat tail-suspension model to simulate microgravity-induced osteopenia. Fractal dimensions were estimated from digitized radiographs obtained from tail-suspended and ambulatory rats. Fifty 4-month-old male Sprague-Dawley rats were divided into groups of 24 ambulatory (control) and 26 suspended (test) animals. Rats of both groups were killed after periods of 1, 4, and 8 weeks. Femurs and tibiae were removed and radiographed with standard intraoral films and digitized using a flatbed scanner. Square regions of interest were cropped at proximal, middle, and distal areas of each bone. Fractal dimensions were estimated from slopes of regression lines fitted to circularly averaged plots of log power vs. log spatial frequency. The results showed that the computed fractal dimensions were significantly greater for images of trabecular bones from tail-suspended groups than for ambulatory groups (p < 0.01) at 1 week. Periods between 1 and 4 weeks likewise yielded significantly different estimates (p < 0.05), consistent with an increase in bone loss. In the tibiae, the proximal regions of the suspended group produced significantly greater fractal dimensions than other regions (p < 0.05), which suggests they were more susceptible to unloading. The data are consistent with other studies demonstrating osteopenia in microgravity environments and the regional response to skeletal unloading. Thus, fractal analysis could be a useful technique to evaluate the structural changes of bone.

10. Fractality à la carte: a general particle aggregation model.

    PubMed

    Nicolás-Carlock, J R; Carrillo-Estrada, J L; Dossetti, V

    2016-01-19

    In nature, fractal structures emerge in a wide variety of systems as a local optimization of entropic and energetic distributions. The fractality of these systems determines many of their physical, chemical and/or biological properties. Thus, to comprehend the mechanisms that originate and control the fractality is highly relevant in many areas of science and technology. In studying clusters grown by aggregation phenomena, simple models have contributed to unveil some of the basic elements that give origin to fractality, however, the specific contribution from each of these elements to fractality has remained hidden in the complex dynamics. Here, we propose a simple and versatile model of particle aggregation that is, on the one hand, able to reveal the specific entropic and energetic contributions to the clusters' fractality and morphology, and, on the other, capable to generate an ample assortment of rich natural-looking aggregates with any prescribed fractal dimension.

11. Fat fractal scaling of drainage networks from a random spatial network model

    USGS Publications Warehouse

    Karlinger, Michael R.; Troutman, Brent M.

    1992-01-01

    An alternative quantification of the scaling properties of river channel networks is explored using a spatial network model. Whereas scaling descriptions of drainage networks previously have been presented using a fractal analysis primarily of the channel lengths, we illustrate the scaling of the surface area of the channels defining the network pattern with an exponent which is independent of the fractal dimension but not of the fractal nature of the network. The methodology presented is a fat fractal analysis in which the drainage basin minus the channel area is considered the fat fractal. Random channel networks within a fixed basin area are generated on grids of different scales. The sample channel networks generated by the model have a common outlet of fixed width and a rule of upstream channel narrowing specified by a diameter branching exponent using hydraulic and geomorphologic principles. Scaling exponents are computed for each sample network on a given grid size and are regressed against network magnitude. Results indicate that the size of the exponents are related to magnitude of the networks and generally decrease as network magnitude increases. Cases showing differences in scaling exponents with like magnitudes suggest a direction of future work regarding other topologic basin characteristics as potential explanatory variables.

12. GENERATING FRACTAL PATTERNS BY USING p-CIRCLE INVERSION

    NASA Astrophysics Data System (ADS)

    Ramírez, José L.; Rubiano, Gustavo N.; Zlobec, Borut Jurčič

    2015-10-01

    In this paper, we introduce the p-circle inversion which generalizes the classical inversion with respect to a circle (p = 2) and the taxicab inversion (p = 1). We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the p-circle inversion.

13. Emergence of fractal geometry on the surface of human cervical epithelial cells during progression towards cancer

    NASA Astrophysics Data System (ADS)

    Dokukin, M. E.; Guz, N. V.; Woodworth, C. D.; Sokolov, I.

    2015-03-01

    Despite considerable advances in understanding the molecular nature of cancer, many biophysical aspects of malignant development are still unclear. Here we study physical alterations of the surface of human cervical epithelial cells during stepwise in vitro development of cancer (from normal to immortal (premalignant), to malignant). We use atomic force microscopy to demonstrate that development of cancer is associated with emergence of simple fractal geometry on the cell surface. Contrary to the previously expected correlation between cancer and fractals, we find that fractal geometry occurs only at a limited period of development when immortal cells become cancerous; further cancer progression demonstrates deviation from fractal. Because of the connection between fractal behaviour and chaos (or far from equilibrium behaviour), these results suggest that chaotic behaviour coincides with the cancer transformation of the immortalization stage of cancer development, whereas further cancer progression recovers determinism of processes responsible for cell surface formation.

14. Electro-chemical manifestation of nanoplasmonics in fractal media

    NASA Astrophysics Data System (ADS)

    Baskin, Emmanuel; Iomin, Alexander

    2013-06-01

    Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.

15. FAST TRACK COMMUNICATION: Weyl law for fat fractals

    NASA Astrophysics Data System (ADS)

    Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos

    2010-10-01

    It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.

16. Effective degrees of freedom of a random walk on a fractal.

    PubMed

    Balankin, Alexander S

    2015-12-01

    We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν-dimensional space F(ν) equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν) and fractal dimensionalities is deduced. The intrinsic time of random walk in F(ν) is inferred. The Laplacian operator in F(ν) is constructed. This allows us to map physical problems on fractals into the corresponding problems in F(ν). In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

17. Effective degrees of freedom of a random walk on a fractal

    NASA Astrophysics Data System (ADS)

    Balankin, Alexander S.

    2015-12-01

    We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

18. Self-Similarity of Plasmon Edge Modes on Koch Fractal Antennas.

    PubMed

    Bellido, Edson P; Bernasconi, Gabriel D; Rossouw, David; Butet, Jérémy; Martin, Olivier J F; Botton, Gianluigi A

    2017-11-28

    We investigate the plasmonic behavior of Koch snowflake fractal geometries and their possible application as broadband optical antennas. Lithographically defined planar silver Koch fractal antennas were fabricated and characterized with high spatial and spectral resolution using electron energy loss spectroscopy. The experimental data are supported by numerical calculations carried out with a surface integral equation method. Multiple surface plasmon edge modes supported by the fractal structures have been imaged and analyzed. Furthermore, by isolating and reproducing self-similar features in long silver strip antennas, the edge modes present in the Koch snowflake fractals are identified. We demonstrate that the fractal response can be obtained by the sum of basic self-similar segments called characteristic edge units. Interestingly, the plasmon edge modes follow a fractal-scaling rule that depends on these self-similar segments formed in the structure after a fractal iteration. As the size of a fractal structure is reduced, coupling of the modes in the characteristic edge units becomes relevant, and the symmetry of the fractal affects the formation of hybrid modes. This analysis can be utilized not only to understand the edge modes in other planar structures but also in the design and fabrication of fractal structures for nanophotonic applications.

19. Fractal dust constrains the collisional history of comets

    NASA Astrophysics Data System (ADS)

    Fulle, M.; Blum, J.

    2017-07-01

    The fractal dust particles observed by Rosetta cannot form in the physical conditions observed today in comet 67P/Churyumov-Gerasimenko (67P hereinafter), being instead consistent with models of the pristine dust aggregates coagulated in the solar nebula. Since bouncing collisions in the protoplanetary disc restructure fractals into compact aggregates (pebbles), the only way to preserve fractals in a comet is the gentle gravitational collapse of a mixture of pebbles and fractals, which must occur before their mutual collision speeds overcome ≈1 m s-1. This condition fixes the pebble radius to ≲1 cm, as confirmed by Comet Nucleus Infrared and Visible Analyser onboard Philae. Here, we show that the flux of fractal particles measured by Rosetta constrains the 67P nucleus in a random packing of cm-sized pebbles, with all the voids among them filled by fractal particles. This structure is inconsistent with any catastrophic collision, which would have compacted or dispersed most fractals, thus leaving empty most voids in the reassembled nucleus. Comets are less numerous than current estimates, as confirmed by lacking small craters on Pluto and Charon. Bilobate comets accreted at speeds <1 m s-1 from cometesimals born in the same disc stream.

20. Perceptual and Physiological Responses to Jackson Pollock's Fractals

    PubMed Central

    Taylor, Richard P.; Spehar, Branka; Van Donkelaar, Paul; Hagerhall, Caroline M.

    2011-01-01

    Fractals have been very successful in quantifying the visual complexity exhibited by many natural patterns, and have captured the imagination of scientists and artists alike. Our research has shown that the poured patterns of the American abstract painter Jackson Pollock are also fractal. This discovery raises an intriguing possibility – are the visual characteristics of fractals responsible for the long-term appeal of Pollock's work? To address this question, we have conducted 10 years of scientific investigation of human response to fractals and here we present, for the first time, a review of this research that examines the inter-relationship between the various results. The investigations include eye tracking, visual preference, skin conductance, and EEG measurement techniques. We discuss the artistic implications of the positive perceptual and physiological responses to fractal patterns. PMID:21734876

1. The 1985 central chile earthquake: a repeat of previous great earthquakes in the region?

   PubMed

   Comte, D; Eisenberg, A; Lorca, E; Pardo, M; Ponce, L; Saragoni, R; Singh, S K; Suárez, G

   1986-07-25

   A great earthquake (surface-wave magnitude, 7.8) occurred along the coast of central Chile on 3 March 1985, causing heavy damage to coastal towns. Intense foreshock activity near the epicenter of the main shock occurred for 11 days before the earthquake. The aftershocks of the 1985 earthquake define a rupture area of 170 by 110 square kilometers. The earthquake was forecast on the basis of the nearly constant repeat time (83 +/- 9 years) of great earthquakes in this region. An analysis of previous earthquakes suggests that the rupture lengths of great shocks in the region vary by a factor of about 3. The nearly constant repeat time and variable rupture lengths cannot be reconciled with time- or slip-predictable models of earthquake recurrence. The great earthquakes in the region seem to involve a variable rupture mode and yet, for unknown reasons, remain periodic. Historical data suggest that the region south of the 1985 rupture zone should now be considered a gap of high seismic potential that may rupture in a great earthquake in the next few tens of years.

2. Transport properties of electrons in fractal magnetic-barrier structures

   NASA Astrophysics Data System (ADS)

   Sun, Lifeng; Fang, Chao; Guo, Yong

   2010-09-01

   Quantum transport properties in fractal magnetically modulated structures are studied by the transfer-matrix method. It is found that the transmission spectra depend sensitively not only on the incident energy and the direction of the wave vector but also on the stage of the fractal structures. Resonance splitting, enhancement, and position shift of the resonance peaks under different magnetic modulation are observed at four different fractal stages, and the relationship between the conductance in the fractal structure and magnetic modulation is also revealed. The results indicate the spectra of the transmission can be considered as fingerprints for the fractal structures, which show the subtle correspondence between magnetic structures and transport behaviors.

3. Characterization of branch complexity by fractal analyses

   USGS Publications Warehouse

   Alados, C.L.; Escos, J.; Emlen, J.M.; Freeman, D.C.

   1999-01-01

   The comparison between complexity in the sense of space occupancy (box-counting fractal dimension D(c) and information dimension D1) and heterogeneity in the sense of space distribution (average evenness index f and evenness variation coefficient J(cv)) were investigated in mathematical fractal objects and natural branch structures. In general, increased fractal dimension was paired with low heterogeneity. Comparisons between branch architecture in Anthyllis cytisoides under different slope exposure and grazing impact revealed that branches were more complex and more homogeneously distributed for plants on northern exposures than southern, while grazing had no impact during a wet year. Developmental instability was also investigated by the statistical noise of the allometric relation between internode length and node order. In conclusion, our study demonstrated that fractal dimension of branch structure can be used to analyze the structural organization of plants, especially if we consider not only fractal dimension but also shoot distribution within the canopy (lacunarity). These indexes together with developmental instability analyses are good indicators of growth responses to the environment.

4. Does fractality in heart rate variability indicate the development of fetal neural processes?

   NASA Astrophysics Data System (ADS)

   Echeverría, J. C.; Woolfson, M. S.; Crowe, J. A.; Hayes-Gill, B. R.; Piéri, Jean F.; Spencer, C. J.; James, D. K.

   2004-10-01

   By using an improved detrended fluctuation analysis we studied the scaling behaviour of 53 long-term series of fetal heart rate fluctuations. Our results suggest that fractality begins to arise around 24 weeks of normal human gestation and that this condition, showing some additional developments, seems to be preserved during gestation. This may provide new evidence of a role played by cortical-to-subcortical pathways in the long-term fractal nature of heart rate variability data.

5. Comparison of Pore Fractal Characteristics Between Marine and Continental Shales

   NASA Astrophysics Data System (ADS)

   Liu, Jun; Yao, Yanbin; Liu, Dameng; Cai, Yidong; Cai, Jianchao

   Fractal characterization offers a quantitative evaluation on the heterogeneity of pore structure which greatly affects gas adsorption and transportation in shales. To compare the fractal characteristics between marine and continental shales, nine samples from the Lower Silurian Longmaxi formation in the Sichuan basin and nine from the Middle Jurassic Dameigou formation in the Qaidam basin were collected. Reservoir properties and fractal dimensions were characterized for all the collected samples. In this study, fractal dimensions were originated from the Frenkel-Halsey-Hill (FHH) model with N2 adsorption data. Compared to continental shale, marine shale has greater values of quartz content, porosity, specific surface area and total pore volume but lower level of clay minerals content, permeability, average pore diameter and methane adsorption capacity. The quartz in marine shale is mostly associated with biogenic origin, while that in continental shale is mainly due to terrigenous debris. The N2 adsorption-desorption isotherms exhibit that marine shale has fewer inkbottle-shaped pores but more plate-like and slit-shaped pores than continental shale. Two fractal dimensions (D1 and D2) were obtained at P/Po of 0-0.5 and 0.5-1. The dimension D2 is commonly greater than D1, suggesting that larger pores (diameter >˜ 4nm) have more complex structures than small pores (diameter <˜ 4nm). The fractal dimensions (both D1 and D2) positively correlate to clay minerals content, specific surface area and methane adsorption capacity, but have negative relationships with porosity, permeability and average pore diameter. The fractal dimensions increase proportionally with the increasing quartz content in marine shale but have no obvious correlation with that in continental shale. The dimension D1 is correlative to the TOC content and permeability of marine shale at a similar degree with dimension D2, while the dimension D1 is more sensitive to those of continental shale than

6. Towards thermomechanics of fractal media

   NASA Astrophysics Data System (ADS)

   Ostoja-Starzewski, Martin

   2007-11-01

   Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.

7. Undergraduate Experiment with Fractal Diffraction Gratings

   ERIC Educational Resources Information Center

   Monsoriu, Juan A.; Furlan, Walter D.; Pons, Amparo; Barreiro, Juan C.; Gimenez, Marcos H.

   2011-01-01

   We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics…

8. The analysis of the influence of fractal structure of stimuli on fractal dynamics in fixational eye movements and EEG signal

   NASA Astrophysics Data System (ADS)

   Namazi, Hamidreza; Kulish, Vladimir V.; Akrami, Amin

   2016-05-01

   One of the major challenges in vision research is to analyze the effect of visual stimuli on human vision. However, no relationship has been yet discovered between the structure of the visual stimulus, and the structure of fixational eye movements. This study reveals the plasticity of human fixational eye movements in relation to the ‘complex’ visual stimulus. We demonstrated that the fractal temporal structure of visual dynamics shifts towards the fractal dynamics of the visual stimulus (image). The results showed that images with higher complexity (higher fractality) cause fixational eye movements with lower fractality. Considering the brain, as the main part of nervous system that is engaged in eye movements, we analyzed the governed Electroencephalogram (EEG) signal during fixation. We have found out that there is a coupling between fractality of image, EEG and fixational eye movements. The capability observed in this research can be further investigated and applied for treatment of different vision disorders.

9. Fractal dimension analysis of complexity in Ligeti piano pieces

   NASA Astrophysics Data System (ADS)

   Bader, Rolf

   2005-04-01

   Fractal correlation dimensional analysis has been performed with whole solo piano pieces by Gyrgy Ligeti at every 50ms interval of the pieces. The resulting curves of development of complexity represented by the fractal dimension showed up a very reasonable correlation with the perceptional density of events during these pieces. The seventh piece of Ligeti's ``Musica ricercata'' was used as a test case. Here, each new part of the piece was followed by an increase of the fractal dimension because of the increase of information at the part changes. The second piece ``Galamb borong,'' number seven of the piano Etudes was used, because Ligeti wrote these Etudes after studying fractal geometry. Although the piece is not fractal in the strict mathematical sense, the overall structure of the psychoacoustic event-density as well as the detailed event development is represented by the fractal dimension plot.

10. Quantitative assessment of early diabetic retinopathy using fractal analysis.

    PubMed

    Cheung, Ning; Donaghue, Kim C; Liew, Gerald; Rogers, Sophie L; Wang, Jie Jin; Lim, Shueh-Wen; Jenkins, Alicia J; Hsu, Wynne; Li Lee, Mong; Wong, Tien Y

    2009-01-01

    Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes. We conducted a cross-sectional study of 729 patients with type 1 diabetes (aged 12-20 years) who had seven-field stereoscopic retinal photographs taken of both eyes. From these photographs, retinopathy was graded according to the modified Airlie House classification, and fractal dimension was quantified using a computer-based program following a standardized protocol. In this study, 137 patients (18.8%) had diabetic retinopathy signs; of these, 105 had mild retinopathy. Median (interquartile range) retinal fractal dimension was 1.46214 (1.45023-1.47217). After adjustment for age, sex, diabetes duration, A1C, blood pressure, and total cholesterol, increasing retinal vascular fractal dimension was significantly associated with increasing odds of retinopathy (odds ratio 3.92 [95% CI 2.02-7.61] for fourth versus first quartile of fractal dimension). In multivariate analysis, each 0.01 increase in retinal vascular fractal dimension was associated with a nearly 40% increased odds of retinopathy (1.37 [1.21-1.56]). This association remained after additional adjustment for retinal vascular caliber. Greater retinal fractal dimension, representing increased geometric complexity of the retinal vasculature, is independently associated with early diabetic retinopathy signs in type 1 diabetes. Fractal analysis of fundus photographs may allow quantitative measurement of early diabetic microvascular damage.

11. Earthquake Hazard Assessment: Basics of Evaluation

    NASA Astrophysics Data System (ADS)

    Kossobokov, Vladimir

    2016-04-01

    Seismic hazard assessment (SHA) is not an easy task that implies a delicate application of statistics to data of limited size and different accuracy. Earthquakes follow the Unified Scaling Law that generalizes the Gutenberg-Richter relationship by taking into account naturally fractal distribution of their sources. Moreover, earthquakes, including the great and mega events, are clustered in time and their sequences have irregular recurrence intervals. Furthermore, earthquake related observations are limited to the recent most decades (or centuries in just a few rare cases). Evidently, all this complicates reliable assessment of seismic hazard and associated risks. Making SHA claims, either termless or time dependent (so-called t-DASH), quantitatively probabilistic in the frames of the most popular objectivists' viewpoint on probability requires a long series of "yes/no" trials, which cannot be obtained without an extended rigorous testing of the method predictions against real observations. Therefore, we reiterate the necessity and possibility of applying the modified tools of Earthquake Prediction Strategies, in particular, the Error Diagram, introduced by G.M. Molchan in early 1990ies for evaluation of SHA, and the Seismic Roulette null-hypothesis as a measure of the alerted space. The set of errors, i.e. the rates of failure and of the alerted space-time volume, compared to those obtained in the same number of random guess trials permits evaluating the SHA method effectiveness and determining the optimal choice of the parameters in regard to specified cost-benefit functions. These and other information obtained in such a testing supplies us with a realistic estimate of confidence in SHA results and related recommendations on the level of risks for decision making in regard to engineering design, insurance, and emergency management. These basics of SHA evaluation are exemplified in brief with a few examples, which analyses in more detail are given in a poster of

12. Using Peano Curves to Construct Laplacians on Fractals

    NASA Astrophysics Data System (ADS)

    Molitor, Denali; Ott, Nadia; Strichartz, Robert

    2015-12-01

    We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.

13. ABC of multi-fractal spacetimes and fractional sea turtles

    NASA Astrophysics Data System (ADS)

    Calcagni, Gianluca

    2016-04-01

    We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.

14. Analysis of the fractal dimension of volcano geomorphology through Synthetic Aperture Radar (SAR) amplitude images acquired in C and X band.

    NASA Astrophysics Data System (ADS)

    Pepe, S.; Di Martino, G.; Iodice, A.; Manzo, M.; Pepe, A.; Riccio, D.; Ruello, G.; Sansosti, E.; Tizzani, P.; Zinno, I.

    2012-04-01

    In the last two decades several aspects relevant to volcanic activity have been analyzed in terms of fractal parameters that effectively describe natural objects geometry. More specifically, these researches have been aimed at the identification of (1) the power laws that governed the magma fragmentation processes, (2) the energy of explosive eruptions, and (3) the distribution of the associated earthquakes. In this paper, the study of volcano morphology via satellite images is dealt with; in particular, we use the complete forward model developed by some of the authors (Di Martino et al., 2012) that links the stochastic characterization of amplitude Synthetic Aperture Radar (SAR) images to the fractal dimension of the imaged surfaces, modelled via fractional Brownian motion (fBm) processes. Based on the inversion of such a model, a SAR image post-processing has been implemented (Di Martino et al., 2010), that allows retrieving the fractal dimension of the observed surfaces, dictating the distribution of the roughness over different spatial scales. The fractal dimension of volcanic structures has been related to the specific nature of materials and to the effects of active geodynamic processes. Hence, the possibility to estimate the fractal dimension from a single amplitude-only SAR image is of fundamental importance for the characterization of volcano structures and, moreover, can be very helpful for monitoring and crisis management activities in case of eruptions and other similar natural hazards. The implemented SAR image processing performs the extraction of the point-by-point fractal dimension of the scene observed by the sensor, providing - as an output product - the map of the fractal dimension of the area of interest. In this work, such an analysis is performed on Cosmo-SkyMed, ERS-1/2 and ENVISAT images relevant to active stratovolcanoes in different geodynamic contexts, such as Mt. Somma-Vesuvio, Mt. Etna, Vulcano and Stromboli in Southern Italy, Shinmoe

15. Fractal morphometry of cell complexity.

    PubMed

    Losa, Gabriele A

    2002-01-01

    Irregularity and self-similarity under scale changes are the main attributes of the morphological complexity of both normal and abnormal cells and tissues. In other words, the shape of a self-similar object does not change when the scale of measurement changes, because each part of it looks similar to the original object. However, the size and geometrical parameters of an irregular object do differ when it is examined at increasing resolution, which reveals more details. Significant progress has been made over the past three decades in understanding how irregular shapes and structures in the physical and biological sciences can be analysed. Dominant influences have been the discovery of a new practical geometry of Nature, now known as fractal geometry, and the continuous improvements in computation capabilities. Unlike conventional Euclidean geometry, which was developed to describe regular and ideal geometrical shapes which are practically unknown in nature, fractal geometry can be used to measure the fractal dimension, contour length, surface area and other dimension parameters of almost all irregular and complex biological tissues. We have used selected examples to illustrate the application of the fractal principle to measuring irregular and complex membrane ultrastructures of cells at specific functional and pathological stage.

16. Fractal dynamics in physiology: Alterations with disease and aging

    PubMed Central

    Goldberger, Ary L.; Amaral, Luis A. N.; Hausdorff, Jeffrey M.; Ivanov, Plamen Ch.; Peng, C.-K.; Stanley, H. Eugene

    2002-01-01

    According to classical concepts of physiologic control, healthy systems are self-regulated to reduce variability and maintain physiologic constancy. Contrary to the predictions of homeostasis, however, the output of a wide variety of systems, such as the normal human heartbeat, fluctuates in a complex manner, even under resting conditions. Scaling techniques adapted from statistical physics reveal the presence of long-range, power-law correlations, as part of multifractal cascades operating over a wide range of time scales. These scaling properties suggest that the nonlinear regulatory systems are operating far from equilibrium, and that maintaining constancy is not the goal of physiologic control. In contrast, for subjects at high risk of sudden death (including those with heart failure), fractal organization, along with certain nonlinear interactions, breaks down. Application of fractal analysis may provide new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as to monitoring the aging process. Similar approaches show promise in assessing other regulatory systems, such as human gait control in health and disease. Elucidating the fractal and nonlinear mechanisms involved in physiologic control and complex signaling networks is emerging as a major challenge in the postgenomic era. PMID:11875196

17. Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel

    PubMed Central

    Shanhua, Xu; Songbo, Ren; Youde, Wang

    2015-01-01

    To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel. PMID:26121468

18. Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.

    PubMed

    Shanhua, Xu; Songbo, Ren; Youde, Wang

    2015-01-01

    To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.

19. Hierarchical socioeconomic fractality: The rich, the poor, and the middle-class

    NASA Astrophysics Data System (ADS)

    Eliazar, Iddo; Cohen, Morrel H.

    2014-05-01

    Since the seminal work of the Italian economist Vilfredo Pareto, the study of wealth and income has been a topic of active scientific exploration engaging researches ranging from economics and political science to econophysics and complex systems. This paper investigates the intrinsic fractality of wealth and income. To that end we introduce and characterize three forms of socioeconomic scale-invariance-poor fractality, rich fractality, and middle-class fractality-and construct hierarchical fractal approximations of general wealth and income distributions, based on the stitching of these three forms of fractality. Intertwining the theoretical results with real-world empirical data we then establish that the three forms of socioeconomic fractality-amalgamated into a composite hierarchical structure-underlie the distributions of wealth and income in human societies. We further establish that the hierarchical socioeconomic fractality of wealth and income is also displayed by empirical rank distributions observed across the sciences.

20. Fractal Dynamics of Heartbeat Interval Fluctuations in Health and Disease

    NASA Astrophysics Data System (ADS)

    Meyer, M.; Marconi, C.; Rahmel, A.; Grassi, B.; Ferretti, G.; Skinner, J. E.; Cerretelli, P.

    The dynamics of heartbeat interval time series were studied by a modified random walk analysis recently introduced as Detrended Fluctuation Analysis. In this analysis, the intrinsic fractal long-range power-law correlation properties of beat-to-beat fluctuations generated by the dynamical system (i.e. cardiac rhythm generator), after decomposition from extrinsic uncorrelated sources, can be quantified by the scaling exponent which, in healthy subjects, is about 1.0. The finding of a scaling coefficient of 1.0, indicating scale-invariant long-range power-law correlations (1/ƒnoise) of heartbeat fluctuations, would reflect a genuinely self-similar fractal process that typically generates fluctuations on a wide range of time scales. Lack of a characteristic time scale suggests that the neuroautonomic system underlying the control of heart rate dynamics helps prevent excessive mode-locking (error tolerance) that would restrict its functional responsiveness (plasticity) to environmental stimuli. The 1/ƒ dynamics of heartbeat interval fluctuations are unaffected by exposure to chronic hypoxia suggesting that the neuroautonomic cardiac control system is preadapted to hypoxia. Functional (hypothermia, cardiac disease) and/or structural (cardiac transplantation, early cardiac development) inactivation of neuroautonomic control is associated with the breakdown or absence of fractal complexity reflected by anticorrelated random walk-like dynamics, indicating that in these conditions the heart is unadapted to its environment.

1. A Tutorial Review on Fractal Spacetime and Fractional Calculus

   NASA Astrophysics Data System (ADS)

   He, Ji-Huan

   2014-11-01

   This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

2. Intraplate triggered earthquakes: Observations and interpretation

   USGS Publications Warehouse

   Hough, S.E.; Seeber, L.; Armbruster, J.G.

   2003-01-01

   We present evidence that at least two of the three 1811-1812 New Madrid, central United States, mainshocks and the 1886 Charleston, South Carolina, earthquake triggered earthquakes at regional distances. In addition to previously published evidence for triggered earthquakes in the northern Kentucky/southern Ohio region in 1812, we present evidence suggesting that triggered events might have occurred in the Wabash Valley, to the south of the New Madrid Seismic Zone, and near Charleston, South Carolina. We also discuss evidence that earthquakes might have been triggered in northern Kentucky within seconds of the passage of surface waves from the 23 January 1812 New Madrid mainshock. After the 1886 Charleston earthquake, accounts suggest that triggered events occurred near Moodus, Connecticut, and in southern Indiana. Notwithstanding the uncertainty associated with analysis of historical accounts, there is evidence that at least three out of the four known Mw 7 earthquakes in the central and eastern United States seem to have triggered earthquakes at distances beyond the typically assumed aftershock zone of 1-2 mainshock fault lengths. We explore the possibility that remotely triggered earthquakes might be common in low-strain-rate regions. We suggest that in a low-strain-rate environment, permanent, nonelastic deformation might play a more important role in stress accumulation than it does in interplate crust. Using a simple model incorporating elastic and anelastic strain release, we show that, for realistic parameter values, faults in intraplate crust remain close to their failure stress for a longer part of the earthquake cycle than do faults in high-strain-rate regions. Our results further suggest that remotely triggered earthquakes occur preferentially in regions of recent and/or future seismic activity, which suggests that faults are at a critical stress state in only some areas. Remotely triggered earthquakes may thus serve as beacons that identify regions of

3. Fractal analysis of scatter imaging signatures to distinguish breast pathologies

   NASA Astrophysics Data System (ADS)

   Eguizabal, Alma; Laughney, Ashley M.; Krishnaswamy, Venkataramanan; Wells, Wendy A.; Paulsen, Keith D.; Pogue, Brian W.; López-Higuera, José M.; Conde, Olga M.

   2013-02-01

   Fractal analysis combined with a label-free scattering technique is proposed for describing the pathological architecture of tumors. Clinicians and pathologists are conventionally trained to classify abnormal features such as structural irregularities or high indices of mitosis. The potential of fractal analysis lies in the fact of being a morphometric measure of the irregular structures providing a measure of the object's complexity and self-similarity. As cancer is characterized by disorder and irregularity in tissues, this measure could be related to tumor growth. Fractal analysis has been probed in the understanding of the tumor vasculature network. This work addresses the feasibility of applying fractal analysis to the scattering power map (as a physical modeling) and principal components (as a statistical modeling) provided by a localized reflectance spectroscopic system. Disorder, irregularity and cell size variation in tissue samples is translated into the scattering power and principal components magnitude and its fractal dimension is correlated with the pathologist assessment of the samples. The fractal dimension is computed applying the box-counting technique. Results show that fractal analysis of ex-vivo fresh tissue samples exhibits separated ranges of fractal dimension that could help classifier combining the fractal results with other morphological features. This contrast trend would help in the discrimination of tissues in the intraoperative context and may serve as a useful adjunct to surgeons.

4. Plasmon confinement in fractal quantum systems

   NASA Astrophysics Data System (ADS)

   Westerhout, Tom; van Veen, Edo; Katsnelson, Mikhail I.; Yuan, Shengjun

   2018-05-01

   Recent progress in the fabrication of materials has made it possible to create arbitrary nonperiodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the quantum plasmonic properties of electron gases in complex geometries. In this work we study systems with a fractal dimension. We calculate the full dielectric functions of two prototypical fractals with different ramification numbers, namely the Sierpinski carpet and gasket. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized plasmon modes with a flat dispersion. This strong plasmon confinement in finitely ramified fractals can provide a novel setting for manipulating light at the quantum level.

5. Multi-Scale Fractal Analysis of Image Texture and Pattern

   NASA Technical Reports Server (NTRS)

   Emerson, Charles W.

   1998-01-01

   Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely independent of scale. Self-similarity is defined as a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. An ideal fractal (or monofractal) curve or surface has a constant dimension over all scales, although it may not be an integer value. This is in contrast to Euclidean or topological dimensions, where discrete one, two, and three dimensions describe curves, planes, and volumes. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution. However, most geographical phenomena are not strictly self-similar at all scales, but they can often be modeled by a stochastic fractal in which the scaling and self-similarity properties of the fractal have inexact patterns that can be described by statistics. Stochastic fractal sets relax the monofractal self-similarity assumption and measure many scales and resolutions in order to represent the varying form of a phenomenon as a function of local variables across space. In image interpretation, pattern is defined as the overall spatial form of related features, and the repetition of certain forms is a characteristic pattern found in many cultural objects and some natural features. Texture is the visual impression of coarseness or smoothness caused by the variability or uniformity of image tone or color. A potential use of fractals concerns the analysis of image texture. In these situations it is commonly observed that the degree of roughness or inexactness in an image or surface is a function of scale and not of experimental technique. The fractal dimension of remote sensing data could yield quantitative insight on the spatial complexity and

6. Investigation into How 8th Grade Students Define Fractals

   ERIC Educational Resources Information Center

   Karakus, Fatih

   2015-01-01

   The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…

7. Association between stride time fractality and gait adaptability during unperturbed and asymmetric walking.

   PubMed

   Ducharme, Scott W; Liddy, Joshua J; Haddad, Jeffrey M; Busa, Michael A; Claxton, Laura J; van Emmerik, Richard E A

   2018-04-01

   speed, fractal dynamics increased closer to 1/f when participants were exposed to asymmetric walking. These findings suggest there may not be a relationship between unperturbed preferred or slow speed walking fractal dynamics and gait adaptability. However, the emergent relationship between asymmetric walking fractal dynamics and limb phase adaptation may represent a functional reorganization of the locomotor system (i.e., improved interactivity between degrees of freedom within the system) to be better suited to attenuate externally generated perturbations at various spatiotemporal scales. Copyright © 2018 Elsevier B.V. All rights reserved.

8. Fractal patterns formed by growth of radial viscous fingers*

   NASA Astrophysics Data System (ADS)

   Praud, Olivier

   2004-03-01

   We examine fractal patterns formed by the injection of air into oil in a thin (0.13 mm) layer contained between two cylindrical glass plates of 288 mm diameter (a Hele-Shaw cell) [1]. The resultant radially grown patterns are similar to those formed in Diffusion Limited Aggregation (DLA), but the relation between the continuum limit of DLA and continuum (Laplacian) growth remains an open question. Our viscous fingering patterns in the limit of very high pressure difference reach an asymptotic state in which they exhibit a fractal dimension of 1.70± 0.02, in good agreement with a calculation of the fractal dimension of a DLA cluster, 1.713± 0.003 [2]. The generalized dimensions are also computed and show that the observed pattern is self-similar with Dq = 1.70 for all q. Further, the probability density function of shielding angles suggests the existence of a critical angle close to 75 degrees. This result is in accord with numerical and analytical evidence of a critical angle in DLA [3]. Thus fractal viscous fingering patterns and Diffusion Limited Aggregation clusters have a similar geometrical structure. *Work conducted in collaboration with H.L. Swinney, M.G. Moore and Eran Sharon [1] E. Sharon, M. G. Moore, W. D. McCormick, and H. L. Swinney, Phys. Rev. Lett. 91, 205504 (2003). [2] B.Davidovitch et A. Levermann and I. Procaccia, Phys. Rev. E 62, 5919 (2000). [3] D. A. Kessler et al., Phys. Rev. E 57, 6913 (1998).

9. Anomalous relaxation in fractal structures

   SciTech Connect

   Fujiwara, S.; Yonezawa, F.

   1995-03-01

   For the purpose of studying some interesting properties of anomalous relaxation in fractal structures, we carry out Monte Carlo simulations of random walks on two-dimensional fractal structures (Sierpinski carpets with different cutouts and site-percolation clusters in a square lattice at the critical concentration). We find that the relaxation is of the Cole-Cole type [J. Chem. Phys. 9, 341 (1941)], which is one of the empirical laws of anomalous relaxation. Scaling properties are found in the relaxation function as well as in the particle density. We also find that, in strucures with almost the same fractal dimension, relaxation in structures withmore » dead ends is slower than that in structures without them. This paper ascertains that the essential aspects of the anomalous relaxation due to many-body effects can be explained in the framework of the one-body model.« less

10. Perception of earthquake risk in Taiwan: effects of gender and past earthquake experience.

    PubMed

    Kung, Yi-Wen; Chen, Sue-Huei

    2012-09-01

    This study explored how individuals in Taiwan perceive the risk of earthquake and the relationship of past earthquake experience and gender to risk perception. Participants (n= 1,405), including earthquake survivors and those in the general population without prior direct earthquake exposure, were selected and interviewed through a computer-assisted telephone interviewing procedure using a random sampling and stratification method covering all 24 regions of Taiwan. A factor analysis of the interview data yielded a two-factor structure of risk perception in regard to earthquake. The first factor, "personal impact," encompassed perception of threat and fear related to earthquakes. The second factor, "controllability," encompassed a sense of efficacy of self-protection in regard to earthquakes. The findings indicated prior earthquake survivors and females reported higher scores on the personal impact factor than males and those with no prior direct earthquake experience, although there were no group differences on the controllability factor. The findings support that risk perception has multiple components, and suggest that past experience (survivor status) and gender (female) affect the perception of risk. Exploration of potential contributions of other demographic factors such as age, education, and marital status to personal impact, especially for females and survivors, is discussed. Future research on and intervention program with regard to risk perception are suggested accordingly. © 2012 Society for Risk Analysis.

11. Correlation of Fractal Dimension Values with Implant Insertion Torque and Resonance Frequency Values at Implant Recipient Sites.

    PubMed

    Suer, Berkay Tolga; Yaman, Zekai; Buyuksarac, Bora

    2016-01-01

    Fractal analysis is a mathematical method used to describe the internal architecture of complex structures such as trabecular bone. Fractal analysis of panoramic radiographs of implant recipient sites could help to predict the quality of the bone prior to implant placement. This study investigated the correlations between the fractal dimension values obtained from panoramic radiographs and the insertion torque and resonance frequency values of mandibular implants. Thirty patients who received a total of 55 implants of the same brand, diameter, and length in the mandibular premolar and molar regions were included in the study. The same surgical procedures were applied to each patient, and the insertion torque and resonance frequency values were recorded for each implant at the time of placement. The radiographic fractal dimensions of the alveolar bone in the implant recipient area were calculated from preoperative panoramic radiographs using a box-counting algorithm. The insertion torque and resonance frequency values were compared with the fractal dimension values using the Spearman test. All implants were successful, and none were lost during the follow-up period. Linear correlations were observed between the fractal dimension and resonance frequency, between the fractal dimension and insertion torque, and between resonance frequency and insertion torque. These results suggest that the noninvasive measurement of the fractal dimension from panoramic radiographs might help to predict the bone quality, and thus the primary stability of dental implants, before implant surgery.

12. Pulse regime in formation of fractal fibers

    SciTech Connect

    Smirnov, B. M., E-mail:

    The pulse regime of vaporization of a bulk metal located in a buffer gas is analyzed as a method of generation of metal atoms under the action of a plasma torch or a laser beam. Subsequently these atoms are transformed into solid nanoclusters, fractal aggregates and then into fractal fibers if the growth process proceeds in an external electric field. We are guided by metals in which transitions between s and d-electrons of their atoms are possible, since these metals are used as catalysts and filters in interaction with gas flows. The resistance of metal fractal structures to a gasmore » flow is evaluated that allows one to find optimal parameters of a fractal structure for gas flow propagation through it. The thermal regime of interaction between a plasma pulse or a laser beam and a metal surface is analyzed. It is shown that the basic energy from an external source is consumed on a bulk metal heating, and the efficiency of atom evaporation from the metal surface, that is the ratio of energy fluxes for vaporization and heating, is 10{sup –3}–10{sup –4} for transient metals under consideration. A typical energy flux (~10{sup 6} W/cm{sup 2}), a typical surface temperature (~3000 K), and a typical pulse duration (~1 μs) provide a sufficient amount of evaporated atoms to generate fractal fibers such that each molecule of a gas flow collides with the skeleton of fractal fibers many times.« less

13. Predicting beauty: fractal dimension and visual complexity in art.

    PubMed

    Forsythe, A; Nadal, M; Sheehy, N; Cela-Conde, C J; Sawey, M

    2011-02-01

    Visual complexity has been known to be a significant predictor of preference for artistic works for some time. The first study reported here examines the extent to which perceived visual complexity in art can be successfully predicted using automated measures of complexity. Contrary to previous findings the most successful predictor of visual complexity was Gif compression. The second study examined the extent to which fractal dimension could account for judgments of perceived beauty. The fractal dimension measure accounts for more of the variance in judgments of perceived beauty in visual art than measures of visual complexity alone, particularly for abstract and natural images. Results also suggest that when colour is removed from an artistic image observers are unable to make meaningful judgments as to its beauty. ©2010 The British Psychological Society.

14. Fractal tomography and its application in 3D vision

    NASA Astrophysics Data System (ADS)

    Trubochkina, N.

    2018-01-01

    A three-dimensional artistic fractal tomography method that implements a non-glasses 3D visualization of fractal worlds in layered media is proposed. It is designed for the glasses-free 3D vision of digital art objects and films containing fractal content. Prospects for the development of this method in art galleries and the film industry are considered.

15. Wetting characteristics of 3-dimensional nanostructured fractal surfaces

    NASA Astrophysics Data System (ADS)

    Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy

    2017-01-01

    This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.

16. Teaching about Fractals.

    ERIC Educational Resources Information Center

    Willson, Stephen J.

    1991-01-01

    Described is a course designed to teach students about fractals using various teaching methods including the computer. Discussed are why the course drew students, prerequisites, clientele, textbook, grading, computer usage, and the syllabus. (KR)

17. Two-Dimensional Animal-Like Fractals in Thin Films

    NASA Astrophysics Data System (ADS)

    Gao, Hong-jun; Xue, Zeng-quan; Wu, Quan-de; Pang, Shi-jin

    1996-02-01

    We present a few unique animal-like fractal patterns in ionized-cluster-beam deposited fullerene-tetracyanoquinodimethane thin films. The fractal patterns consisting of animal-like aggregates such as "fishes" and "quasi-seahorses" have been characterized by transmission electron microscopy. The results indicate that the small aggregates of the animal-like body are composed of many single crystals whose crystalline directions are generally different. The formation of the fractal patterns can be attributed to the cluster-diffusion-limited aggregation.

18. A fractal nature for polymerized laminin.

    PubMed

    Hochman-Mendez, Camila; Cantini, Marco; Moratal, David; Salmeron-Sanchez, Manuel; Coelho-Sampaio, Tatiana

    2014-01-01

    Polylaminin (polyLM) is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM), scanning electron microscopy (SEM) and atomic force microscopy (AFM) to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM) was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.

19. Flat bands in fractal-like geometry

    NASA Astrophysics Data System (ADS)

    Pal, Biplab; Saha, Kush

    2018-05-01

    We report the presence of multiple flat bands in a class of two-dimensional lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic unit cells. Solving the tight-binding Hamiltonian for such lattices with different generations of a SPG network, we find multiple degenerate and nondegenerate completely flat bands, depending on the configuration of parameters of the Hamiltonian. Moreover, we establish a generic formula to determine the number of such bands as a function of the generation index ℓ of the fractal geometry. We show that the flat bands and their neighboring dispersive bands have remarkable features, the most interesting one being the spin-1 conical-type spectrum at the band center without any staggered magnetic flux, in contrast to the kagome lattice. We furthermore investigate the effect of magnetic flux in these lattice settings and show that different combinations of fluxes through such fractal unit cells lead to a richer spectrum with a single isolated flat band or gapless electron- or holelike flat bands. Finally, we discuss a possible experimental setup to engineer such a fractal flat-band network using single-mode laser-induced photonic waveguides.

20. Fractals and Transformations.

    ERIC Educational Resources Information Center

    Bannon, Thomas J.

    1991-01-01

    Discussed are several different transformations based on the generation of fractals including self-similar designs, the chaos game, the koch curve, and the Sierpinski Triangle. Three computer programs which illustrate these concepts are provided. (CW)

1. Missing great earthquakes

   USGS Publications Warehouse

   Hough, Susan E.

   2013-01-01

   The occurrence of three earthquakes with moment magnitude (Mw) greater than 8.8 and six earthquakes larger than Mw 8.5, since 2004, has raised interest in the long-term global rate of great earthquakes. Past studies have focused on the analysis of earthquakes since 1900, which roughly marks the start of the instrumental era in seismology. Before this time, the catalog is less complete and magnitude estimates are more uncertain. Yet substantial information is available for earthquakes before 1900, and the catalog of historical events is being used increasingly to improve hazard assessment. Here I consider the catalog of historical earthquakes and show that approximately half of all Mw ≥ 8.5 earthquakes are likely missing or underestimated in the 19th century. I further present a reconsideration of the felt effects of the 8 February 1843, Lesser Antilles earthquake, including a first thorough assessment of felt reports from the United States, and show it is an example of a known historical earthquake that was significantly larger than initially estimated. The results suggest that incorporation of best available catalogs of historical earthquakes will likely lead to a significant underestimation of seismic hazard and/or the maximum possible magnitude in many regions, including parts of the Caribbean.

2. Decoding the Margins: What Can the Fractal Geometry of Basaltic Flow Margins Tell Us?

   NASA Astrophysics Data System (ADS)

   Schaefer, E. I.; Hamilton, C.; Neish, C.; Beard, S. P.; Bramson, A. M.; Sori, M.; Rader, E. L.

   2016-12-01

   Studying lava flows on other planetary bodies is essential to characterizing eruption styles and constraining the bodies' thermal evolution. Although planetary basaltic flows are common, many key features are not resolvable in orbital imagery. We are thus developing a technique to characterize basaltic flow type, sub-meter roughness, and sediment mantling from these data. We will present the results from upcoming fieldwork at Craters of the Moon National Monument and Preserve with FINESSE (August) and at Hawai'i Volcanoes National Park (September). We build on earlier work that showed that basaltic flow margins are approximately fractal [Bruno et al., 1992; Gaonac'h et al., 1992] and that their fractal dimensions (D) have distinct `a`ā and pāhoehoe ranges under simple conditions [Bruno et al., 1994]. Using a differential GPS rover, we have recently shown that the margin of Iceland's 2014 Holuhraun flow exhibits near-perfect (R2=0.9998) fractality for ≥24 km across dm to km scales [Schaefer et al., 2016]. This finding suggests that a fractal-based technique has significant potential to characterize flows at sub-resolution scales. We are simultaneously seeking to understand how margin fractality can be modified. A preliminary result for an `a'ā flow in Hawaii's Ka'ū Desert suggests that although aeolian mantling obscures the original flow margin, the apparent margin (i.e., sediment-lava interface) remains fractal [Schaefer et al., 2015]. Further, the apparent margin's D is likely significantly modified from that of the original margin. Other factors that we are exploring include erosion, transitional flow types, and topographic confinement. We will also rigorously test the intriguing possibility that margin D correlates with the sub-meter Hurst exponent H of the flow surface, a common metric of roughness scaling [e.g., Shepard et al., 2001]. This hypothesis is based on geometric arguments [Turcotte, 1997] and is qualitatively consistent with all results so far.

3. A Complex Story: Universal Preference vs. Individual Differences Shaping Aesthetic Response to Fractals Patterns

   PubMed Central

   Street, Nichola; Forsythe, Alexandra M.; Reilly, Ronan; Taylor, Richard; Helmy, Mai S.

   2016-01-01

   Fractal patterns offer one way to represent the rough complexity of the natural world. Whilst they dominate many of our visual experiences in nature, little large-scale perceptual research has been done to explore how we respond aesthetically to these patterns. Previous research (Taylor et al., 2011) suggests that the fractal patterns with mid-range fractal dimensions (FDs) have universal aesthetic appeal. Perceptual and aesthetic responses to visual complexity have been more varied with findings suggesting both linear (Forsythe et al., 2011) and curvilinear (Berlyne, 1970) relationships. Individual differences have been found to account for many of the differences we see in aesthetic responses but some, such as culture, have received little attention within the fractal and complexity research fields. This two-study article aims to test preference responses to FD and visual complexity, using a large cohort (N = 443) of participants from around the world to allow universality claims to be tested. It explores the extent to which age, culture and gender can predict our preferences for fractally complex patterns. Following exploratory analysis that found strong correlations between FD and visual complexity, a series of linear mixed-effect models were implemented to explore if each of the individual variables could predict preference. The first tested a linear complexity model (likelihood of selecting the more complex image from the pair of images) and the second a mid-range FD model (likelihood of selecting an image within mid-range). Results show that individual differences can reliably predict preferences for complexity across culture, gender and age. However, in fitting with current findings the mid-range models show greater consistency in preference not mediated by gender, age or culture. This article supports the established theory that the mid-range fractal patterns appear to be a universal construct underlying preference but also highlights the fragility of

4. A Complex Story: Universal Preference vs. Individual Differences Shaping Aesthetic Response to Fractals Patterns.

   PubMed

   Street, Nichola; Forsythe, Alexandra M; Reilly, Ronan; Taylor, Richard; Helmy, Mai S

   2016-01-01

   Fractal patterns offer one way to represent the rough complexity of the natural world. Whilst they dominate many of our visual experiences in nature, little large-scale perceptual research has been done to explore how we respond aesthetically to these patterns. Previous research (Taylor et al., 2011) suggests that the fractal patterns with mid-range fractal dimensions (FDs) have universal aesthetic appeal. Perceptual and aesthetic responses to visual complexity have been more varied with findings suggesting both linear (Forsythe et al., 2011) and curvilinear (Berlyne, 1970) relationships. Individual differences have been found to account for many of the differences we see in aesthetic responses but some, such as culture, have received little attention within the fractal and complexity research fields. This two-study article aims to test preference responses to FD and visual complexity, using a large cohort (N = 443) of participants from around the world to allow universality claims to be tested. It explores the extent to which age, culture and gender can predict our preferences for fractally complex patterns. Following exploratory analysis that found strong correlations between FD and visual complexity, a series of linear mixed-effect models were implemented to explore if each of the individual variables could predict preference. The first tested a linear complexity model (likelihood of selecting the more complex image from the pair of images) and the second a mid-range FD model (likelihood of selecting an image within mid-range). Results show that individual differences can reliably predict preferences for complexity across culture, gender and age. However, in fitting with current findings the mid-range models show greater consistency in preference not mediated by gender, age or culture. This article supports the established theory that the mid-range fractal patterns appear to be a universal construct underlying preference but also highlights the fragility of

5. Estimation of Fractal Dimension in Differential Diagnosis of Pigmented Skin Lesions

   NASA Astrophysics Data System (ADS)

   Aralica, Gorana; Milošević, Danko; Konjevoda, Paško; Seiwerth, Sven; Štambuk, Nikola

   Medical differential diagnosis is a method of identifying the presence of a particular entity (disease) within a set of multiple possible alternatives. The significant problem in dermatology and pathology is the differential diagnosis of malignant melanoma and other pigmented skin lesions, especially of dysplastic nevi. Malignant melanoma is the most malignant skin neoplasma, with increasing incidence in various parts of the world. It is hoped that the methods of quantitative pathology, i.e. morphometry, can help objectification of the diagnostic process, since early discovery of melanoma results in 10-year survival rate of 90%. The aim of the study was to use fractal dimension calculated from the perimeter-area relation of the cell nuclei as a tool for the differential diagnosis of pigmented skin lesions. We analyzed hemalaun-eosin stained pathohistological slides of pigmented skin lesions: intradermal naevi (n = 45), dysplastic naevi (n = 47), and malignant melanoma (n = 50). It was found that fractal dimension of malignant melanoma cell nuclei differs significantly from the intradermal and dysplastic naevi (p ≤ 0. 001, Steel-Dwass Multiple Comparison Test). Additionaly, ROC analysis confirmed the value of fractal dimension based evaluation. It is suggested that the estimation of fractal dimension from the perimeter-area relation of the cell nuclei may be a potentially useful morphometric parameter in the medical differential diagnosis of pigmented skin lesions.

6. Surface and mass fractals in vapor-phase aggregates

   NASA Astrophysics Data System (ADS)

   Hurd, Alan J.; Schaefer, Dale W.; Martin, James E.

   1987-03-01

   Several types of fumed-silica aggregates with differing surface areas were studied over a wide range of spatial resolution by employing both light and neutron scattering. At intermediate length scales, between 100 and 1000 Å, the aggregates are mass fractals with Dm~=1.7-2.0, in basic agreement with simulations of aggregating clusters. At short length scales below 100 Å where the nature of the surfaces of the primary particles dominates the scattering, some of the samples appear to be fractally rough. In particular, a higher surface area seems to be correlated not with smaller primary particles in the aggregates, as previously assumed, but with fractally rough surfaces having Ds as high as 2.5. These may be the first materials discovered to have both mass and surface fractal structure.

7. Fractal analysis of bone structure with applications to osteoporosis and microgravity effects

   NASA Astrophysics Data System (ADS)

   Acharya, Raj S.; LeBlanc, Adrian; Shackelford, Linda; Swarnakar, Vivek; Krishnamurthy, Ram; Hausman, E.; Lin, Chin-Shoou

   1995-05-01

   We characterize the trabecular structure with the aid of fractal dimension. We use alternating sequential filters (ASF) to generate a nonlinear pyramid for fractal dimension computations. We do not make any assumptions of the statistical distributions of the underlying fractal bone structure. The only assumption of our scheme is the rudimentary definition of self-similarity. This allows us the freedom of not being constrained by statistical estimation schemes. With mathematical simulations, we have shown that the ASF methods outperform other existing methods for fractal dimension estimation. We have shown that the fractal dimension remains the same when computed with both the x-ray images and the MRI images of the patella. We have shown that the fractal dimension of osteoporotic subjects is lower than that of the normal subjects. In animal models, we have shown that the fractal dimension of osteoporotic rats was lower than that of the normal rats. In a 17 week bedrest study, we have shown that the subject's prebedrest fractal dimension is higher than that of the postbedrest fractal dimension.

8. TEC variations over the Mediterranean before and during the strong earthquake (M = 6.5) of 12th October 2013 in Crete, Greece

   NASA Astrophysics Data System (ADS)

   Contadakis, M. E.; Arabelos, D. N.; Vergos, G.; Spatalas, S. D.; Skordilis, M.

   In this paper, the total electron content (TEC) data from eight global positioning system (GPS) stations of the EUREF network, provided by IONOLAB (Turkey), were analyzed using discrete Fourier analysis to investigate the TEC variations over the Mediterranean before and during the strong earthquake of 12th October 2013, which occurred west of Crete, Greece. In accordance with the results of similar analyses in the area, the main conclusions of this study are the following: (a) TEC oscillations in a broad range of frequencies occur randomly over an area of several hundred km from the earthquake and (b) high frequency oscillations (f ⩾ 0.0003 Hz, periods T ⩽ 60 m) may point to the location of the earthquake with questionable accuracy. The fractal characteristics of the frequency distribution may point to the locus of the earthquake with higher accuracy. We conclude that the lithosphere-atmosphere-ionosphere coupling (LAIC) mechanism through acoustic or gravity waves could explain this phenomenology.

9. Fractals and the irreducibility of consciousness in plants and animals.

   PubMed

   Gardiner, John

   2013-08-01

   In both plants and animals consciousness is fractal. Since fractals can only pass information in one direction it is impossible to extrapolate backward to find the rule that governs the fractal. Thus, similarly, it will be impossible to completely determine the rule or rules that govern consciousness.

10. A new numerical approximation of the fractal ordinary differential equation

    NASA Astrophysics Data System (ADS)

    Atangana, Abdon; Jain, Sonal

    2018-02-01

    The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.

11. Fractal Viscous Fingering in Fracture Networks

    NASA Astrophysics Data System (ADS)

    Boyle, E.; Sams, W.; Ferer, M.; Smith, D. H.

    2007-12-01

    We have used two very different physical models and computer codes to study miscible injection of a low- viscosity fluid into a simple fracture network, where it displaces a much-more viscous "defending" fluid through "rock" that is otherwise impermeable. The one code (NETfLow) is a standard pore level model, originally intended to treat laboratory-scale experiments; it assumes negligible mixing of the two fluids. The other code (NFFLOW) was written to treat reservoir-scale engineering problems; It explicitly treats the flow through the fractures and allows for significant mixing of the fluids at the interface. Both codes treat the fractures as parallel plates, of different effective apertures. Results are presented for the composition profiles from both codes. Independent of the degree of fluid-mixing, the profiles from both models have a functional form identical to that for fractal viscous fingering (i.e., diffusion limited aggregation, DLA). The two codes that solve the equations for different models gave similar results; together they suggest that the injection of a low-viscosity fluid into large- scale fracture networks may be much more significantly affected by fractal fingering than previously illustrated.

12. Earthquake triggering by seismic waves following the landers and hector mine earthquakes

    USGS Publications Warehouse

    Gomberg, J.; Reasenberg, P.A.; Bodin, P.; Harris, R.A.

    2001-01-01

    The proximity and similarity of the 1992, magnitude 7.3 Landers and 1999, magnitude 7.1 Hector Mine earthquakes in California permit testing of earthquake triggering hypotheses not previously possible. The Hector Mine earthquake confirmed inferences that transient, oscillatory 'dynamic' deformations radiated as seismic waves can trigger seismicity rate increases, as proposed for the Landers earthquake1-6. Here we quantify the spatial and temporal patterns of the seismicity rate changes7. The seismicity rate increase was to the north for the Landers earthquake and primarily to the south for the Hector Mine earthquake. We suggest that rupture directivity results in elevated dynamic deformations north and south of the Landers and Hector Mine faults, respectively, as evident in the asymmetry of the recorded seismic velocity fields. Both dynamic and static stress changes seem important for triggering in the near field with dynamic stress changes dominating at greater distances. Peak seismic velocities recorded for each earthquake suggest the existence of, and place bounds on, dynamic triggering thresholds. These thresholds vary from a few tenths to a few MPa in most places, depend on local conditions, and exceed inferred static thresholds by more than an order of magnitude. At some sites, the onset of triggering was delayed until after the dynamic deformations subsided. Physical mechanisms consistent with all these observations may be similar to those that give rise to liquefaction or cyclic fatigue.

13. Fractality of eroded coastlines of correlated landscapes.

    PubMed

    Morais, P A; Oliveira, E A; Araújo, N A M; Herrmann, H J; Andrade, J S

    2011-07-01

    Using numerical simulations of a simple sea-coast mechanical erosion model, we investigate the effect of spatial long-range correlations in the lithology of coastal landscapes on the fractal behavior of the corresponding coastlines. In the model, the resistance of a coast section to erosion depends on the local lithology configuration as well as on the number of neighboring sea sides. For weak sea forces, the sea is trapped by the coastline and the eroding process stops after some time. For strong sea forces erosion is perpetual. The transition between these two regimes takes place at a critical sea force, characterized by a fractal coastline front. For uncorrelated landscapes, we obtain, at the critical value, a fractal dimension D=1.33, which is consistent with the dimension of the accessible external perimeter of the spanning cluster in two-dimensional percolation. For sea forces above the critical value, our results indicate that the coastline is self-affine and belongs to the Kardar-Parisi-Zhang universality class. In the case of landscapes generated with power-law spatial long-range correlations, the coastline fractal dimension changes continuously with the Hurst exponent H, decreasing from D=1.34 to 1.04, for H=0 and 1, respectively. This nonuniversal behavior is compatible with the multitude of fractal dimensions found for real coastlines.

14. Fractals and the irreducibility of consciousness in plants and animals

    PubMed Central

    Gardiner, John

    2013-01-01

    In both plants and animals consciousness is fractal. Since fractals can only pass information in one direction it is impossible to extrapolate backward to find the rule that governs the fractal. Thus, similarly, it will be impossible to completely determine the rule or rules that govern consciousness. PMID:23759545

15. Persistent fluctuations in stride intervals under fractal auditory stimulation.

    PubMed

    Marmelat, Vivien; Torre, Kjerstin; Beek, Peter J; Daffertshofer, Andreas

    2014-01-01

    Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.

16. Methods of nanoassembly of a fractal polymer and materials formed thereby

    SciTech Connect

    Newkome, George R; Moorefield, Charles N

    2012-07-24

    The invention relates to the formation of synthesized fractal constructs and the methods of chemical self-assembly for the preparation of a non-dendritic, nano-scale, fractal constructs or molecules. More particularly, the invention relates to fractal constructs formed by molecular self-assembly, to create synthetic, nanometer-scale fractal shapes. In an embodiment, a nanoscale Sierpinski hexagonal gasket is formed. This non-dendritic, perfectly self-similar fractal macromolecule is comprised of bisterpyridine building blocks that are bound together by coordination to 36 Ru and 6 Fe ions to form a nearly planar array of increasingly larger hexagons around a hollow center.

17. Methods of nanoassembly of a fractal polymer and materials formed thereby

    SciTech Connect

    Newkome, George R; Moorefield, Charles N

    2014-09-23

    The invention relates to the formation of synthesized fractal constructs and the methods of chemical self-assembly for the preparation of a non-dendritic, nano-scale, fractal constructs or molecules. More particularly, the invention relates to fractal constructs formed by molecular self-assembly, to create synthetic, nanometer-scale fractal shapes. In an embodiment, a nanoscale Sierpinski hexagonal gasket is formed. This non-dendritic, perfectly self-similar fractal macromolecule is comprised of bisterpyridine building blocks that are bound together by coordination to (36) Ru and (6) Fe ions to form a nearly planar array of increasingly larger hexagons around a hollow center.

18. Applications of fractals in ecology.

    PubMed

    Sugihara, G; M May, R

    1990-03-01

    Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems. Copyright © 1990. Published by Elsevier Ltd.

19. Multi-Scale Fractal Analysis of Image Texture and Pattern

    NASA Technical Reports Server (NTRS)

    Emerson, Charles W.; Lam, Nina Siu-Ngan; Quattrochi, Dale A.

    1999-01-01

    Analyses of the fractal dimension of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat Thematic Mapper images of the East Humboldt Range in Nevada taken four months apart show a more complex relation between pixel size and fractal dimension. The major visible difference between the spring and late summer NDVI images is the absence of high elevation snow cover in the summer image. This change significantly alters the relation between fractal dimension and pixel size. The slope of the fractal dimension-resolution relation provides indications of how image classification or feature identification will be affected by changes in sensor spatial resolution.

20. Multi-Scale Fractal Analysis of Image Texture and Pattern

    NASA Technical Reports Server (NTRS)

    Emerson, Charles W.; Lam, Nina Siu-Ngan; Quattrochi, Dale A.

    1999-01-01

    Analyses of the fractal dimension of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat Thematic Mapper images of the East Humboldt Range in Nevada taken four months apart show a more complex relation between pixel size and fractal dimension. The major visible difference between the spring and late summer NDVI images of the absence of high elevation snow cover in the summer image. This change significantly alters the relation between fractal dimension and pixel size. The slope of the fractal dimensional-resolution relation provides indications of how image classification or feature identification will be affected by changes in sensor spatial resolution.

1. Fractal rigidity in migraine

   NASA Astrophysics Data System (ADS)

   Latka, Miroslaw; Glaubic-Latka, Marta; Latka, Dariusz; West, Bruce J.

   2004-04-01

   We study the middle cerebral artery blood flow velocity (MCAfv) in humans using transcranial Doppler ultrasonography (TCD). Scaling properties of time series of the axial flow velocity averaged over a cardiac beat interval may be characterized by two exponents. The short time scaling exponent (STSE) determines the statistical properties of fluctuations of blood flow velocities in short-time intervals while the Hurst exponent describes the long-term fractal properties. In many migraineurs the value of the STSE is significantly reduced and may approach that of the Hurst exponent. This change in dynamical properties reflects the significant loss of short-term adaptability and the overall hyperexcitability of the underlying cerebral blood flow control system. We call this effect fractal rigidity.

2. Fractal analysis of bone structure with applications to osteoporosis and microgravity effects

   SciTech Connect

   Acharya, R.S.; Swarnarkar, V.; Krishnamurthy, R.

   1995-12-31

   The authors characterize the trabecular structure with the aid of fractal dimension. The authors use Alternating Sequential filters to generate a nonlinear pyramid for fractal dimension computations. The authors do not make any assumptions of the statistical distributions of the underlying fractal bone structure. The only assumption of the scheme is the rudimentary definition of self similarity. This allows them the freedom of not being constrained by statistical estimation schemes. With mathematical simulations, the authors have shown that the ASF methods outperform other existing methods for fractal dimension estimation. They have shown that the fractal dimension remains the same whenmore » computed with both the X-Ray images and the MRI images of the patella. They have shown that the fractal dimension of osteoporotic subjects is lower than that of the normal subjects. In animal models, the authors have shown that the fractal dimension of osteoporotic rats was lower than that of the normal rats. In a 17 week bedrest study, they have shown that the subject`s prebedrest fractal dimension is higher than that of the postbedrest fractal dimension.« less

3. Fractal Music: The Mathematics Behind "Techno" Music

   ERIC Educational Resources Information Center

   Padula, Janice

   2005-01-01

   This article describes sound waves, their basis in the sine curve, Fourier's theorem of infinite series, the fractal equation and its application to the composition of music, together with algorithms (such as those employed by meteorologist Edward Lorenz in his discovery of chaos theory) that are now being used to compose fractal music on…

4. Fractal dimension and the navigational information provided by natural scenes.

   PubMed

   Shamsyeh Zahedi, Moosarreza; Zeil, Jochen

   2018-01-01

   Recent work on virtual reality navigation in humans has suggested that navigational success is inversely correlated with the fractal dimension (FD) of artificial scenes. Here we investigate the generality of this claim by analysing the relationship between the fractal dimension of natural insect navigation environments and a quantitative measure of the navigational information content of natural scenes. We show that the fractal dimension of natural scenes is in general inversely proportional to the information they provide to navigating agents on heading direction as measured by the rotational image difference function (rotIDF). The rotIDF determines the precision and accuracy with which the orientation of a reference image can be recovered or maintained and the range over which a gradient descent in image differences will find the minimum of the rotIDF, that is the reference orientation. However, scenes with similar fractal dimension can differ significantly in the depth of the rotIDF, because FD does not discriminate between the orientations of edges, while the rotIDF is mainly affected by edge orientation parallel to the axis of rotation. We present a new equation for the rotIDF relating navigational information to quantifiable image properties such as contrast to show (1) that for any given scene the maximum value of the rotIDF (its depth) is proportional to pixel variance and (2) that FD is inversely proportional to pixel variance. This contrast dependence, together with scene differences in orientation statistics, explains why there is no strict relationship between FD and navigational information. Our experimental data and their numerical analysis corroborate these results.

5. Enhanced Graphene Photodetector with Fractal Metasurface.

   PubMed

   Fang, Jieran; Wang, Di; DeVault, Clayton T; Chung, Ting-Fung; Chen, Yong P; Boltasseva, Alexandra; Shalaev, Vladimir M; Kildishev, Alexander V

   2017-01-11

   Graphene has been demonstrated to be a promising photodetection material because of its ultrabroadband optical absorption, compatibility with CMOS technology, and dynamic tunability in optical and electrical properties. However, being a single atomic layer thick, graphene has intrinsically small optical absorption, which hinders its incorporation with modern photodetecting systems. In this work, we propose a gold snowflake-like fractal metasurface design to realize broadband and polarization-insensitive plasmonic enhancement in graphene photodetector. We experimentally obtain an enhanced photovoltage from the fractal metasurface that is an order of magnitude greater than that generated at a plain gold-graphene edge and such an enhancement in the photovoltage sustains over the entire visible spectrum. We also observed a relatively constant photoresponse with respect to polarization angles of incident light, as a result of the combination of two orthogonally oriented concentric hexagonal fractal geometries in one metasurface.

6. A Fractal Permeability Model for Shale Oil Reservoir

   NASA Astrophysics Data System (ADS)

   Zhang, Tao; Dong, Mingzhe; Li, Yajun

   2018-01-01

   In this work, a fractal analytical model is proposed to predict the permeability of shale reservoir. The proposed model explicitly relates the permeability to the micro-structural parameters (tortuosity, pore area fractal dimensions, porosity and slip velocity coefficient) of shale.

7. Dynamic fractals in spatial evolutionary games

   NASA Astrophysics Data System (ADS)

   Kolotev, Sergei; Malyutin, Aleksandr; Burovski, Evgeni; Krashakov, Sergei; Shchur, Lev

   2018-06-01

   We investigate critical properties of a spatial evolutionary game based on the Prisoner's Dilemma. Simulations demonstrate a jump in the component densities accompanied by drastic changes in average sizes of the component clusters. We argue that the cluster boundary is a random fractal. Our simulations are consistent with the fractal dimension of the boundary being equal to 2, and the cluster boundaries are hence asymptotically space filling as the system size increases.

8. Earthquake potential revealed by tidal influence on earthquake size-frequency statistics

   NASA Astrophysics Data System (ADS)

   Ide, Satoshi; Yabe, Suguru; Tanaka, Yoshiyuki

   2016-11-01

   The possibility that tidal stress can trigger earthquakes is long debated. In particular, a clear causal relationship between small earthquakes and the phase of tidal stress is elusive. However, tectonic tremors deep within subduction zones are highly sensitive to tidal stress levels, with tremor rate increasing at an exponential rate with rising tidal stress. Thus, slow deformation and the possibility of earthquakes at subduction plate boundaries may be enhanced during periods of large tidal stress. Here we calculate the tidal stress history, and specifically the amplitude of tidal stress, on a fault plane in the two weeks before large earthquakes globally, based on data from the global, Japanese, and Californian earthquake catalogues. We find that very large earthquakes, including the 2004 Sumatran, 2010 Maule earthquake in Chile and the 2011 Tohoku-Oki earthquake in Japan, tend to occur near the time of maximum tidal stress amplitude. This tendency is not obvious for small earthquakes. However, we also find that the fraction of large earthquakes increases (the b-value of the Gutenberg-Richter relation decreases) as the amplitude of tidal shear stress increases. The relationship is also reasonable, considering the well-known relationship between stress and the b-value. This suggests that the probability of a tiny rock failure expanding to a gigantic rupture increases with increasing tidal stress levels. We conclude that large earthquakes are more probable during periods of high tidal stress.

9. Fractal continuum model for tracer transport in a porous medium.

   PubMed

   Herrera-Hernández, E C; Coronado, M; Hernández-Coronado, H

   2013-12-01

   A model based on the fractal continuum approach is proposed to describe tracer transport in fractal porous media. The original approach has been extended to treat tracer transport and to include systems with radial and uniform flow, which are cases of interest in geoscience. The models involve advection due to the fluid motion in the fractal continuum and dispersion whose mathematical expression is taken from percolation theory. The resulting advective-dispersive equations are numerically solved for continuous and for pulse tracer injection. The tracer profile and the tracer breakthrough curve are evaluated and analyzed in terms of the fractal parameters. It has been found in this work that anomalous transport frequently appears, and a condition on the fractal parameter values to predict when sub- or superdiffusion might be expected has been obtained. The fingerprints of fractality on the tracer breakthrough curve in the explored parameter window consist of an early tracer breakthrough and long tail curves for the spherical and uniform flow cases, and symmetric short tailed curves for the radial flow case.

10. Multifractal Detrended Fluctuation Analysis of Self-Potential Field Prior to the M 6.5, October 24, 1993 Earthquake in MÉXICO

    NASA Astrophysics Data System (ADS)

    Cervantes, F.; González-Trejo, J. I.; Real-Ramírez, C. A.; Hoyos-Reyes, L. F.; Area de Sistemas Computacionales

    2013-05-01

    In the current literature on seismo electromagnetic, it has been reported many earthquakes which present electromagnetic anomalies as probable precursors of their occurrences. Although this methodology remains yet under discussion, is relevant to study many particular cases. In this work, we report a multifractal detrended fluctuation analysis (MFDFA) of electroseismic signals recorded in the Acapulco station during 1993. In October 24, 1993, occurred and earthquake (EQ) with M 6.5, with epicenter at (16.54 N, 98.98 W), 100Km away from the mentioned station. The multifractal spectrum identifies the deviations in fractal structure within time periods with large and small fluctuations. We discuss the dynamical meaning of this analysis and its possible relation with the mentioned EQ.

11. Persistent Fluctuations in Stride Intervals under Fractal Auditory Stimulation

    PubMed Central

    Marmelat, Vivien; Torre, Kjerstin; Beek, Peter J.; Daffertshofer, Andreas

    2014-01-01

    Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals. PMID:24651455

12. Multispectral image fusion based on fractal features

    NASA Astrophysics Data System (ADS)

    Tian, Jie; Chen, Jie; Zhang, Chunhua

    2004-01-01

    Imagery sensors have been one indispensable part of the detection and recognition systems. They are widely used to the field of surveillance, navigation, control and guide, et. However, different imagery sensors depend on diverse imaging mechanisms, and work within diverse range of spectrum. They also perform diverse functions and have diverse circumstance requires. So it is unpractical to accomplish the task of detection or recognition with a single imagery sensor under the conditions of different circumstances, different backgrounds and different targets. Fortunately, the multi-sensor image fusion technique emerged as important route to solve this problem. So image fusion has been one of the main technical routines used to detect and recognize objects from images. While, loss of information is unavoidable during fusion process, so it is always a very important content of image fusion how to preserve the useful information to the utmost. That is to say, it should be taken into account before designing the fusion schemes how to avoid the loss of useful information or how to preserve the features helpful to the detection. In consideration of these issues and the fact that most detection problems are actually to distinguish man-made objects from natural background, a fractal-based multi-spectral fusion algorithm has been proposed in this paper aiming at the recognition of battlefield targets in the complicated backgrounds. According to this algorithm, source images are firstly orthogonally decomposed according to wavelet transform theories, and then fractal-based detection is held to each decomposed image. At this step, natural background and man-made targets are distinguished by use of fractal models that can well imitate natural objects. Special fusion operators are employed during the fusion of area that contains man-made targets so that useful information could be preserved and features of targets could be extruded. The final fused image is reconstructed from the

13. Fractal characterization of a fractured chalk reservoir - The Laegerdorf case

    SciTech Connect

    Stoelum, H.H.; Koestler, A.G.; Feder, J.

    1991-03-01

    What is the matrix block size distribution of a fractured reservoir In order to answer this question and assess the potential of fractal geometry as a method of characterization of fracture networks, a pilot study has been done of the fractured chalk quarry in Laegerdorf. The fractures seen on the quarry walls were traced in the field for a total area of {approximately}200 {times} 45 m. The digitized pictures have been analyzed by a standard box-counting method. This analysis gave a fractal dimension of similarity varying from 1.33 for fractured areas between faults, to 1.43 for the fault zone, andmore » 1.53 for the highly deformed fault gouge. The amplitude showed a similar trend. The fractal dimension for the whole system of fractures is {approximately}1.55. In other words, fracture networks in chalk have a nonlinear, fractal geometry, and so matrix block size is a scaling property of chalk reservoirs. In terms of rock mechanics, the authors interpret the variation of the fractal dimension as follows: A small fractal dimension and amplitude are associated with brittle deformation in the elastic regime, while a large fractal dimension and amplitude are associated with predominantly ductile, strain softening deformation in the plastic regime. The interaction between the two regimes of deformation in the rock body is a key element of successful characterization and may be approached by seeing the rock as a non-Newtonian viscoelastic medium. The fractal dimension for the whole is close to a material independent limit that constrains the development of fractures.« less

14. Fractal and multifractal analyses of bipartite networks

    NASA Astrophysics Data System (ADS)

    Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

    2017-03-01

    Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

15. Fractal and multifractal analyses of bipartite networks.

    PubMed

    Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

    2017-03-31

    Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

16. Fractal and multifractal analyses of bipartite networks

    PubMed Central

    Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

    2017-01-01

    Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions. PMID:28361962

17. Hyper-Fractal Analysis: A visual tool for estimating the fractal dimension of 4D objects

    NASA Astrophysics Data System (ADS)

    Grossu, I. V.; Grossu, I.; Felea, D.; Besliu, C.; Jipa, Al.; Esanu, T.; Bordeianu, C. C.; Stan, E.

    2013-04-01

    This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03) Catalogue identifier: AEEG_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 745761 No. of bytes in distributed program, including test data, etc.: 12544491 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 100M Classification: 14 Catalogue identifier of previous version: AEEG_v2_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831-832 Does the new version supersede the previous version? Yes Nature of problem: Estimating the fractal dimension of 4D images. Solution method: Optimized implementation of the 4D box-counting algorithm. Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images. The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files. A new form was added for generating 2D, 3D, and 4D test data. The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1). The algorithm could be extended, with minimum effort, to

18. Passenger flow analysis of Beijing urban rail transit network using fractal approach

    NASA Astrophysics Data System (ADS)

    Li, Xiaohong; Chen, Peiwen; Chen, Feng; Wang, Zijia

    2018-04-01

    To quantify the spatiotemporal distribution of passenger flow and the characteristics of an urban rail transit network, we introduce four radius fractal dimensions and two branch fractal dimensions by combining a fractal approach with passenger flow assignment model. These fractal dimensions can numerically describe the complexity of passenger flow in the urban rail transit network and its change characteristics. Based on it, we establish a fractal quantification method to measure the fractal characteristics of passenger follow in the rail transit network. Finally, we validate the reasonability of our proposed method by using the actual data of Beijing subway network. It has been shown that our proposed method can effectively measure the scale-free range of the urban rail transit network, network development and the fractal characteristics of time-varying passenger flow, which further provides a reference for network planning and analysis of passenger flow.

19. Ulam method and fractal Weyl law for Perron-Frobenius operators

    NASA Astrophysics Data System (ADS)

    Ermann, L.; Shepelyansky, D. L.

    2010-06-01

    We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we numerically find the Weyl exponent ν = d/2 where d is the fractal dimension of strange attractor. The Weyl exponent can be also expressed via the relation ν = d0/2 where d0 is the fractal dimension of the invariant sets. We also discuss the properties of eigenvalues and eigenvectors of such operators characterized by the fractal Weyl law.

20. Resource Letter FR-1: Fractals

    NASA Astrophysics Data System (ADS)

    Hurd, Alan J.

    1988-11-01

    This Resource Letter provides a guide to the literature on fractals. Although ``fractal'' is a relatively new term in science, unifying many new ideas with established ones, its wide application and general popularity have made it one of the fastest growing fields in statistical physics. The letter E after an item indicates elementary level or material of general interest to persons becoming informed in the field; the letter I, for intermediate level, indicates material of somewhat more specialized nature; and the letter A indicates rather specialized or advanced material. An asterisk (*) indicates those articles to be included in an accompanying Reprint Book.

1. Fractal universe and quantum gravity.

   PubMed

   Calcagni, Gianluca

   2010-06-25

   We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.

2. Surface areas of fractally rough particles studied by scattering

   NASA Astrophysics Data System (ADS)

   Hurd, Alan J.; Schaefer, Dale W.; Smith, Douglas M.; Ross, Steven B.; Le Méhauté, Alain; Spooner, Steven

   1989-05-01

   The small-angle scattering from fractally rough surfaces has the potential to give information on the surface area at a given resolution. By use of quantitative neutron and x-ray scattering, a direct comparison of surface areas of fractally rough powders was made between scattering and adsorption techniques. This study supports a recently proposed correction to the theory for scattering from fractal surfaces. In addition, the scattering data provide an independent calibration of molecular adsorbate areas.

3. a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution

   NASA Astrophysics Data System (ADS)

   Xia, Yuxuan; Cai, Jianchao; Wei, Wei; Hu, Xiangyun; Wang, Xin; Ge, Xinmin

   Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.

4. Process for applying control variables having fractal structures

   DOEpatents

   Bullock, IV, Jonathan S.; Lawson, Roger L.

   1996-01-01

   A process and apparatus for the application of a control variable having a fractal structure to a body or process. The process of the present invention comprises the steps of generating a control variable having a fractal structure and applying the control variable to a body or process reacting in accordance with the control variable. The process is applicable to electroforming where first, second and successive pulsed-currents are applied to cause the deposition of material onto a substrate, such that the first pulsed-current, the second pulsed-current, and successive pulsed currents form a fractal pulsed-current waveform.

5. Process for applying control variables having fractal structures

   DOEpatents

   Bullock, J.S. IV; Lawson, R.L.

   1996-01-23

   A process and apparatus are disclosed for the application of a control variable having a fractal structure to a body or process. The process of the present invention comprises the steps of generating a control variable having a fractal structure and applying the control variable to a body or process reacting in accordance with the control variable. The process is applicable to electroforming where first, second and successive pulsed-currents are applied to cause the deposition of material onto a substrate, such that the first pulsed-current, the second pulsed-current, and successive pulsed currents form a fractal pulsed-current waveform. 3 figs.

6. Comprehensive Fractal Description of Porosity of Coal of Different Ranks

   PubMed Central

   Ren, Jiangang; Zhang, Guocheng; Song, Zhimin; Liu, Gaofeng; Li, Bing

   2014-01-01

   We selected, as the objects of our research, lignite from the Beizao Mine, gas coal from the Caiyuan Mine, coking coal from the Xiqu Mine, and anthracite from the Guhanshan Mine. We used the mercury intrusion method and the low-temperature liquid nitrogen adsorption method to analyze the structure and shape of the coal pores and calculated the fractal dimensions of different aperture segments in the coal. The experimental results show that the fractal dimension of the aperture segment of lignite, gas coal, and coking coal with an aperture of greater than or equal to 10 nm, as well as the fractal dimension of the aperture segment of anthracite with an aperture of greater than or equal to 100 nm, can be calculated using the mercury intrusion method; the fractal dimension of the coal pore, with an aperture range between 2.03 nm and 361.14 nm, can be calculated using the liquid nitrogen adsorption method, of which the fractal dimensions bounded by apertures of 10 nm and 100 nm are different. Based on these findings, we defined and calculated the comprehensive fractal dimensions of the coal pores and achieved the unity of fractal dimensions for full apertures of coal pores, thereby facilitating, overall characterization for the heterogeneity of the coal pore structure. PMID:24955407

7. Experimental investigation of the flow field and power consumption characteristics of regular and fractal blade impellers in a dynamic mixer

   NASA Astrophysics Data System (ADS)

   Steiros, K.; Bruce, P. J. K.; Buxton, O. R. H.; Vassilicos, J. C.

   2015-11-01

   Experiments have been performed in an octagonal un-baffled water tank, stirred by three radial turbines with different geometry impellers: (1) regular rectangular blades; (2) single-iteration fractal blades; (3) two-iteration fractal blades. Shaft torque was monitored and the power number calculated for each case. Both impellers with fractal geometry blades exhibited a decrease of turbine power number compared to the regular one (15% decrease for single-iteration and 19% for two iterations). Phase locked PIV in the discharge region of the blades revealed that the vortices emanating from the regular blades are more coherent, have higher kinetic energy, and advect faster towards the tank's walls where they are dissipated, compared to their fractal counterparts. This suggests a strong link between vortex production and behaviour and the energy input for the different impellers. Planar PIV measurements in the bulk of the tank showed an increase of turbulence intensity of over 20% for the fractal geometry blades, suggesting higher mixing efficiency. Experiments with pressure measurements on the different geometry blade surfaces are ongoing to investigate the distribution of forces, and calculate hydrodynamic centres of pressure. The authors would like to acknowledge the financial support given by European Union FP7 Marie Curie MULTISOLVE project (Grant Agreement No. 317269).

8. Fractal Dimensions of Umbral and Penumbral Regions of Sunspots

   NASA Astrophysics Data System (ADS)

   Rajkumar, B.; Haque, S.; Hrudey, W.

   2017-11-01

   The images of sunspots in 16 active regions taken at the University College of the Cayman Islands (UCCI) Observatory on Grand Cayman during June-November 2015 were used to determine their fractal dimensions using the perimeter-area method for the umbral and the penumbral region. Scale-free fractal dimensions of 2.09 ±0.42 and 1.72 ±0.4 were found, respectively. This value was higher than the value determined by Chumak and Chumak ( Astron. Astrophys. Trans. 10, 329, 1996), who used a similar method, but only for the penumbral region of their sample set. The umbral and penumbral fractal dimensions for the specific sunspots are positively correlated with r = 0.58. Furthermore, a similar time-series analysis was performed on eight images of AR 12403, from 21 August 2015 to 28 August 2015 taken from the Debrecen Photoheliographic Data (DPD). The correlation is r = 0.623 between the umbral and penumbral fractal dimensions in the time series, indicating that the complexity in morphology indicated by the fractal dimension between the umbra and penumbra followed each other in time as well.

9. Impact of earthquakes on sex ratio at birth: Eastern Marmara earthquakes

   PubMed Central

   Doğer, Emek; Çakıroğlu, Yiğit; Köpük, Şule Yıldırım; Ceylan, Yasin; Şimşek, Hayal Uzelli; Çalışkan, Eray

   2013-01-01

   Objective: Previous reports suggest that maternal exposure to acute stress related to earthquakes affects the sex ratio at birth. Our aim was to examine the change in sex ratio at birth after Eastern Marmara earthquake disasters. Material and Methods: This study was performed using the official birth statistics from January 1997 to December 2002 – before and after 17 August 1999, the date of the Golcuk Earthquake – supplied from the Turkey Statistics Institute. The secondary sex ratio was expressed as the male proportion at birth, and the ratio of both affected and unaffected areas were calculated and compared on a monthly basis using data from gender with using the Chi-square test. Results: We observed significant decreases in the secondary sex ratio in the 4th and 8th months following an earthquake in the affected region compared to the unaffected region (p= 0.001 and p= 0.024). In the earthquake region, the decrease observed in the secondary sex ratio during the 8th month after an earthquake was specific to the period after the earthquake. Conclusion: Our study indicated a significant reduction in the secondary sex ratio after an earthquake. With these findings, events that cause sudden intense stress such as earthquakes can have an effect on the sex ratio at birth. PMID:24592082

10. Results of the Regional Earthquake Likelihood Models (RELM) test of earthquake forecasts in California.

    PubMed

    Lee, Ya-Ting; Turcotte, Donald L; Holliday, James R; Sachs, Michael K; Rundle, John B; Chen, Chien-Chih; Tiampo, Kristy F

    2011-10-04

    The Regional Earthquake Likelihood Models (RELM) test of earthquake forecasts in California was the first competitive evaluation of forecasts of future earthquake occurrence. Participants submitted expected probabilities of occurrence of M ≥ 4.95 earthquakes in 0.1° × 0.1° cells for the period 1 January 1, 2006, to December 31, 2010. Probabilities were submitted for 7,682 cells in California and adjacent regions. During this period, 31 M ≥ 4.95 earthquakes occurred in the test region. These earthquakes occurred in 22 test cells. This seismic activity was dominated by earthquakes associated with the M = 7.2, April 4, 2010, El Mayor-Cucapah earthquake in northern Mexico. This earthquake occurred in the test region, and 16 of the other 30 earthquakes in the test region could be associated with it. Nine complete forecasts were submitted by six participants. In this paper, we present the forecasts in a way that allows the reader to evaluate which forecast is the most "successful" in terms of the locations of future earthquakes. We conclude that the RELM test was a success and suggest ways in which the results can be used to improve future forecasts.

11. Results of the Regional Earthquake Likelihood Models (RELM) test of earthquake forecasts in California

    PubMed Central

    Lee, Ya-Ting; Turcotte, Donald L.; Holliday, James R.; Sachs, Michael K.; Rundle, John B.; Chen, Chien-Chih; Tiampo, Kristy F.

    2011-01-01

    The Regional Earthquake Likelihood Models (RELM) test of earthquake forecasts in California was the first competitive evaluation of forecasts of future earthquake occurrence. Participants submitted expected probabilities of occurrence of M≥4.95 earthquakes in 0.1° × 0.1° cells for the period 1 January 1, 2006, to December 31, 2010. Probabilities were submitted for 7,682 cells in California and adjacent regions. During this period, 31 M≥4.95 earthquakes occurred in the test region. These earthquakes occurred in 22 test cells. This seismic activity was dominated by earthquakes associated with the M = 7.2, April 4, 2010, El Mayor–Cucapah earthquake in northern Mexico. This earthquake occurred in the test region, and 16 of the other 30 earthquakes in the test region could be associated with it. Nine complete forecasts were submitted by six participants. In this paper, we present the forecasts in a way that allows the reader to evaluate which forecast is the most “successful” in terms of the locations of future earthquakes. We conclude that the RELM test was a success and suggest ways in which the results can be used to improve future forecasts. PMID:21949355

12. Turbulent premixed flames on fractal-grid-generated turbulence

    NASA Astrophysics Data System (ADS)

    Soulopoulos, N.; Kerl, J.; Sponfeldner, T.; Beyrau, F.; Hardalupas, Y.; Taylor, A. M. K. P.; Vassilicos, J. C.

    2013-12-01

    A space-filling, low blockage fractal grid is used as a novel turbulence generator in a premixed turbulent flame stabilized by a rod. The study compares the flame behaviour with a fractal grid to the behaviour when a standard square mesh grid with the same effective mesh size and solidity as the fractal grid is used. The isothermal gas flow turbulence characteristics, including mean flow velocity and rms of velocity fluctuations and Taylor length, were evaluated from hot-wire measurements. The behaviour of the flames was assessed with direct chemiluminescence emission from the flame and high-speed OH-laser-induced fluorescence. The characteristics of the two flames are considered in terms of turbulent flame thickness, local flame curvature and turbulent flame speed. It is found that, for the same flow rate and stoichiometry and at the same distance downstream of the location of the grid, fractal-grid-generated turbulence leads to a more turbulent flame with enhanced burning rate and increased flame surface area.

13. Self-stabilized Fractality of Sea-coasts Through Damped Erosion

    NASA Astrophysics Data System (ADS)

    Sapoval, B.; Baldassari, A.; Gabrielli, A.

    2004-05-01

    Coastline morphology is of current interest in geophysical research and coastline erosion has important economic consequences. At the same time, although the geometry of seacoasts is often used as an introductory archetype of fractal morphology in nature there has been no explanation about which physical mechanism could justify that empirical observation. The present work propose a minimal, but robust, model of evolution of rocky coasts towards fractality. The model describes how a stationary fractal geometry arises spontaneously from the mutual self-stabilization of a rocky coast morphology and sea eroding power. If, on one hand, erosion generally increases the geometrical irregularity of the coast, on the other hand this increase creates a stronger damping of the sea and a consequent diminution of its eroding power. The increased damping argument relies on the studies of fractal acoustical cavities, which have shown that viscous damping is augmented on a longer, irregular, surface. A minimal two-dimensional model of erosion is introduced which leads to the through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with dimension close to 4/3. Fractal geometry plays here the role of a morphological attractor directly related to percolation geometry. The model reproduces at least qualitatively some of the features of real coasts using only simple ingredients: the randomness of the lithology and the decrease of the erosion power of the sea. B. Sapoval, Fractals (Aditech, Paris, 1989). B. Sapoval, O. Haeberlé, and S.Russ, J. Acoust. Soc. Am., 2014 (1997). B. Hébert B., B. Sapoval, and S.Russ, J. Acoust. Soc. Am., 1567 (1999).

14. Fractal cometary dust - a window into the early Solar system

    NASA Astrophysics Data System (ADS)

    Mannel, T.; Bentley, M. S.; Schmied, R.; Jeszenszky, H.; Levasseur-Regourd, A. C.; Romstedt, J.; Torkar, K.

    2016-11-01

    The properties of dust in the protoplanetary disc are key to understanding the formation of planets in our Solar system. Many models of dust growth predict the development of fractal structures which evolve into non-fractal, porous dust pebbles representing the main component for planetesimal accretion. In order to understand comets and their origins, the Rosetta orbiter followed comet 67P/Churyumov-Gerasimenko for over two years and carried a dedicated instrument suite for dust analysis. One of these instruments, the MIDAS (Micro-Imaging Dust Analysis System) atomic force microscope, recorded the 3D topography of micro- to nanometre-sized dust. All particles analysed to date have been found to be hierarchical agglomerates. Most show compact packing; however, one is extremely porous. This paper contains a structural description of a compact aggregate and the outstanding porous one. Both particles are tens of micrometres in size and show rather narrow subunit size distributions with noticeably similar mean values of 1.48^{+0.13}_{-0.59} μm for the porous particle and 1.36^{+0.15}_{-0.59} μm for the compact. The porous particle allows a fractal analysis, where a density-density correlation function yields a fractal dimension of Df = 1.70 ± 0.1. GIADA, another dust analysis instrument on board Rosetta, confirms the existence of a dust population with a similar fractal dimension. The fractal particles are interpreted as pristine agglomerates built in the protoplanetary disc and preserved in the comet. The similar subunits of both fractal and compact dust indicate a common origin which is, given the properties of the fractal, dominated by slow agglomeration of equally sized aggregates known as cluster-cluster agglomeration.

15. Fractal Geometry in the Arts: AN Overview across the Different Cultures

    NASA Astrophysics Data System (ADS)

    Sala, Nicoletta

    Fractal, in mathematics, is a geometric shape that is complex and detailed in structure at any level of magnification. The word "fractal" was coined less than thirty years ago by one of history's most creative and mathematicians, Benoit Mandelbrot, whose work, The Fractal Geometry of Nature, first introduced and explained concepts underlying this new vision of the geometry. Although other mathematical thinkers like Georg Cantor (1845-1918), Felix Hausdorff (1868-1942), Gaston Julia (1893-1978), Helge von Koch (1870-1924), Giuseppe Peano (1858-1932), Lewis Richardson (1891-1953), Waclaw Sierpinski (1882-1969) and others had attained isolated insights of fractal understanding, such ideas were largely ignored until Mandelbrot's genius forged them at a single blow into a gorgeously coherent and fascinating discipline. Fractal geometry is applied in different field now: engineering, physics, chemistry, biology, and architecture. The aim of this paper is to introduce an approach where the arts are analysed using a fractal point of view.

16. Fractal analysis as a potential tool for surface morphology of thin films

    NASA Astrophysics Data System (ADS)

    Soumya, S.; Swapna, M. S.; Raj, Vimal; Mahadevan Pillai, V. P.; Sankararaman, S.

    2017-12-01

    Fractal geometry developed by Mandelbrot has emerged as a potential tool for analyzing complex systems in the diversified fields of science, social science, and technology. Self-similar objects having the same details in different scales are referred to as fractals and are analyzed using the mathematics of non-Euclidean geometry. The present work is an attempt to correlate fractal dimension for surface characterization by Atomic Force Microscopy (AFM). Taking the AFM images of zinc sulphide (ZnS) thin films prepared by pulsed laser deposition (PLD) technique, under different annealing temperatures, the effect of annealing temperature and surface roughness on fractal dimension is studied. The annealing temperature and surface roughness show a strong correlation with fractal dimension. From the regression equation set, the surface roughness at a given annealing temperature can be calculated from the fractal dimension. The AFM images are processed using Photoshop and fractal dimension is calculated by box-counting method. The fractal dimension decreases from 1.986 to 1.633 while the surface roughness increases from 1.110 to 3.427, for a change of annealing temperature 30 ° C to 600 ° C. The images are also analyzed by power spectrum method to find the fractal dimension. The study reveals that the box-counting method gives better results compared to the power spectrum method.

17. Influence of Turbulent Flow and Fractal Scaling on Effective Permeability of Fracture Network

    NASA Astrophysics Data System (ADS)

    Zhu, J.

    2017-12-01

    A new approach is developed to calculate hydraulic gradient dependent effective permeability of a fractal fracture network where both laminar and turbulent flows may occur in individual fractures. A critical fracture length is used to distinguish flow characteristics in individual fractures. The developed new solutions can be used for the case of a general scaling relationship, an extension to the linear scaling. We examine the impact on the effective permeability of the network of fractal fracture network characteristics, which include the fractal scaling coefficient and exponent, fractal dimension, ratio of minimum over maximum fracture lengths. Results demonstrate that the developed solution can explain more variations of the effective permeability in relation to the fractal dimensions estimated from the field observations. At high hydraulic gradient the effective permeability decreases with the fractal scaling exponent, but increases with the fractal scaling exponent at low gradient. The effective permeability increases with the scaling coefficient, fractal dimension, fracture length ratio and maximum fracture length.

18. Fractal based curves in musical creativity: A critical annotation

    NASA Astrophysics Data System (ADS)

    Georgaki, Anastasia; Tsolakis, Christos

    In this article we examine fractal curves and synthesis algorithms in musical composition and research. First we trace the evolution of different approaches for the use of fractals in music since the 80's by a literature review. Furthermore, we review representative fractal algorithms and platforms that implement them. Properties such as self-similarity (pink noise), correlation, memory (related to the notion of Brownian motion) or non correlation at multiple levels (white noise), can be used to develop hierarchy of criteria for analyzing different layers of musical structure. L-systems can be applied in the modelling of melody in different musical cultures as well as in the investigation of musical perception principles. Finally, we propose a critical investigation approach for the use of artificial or natural fractal curves in systematic musicology.

19. Study on Conversion Between Momentum and Contrarian Based on Fractal Game

    NASA Astrophysics Data System (ADS)

    Wu, Xu; Song, Guanghui; Deng, Yan; Xu, Lin

    2015-06-01

    Based on the fractal game which is performed by the majority and the minority, the fractal market theory (FMT) is employed to describe the features of investors' decision-making. Accordingly, the process of fractal games is formed in order to analyze the statistical features of conversion between momentum and contrarian. The result shows that among three fractal game mechanisms, the statistical feature of simulated return rate series is much more similar to log returns on actual series. In addition, the conversion between momentum and contrarian is also extremely similar to real situation, which can reflect the effectiveness of using fractal game in analyzing the conversion between momentum and contrarian. Moreover, it also provides decision-making reference which helps investors develop effective investment strategy.

20. Investigation of changes in fractal dimension from layered retinal structures of healthy and diabetic eyes with optical coherence tomography

    NASA Astrophysics Data System (ADS)

    Gao, Wei; Zakharov, Valery P.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Artemyev, Dmitry N.; Kornilin, Dmitry V.

    2015-07-01

    Optical coherence tomography (OCT) is usually employed for the measurement of retinal thickness characterizing the structural changes of tissue. However, fractal dimension (FD) could also character the structural changes of tissue. Therefore, fractal dimension changes may provide further information regarding cellular layers and early damage in ocular diseases. We investigated the possibility of OCT in detecting changes in fractal dimension from layered retinal structures. OCT images were obtained from diabetic patients without retinopathy (DM, n = 38 eyes) or mild diabetic retinopathy (MDR, n = 43 eyes) and normal healthy subjects (Controls, n = 74 eyes). Fractal dimension was calculated using the differentiate box counting methodology. We evaluated the usefulness of quantifying fractal dimension of layered structures in the detection of retinal damage. Generalized estimating equations considering within-subject intereye relations were used to test for differences between the groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of fractal dimension to discriminate between the eyes of DM, MDR and healthy eyes. Significant decreases of fractal dimension were observed in all layers in the MDR eyes compared with controls except in the inner nuclear layer (INL). Significant decreases of fractal dimension were also observed in all layers in the MDR eyes compared with DM eyes. The highest area under receiver operating characteristic curve (AUROC) values estimated for fractal dimension were observed for the outer plexiform layer (OPL) and outer segment photoreceptors (OS) when comparing MDR eyes with controls. The highest AUROC value estimated for fractal dimension were also observed for the retinal nerve fiber layer (RNFL) and OS when comparing MDR eyes with DM eyes. Our results suggest that fractal dimension of the intraretinal layers may provide useful

1. Launching the chaotic realm of iso-fractals: A short remark

   SciTech Connect

   O'Schmidt, Nathan; Katebi, Reza; Corda, Christian

   In this brief note, we introduce the new, emerging sub-discipline of iso-fractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, non-linear, and self-similar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the iso-fractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot iso-sets. Third, we present the cutting-edge notion of dynamic iso-spaces and explain how a mathematical space can be iso-topically lifted with iso-unit functions that (continuously or discretely) change; in the discrete casemore » examples, we mention that iteratively generated sequences like Fibonacci’s numbers and (the complex moduli of) Mandelbrot’s numbers can supply a deterministic chain of iso-units to construct an ordered series of (magnified and/or de-magnified) iso-spaces that are locally iso-morphic. Fourth, we consider the initiation of iso-fractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D iso-spaces. In total, the reviewed iso-fractal results are a significant improvement over traditional fractals because the application of Santilli’s iso-mathematics arms us an extra degree of freedom for attacking problems in chaos. Finally, we conclude by proposing some questions and ideas for future research work.« less

2. Earthquake Damage Assessment Using Objective Image Segmentation: A Case Study of 2010 Haiti Earthquake

   NASA Technical Reports Server (NTRS)

   Oommen, Thomas; Rebbapragada, Umaa; Cerminaro, Daniel

   2012-01-01

   In this study, we perform a case study on imagery from the Haiti earthquake that evaluates a novel object-based approach for characterizing earthquake induced surface effects of liquefaction against a traditional pixel based change technique. Our technique, which combines object-oriented change detection with discriminant/categorical functions, shows the power of distinguishing earthquake-induced surface effects from changes in buildings using the object properties concavity, convexity, orthogonality and rectangularity. Our results suggest that object-based analysis holds promise in automatically extracting earthquake-induced damages from high-resolution aerial/satellite imagery.

3. Fractal model of polarization switching kinetics in ferroelectrics under nonequilibrium conditions of electron irradiation

   NASA Astrophysics Data System (ADS)

   Maslovskaya, A. G.; Barabash, T. K.

   2018-03-01

   The paper presents the results of the fractal and multifractal analysis of polarization switching current in ferroelectrics under electron irradiation, which allows statistical memory effects to be estimated at dynamics of domain structure. The mathematical model of formation of electron beam-induced polarization current in ferroelectrics was suggested taking into account the fractal nature of domain structure dynamics. In order to realize the model the computational scheme was constructed using the numerical solution approximation of fractional differential equation. Evidences of electron beam-induced polarization switching process in ferroelectrics were specified at a variation of control model parameters.

4. [Recent progress of research and applications of fractal and its theories in medicine].

   PubMed

   Cai, Congbo; Wang, Ping

   2014-10-01

   Fractal, a mathematics concept, is used to describe an image of self-similarity and scale invariance. Some organisms have been discovered with the fractal characteristics, such as cerebral cortex surface, retinal vessel structure, cardiovascular network, and trabecular bone, etc. It has been preliminarily confirmed that the three-dimensional structure of cells cultured in vitro could be significantly enhanced by bionic fractal surface. Moreover, fractal theory in clinical research will help early diagnosis and treatment of diseases, reducing the patient's pain and suffering. The development process of diseases in the human body can be expressed by the fractal theories parameter. It is of considerable significance to retrospectively review the preparation and application of fractal surface and its diagnostic value in medicine. This paper gives an application of fractal and its theories in the medical science, based on the research achievements in our laboratory.

5. Fractal markets: Liquidity and investors on different time horizons

   NASA Astrophysics Data System (ADS)

   Li, Da-Ye; Nishimura, Yusaku; Men, Ming

   2014-08-01

   In this paper, we propose a new agent-based model to study the source of liquidity and the “emergent” phenomenon in financial market with fractal structure. The model rests on fractal market hypothesis and agents with different time horizons of investments. What is interesting is that though the agent-based model reveals that the interaction between these heterogeneous agents affects the stability and liquidity of the financial market the real world market lacks detailed data to bring it to light since it is difficult to identify and distinguish the investors with different time horizons in the empirical approach. results show that in a relatively short period of time fractal market provides liquidity from investors with different horizons and the market gains stability when the market structure changes from uniformity to diversification. In the real world the fractal structure with the finite of horizons can only stabilize the market within limits. With the finite maximum horizons, the greater diversity of the investors and the fractal structure will not necessarily bring more stability to the market which might come with greater fluctuation in large time scale.

6. Is fractal 1/f scaling in stream chemistry universal?

   NASA Astrophysics Data System (ADS)

   Hrachowitz, Markus

   2016-04-01

   Stream water chemistry data from catchments worldwide suggest that catchments act as filters that transform white noise, i.e. random, input signals such as in precipitation, into 1/f^α noise whose slope in a power spectrum typically ranges between -0.5>α>-1.5. This previously lead to the hypothesis that catchments act as fractal filters. In other words, it was posed that considering uncertainty, a slope of α=-1 may be a universal and intrinsic property of catchments. Such fractal scaling characteristics would have considerable implications on the predictability of stream water chemistry, as both, temporal short- and long-range interdependence and memory control the system response. While short memories and thus flatter slopes with α closer to 0 indicate poor short term but good long-term predictability, steeper slopes with values of α <<-1 indicate the opposite. In fractal systems, i.e. where α=-1, this therefore leads to inherent problems of robustly predicting both, short and long-term response patterns. The hypothesis of catchments acting as fractal filters (α=-1), however, remains to be tested more profoundly. It is, for example, not yet clear, if the observed inter-catchment variations in α indeed need to be interpreted as uncertainty and noise in the signal or if the variations underlie a systematic pattern and can be explained by some characteristic of catchment function, as was recently suggested in a modelling study based two experimental catchments (Hrachowitz et al., 2015). Here we will therefore further test the hypothesis that the spectral slope of stream water chemistry is not necessarily α=-1 and that catchments therefore do not inherently act as fractal filters. Further, it will be tested if closer links between the variations in spectral slope and hydrological function of catchments can be identified. The combined data-analysis and modelling study uses hydrochemical data (i.e. Cl- and O-18) from a wide range of catchments worldwide to

7. A comparison of the fractal and JPEG algorithms

   NASA Technical Reports Server (NTRS)

   Cheung, K.-M.; Shahshahani, M.

   1991-01-01

   A proprietary fractal image compression algorithm and the Joint Photographic Experts Group (JPEG) industry standard algorithm for image compression are compared. In every case, the JPEG algorithm was superior to the fractal method at a given compression ratio according to a root mean square criterion and a peak signal to noise criterion.

8. a Fractal Permeability Model Coupling Boundary-Layer Effect for Tight Oil Reservoirs

   NASA Astrophysics Data System (ADS)

   Wang, Fuyong; Liu, Zhichao; Jiao, Liang; Wang, Congle; Guo, Hu

   A fractal permeability model coupling non-flowing boundary-layer effect for tight oil reservoirs was proposed. Firstly, pore structures of tight formations were characterized with fractal theory. Then, with the empirical equation of boundary-layer thickness, Hagen-Poiseuille equation and fractal theory, a fractal torturous capillary tube model coupled with boundary-layer effect was developed, and verified with experimental data. Finally, the parameters influencing effective liquid permeability were quantitatively investigated. The research results show that effective liquid permeability of tight formations is not only decided by pore structures, but also affected by boundary-layer distributions, and effective liquid permeability is the function of fluid type, fluid viscosity, pressure gradient, fractal dimension, tortuosity fractal dimension, minimum pore radius and maximum pore radius. For the tight formations dominated with nanoscale pores, boundary-layer effect can significantly reduce effective liquid permeability, especially under low pressure gradient.

9. Are fractal dimensions of the spatial distribution of mineral deposits meaningful?

   USGS Publications Warehouse

   Raines, G.L.

   2008-01-01

   definition of the permissive area. Density functions for porphyry copper deposits appear to be significantly different for regions in the Andes, Mexico, United States, and western Canada. Consequently, depending on which regional density function is used, quite different estimates of numbers of undiscovered deposits can be obtained. These fractal properties suggest that geologic studies based on mapping at scales of 1:24,000 to 1:100,000 may not recognize processes that are important in the formation of mineral deposits at scales larger than the crossover points at 30-60 km. ?? 2008 International Association for Mathematical Geology.

10. The Fractal Behavior of Crystal Distribution of la Gloria Pluton, Chile

    NASA Astrophysics Data System (ADS)

    Gutiérrez, F. J.; Payacán, I. J.; Pasten, D.; Aravena, A.; Gelman, S. E.; Bachmann, O.; Parada, M. A.

    2013-12-01

    We utilize fractal analysis to study the spatial distributions of crystals in a 10 Ma granitic intrusion (La Gloria pluton) located in the central Chilean Andes. Previous work determined the crystal size distribution (CSD) and anisotropy of magnetic susceptibility (AMS) tensors throughout this pluton. Using orthogonal thin sections oriented along the AMS tensor axes, we have applied fractal analysis in three magmatic crystal families: plagioclase, ferromagnesian minerals (biotite and amphibole), and Fe-Ti oxides (magnetite with minor ilmenite). We find that plagioclase and ferromagnesian minerals have a Semi-logarithmic CSD (S-CSD), given by: log(n/n0)= -L/C (1) where n [mm-4], n0 [mm-4], L [mm] and C [mm] are crystal density, intercept (nucleation density; L=0), size of crystals (three axes) and characteristic length, respectively. In contrast, Fe-Ti oxides have a Fractal CSD (F-CSD, power law size distribution), given by: log(n)= - Dn log(L) + n1 (2) where Dn and n1 [log(mm-4)] are a non-dimensional proportionality constant and the logarithm of the initial crystallization density (n1 = log(n(L=1 mm))), respectively. Finally, we calculate the fractal dimension (D0) by applying the box-counting method on each crystal thin section image, using: log(N) = -D0 log(ɛ) (3) where N and ɛ are the number of boxes occupied by minerals and the length of the square box, respectively. Results indicate that D0 values (eq. 3) are well defined for all minerals, and are higher for plagioclase than for ferromagnesian minerals and lowest for Fe-Ti oxides. D0 values are correlated with n0 and -1/C for S-CSD (eq. 1), and with n1 values for F-CSD (eq. 2). These correlations between fractal dimensions with CSD parameters suggest crystal growth follows a fractal behaviour in magmatic systems. Fractal behaviour of CSD means that the spatial distribution of crystals follows an all-scale pattern as part of a self-organized magmatic system. We interpret S-CSD of plagioclase and

11. A Fractal Excursion.

    ERIC Educational Resources Information Center

    Camp, Dane R.

    1991-01-01

    After introducing the two-dimensional Koch curve, which is generated by simple recursions on an equilateral triangle, the process is extended to three dimensions with simple recursions on a regular tetrahedron. Included, for both fractal sequences, are iterative formulae, illustrations of the first several iterations, and a sample PASCAL program.…

12. Characterisation of human non-proliferative diabetic retinopathy using the fractal analysis

    PubMed Central

    Ţălu, Ştefan; Călugăru, Dan Mihai; Lupaşcu, Carmen Alina

    2015-01-01

    AIM To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method. METHODS This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding to both normal (24 images) and pathological (148 images) states of the retina were examined. An automatic unsupervised method for retinal vessel segmentation was applied before fractal analysis. The fractal analyses of the retinal digital images were performed using the fractal analysis software ImageJ. Statistical analyses were performed for these groups using Microsoft Office Excel 2003 and GraphPad InStat software. RESULTS It was found that subtle changes in the vascular network geometry of the human retina are influenced by diabetic retinopathy (DR) and can be estimated using the fractal geometry. The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is slightly lower than the corresponding values of mild non-proliferative DR (NPDR) images (segmented and skeletonized versions). The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is higher than the corresponding values of moderate NPDR images (segmented and skeletonized versions). The lowest values were found for the corresponding values of severe NPDR images (segmented and skeletonized versions). CONCLUSION The fractal analysis of fundus photographs may be used for a more complete undeTrstanding of the early and basic pathophysiological mechanisms of diabetes. The architecture of the retinal microvasculature in diabetes can be quantitative quantified by means of the fractal dimension. Microvascular abnormalities on retinal imaging may elucidate early mechanistic pathways for microvascular complications and distinguish patients with DR from

13. Characterisation of human non-proliferative diabetic retinopathy using the fractal analysis.

    PubMed

    Ţălu, Ştefan; Călugăru, Dan Mihai; Lupaşcu, Carmen Alina

    2015-01-01

    To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method. This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding to both normal (24 images) and pathological (148 images) states of the retina were examined. An automatic unsupervised method for retinal vessel segmentation was applied before fractal analysis. The fractal analyses of the retinal digital images were performed using the fractal analysis software ImageJ. Statistical analyses were performed for these groups using Microsoft Office Excel 2003 and GraphPad InStat software. It was found that subtle changes in the vascular network geometry of the human retina are influenced by diabetic retinopathy (DR) and can be estimated using the fractal geometry. The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is slightly lower than the corresponding values of mild non-proliferative DR (NPDR) images (segmented and skeletonized versions). The average of fractal dimensions D for the normal images (segmented and skeletonized versions) is higher than the corresponding values of moderate NPDR images (segmented and skeletonized versions). The lowest values were found for the corresponding values of severe NPDR images (segmented and skeletonized versions). The fractal analysis of fundus photographs may be used for a more complete undeTrstanding of the early and basic pathophysiological mechanisms of diabetes. The architecture of the retinal microvasculature in diabetes can be quantitative quantified by means of the fractal dimension. Microvascular abnormalities on retinal imaging may elucidate early mechanistic pathways for microvascular complications and distinguish patients with DR from healthy individuals.

14. A fractal growth model: Exploring the connection pattern of hubs in complex networks

    NASA Astrophysics Data System (ADS)

    Li, Dongyan; Wang, Xingyuan; Huang, Penghe

    2017-04-01

    Fractal is ubiquitous in many real-world networks. Previous researches showed that the strong disassortativity between the hub-nodes on all length scales was the key principle that gave rise to the fractal architecture of networks. Although fractal property emerged in some models, there were few researches about the fractal growth model and quantitative analyses about the strength of the disassortativity for fractal model. In this paper, we proposed a novel inverse renormalization method, named Box-based Preferential Attachment (BPA), to build the fractal growth models in which the Preferential Attachment was performed at box level. The proposed models provided a new framework that demonstrated small-world-fractal transition. Also, we firstly demonstrated the statistical characteristic of connection patterns of the hubs in fractal networks. The experimental results showed that, given proper growing scale and added edges, the proposed models could clearly show pure small-world or pure fractal or both of them. It also showed that the hub connection ratio showed normal distribution in many real-world networks. At last, the comparisons of connection pattern between the proposed models and the biological and technical networks were performed. The results gave useful reference for exploring the growth principle and for modeling the connection patterns for real-world networks.

15. Numerical study of electromagnetic scattering from one-dimensional nonlinear fractal sea surface

    NASA Astrophysics Data System (ADS)

    Xie, Tao; He, Chao; William, Perrie; Kuang, Hai-Lan; Zou, Guang-Hui; Chen, Wei

    2010-02-01

    In recent years, linear fractal sea surface models have been developed for the sea surface in order to establish an electromagnetic backscattering model. Unfortunately, the sea surface is always nonlinear, particularly at high sea states. We present a nonlinear fractal sea surface model and derive an electromagnetic backscattering model. Using this model, we numerically calculate the normalized radar cross section (NRCS) of a nonlinear sea surface. Comparing the averaged NRCS between linear and nonlinear fractal models, we show that the NRCS of a linear fractal sea surface underestimates the NRCS of the real sea surface, especially for sea states with high fractal dimensions, and for dominant ocean surface gravity waves that are either very short or extremely long.

16. Analysis of fractal dimensions of rat bones from film and digital images

    NASA Technical Reports Server (NTRS)

    Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Yamauchi, M.

    2001-01-01

    OBJECTIVES: (1) To compare the effect of two different intra-oral image receptors on estimates of fractal dimension; and (2) to determine the variations in fractal dimensions between the femur, tibia and humerus of the rat and between their proximal, middle and distal regions. METHODS: The left femur, tibia and humerus from 24 4-6-month-old Sprague-Dawley rats were radiographed using intra-oral film and a charge-coupled device (CCD). Films were digitized at a pixel density comparable to the CCD using a flat-bed scanner. Square regions of interest were selected from proximal, middle, and distal regions of each bone. Fractal dimensions were estimated from the slope of regression lines fitted to plots of log power against log spatial frequency. RESULTS: The fractal dimensions estimates from digitized films were significantly greater than those produced from the CCD (P=0.0008). Estimated fractal dimensions of three types of bone were not significantly different (P=0.0544); however, the three regions of bones were significantly different (P=0.0239). The fractal dimensions estimated from radiographs of the proximal and distal regions of the bones were lower than comparable estimates obtained from the middle region. CONCLUSIONS: Different types of image receptors significantly affect estimates of fractal dimension. There was no difference in the fractal dimensions of the different bones but the three regions differed significantly.

17. Surface fractal dimension, water adsorption efficiency, and cloud nucleation activity of insoluble aerosol.

    PubMed

    Laaksonen, Ari; Malila, Jussi; Nenes, Athanasios; Hung, Hui-Ming; Chen, Jen-Ping

    2016-05-03

    Surface porosity affects the ability of a substance to adsorb gases. The surface fractal dimension D is a measure that indicates the amount that a surface fills a space, and can thereby be used to characterize the surface porosity. Here we propose a new method for determining D, based on measuring both the water vapour adsorption isotherm of a given substance, and its ability to act as a cloud condensation nucleus when introduced to humidified air in aerosol form. We show that our method agrees well with previous methods based on measurement of nitrogen adsorption. Besides proving the usefulness of the new method for general surface characterization of materials, our results show that the surface fractal dimension is an important determinant in cloud drop formation on water insoluble particles. We suggest that a closure can be obtained between experimental critical supersaturation for cloud drop activation and that calculated based on water adsorption data, if the latter is corrected using the surface fractal dimension of the insoluble cloud nucleus.

18. Surface fractal dimension, water adsorption efficiency, and cloud nucleation activity of insoluble aerosol

    NASA Astrophysics Data System (ADS)

    Laaksonen, Ari; Malila, Jussi; Nenes, Athanasios; Hung, Hui-Ming; Chen, Jen-Ping

    2016-05-01

    Surface porosity affects the ability of a substance to adsorb gases. The surface fractal dimension D is a measure that indicates the amount that a surface fills a space, and can thereby be used to characterize the surface porosity. Here we propose a new method for determining D, based on measuring both the water vapour adsorption isotherm of a given substance, and its ability to act as a cloud condensation nucleus when introduced to humidified air in aerosol form. We show that our method agrees well with previous methods based on measurement of nitrogen adsorption. Besides proving the usefulness of the new method for general surface characterization of materials, our results show that the surface fractal dimension is an important determinant in cloud drop formation on water insoluble particles. We suggest that a closure can be obtained between experimental critical supersaturation for cloud drop activation and that calculated based on water adsorption data, if the latter is corrected using the surface fractal dimension of the insoluble cloud nucleus.

19. Universal characteristics of fractal fluctuations in prime number distribution

    NASA Astrophysics Data System (ADS)

    Selvam, A. M.

    2014-11-01

    The frequency of occurrence of prime numbers at unit number spacing intervals exhibits self-similar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows, stock market fluctuations and population dynamics. The physics of long-range correlations exhibited by fractals is not yet identified. A recently developed general systems theory visualizes the eddy continuum underlying fractals to result from the growth of large eddies as the integrated mean of enclosed small scale eddies, thereby generating a hierarchy of eddy circulations or an inter-connected network with associated long-range correlations. The model predictions are as follows: (1) The probability distribution and power spectrum of fractals follow the same inverse power law which is a function of the golden mean. The predicted inverse power law distribution is very close to the statistical normal distribution for fluctuations within two standard deviations from the mean of the distribution. (2) Fractals signify quantum-like chaos since variance spectrum represents probability density distribution, a characteristic of quantum systems such as electron or photon. (3) Fractal fluctuations of frequency distribution of prime numbers signify spontaneous organization of underlying continuum number field into the ordered pattern of the quasiperiodic Penrose tiling pattern. The model predictions are in agreement with the probability distributions and power spectra for different sets of frequency of occurrence of prime numbers at unit number interval for successive 1000 numbers. Prime numbers in the first 10 million numbers were used for the study.

20. A tale of two fractals: The Hofstadter butterfly and the integral Apollonian gaskets

    NASA Astrophysics Data System (ADS)

    Satija, Indubala I.

    2016-11-01

    This paper unveils a mapping between a quantum fractal that describes a physical phenomena, and an abstract geometrical fractal. The quantum fractal is the Hofstadter butterfly discovered in 1976 in an iconic condensed matter problem of electrons moving in a two-dimensional lattice in a transverse magnetic field. The geometric fractal is the integer Apollonian gasket characterized in terms of a 300 BC problem of mutually tangent circles. Both of these fractals are made up of integers. In the Hofstadter butterfly, these integers encode the topological quantum numbers of quantum Hall conductivity. In the Apollonian gaskets an infinite number of mutually tangent circles are nested inside each other, where each circle has integer curvature. The mapping between these two fractals reveals a hidden D3 symmetry embedded in the kaleidoscopic images that describe the asymptotic scaling properties of the butterfly. This paper also serves as a mini review of these fractals, emphasizing their hierarchical aspects in terms of Farey fractions.

1. A fractal comparison of real and Austrian business cycle models

   NASA Astrophysics Data System (ADS)

   Mulligan, Robert F.

   2010-06-01

   Rescaled range and power spectral density analysis are applied to examine a diverse set of macromonetary data for fractal character and stochastic dependence. Fractal statistics are used to evaluate two competing models of the business cycle, Austrian business cycle theory and real business cycle theory. Strong evidence is found for antipersistent stochastic dependence in transactions money (M1) and components of the monetary aggregates most directly concerned with transactions, which suggests an activist monetary policy. Savings assets exhibit persistent long memory, as do those monetary aggregates which include savings assets, such as savings money (M2), M2 minus small time deposits, and money of zero maturity (MZM). Virtually all measures of economic activity display antipersistence, and this finding is invariant to whether the measures are adjusted for inflation, including real gross domestic product, real consumption expenditures, real fixed private investment, and labor productivity. This strongly disconfirms real business cycle theory.

2. Applications of Fractal Analytical Techniques in the Estimation of Operational Scale

   NASA Technical Reports Server (NTRS)

   Emerson, Charles W.; Quattrochi, Dale A.

   2000-01-01

   The observational scale and the resolution of remotely sensed imagery are essential considerations in the interpretation process. Many atmospheric, hydrologic, and other natural and human-influenced spatial phenomena are inherently scale dependent and are governed by different physical processes at different spatial domains. This spatial and operational heterogeneity constrains the ability to compare interpretations of phenomena and processes observed in higher spatial resolution imagery to similar interpretations obtained from lower resolution imagery. This is a particularly acute problem, since longterm global change investigations will require high spatial resolution Earth Observing System (EOS), Landsat 7, or commercial satellite data to be combined with lower resolution imagery from older sensors such as Landsat TM and MSS. Fractal analysis is a useful technique for identifying the effects of scale changes on remotely sensed imagery. The fractal dimension of an image is a non-integer value between two and three which indicates the degree of complexity in the texture and shapes depicted in the image. A true fractal surface exhibits self-similarity, a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution, and the slope of the fractal dimension-resolution relationship would be zero. Most geographical phenomena, however, are not self-similar at all scales, but they can be modeled by a stochastic fractal in which the scaling properties of the image exhibit patterns that can be described by statistics such as area-perimeter ratios and autocovariances. Stochastic fractal sets relax the self-similarity assumption and measure many scales and

3. Revisiting the 1872 Owens Valley, California, Earthquake

   USGS Publications Warehouse

   Hough, S.E.; Hutton, K.

   2008-01-01

   The 26 March 1872 Owens Valley earthquake is among the largest historical earthquakes in California. The felt area and maximum fault displacements have long been regarded as comparable to, if not greater than, those of the great San Andreas fault earthquakes of 1857 and 1906, but mapped surface ruptures of the latter two events were 2-3 times longer than that inferred for the 1872 rupture. The preferred magnitude estimate of the Owens Valley earthquake has thus been 7.4, based largely on the geological evidence. Reinterpreting macroseismic accounts of the Owens Valley earthquake, we infer generally lower intensity values than those estimated in earlier studies. Nonetheless, as recognized in the early twentieth century, the effects of this earthquake were still generally more dramatic at regional distances than the macroseismic effects from the 1906 earthquake, with light damage to masonry buildings at (nearest-fault) distances as large as 400 km. Macroseismic observations thus suggest a magnitude greater than that of the 1906 San Francisco earthquake, which appears to be at odds with geological observations. However, while the mapped rupture length of the Owens Valley earthquake is relatively low, the average slip was high. The surface rupture was also complex and extended over multiple fault segments. It was first mapped in detail over a century after the earthquake occurred, and recent evidence suggests it might have been longer than earlier studies indicated. Our preferred magnitude estimate is Mw 7.8-7.9, values that we show are consistent with the geological observations. The results of our study suggest that either the Owens Valley earthquake was larger than the 1906 San Francisco earthquake or that, by virtue of source properties and/or propagation effects, it produced systematically higher ground motions at regional distances. The latter possibility implies that some large earthquakes in California will generate significantly larger ground motions than San

4. Temporal fractals in seabird foraging behaviour: diving through the scales of time

   PubMed Central

   MacIntosh, Andrew J. J.; Pelletier, Laure; Chiaradia, Andre; Kato, Akiko; Ropert-Coudert, Yan

   2013-01-01

   Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (Eudyptula minor) across full-day foraging trips (216 data points; 4 orders of temporal magnitude). Results from 4 fractal methods show that dive sequences are long-range dependent and persistent across ca. 2 orders of magnitude. This fractal structure correlated with trip length and time spent underwater, but individual traits had little effect. Fractal time is a fundamental characteristic of penguin foraging behaviour, and its investigation is thus a promising avenue for research on interactions between animals and their environments. PMID:23703258

5. Fractal symmetry of protein interior: what have we learned?

   PubMed

   Banerji, Anirban; Ghosh, Indira

   2011-08-01

   The application of fractal dimension-based constructs to probe the protein interior dates back to the development of the concept of fractal dimension itself. Numerous approaches have been tried and tested over a course of (almost) 30 years with the aim of elucidating the various facets of symmetry of self-similarity prevalent in the protein interior. In the last 5 years especially, there has been a startling upsurge of research that innovatively stretches the limits of fractal-based studies to present an array of unexpected results on the biophysical properties of protein interior. In this article, we introduce readers to the fundamentals of fractals, reviewing the commonality (and the lack of it) between these approaches before exploring the patterns in the results that they produced. Clustering the approaches in major schools of protein self-similarity studies, we describe the evolution of fractal dimension-based methodologies. The genealogy of approaches (and results) presented here portrays a clear picture of the contemporary state of fractal-based studies in the context of the protein interior. To underline the utility of fractal dimension-based measures further, we have performed a correlation dimension analysis on all of the available non-redundant protein structures, both at the level of an individual protein and at the level of structural domains. In this investigation, we were able to separately quantify the self-similar symmetries in spatial correlation patterns amongst peptide-dipole units, charged amino acids, residues with the π-electron cloud and hydrophobic amino acids. The results revealed that electrostatic environments in the interiors of proteins belonging to 'α/α toroid' (all-α class) and 'PLP-dependent transferase-like' domains (α/β class) are highly conducive. In contrast, the interiors of 'zinc finger design' ('designed proteins') and 'knottins' ('small proteins') were identified as folds with the least conducive electrostatic

6. Earthquakes and emergence

   NASA Astrophysics Data System (ADS)

   Earthquakes and emerging infections may not have a direct cause and effect relationship like tax evasion and jail, but new evidence suggests that there may be a link between the two human health hazards. Various media accounts have cited a massive 1993 earthquake in Maharashtra as a potential catalyst of the recent outbreak of plague in India that has claimed more than 50 lives and alarmed the world. The hypothesis is that the earthquake may have uprooted underground rat populations that carry the fleas infected with the bacterium that causes bubonic plague and can lead to the pneumonic form of the disease that is spread through the air.

7. Fractals in the neurosciences, Part II: clinical applications and future perspectives.

   PubMed

   Di Ieva, Antonio; Esteban, Francisco J; Grizzi, Fabio; Klonowski, Wlodzimierz; Martín-Landrove, Miguel

   2015-02-01

   It has been ascertained that the human brain is a complex system studied at multiple scales, from neurons and microcircuits to macronetworks. The brain is characterized by a hierarchical organization that gives rise to its highly topological and functional complexity. Over the last decades, fractal geometry has been shown as a universal tool for the analysis and quantification of the geometric complexity of natural objects, including the brain. The fractal dimension has been identified as a quantitative parameter for the evaluation of the roughness of neural structures, the estimation of time series, and the description of patterns, thus able to discriminate different states of the brain in its entire physiopathological spectrum. Fractal-based computational analyses have been applied to the neurosciences, particularly in the field of clinical neurosciences including neuroimaging and neuroradiology, neurology and neurosurgery, psychiatry and psychology, and neuro-oncology and neuropathology. After a review of the basic concepts of fractal analysis and its main applications to the basic neurosciences in part I of this series, here, we review the main applications of fractals to the clinical neurosciences for a holistic approach towards a fractal geometry model of the brain. © The Author(s) 2013.

8. Analysis of Fractional Flow for Transient Two-Phase Flow in Fractal Porous Medium

   NASA Astrophysics Data System (ADS)

   Lu, Ting; Duan, Yonggang; Fang, Quantang; Dai, Xiaolu; Wu, Jinsui

   2016-03-01

   Prediction of fractional flow in fractal porous medium is important for reservoir engineering and chemical engineering as well as hydrology. A physical conceptual fractional flow model of transient two-phase flow is developed in fractal porous medium based on the fractal characteristics of pore-size distribution and on the approximation that porous medium consist of a bundle of tortuous capillaries. The analytical expression for fractional flow for wetting phase is presented, and the proposed expression is the function of structural parameters (such as tortuosity fractal dimension, pore fractal dimension, maximum and minimum diameters of capillaries) and fluid properties (such as contact angle, viscosity and interfacial tension) in fractal porous medium. The sensitive parameters that influence fractional flow and its derivative are formulated, and their impacts on fractional flow are discussed.

9. Technologically important extremophile 16S rRNA sequence Shannon entropy and fractal property comparison with long term dormant microbes

   NASA Astrophysics Data System (ADS)

   Holden, Todd; Gadura, N.; Dehipawala, S.; Cheung, E.; Tuffour, M.; Schneider, P.; Tremberger, G., Jr.; Lieberman, D.; Cheung, T.

   2011-10-01

   Technologically important extremophiles including oil eating microbes, uranium and rocket fuel perchlorate reduction microbes, electron producing microbes and electrode electrons feeding microbes were compared in terms of their 16S rRNA sequences, a standard targeted sequence in comparative phylogeny studies. Microbes that were reported to have survived a prolonged dormant duration were also studied. Examples included the recently discovered microbe that survives after 34,000 years in a salty environment while feeding off organic compounds from other trapped dead microbes. Shannon entropy of the 16S rRNA nucleotide composition and fractal dimension of the nucleotide sequence in terms of its atomic number fluctuation analyses suggest a selected range for these extremophiles as compared to other microbes; consistent with the experience of relatively mild evolutionary pressure. However, most of the microbes that have been reported to survive in prolonged dormant duration carry sequences with fractal dimension between 1.995 and 2.005 (N = 10 out of 13). Similar results are observed for halophiles, red-shifted chlorophyll and radiation resistant microbes. The results suggest that prolonged dormant duration, in analogous to high salty or radiation environment, would select high fractal 16S rRNA sequences. Path analysis in structural equation modeling supports a causal relation between entropy and fractal dimension for the studied 16S rRNA sequences (N = 7). Candidate choices for high fractal 16S rRNA microbes could offer protection for prolonged spaceflights. BioBrick gene network manipulation could include extremophile 16S rRNA sequences in synthetic biology and shed more light on exobiology and future colonization in shielded spaceflights. Whether the high fractal 16S rRNA sequences contain an asteroidlike extra-terrestrial source could be speculative but interesting.

10. Fractal and Multifractal Analysis of Human Gait

    NASA Astrophysics Data System (ADS)

    Muñoz-Diosdado, A.; del Río Correa, J. L.; Angulo-Brown, F.

    2003-09-01

    We carried out a fractal and multifractal analysis of human gait time series of young and old individuals, and adults with three illnesses that affect the march: The Parkinson's and Huntington's diseases and the amyotrophic lateral sclerosis (ALS). We obtained cumulative plots of events, the correlation function, the Hurst exponent and the Higuchi's fractal dimension of these time series and found that these fractal markers could be a factor to characterize the march, since we obtained different values of these quantities for youths and adults and they are different also for healthy and ill persons and the most anomalous values belong to ill persons. In other physiological signals there is complexity lost related with the age and the illness, in the case of the march the opposite occurs. The multifractal analysis could be also a useful tool to understand the dynamics of these and other complex systems.

11. Fractal characterization and wettability of ion treated silicon surfaces

    NASA Astrophysics Data System (ADS)

    Yadav, R. P.; Kumar, Tanuj; Baranwal, V.; Vandana, Kumar, Manvendra; Priya, P. K.; Pandey, S. N.; Mittal, A. K.

    2017-02-01

    Fractal characterization of surface morphology can be useful as a tool for tailoring the wetting properties of solid surfaces. In this work, rippled surfaces of Si (100) are grown using 200 keV Ar+ ion beam irradiation at different ion doses. Relationship between fractal and wetting properties of these surfaces are explored. The height-height correlation function extracted from atomic force microscopic images, demonstrates an increase in roughness exponent with an increase in ion doses. A steep variation in contact angle values is found for low fractal dimensions. Roughness exponent and fractal dimensions are found correlated with the static water contact angle measurement. It is observed that after a crossover of the roughness exponent, the surface morphology has a rippled structure. Larger values of interface width indicate the larger ripples on the surface. The contact angle of water drops on such surfaces is observed to be lowest. Autocorrelation function is used for the measurement of ripple wavelength.

12. Two Dimensional Drug Diffusion Between Nanoparticles and Fractal Tumors

    NASA Astrophysics Data System (ADS)

    Samioti, S. E.; Karamanos, K.; Tsiantis, A.; Papathanasiou, A.; Sarris, I.

    2017-11-01

    Drug delivery methods based on nanoparticles are some of the most promising medical applications in nanotechnology to treat cancer. It is observed that drug released by nanoparticles to the cancer tumors may be driven by diffusion. A fractal tumor boundary of triangular Von Koch shape is considered here and the diffusion mechanism is studied for different drug concentrations and increased fractality. A high order Finite Elements method based on the Fenics library is incorporated in fine meshes to fully resolve these irregular boundaries. Drug concentration, its transfer rates and entropy production are calculated in an up to forth order fractal iteration boundaries. We observed that diffusion rate diminishes for successive prefractal generations. Also, the entropy production around the system changes greatly as the order of the fractal curve increases. Results indicate with precision where the active sites are, in which most of the diffusion takes place and thus drug arrives to the tumor.

13. Frequency-Specific Fractal Analysis of Postural Control Accounts for Control Strategies

    PubMed Central

    Gilfriche, Pierre; Deschodt-Arsac, Véronique; Blons, Estelle; Arsac, Laurent M.

    2018-01-01

    Diverse indicators of postural control in Humans have been explored for decades, mostly based on the trajectory of the center-of-pressure. Classical approaches focus on variability, based on the notion that if a posture is too variable, the subject is not stable. Going deeper, an improved understanding of underlying physiology has been gained from studying variability in different frequency ranges, pointing to specific short-loops (proprioception), and long-loops (visuo-vestibular) in neural control. More recently, fractal analyses have proliferated and become useful additional metrics of postural control. They allowed identifying two scaling phenomena, respectively in short and long timescales. Here, we show that one of the most widely used methods for fractal analysis, Detrended Fluctuation Analysis, could be enhanced to account for scalings on specific frequency ranges. By computing and filtering a bank of synthetic fractal signals, we established how scaling analysis can be focused on specific frequency components. We called the obtained method Frequency-specific Fractal Analysis (FsFA) and used it to associate the two scaling phenomena of postural control to proprioceptive-based control loop and visuo-vestibular based control loop. After that, convincing arguments of method validity came from an application on the study of unaltered vs. altered postural control in athletes. Overall, the analysis suggests that at least two timescales contribute to postural control: a velocity-based control in short timescales relying on proprioceptive sensors, and a position-based control in longer timescales with visuo-vestibular sensors, which is a brand-new vision of postural control. Frequency-specific scaling exponents are promising markers of control strategies in Humans. PMID:29643816

14. Model for growth of fractal solid state surface and possibility of its verification by means of atomic force microscopy

    NASA Astrophysics Data System (ADS)

    Kulikov, D. A.; Potapov, A. A.; Rassadin, A. E.; Stepanov, A. V.

    2017-10-01

    In the paper, methods of verification of models for growth of solid state surface by means of atomic force microscopy are suggested. Simulation of growth of fractals with cylindrical generatrix on the solid state surface is presented. Our mathematical model of this process is based on generalization of the Kardar-Parisi-Zhang equation. Corner stones of this generalization are both conjecture of anisotropy of growth of the surface and approximation of small angles. The method of characteristics has been applied to solve the Kardar-Parisi-Zhang equation. Its solution should be considered up to the gradient catastrophe. The difficulty of nondifferentiability of fractal initial generatrix has been overcome by transition from a mathematical fractal to a physical one.

15. Small-angle scattering from the Cantor surface fractal on the plane and the Koch snowflake

    NASA Astrophysics Data System (ADS)

    Cherny, Alexander Yu.; Anitas, Eugen M.; Osipov, Vladimir A.; Kuklin, Alexander I.

    The small-angle scattering (SAS) from the Cantor surface fractal on the plane and Koch snowflake is considered. We develop the construction algorithm for the Koch snowflake, which makes possible the recurrence relation for the scattering amplitude. The surface fractals can be decomposed into a sum of surface mass fractals for arbitrary fractal iteration, which enables various approximations for the scattering intensity. It is shown that for the Cantor fractal, one can neglect with a good accuracy the correlations between the mass fractal amplitudes, while for the Koch snowflake, these correlations are important. It is shown that nevertheless, the correlations can be build in the mass fractal amplitudes, which explains the decay of the scattering intensity $I(q)\\sim q^{D_{\\mathrm{s}}-4}$ with $1 < D_{\\mathrm{s}} < 2$ being the fractal dimension of the perimeter. The curve $I(q)q^{4-D_{\\mathrm{s}}}$ is found to be log-periodic in the fractal region with the period equal to the scaling factor of the fractal. The log-periodicity arises from the self-similarity of sizes of basic structural units rather than from correlations between their distances. A recurrence relation is obtained for the radius of gyration of Koch snowflake, which is solved in the limit of infinite iterations. The present analysis allows us to obtain additional information from SAS data, such as the edges of the fractal regions, the fractal iteration number and the scaling factor.

16. Fractal and Multifractal Models Applied to Porous Media - Editorial

    USDA-ARS?s Scientific Manuscript database

    Given the current high level of interest in the use of fractal geometry to characterize natural porous media, a special issue of the Vadose Zone Journal was organized in order to expose established fractal analysis techniques and cutting-edge new developments to a wider Earth science audience. The ...

17. Robust estimation of fractal measures for characterizing the structural complexity of the human brain: optimization and reproducibility

    PubMed Central

    Goñi, Joaquín; Sporns, Olaf; Cheng, Hu; Aznárez-Sanado, Maite; Wang, Yang; Josa, Santiago; Arrondo, Gonzalo; Mathews, Vincent P; Hummer, Tom A; Kronenberger, William G; Avena-Koenigsberger, Andrea; Saykin, Andrew J.; Pastor, María A.

    2013-01-01

    High-resolution isotropic three-dimensional reconstructions of human brain gray and white matter structures can be characterized to quantify aspects of their shape, volume and topological complexity. In particular, methods based on fractal analysis have been applied in neuroimaging studies to quantify the structural complexity of the brain in both healthy and impaired conditions. The usefulness of such measures for characterizing individual differences in brain structure critically depends on their within-subject reproducibility in order to allow the robust detection of between-subject differences. This study analyzes key analytic parameters of three fractal-based methods that rely on the box-counting algorithm with the aim to maximize within-subject reproducibility of the fractal characterizations of different brain objects, including the pial surface, the cortical ribbon volume, the white matter volume and the grey matter/white matter boundary. Two separate datasets originating from different imaging centers were analyzed, comprising, 50 subjects with three and 24 subjects with four successive scanning sessions per subject, respectively. The reproducibility of fractal measures was statistically assessed by computing their intra-class correlations. Results reveal differences between different fractal estimators and allow the identification of several parameters that are critical for high reproducibility. Highest reproducibility with intra-class correlations in the range of 0.9–0.95 is achieved with the correlation dimension. Further analyses of the fractal dimensions of parcellated cortical and subcortical gray matter regions suggest robustly estimated and region-specific patterns of individual variability. These results are valuable for defining appropriate parameter configurations when studying changes in fractal descriptors of human brain structure, for instance in studies of neurological diseases that do not allow repeated measurements or for disease

18. A New Fractal Model of Chromosome and DNA Processes

    NASA Astrophysics Data System (ADS)

    Bouallegue, K.

    Dynamic chromosome structure remains unknown. Can fractals and chaos be used as new tools to model, identify and generate a structure of chromosomes?Fractals and chaos offer a rich environment for exploring and modeling the complexity of nature. In a sense, fractal geometry is used to describe, model, and analyze the complex forms found in nature. Fractals have also been widely not only in biology but also in medicine. To this effect, a fractal is considered an object that displays self-similarity under magnification and can be constructed using a simple motif (an image repeated on ever-reduced scales).It is worth noting that the problem of identifying a chromosome has become a challenge to find out which one of the models it belongs to. Nevertheless, the several different models (a hierarchical coiling, a folded fiber, and radial loop) have been proposed for mitotic chromosome but have not reached a dynamic model yet.This paper is an attempt to solve topological problems involved in the model of chromosome and DNA processes. By combining the fractal Julia process and the numerical dynamical system, we have finally found out four main points. First, we have developed not only a model of chromosome but also a model of mitosis and one of meiosis. Equally important, we have identified the centromere position through the numerical model captured below. More importantly, in this paper, we have discovered the processes of the cell divisions of both mitosis and meiosis. All in all, the results show that this work could have a strong impact on the welfare of humanity and can lead to a cure of genetic diseases.

19. Increased Earthquake Rates in the Central and Eastern US Portend Higher Earthquake Hazards

    NASA Astrophysics Data System (ADS)

    Llenos, A. L.; Rubinstein, J. L.; Ellsworth, W. L.; Mueller, C. S.; Michael, A. J.; McGarr, A.; Petersen, M. D.; Weingarten, M.; Holland, A. A.

    2014-12-01

    Since 2009 the central and eastern United States has experienced an unprecedented increase in the rate of M≥3 earthquakes that is unlikely to be due to natural variation. Where the rates have increased so has the seismic hazard, making it important to understand these changes. Areas with significant seismicity increases are limited to areas where oil and gas production take place. By far the largest contributor to the seismicity increase is Oklahoma, where recent studies suggest that these rate changes may be due to fluid injection (e.g., Keranen et al., Geology, 2013; Science, 2014). Moreover, the area of increased seismicity in northern Oklahoma that began in 2013 coincides with the Mississippi Lime play, where well completions greatly increased the year before the seismicity increase. This suggests a link to oil and gas production either directly or from the disposal of significant amounts of produced water within the play. For the purpose of assessing the hazard due to these earthquakes, should they be treated differently from natural earthquakes? Previous studies suggest that induced seismicity may differ from natural seismicity in clustering characteristics or frequency-magnitude distributions (e.g., Bachmann et al., GJI, 2011; Llenos and Michael, BSSA, 2013). These differences could affect time-independent hazard computations, which typically assume that clustering and size distribution remain constant. In Oklahoma, as well as other areas of suspected induced seismicity, we find that earthquakes since 2009 tend to be considerably more clustered in space and time than before 2009. However differences between various regional and national catalogs leave unclear whether there are significant changes in magnitude distribution. Whether they are due to natural or industrial causes, the increased earthquake rates in these areas could increase the hazard in ways that are not accounted for in current hazard assessment practice. Clearly the possibility of induced

20. Connecting slow earthquakes to huge earthquakes.

    PubMed

    Obara, Kazushige; Kato, Aitaro

    2016-07-15

    Slow earthquakes are characterized by a wide spectrum of fault slip behaviors and seismic radiation patterns that differ from those of traditional earthquakes. However, slow earthquakes and huge megathrust earthquakes can have common slip mechanisms and are located in neighboring regions of the seismogenic zone. The frequent occurrence of slow earthquakes may help to reveal the physics underlying megathrust events as useful analogs. Slow earthquakes may function as stress meters because of their high sensitivity to stress changes in the seismogenic zone. Episodic stress transfer to megathrust source faults leads to an increased probability of triggering huge earthquakes if the adjacent locked region is critically loaded. Careful and precise monitoring of slow earthquakes may provide new information on the likelihood of impending huge earthquakes. Copyright © 2016, American Association for the Advancement of Science.

1. Comparative Study of Earthquake Clustering in Relation to Hydraulic Activities at Geothermal Fields in California

   NASA Astrophysics Data System (ADS)

   Martínez-Garzón, P.; Zaliapin, I. V.; Ben-Zion, Y.; Kwiatek, G.; Bohnhoff, M.

   2017-12-01

   We investigate earthquake clustering properties from three geothermal reservoirs to clarify how earthquake patterns respond to hydraulic activities. We process ≈ 9 years from four datasets corresponding to the Geysers (both the entire field and a local subset), Coso and Salton Sea geothermal fields, California. For each, the completeness magnitude, b-value and fractal dimension are calculated and used to identify seismicity clusters using the nearest-neighbor approach of Zaliapin and Ben-Zion [2013a, 2013b]. Estimations of temporal evolution of different clustering properties in relation to hydraulic parameters point to different responses of earthquake dynamics to hydraulic operations in each case study. The clustering at the Geysers at local scale and Salton Sea are most and least affected by hydraulic activities, respectively. The response of the earthquake clustering from different datasets to the hydraulic activities may reflect the regional seismo-tectonic complexity as well as the dimension of the geothermal activities performed (e.g. number of active wells and superposition of injection + production activities).Two clustering properties significantly respond to hydraulic changes across all datasets: the background rates and the proportion of clusters consisting of a single event. Background rates are larger at the Geysers and Coso during high injection-production periods, while the opposite holds for the Salton Sea. This possibly reflects the different physical mechanisms controlling seismicity at each geothermal field. Additionally, a lower proportion of singles is found during time periods with higher injection-production rates. This may reflect decreasing effective stress in areas subjected to higher pore pressure and larger earthquake triggering by stress transfer.

2. Navigation performance in virtual environments varies with fractal dimension of landscape.

   PubMed

   Juliani, Arthur W; Bies, Alexander J; Boydston, Cooper R; Taylor, Richard P; Sereno, Margaret E

   2016-09-01

   Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans' ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D. In Experiment 2, participants completed a map-reading and location-judgment task in separate sets of fractal landscapes. In both experiments, task performance was highest at the low-to-mid range of D, which was previously reported as most preferred and discriminable in studies of fractal aesthetics and discrimination, respectively, supporting a theory of visual fluency. The applicability of these findings to architecture, urban planning, and the general design of constructed spaces is discussed.

3. Complex Patterns in Financial Time Series Through HIGUCHI’S Fractal Dimension

   NASA Astrophysics Data System (ADS)

   Grace Elizabeth Rani, T. G.; Jayalalitha, G.

   2016-11-01

   This paper analyzes the complexity of stock exchanges through fractal theory. Closing price indices of four stock exchanges with different industry sectors are selected. Degree of complexity is assessed through Higuchi’s fractal dimension. Various window sizes are considered in evaluating the fractal dimension. It is inferred that the data considered as a whole represents random walk for all the four indices. Analysis of financial data through windowing procedure exhibits multi-fractality. Attempts to apply moving averages to reduce noise in the data revealed lower estimates of fractal dimension, which was verified using fractional Brownian motion. A change in the normalization factor in Higuchi’s algorithm did improve the results. It is quintessential to focus on rural development to realize a standard and steady growth of economy. Tools must be devised to settle the issues in this regard. Micro level institutions are necessary for the economic growth of a country like India, which would induce a sporadic development in the present global economical scenario.

4. Demand surge following earthquakes

   USGS Publications Warehouse

   Olsen, Anna H.

   2012-01-01

   Demand surge is understood to be a socio-economic phenomenon where repair costs for the same damage are higher after large- versus small-scale natural disasters. It has reportedly increased monetary losses by 20 to 50%. In previous work, a model for the increased costs of reconstruction labor and materials was developed for hurricanes in the Southeast United States. The model showed that labor cost increases, rather than the material component, drove the total repair cost increases, and this finding could be extended to earthquakes. A study of past large-scale disasters suggested that there may be additional explanations for demand surge. Two such explanations specific to earthquakes are the exclusion of insurance coverage for earthquake damage and possible concurrent causation of damage from an earthquake followed by fire or tsunami. Additional research into these aspects might provide a better explanation for increased monetary losses after large- vs. small-scale earthquakes.

5. A physically-based earthquake recurrence model for estimation of long-term earthquake probabilities

   USGS Publications Warehouse

   Ellsworth, William L.; Matthews, Mark V.; Nadeau, Robert M.; Nishenko, Stuart P.; Reasenberg, Paul A.; Simpson, Robert W.

   1999-01-01

   A physically-motivated model for earthquake recurrence based on the Brownian relaxation oscillator is introduced. The renewal process defining this point process model can be described by the steady rise of a state variable from the ground state to failure threshold as modulated by Brownian motion. Failure times in this model follow the Brownian passage time (BPT) distribution, which is specified by the mean time to failure, μ, and the aperiodicity of the mean, α (equivalent to the familiar coefficient of variation). Analysis of 37 series of recurrent earthquakes, M -0.7 to 9.2, suggests a provisional generic value of α = 0.5. For this value of α, the hazard function (instantaneous failure rate of survivors) exceeds the mean rate for times > μ⁄2, and is ~ ~ 2 ⁄ μ for all times > μ. Application of this model to the next M 6 earthquake on the San Andreas fault at Parkfield, California suggests that the annual probability of the earthquake is between 1:10 and 1:13.

6. Fuzzy fractals, chaos, and noise

   SciTech Connect

   Zardecki, A.

   1997-05-01

   To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the conceptmore » of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.« less

7. Fractal Measure and Microscopic Modeling of Osseointegration.

   PubMed

   Santos, Leonardo Cavalcanti Bezerra; Carvalho, Alessandra Albuquerque; Leão, Jair Carneiro; Neto, Paulo Jose; Stosic, Tatijana; Stosic, Borko

   2015-01-01

   In this study, the process of osseointegration on titanium implant surfaces with different physicochemical treatments subjected to a simulated corporal fluid submersion was evaluated using the concept of fractal dimension. It was found that different treatments led to rather different calcium phosphate crystal growth patterns, with fractal dimension ranging from 1.68 to 1.93. The observed crystal patterns may be explained by a general deposition, diffusion, and aggregation growth mechanism, where diffusing particle sticking probability plays a fundamental role.

8. Fractal pharmacokinetics of the drug mibefradil in the liver

   NASA Astrophysics Data System (ADS)

   Fuite, J.; Marsh, R.; Tuszyński, J.

   2002-08-01

   We explore the ramifications of the fractal geometry of the key organ for drug elimination, the liver, on pharmacokinetic data analysis. A formalism is developed for the use of a combination of well-stirred Euclidean and fractal compartments in the body. Perturbation analysis is carried out to obtain analytical solutions for the drug concentration time evolution. These results are then fitted to experimental data collected from clinically instrumented dogs [see, A. Skerjanec et al., J. Pharm. Sci. 85, 189 (1995)] using the drug mibefradil. The thus obtained spectral fractal dimension has a range of values that is consistent with the value found in independently performed ultrasound experiments on the liver.

9. Relationship between the anomalous diffusion and the fractal dimension of the environment

   NASA Astrophysics Data System (ADS)

   Zhokh, Alexey; Trypolskyi, Andrey; Strizhak, Peter

   2018-03-01

   In this letter, we provide an experimental study highlighting a relation between the anomalous diffusion and the fractal dimension of the environment using the methanol anomalous transport through the porous solid pellets with various pores geometries and different chemical compositions. The anomalous diffusion exponent was derived from the non-integer order of the time-fractional diffusion equation that describes the methanol anomalous transport through the solid media. The surface fractal dimension was estimated from the nitrogen adsorption isotherms using the Frenkel-Halsey-Hill method. Our study shows that decreasing the fractal dimension leads to increasing the anomalous diffusion exponent, whereas the anomalous diffusion constant is independent on the fractal dimension. We show that the obtained results are in a good agreement with the anomalous diffusion model on a fractal mesh.

10. New 5-adic Cantor sets and fractal string.

    PubMed

    Kumar, Ashish; Rani, Mamta; Chugh, Renu

    2013-01-01

    In the year (1879-1884), George Cantor coined few problems and consequences in the field of set theory. One of them was the Cantor ternary set as a classical example of fractals. In this paper, 5-adic Cantor one-fifth set as an example of fractal string have been introduced. Moreover, the applications of 5-adic Cantor one-fifth set in string theory have also been studied.

11. Landslides, forest fires, and earthquakes: examples of self-organized critical behavior

    NASA Astrophysics Data System (ADS)

    Turcotte, Donald L.; Malamud, Bruce D.

    2004-09-01

    Per Bak conceived self-organized criticality as an explanation for the behavior of the sandpile model. Subsequently, many cellular automata models were found to exhibit similar behavior. Two examples are the forest-fire and slider-block models. Each of these models can be associated with a serious natural hazard: the sandpile model with landslides, the forest-fire model with actual forest fires, and the slider-block model with earthquakes. We examine the noncumulative frequency-area statistics for each natural hazard, and show that each has a robust power-law (fractal) distribution. We propose an inverse-cascade model as a general explanation for the power-law frequency-area statistics of the three cellular-automata models and their ‘associated’ natural hazards.

12. A simple method for estimating the size of nuclei on fractal surfaces

    NASA Astrophysics Data System (ADS)

    Zeng, Qiang

    2017-10-01

    Determining the size of nuclei on complex surfaces remains a big challenge in aspects of biological, material and chemical engineering. Here the author reported a simple method to estimate the size of the nuclei in contact with complex (fractal) surfaces. The established approach was based on the assumptions of contact area proportionality for determining nucleation density and the scaling congruence between nuclei and surfaces for identifying contact regimes. It showed three different regimes governing the equations for estimating the nucleation site density. Nuclei in the size large enough could eliminate the effect of fractal structure. Nuclei in the size small enough could lead to the independence of nucleation site density on fractal parameters. Only when nuclei match the fractal scales, the nucleation site density is associated with the fractal parameters and the size of the nuclei in a coupling pattern. The method was validated by the experimental data reported in the literature. The method may provide an effective way to estimate the size of nuclei on fractal surfaces, through which a number of promising applications in relative fields can be envisioned.

13. Aqueous synthesis of LiFePO4 with Fractal Granularity.

    PubMed

    Cabán-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P; Gómez-Romero, Pedro

    2016-06-03

    Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes.

14. Aqueous synthesis of LiFePO4 with Fractal Granularity

    PubMed Central

    Cabán-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P.; Gómez-Romero, Pedro

    2016-01-01

    Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes. PMID:27256504

15. Aqueous synthesis of LiFePO4 with Fractal Granularity

    NASA Astrophysics Data System (ADS)

    Cabán-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P.; Gómez-Romero, Pedro

    2016-06-01

    Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes.

16. Electrical conductivity modeling in fractal non-saturated porous media

    NASA Astrophysics Data System (ADS)

    Wei, W.; Cai, J.; Hu, X.; Han, Q.

    2016-12-01

    The variety of electrical conductivity in non-saturated conditions is important to study electric conduction in natural sedimentary rocks. The electrical conductivity in completely saturated porous media is a porosity-function representing the complex connected behavior of single conducting phases (pore fluid). For partially saturated conditions, the electrical conductivity becomes even more complicated since the connectedness of pore. Archie's second law is an empirical electrical conductivity-porosity and -saturation model that has been used to predict the formation factor of non-saturated porous rock. However, the physical interpretation of its parameters, e.g., the cementation exponent m and the saturation exponent n, remains questionable. On basis of our previous work, we combine the pore-solid fractal (PSF) model to build an electrical conductivity model in non-saturated porous media. Our theoretical porosity- and saturation-dependent models contain endmember properties, such as fluid electrical conductivities, pore fractal dimension and tortuosity fractal dimension (representing the complex degree of electrical flowing path). We find the presented model with non-saturation-dependent electrical conductivity datasets indicate excellent match between theory and experiments. This means the value of pore fractal dimension and tortuosity fractal dimension change from medium to medium and depends not only on geometrical properties of pore structure but also characteristics of electrical current flowing in the non-saturated porous media.

17. Fractal geometry in an expanding, one-dimensional, Newtonian universe.

    PubMed

    Miller, Bruce N; Rouet, Jean-Louis; Le Guirriec, Emmanuel

    2007-09-01

    Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional N-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the mu (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure.

18. Fractal structure of the interplanetary magnetic field

    NASA Technical Reports Server (NTRS)

    Burlaga, L. F.; Klein, L. W.

    1985-01-01

    Under some conditions, time series of the interplanetary magnetic field strength and components have the properties of fractal curves. Magnetic field measurements made near 8.5 AU by Voyager 2 from June 5 to August 24, 1981 were self-similar over time scales from approximately 20 sec to approximately 3 x 100,000 sec, and the fractal dimension of the time series of the strength and components of the magnetic field was D = 5/3, corresponding to a power spectrum P(f) approximately f sup -5/3. Since the Kolmogorov spectrum for homogeneous, isotropic, stationary turbulence is also f sup -5/3, the Voyager 2 measurements are consistent with the observation of an inertial range of turbulence extending over approximately four decades in frequency. Interaction regions probably contributed most of the power in this interval. As an example, one interaction region is discussed in which the magnetic field had a fractal dimension D = 5/3.

19. Fractality of sensations and the brain health: the theory linking neurodegenerative disorder with distortion of spatial and temporal scale-invariance and fractal complexity of the visible world

    PubMed Central

    Zueva, Marina V.

    2015-01-01

    The theory that ties normal functioning and pathology of the brain and visual system with the spatial–temporal structure of the visual and other sensory stimuli is described for the first time in the present study. The deficit of fractal complexity of environmental influences can lead to the distortion of fractal complexity in the visual pathways of the brain and abnormalities of development or aging. The use of fractal light stimuli and fractal stimuli of other modalities can help to restore the functions of the brain, particularly in the elderly and in patients with neurodegenerative disorders or amblyopia. Non-linear dynamics of these physiological processes have a strong base of evidence, which is seen in the impaired fractal regulation of rhythmic activity in aged and diseased brains. From birth to old age, we live in a non-linear world, in which objects and processes with the properties of fractality and non-linearity surround us. Against this background, the evolution of man took place and all periods of life unfolded. Works of art created by man may also have fractal properties. The positive influence of music on cognitive functions is well-known. Insufficiency of sensory experience is believed to play a crucial role in the pathogenesis of amblyopia and age-dependent diseases. The brain is very plastic in its early development, and the plasticity decreases throughout life. However, several studies showed the possibility to reactivate the adult’s neuroplasticity in a variety of ways. We propose that a non-linear structure of sensory information on many spatial and temporal scales is crucial to the brain health and fractal regulation of physiological rhythms. Theoretical substantiation of the author’s theory is presented. Possible applications and the future research that can experimentally confirm or refute the theoretical concept are considered. PMID:26236232

20. Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.

    PubMed

    Quodbach, Julian; Moussavi, Amir; Tammer, Roland; Frahm, Jens; Kleinebudde, Peter

    2014-11-20

    An efficient disintegrant is capable of breaking up a tablet in the smallest possible particles in the shortest time. Until now, comparative data on the efficacy of different disintegrants is based on dissolution studies or the disintegration time. Extending these approaches, this study introduces a method, which defines the evolution of fractal dimensions of tablets as surrogate parameter for the available surface area. Fractal dimensions are a measure for the tortuosity of a line, in this case the upper surface of a disintegrating tablet. High-resolution real-time MRI was used to record videos of disintegrating tablets. The acquired video images were processed to depict the upper surface of the tablets and a box-counting algorithm was used to estimate the fractal dimensions. The influence of six different disintegrants, of different relative tablet density, and increasing disintegrant concentration was investigated to evaluate the performance of the novel method. Changing relative densities hardly affect the progression of fractal dimensions, whereas an increase in disintegrant concentration causes increasing fractal dimensions during disintegration, which are also reached quicker. Different disintegrants display only minor differences in the maximal fractal dimension, yet the kinetic in which the maximum is reached allows a differentiation and classification of disintegrants. Copyright © 2014 Elsevier B.V. All rights reserved.

1. Earthquake triggering in southeast Africa following the 2012 Indian Ocean earthquake

   NASA Astrophysics Data System (ADS)

   Neves, Miguel; Custódio, Susana; Peng, Zhigang; Ayorinde, Adebayo

   2018-02-01

   In this paper we present evidence of earthquake dynamic triggering in southeast Africa. We analysed seismic waveforms recorded at 53 broad-band and short-period stations in order to identify possible increases in the rate of microearthquakes and tremor due to the passage of teleseismic waves generated by the Mw8.6 2012 Indian Ocean earthquake. We found evidence of triggered local earthquakes and no evidence of triggered tremor in the region. We assessed the statistical significance of the increase in the number of local earthquakes using β-statistics. Statistically significant dynamic triggering of local earthquakes was observed at 7 out of the 53 analysed stations. Two of these stations are located in the northeast coast of Madagascar and the other five stations are located in the Kaapvaal Craton, southern Africa. We found no evidence of dynamically triggered seismic activity in stations located near the structures of the East African Rift System. Hydrothermal activity exists close to the stations that recorded dynamic triggering, however, it also exists near the East African Rift System structures where no triggering was observed. Our results suggest that factors other than solely tectonic regime and geothermalism are needed to explain the mechanisms that underlie earthquake triggering.

2. Fractal fluctuations in spatiotemporal variables when walking on a self-paced treadmill.

   PubMed

   Choi, Jin-Seung; Kang, Dong-Won; Seo, Jeong-Woo; Tack, Gye-Rae

   2017-12-08

   This study investigated the fractal dynamic properties of stride time (ST), stride length (SL) and stride speed (SS) during walking on a self-paced treadmill (STM) in which the belt speed is automatically controlled by the walking speed. Twelve healthy young subjects participated in the study. The subjects walked at their preferred walking speed under four conditions: STM, STM with a metronome (STM+met), fixed-speed (conventional) treadmill (FTM), and FTM with a metronome (FTM+met). To compare the fractal dynamics between conditions, the mean, variability, and fractal dynamics of ST, SL, and SS were compared. Moreover, the relationship among the variables was examined under each walking condition using three types of surrogates. The mean values of all variables did not differ between the two treadmills, and the variability of all variables was generally larger for STM than for FTM. The use of a metronome resulted in a decrease in variability in ST and SS for all conditions. The fractal dynamic characteristics of SS were maintained with STM, in contrast to FTM, and only the fractal dynamic characteristics of ST disappeared when using a metronome. In addition, the fractal dynamic patterns of the cross-correlated surrogate results were identical to those of all variables for the two treadmills. In terms of the fractal dynamic properties, STM walking was generally closer to overground walking than FTM walking. Although further research is needed, the present results will be useful in research on gait fractal dynamics and rehabilitation. Copyright © 2017 Elsevier Ltd. All rights reserved.

3. Bayesian historical earthquake relocation: an example from the 1909 Taipei earthquake

   USGS Publications Warehouse

   Minson, Sarah E.; Lee, William H.K.

   2014-01-01

   Locating earthquakes from the beginning of the modern instrumental period is complicated by the fact that there are few good-quality seismograms and what traveltimes do exist may be corrupted by both large phase-pick errors and clock errors. Here, we outline a Bayesian approach to simultaneous inference of not only the hypocentre location but also the clock errors at each station and the origin time of the earthquake. This methodology improves the solution for the source location and also provides an uncertainty analysis on all of the parameters included in the inversion. As an example, we applied this Bayesian approach to the well-studied 1909 Mw 7 Taipei earthquake. While our epicentre location and origin time for the 1909 Taipei earthquake are consistent with earlier studies, our focal depth is significantly shallower suggesting a higher seismic hazard to the populous Taipei metropolitan area than previously supposed.

4. A fractal process of hydrogen diffusion in a-Si:H with exponential energy distribution

   NASA Astrophysics Data System (ADS)

   Hikita, Harumi; Ishikawa, Hirohisa; Morigaki, Kazuo

   2017-04-01

   Hydrogen diffusion in a-Si:H with exponential distribution of the states in energy exhibits the fractal structure. It is shown that a probability P(t) of the pausing time t has a form of tα (α: fractal dimension). It is shown that the fractal dimension α = Tr/T0 (Tr: hydrogen temperature, T0: a temperature corresponding to the width of exponential distribution of the states in energy) is in agreement with the Hausdorff dimension. A fractal graph for the case of α ≤ 1 is like the Cantor set. A fractal graph for the case of α > 1 is like the Koch curves. At α = ∞, hydrogen migration exhibits Brownian motion. Hydrogen diffusion in a-Si:H should be the fractal process.

5. Urban Earthquakes - Reducing Building Collapse Through Education

   NASA Astrophysics Data System (ADS)

   Bilham, R.

   2004-12-01

   Fatalities from earthquakes rose from 6000k to 9000k/year in the past decade, yet the ratio of numbers of earthquake fatalities to instantaneous population continues to fall. Since 1950 the ratio declined worldwide by a factor of three, but in some countries the ratio has changed little. E.g in Iran, 1 in 3000 people can expect to die in an earthquake, a percentage that has not changed significantly since 1890. Fatalities from earthquakes remain high in those countries that have traditionally suffered from frequent large earthquakes (Turkey, Iran, Japan, and China), suggesting that the exposure time of recently increased urban populations in other countries may be too short to have interacted with earthquakes with long recurrence intervals. This in turn, suggests that disasters of unprecendented size will occur (more than 1 million fatalities) when future large earthquakes occur close to megacities. However, population growth is most rapid in cities of less than 1 million people in the developing nations, where the financial ability to implement earthquake resistant construction methods is limited. In that structural collapse can often be traced to ignorance about the forces at work in an earthquake, the future collapse of buildings presently under construction could be much reduced were contractors, builders and occupants educated in the principles of earthquake resistant assembly. Education of builders who are tempted to cut assembly costs is likely to be more cost effective than material aid.

6. The fractal geometry of Hartree-Fock

   NASA Astrophysics Data System (ADS)

   Theel, Friethjof; Karamatskou, Antonia; Santra, Robin

   2017-12-01

   The Hartree-Fock method is an important approximation for the ground-state electronic wave function of atoms and molecules so that its usage is widespread in computational chemistry and physics. The Hartree-Fock method is an iterative procedure in which the electronic wave functions of the occupied orbitals are determined. The set of functions found in one step builds the basis for the next iteration step. In this work, we interpret the Hartree-Fock method as a dynamical system since dynamical systems are iterations where iteration steps represent the time development of the system, as encountered in the theory of fractals. The focus is put on the convergence behavior of the dynamical system as a function of a suitable control parameter. In our case, a complex parameter λ controls the strength of the electron-electron interaction. An investigation of the convergence behavior depending on the parameter λ is performed for helium, neon, and argon. We observe fractal structures in the complex λ-plane, which resemble the well-known Mandelbrot set, determine their fractal dimension, and find that with increasing nuclear charge, the fragmentation increases as well.

7. The initial subevent of the 1994 Northridge, California, earthquake: Is earthquake size predictable?

   USGS Publications Warehouse

   Kilb, Debi; Gomberg, J.

   1999-01-01

   We examine the initial subevent (ISE) of the M?? 6.7, 1994 Northridge, California, earthquake in order to discriminate between two end-member rupture initiation models: the 'preslip' and 'cascade' models. Final earthquake size may be predictable from an ISE's seismic signature in the preslip model but not in the cascade model. In the cascade model ISEs are simply small earthquakes that can be described as purely dynamic ruptures. In this model a large earthquake is triggered by smaller earthquakes; there is no size scaling between triggering and triggered events and a variety of stress transfer mechanisms are possible. Alternatively, in the preslip model, a large earthquake nucleates as an aseismically slipping patch in which the patch dimension grows and scales with the earthquake's ultimate size; the byproduct of this loading process is the ISE. In this model, the duration of the ISE signal scales with the ultimate size of the earthquake, suggesting that nucleation and earthquake size are determined by a more predictable, measurable, and organized process. To distinguish between these two end-member models we use short period seismograms recorded by the Southern California Seismic Network. We address questions regarding the similarity in hypocenter locations and focal mechanisms of the ISE and the mainshock. We also compare the ISE's waveform characteristics to those of small earthquakes and to the beginnings of earthquakes with a range of magnitudes. We find that the focal mechanisms of the ISE and mainshock are indistinguishable, and both events may have nucleated on and ruptured the same fault plane. These results satisfy the requirements for both models and thus do not discriminate between them. However, further tests show the ISE's waveform characteristics are similar to those of typical small earthquakes in the vicinity and more importantly, do not scale with the mainshock magnitude. These results are more consistent with the cascade model.

8. Prediction of pork quality parameters by applying fractals and data mining on MRI.

   PubMed

   Caballero, Daniel; Pérez-Palacios, Trinidad; Caro, Andrés; Amigo, José Manuel; Dahl, Anders B; ErsbØll, Bjarne K; Antequera, Teresa

   2017-09-01

   This work firstly investigates the use of MRI, fractal algorithms and data mining techniques to determine pork quality parameters non-destructively. The main objective was to evaluate the capability of fractal algorithms (Classical Fractal algorithm, CFA; Fractal Texture Algorithm, FTA and One Point Fractal Texture Algorithm, OPFTA) to analyse MRI in order to predict quality parameters of loin. In addition, the effect of the sequence acquisition of MRI (Gradient echo, GE; Spin echo, SE and Turbo 3D, T3D) and the predictive technique of data mining (Isotonic regression, IR and Multiple linear regression, MLR) were analysed. Both fractal algorithm, FTA and OPFTA are appropriate to analyse MRI of loins. The sequence acquisition, the fractal algorithm and the data mining technique seems to influence on the prediction results. For most physico-chemical parameters, prediction equations with moderate to excellent correlation coefficients were achieved by using the following combinations of acquisition sequences of MRI, fractal algorithms and data mining techniques: SE-FTA-MLR, SE-OPFTA-IR, GE-OPFTA-MLR, SE-OPFTA-MLR, with the last one offering the best prediction results. Thus, SE-OPFTA-MLR could be proposed as an alternative technique to determine physico-chemical traits of fresh and dry-cured loins in a non-destructive way with high accuracy. Copyright © 2017. Published by Elsevier Ltd.

9. The Electronic Encyclopedia of Earthquakes

   NASA Astrophysics Data System (ADS)

   Benthien, M.; Marquis, J.; Jordan, T.

   2003-12-01

   complete 450 entries, which will populate the E3 collection to a level that fully spans earthquake science and engineering. Scientists, engineers, and educators who have suggestions for content to be included in the Encyclopedia can visit www.earthquake.info now to complete the "Suggest a Web Page" form.

10. Correlating brain blood oxygenation level dependent (BOLD) fractal dimension mapping with magnetic resonance spectroscopy (MRS) in Alzheimer's disease.

    PubMed

    Warsi, Mohammed A; Molloy, William; Noseworthy, Michael D

    2012-10-01

    To correlate temporal fractal structure of resting state blood oxygen level dependent (rsBOLD) functional magnetic resonance imaging (fMRI) with in vivo proton magnetic resonance spectroscopy ((1)H-MRS), in Alzheimer's disease (AD) and healthy age-matched normal controls (NC). High temporal resolution (4 Hz) rsBOLD signal and single voxel (left putamen) magnetic resonance spectroscopy data was acquired in 33 AD patients and 13 NC. The rsBOLD data was analyzed using two types of fractal dimension (FD) analysis based on relative dispersion and frequency power spectrum. Comparisons in FD were performed between AD and NC, and FD measures were correlated with (1)H-MRS findings. Temporal fractal analysis of rsBOLD, was able to differentiate AD from NC subjects (P = 0.03). Low FD correlated with markers of AD severity including decreased concentrations of N-acetyl aspartate (R = 0.44, P = 0.015) and increased myoinositol (mI) (R = -0.45, P = 0.012). Based on these results we suggest fractal analysis of rsBOLD could provide an early marker of AD.

11. Fractal Theory for Permeability Prediction, Venezuelan and USA Wells

    NASA Astrophysics Data System (ADS)

    Aldana, Milagrosa; Altamiranda, Dignorah; Cabrera, Ana

    2014-05-01

    Inferring petrophysical parameters such as permeability, porosity, water saturation, capillary pressure, etc, from the analysis of well logs or other available core data has always been of critical importance in the oil industry. Permeability in particular, which is considered to be a complex parameter, has been inferred using both empirical and theoretical techniques. The main goal of this work is to predict permeability values on different wells using Fractal Theory, based on a method proposed by Pape et al. (1999). This approach uses the relationship between permeability and the geometric form of the pore space of the rock. This method is based on the modified equation of Kozeny-Carman and a fractal pattern, which allows determining permeability as a function of the cementation exponent, porosity and the fractal dimension. Data from wells located in Venezuela and the United States of America are analyzed. Employing data of porosity and permeability obtained from core samples, and applying the Fractal Theory method, we calculated the prediction equations for each well. At the beginning, this was achieved by training with 50% of the data available for each well. Afterwards, these equations were tested inferring over 100% of the data to analyze possible trends in their distribution. This procedure gave excellent results in all the wells in spite of their geographic distance, generating permeability models with the potential to accurately predict permeability logs in the remaining parts of the well for which there are no core samples, using even porority logs. Additionally, empirical models were used to determine permeability and the results were compared with those obtained by applying the fractal method. The results indicated that, although there are empirical equations that give a proper adjustment, the prediction results obtained using fractal theory give a better fit to the core reference data.

12. Optimal spinneret layout in Von Koch curves of fractal theory based needleless electrospinning process

    NASA Astrophysics Data System (ADS)

    Yang, Wenxiu; Liu, Yanbo; Zhang, Ligai; Cao, Hong; Wang, Yang; Yao, Jinbo

    2016-06-01

    Needleless electrospinning technology is considered as a better avenue to produce nanofibrous materials at large scale, and electric field intensity and its distribution play an important role in controlling nanofiber diameter and quality of the nanofibrous web during electrospinning. In the current study, a novel needleless electrospinning method was proposed based on Von Koch curves of Fractal configuration, simulation and analysis on electric field intensity and distribution in the new electrospinning process were performed with Finite element analysis software, Comsol Multiphysics 4.4, based on linear and nonlinear Von Koch fractal curves (hereafter called fractal models). The result of simulation and analysis indicated that Second level fractal structure is the optimal linear electrospinning spinneret in terms of field intensity and uniformity. Further simulation and analysis showed that the circular type of Fractal spinneret has better field intensity and distribution compared to spiral type of Fractal spinneret in the nonlinear Fractal electrospinning technology. The electrospinning apparatus with the optimal Von Koch fractal spinneret was set up to verify the theoretical analysis results from Comsol simulation, achieving more uniform electric field distribution and lower energy cost, compared to the current needle and needleless electrospinning technologies.

13. The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction.

    PubMed

    Najafi, Elham; Darooneh, Amir H

    2015-01-01

    A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction.

14. The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction

    PubMed Central

    Najafi, Elham; Darooneh, Amir H.

    2015-01-01

    A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction. PMID:26091207

15. Communities and classes in symmetric fractals

    NASA Astrophysics Data System (ADS)

    Krawczyk, Małgorzata J.

    2015-07-01

    Two aspects of fractal networks are considered: the community structure and the class structure, where classes of nodes appear as a consequence of a local symmetry of nodes. The analyzed systems are the networks constructed for two selected symmetric fractals: the Sierpinski triangle and the Koch curve. Communities are searched for by means of a set of differential equations. Overlapping nodes which belong to two different communities are identified by adding some noise to the initial connectivity matrix. Then, a node can be characterized by a spectrum of probabilities of belonging to different communities. Our main goal is that the overlapping nodes with the same spectra belong to the same class.

16. [Modeling continuous scaling of NDVI based on fractal theory].

    PubMed

    Luan, Hai-Jun; Tian, Qing-Jiu; Yu, Tao; Hu, Xin-Li; Huang, Yan; Du, Ling-Tong; Zhao, Li-Min; Wei, Xi; Han, Jie; Zhang, Zhou-Wei; Li, Shao-Peng

    2013-07-01

    Scale effect was one of the very important scientific problems of remote sensing. The scale effect of quantitative remote sensing can be used to study retrievals' relationship between different-resolution images, and its research became an effective way to confront the challenges, such as validation of quantitative remote sensing products et al. Traditional up-scaling methods cannot describe scale changing features of retrievals on entire series of scales; meanwhile, they are faced with serious parameters correction issues because of imaging parameters' variation of different sensors, such as geometrical correction, spectral correction, etc. Utilizing single sensor image, fractal methodology was utilized to solve these problems. Taking NDVI (computed by land surface radiance) as example and based on Enhanced Thematic Mapper Plus (ETM+) image, a scheme was proposed to model continuous scaling of retrievals. Then the experimental results indicated that: (a) For NDVI, scale effect existed, and it could be described by fractal model of continuous scaling; (2) The fractal method was suitable for validation of NDVI. All of these proved that fractal was an effective methodology of studying scaling of quantitative remote sensing.

17. Self-organized network of fractal-shaped components coupled through statistical interaction.

    PubMed

    Ugajin, R

    2001-09-01

    A dissipative dynamics is introduced to generate self-organized networks of interacting objects, which we call coupled-fractal networks. The growth model is constructed based on a growth hypothesis in which the growth rate of each object is a product of the probability of receiving source materials from faraway and the probability of receiving adhesives from other grown objects, where each object grows to be a random fractal if isolated, but connects with others if glued. The network is governed by the statistical interaction between fractal-shaped components, which can only be identified in a statistical manner over ensembles. This interaction is investigated using the degree of correlation between fractal-shaped components, enabling us to determine whether it is attractive or repulsive.

18. Jupiter Fractal Art

    NASA Image and Video Library

    2017-08-10

    See Jupiter's Great Red Spot as you've never seen it before in this new Jovian work of art. Artist Mik Petter created this unique, digital artwork using data from the JunoCam imager on NASA's Juno spacecraft. The art form, known as fractals, uses mathematical formulas to create art with an infinite variety of form, detail, color and light. The tumultuous atmospheric zones in and around the Great Red Spot are highlighted by the author's use of colorful fractals. Vibrant colors of various tints and hues, combined with the almost organic-seeming shapes, make this image seem to be a colorized and crowded petri dish of microorganisms, or a close-up view of microscopic and wildly-painted seashells. The original JunoCam image was taken on July 10, 2017 at 7:10 p.m. PDT (10:10 p.m. EDT), as the Juno spacecraft performed its seventh close flyby of Jupiter. The spacecraft captured the image from about 8,648 miles (13,917 kilometers) above the tops of the clouds of the planet at a latitude of -32.6 degrees. https://photojournal.jpl.nasa.gov/catalog/PIA21777

19. Implementation for wideband applications using UWB fractal patch antenna

    NASA Astrophysics Data System (ADS)

    Kumar, D. Naresh

    2018-04-01

    This paper defines in detail about the diverse fractal patch antenna. Microstrip patch antennas has evolved in the field of research and development extending its impact across wide range of applications. A combination of patch antenna with fractal patterns has become a tryout to outspread it further. Because of its low profile nature patch antennas have added to a lot of prominence. Apart from have this property it can also be renovated further for wide bandwidth (2929 MHz) applications, as it exhibits self-analogous property. This antenna is premeditated on a patch using Sierpinski(4.040 GHz, 6.566 GHz) and Koch fractal geometries respectively. The antenna is designed using HFSS software.

20. Earthquake triggering at alaskan volcanoes following the 3 November 2002 denali fault earthquake

    USGS Publications Warehouse

    Moran, S.C.; Power, J.A.; Stihler, S.D.; Sanchez, J.J.; Caplan-Auerbach, J.

    2004-01-01

    The 3 November 2002 Mw 7.9 Denali fault earthquake provided an excellent opportunity to investigate triggered earthquakes at Alaskan volcanoes. The Alaska Volcano Observatory operates short-period seismic networks on 24 historically active volcanoes in Alaska, 247-2159 km distant from the mainshock epicenter. We searched for evidence of triggered seismicity by examining the unfiltered waveforms for all stations in each volcano network for ???1 hr after the Mw 7.9 arrival time at each network and for significant increases in located earthquakes in the hours after the mainshock. We found compelling evidence for triggering only at the Katmai volcanic cluster (KVC, 720-755 km southwest of the epicenter), where small earthquakes with distinct P and 5 arrivals appeared within the mainshock coda at one station and a small increase in located earthquakes occurred for several hours after the mainshock. Peak dynamic stresses of ???0.1 MPa at Augustine Volcano (560 km southwest of the epicenter) are significantly lower than those recorded in Yellowstone and Utah (>3000 km southeast of the epicenter), suggesting that strong directivity effects were at least partly responsible for the lack of triggering at Alaskan volcanoes. We describe other incidents of earthquake-induced triggering in the KVC, and outline a qualitative magnitude/distance-dependent triggering threshold. We argue that triggering results from the perturbation of magmatic-hydrothermal systems in the KVC and suggest that the comparative lack of triggering at other Alaskan volcanoes could be a result of differences in the nature of magmatic-hydrothermal systems.

1. Fractal mechanisms and heart rate dynamics. Long-range correlations and their breakdown with disease

   NASA Technical Reports Server (NTRS)

   Peng, C. K.; Havlin, S.; Hausdorff, J. M.; Mietus, J. E.; Stanley, H. E.; Goldberger, A. L.

   1995-01-01

   Under healthy conditions, the normal cardiac (sinus) interbeat interval fluctuates in a complex manner. Quantitative analysis using techniques adapted from statistical physics reveals the presence of long-range power-law correlations extending over thousands of heartbeats. This scale-invariant (fractal) behavior suggests that the regulatory system generating these fluctuations is operating far from equilibrium. In contrast, it is found that for subjects at high risk of sudden death (e.g., congestive heart failure patients), these long-range correlations break down. Application of fractal scaling analysis and related techniques provides new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as motivating development of novel physiologic models of systems that appear to be heterodynamic rather than homeostatic.

2. Fractality of profit landscapes and validation of time series models for stock prices

   NASA Astrophysics Data System (ADS)

   Yi, Il Gu; Oh, Gabjin; Kim, Beom Jun

   2013-08-01

   We apply a simple trading strategy for various time series of real and artificial stock prices to understand the origin of fractality observed in the resulting profit landscapes. The strategy contains only two parameters p and q, and the sell (buy) decision is made when the log return is larger (smaller) than p (-q). We discretize the unit square (p,q) ∈ [0,1] × [0,1] into the N × N square grid and the profit Π(p,q) is calculated at the center of each cell. We confirm the previous finding that local maxima in profit landscapes are scattered in a fractal-like fashion: the number M of local maxima follows the power-law form M ˜ Na, but the scaling exponent a is found to differ for different time series. From comparisons of real and artificial stock prices, we find that the fat-tailed return distribution is closely related to the exponent a ≈ 1.6 observed for real stock markets. We suggest that the fractality of profit landscape characterized by a ≈ 1.6 can be a useful measure to validate time series model for stock prices.

3. Are Earthquakes Predictable? A Study on Magnitude Correlations in Earthquake Catalog and Experimental Data

   NASA Astrophysics Data System (ADS)

   Stavrianaki, K.; Ross, G.; Sammonds, P. R.

   2015-12-01

   The clustering of earthquakes in time and space is widely accepted, however the existence of correlations in earthquake magnitudes is more questionable. In standard models of seismic activity, it is usually assumed that magnitudes are independent and therefore in principle unpredictable. Our work seeks to test this assumption by analysing magnitude correlation between earthquakes and their aftershocks. To separate mainshocks from aftershocks, we perform stochastic declustering based on the widely used Epidemic Type Aftershock Sequence (ETAS) model, which allows us to then compare the average magnitudes of aftershock sequences to that of their mainshock. The results of earthquake magnitude correlations were compared with acoustic emissions (AE) from laboratory analog experiments, as fracturing generates both AE at the laboratory scale and earthquakes on a crustal scale. Constant stress and constant strain rate experiments were done on Darley Dale sandstone under confining pressure to simulate depth of burial. Microcracking activity inside the rock volume was analyzed by the AE technique as a proxy for earthquakes. Applying the ETAS model to experimental data allowed us to validate our results and provide for the first time a holistic view on the correlation of earthquake magnitudes. Additionally we search the relationship between the conditional intensity estimates of the ETAS model and the earthquake magnitudes. A positive relation would suggest the existence of magnitude correlations. The aim of this study is to observe any trends of dependency between the magnitudes of aftershock earthquakes and the earthquakes that trigger them.

4. A user-friendly modified pore-solid fractal model

   PubMed Central

   Ding, Dian-yuan; Zhao, Ying; Feng, Hao; Si, Bing-cheng; Hill, Robert Lee

   2016-01-01

   The primary objective of this study was to evaluate a range of calculation points on water retention curves (WRC) instead of the singularity point at air-entry suction in the pore-solid fractal (PSF) model, which additionally considered the hysteresis effect based on the PSF theory. The modified pore-solid fractal (M-PSF) model was tested using 26 soil samples from Yangling on the Loess Plateau in China and 54 soil samples from the Unsaturated Soil Hydraulic Database. The derivation results showed that the M-PSF model is user-friendly and flexible for a wide range of calculation point options. This model theoretically describes the primary differences between the soil moisture desorption and the adsorption processes by the fractal dimensions. The M-PSF model demonstrated good performance particularly at the calculation points corresponding to the suctions from 100 cm to 1000 cm. Furthermore, the M-PSF model, used the fractal dimension of the particle size distribution, exhibited an accepted performance of WRC predictions for different textured soils when the suction values were ≥100 cm. To fully understand the function of hysteresis in the PSF theory, the role of allowable and accessible pores must be examined. PMID:27996013

5. Fractal-Based Analysis of the Influence of Music on Human Respiration

   NASA Astrophysics Data System (ADS)

   Reza Namazi, H.

   An important challenge in respiration related studies is to investigate the influence of external stimuli on human respiration. Auditory stimulus is an important type of stimuli that influences human respiration. However, no one discovered any trend, which relates the characteristics of the auditory stimuli to the characteristics of the respiratory signal. In this paper, we investigate the correlation between auditory stimuli and respiratory signal from fractal point of view. We found out that the fractal structure of respiratory signal is correlated with the fractal structure of the applied music. Based on the obtained results, the music with greater fractal dimension will result in respiratory signal with smaller fractal dimension. In order to verify this result, we benefit from approximate entropy. The results show the respiratory signal will have smaller approximate entropy by choosing the music with smaller approximate entropy. The method of analysis could be further investigated to analyze the variations of different physiological time series due to the various types of stimuli when the complexity is the main concern.

6. A fractal analysis of pathogen detection by biosensors

   NASA Astrophysics Data System (ADS)

   Doke, Atul M.; Sadana, Ajit

   2006-05-01

   A fractal analysis is presented for the detection of pathogens such as Franscisela tularensis, and Yersinia pestis (the bacterium that causes plague) using a CANARY (cellular analysis and notification of antigens risks and yields) biosensor (Rider et al., 2003). In general, the binding and dissociation rate coefficients may be adequately described by either a single- or a dual-fractal analysis. An attempt is made to relate the binding rate coefficient to the degree of heterogeneity (fractal dimension value) present on the biosensor surface. Binding and dissociation rate coefficient values obtained are presented. The kinetics aspects along with the affinity values presented are of interest, and should along with the rate coefficients presented for the binding and the dissociation phase be of significant interest in help designing better biosensors for an application area that is bound to gain increasing importance in the future.

7. Fractal Interfaces for Stimulating and Recording Neural Implants

   NASA Astrophysics Data System (ADS)

   Watterson, William James

   From investigating movement in an insect to deciphering cognition in a human brain to treating Parkinson's disease, hearing loss, or even blindness, electronic implants are an essential tool for understanding the brain and treating neural diseases. Currently, the stimulating and recording resolution of these implants remains low. For instance, they can record all the neuron activity associated with movement in an insect, but are quite far from recording, at an individual neuron resolution, the large volumes of brain tissue associated with cognition. Likewise, there is remarkable success in the cochlear implant restoring hearing due to the relatively simple anatomy of the auditory nerves, but are failing to restore vision to the blind due to poor signal fidelity and transmission in stimulating the more complex anatomy of the visual nerves. The critically important research needed to improve the resolution of these implants is to optimize the neuron-electrode interface. This thesis explores geometrical and material modifications to both stimulating and recording electrodes which can improve the neuron-electrode interface. First, we introduce a fractal electrode geometry which radically improves the restored visual acuity achieved by retinal implants and leads to safe, long-term operation of the implant. Next, we demonstrate excellent neuron survival and neurite outgrowth on carbon nanotube electrodes, thus providing a safe biomaterial which forms a strong connection between the electrode and neurons. Additional preliminary evidence suggests carbon nanotubes patterned into a fractal geometry will provide further benefits in improving the electrode-neuron interface. Finally, we propose a novel implant based off field effect transistor technology which utilizes an interconnecting fractal network of semiconducting carbon nanotubes to record from thousands of neurons simutaneously at an individual neuron resolution. Taken together, these improvements have the potential to

8. Design of inside cut von koch fractal UWB MIMO antenna

   NASA Astrophysics Data System (ADS)

   Tharani, V.; Shanmuga Priya, N.; Rajesh, A.

   2017-11-01

   An Inside Cut Hexagonal Von Koch fractal MIMO antenna is designed for UWB applications and its characteristics behaviour are studied. Self-comparative and space filling properties of Koch fractal structure are utilized in the antenna design which leads to the desired miniaturization and wideband characteristics. The hexagonal shaped Von Koch Fractal antenna with Defected Ground Structure (DGS) is designed on FR4 substrate with a compact size of 30mm x 20mm x 1.6mm. The antenna achieves a maximum of -44dB and -51dB at 7.1GHz for 1-element and 2-element case respectively.

9. Spatial analysis of cities using Renyi entropy and fractal parameters

   NASA Astrophysics Data System (ADS)

   Chen, Yanguang; Feng, Jian

   2017-12-01

   The spatial distributions of cities fall into two groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law distribution). The latter belongs to scale-free distributions, which can be modeled with fractal geometry. However, fractal dimension is not suitable for the former distribution. In contrast, spatial entropy can be used to measure any types of urban distributions. This paper is devoted to generalizing multifractal parameters by means of dual relation between Euclidean and fractal geometries. The main method is mathematical derivation and empirical analysis, and the theoretical foundation is the discovery that the normalized fractal dimension is equal to the normalized entropy. Based on this finding, a set of useful spatial indexes termed dummy multifractal parameters are defined for geographical analysis. These indexes can be employed to describe both the simple distributions and complex distributions. The dummy multifractal indexes are applied to the population density distribution of Hangzhou city, China. The calculation results reveal the feature of spatio-temporal evolution of Hangzhou's urban morphology. This study indicates that fractal dimension and spatial entropy can be combined to produce a new methodology for spatial analysis of city development.

10. Fractal properties and denoising of lidar signals from cirrus clouds

    NASA Astrophysics Data System (ADS)

    van den Heuvel, J. C.; Driesenaar, M. L.; Lerou, R. J. L.

    2000-02-01

    Airborne lidar signals of cirrus clouds are analyzed to determine the cloud structure. Climate modeling and numerical weather prediction benefit from accurate modeling of cirrus clouds. Airborne lidar measurements of the European Lidar in Space Technology Experiment (ELITE) campaign were analyzed by combining shots to obtain the backscatter at constant altitude. The signal at high altitude was analyzed for horizontal structure of cirrus clouds. The power spectrum and the structure function show straight lines on a double logarithmic plot. This behavior is characteristic for a Brownian fractal. Wavelet analysis using the Haar wavelet confirms the fractal aspects. It is shown that the horizontal structure of cirrus can be described by a fractal with a dimension of 1.8 over length scales that vary 4 orders of magnitude. We use the fractal properties in a new denoising method. Denoising is required for future lidar measurements from space that have a low signal to noise ratio. Our wavelet denoising is based on the Haar wavelet and uses the statistical fractal properties of cirrus clouds in a method based on the maximum a posteriori (MAP) probability. This denoising based on wavelets is tested on airborne lidar signals from ELITE using added Gaussian noise. Superior results with respect to averaging are obtained.

11. Collective properties of injection-induced earthquake sequences: 1. Model description and directivity bias

    NASA Astrophysics Data System (ADS)

    Dempsey, David; Suckale, Jenny

    2016-05-01

    Induced seismicity is of increasing concern for oil and gas, geothermal, and carbon sequestration operations, with several M > 5 events triggered in recent years. Modeling plays an important role in understanding the causes of this seismicity and in constraining seismic hazard. Here we study the collective properties of induced earthquake sequences and the physics underpinning them. In this first paper of a two-part series, we focus on the directivity ratio, which quantifies whether fault rupture is dominated by one (unilateral) or two (bilateral) propagating fronts. In a second paper, we focus on the spatiotemporal and magnitude-frequency distributions of induced seismicity. We develop a model that couples a fracture mechanics description of 1-D fault rupture with fractal stress heterogeneity and the evolving pore pressure distribution around an injection well that triggers earthquakes. The extent of fault rupture is calculated from the equations of motion for two tips of an expanding crack centered at the earthquake hypocenter. Under tectonic loading conditions, our model exhibits a preference for unilateral rupture and a normal distribution of hypocenter locations, two features that are consistent with seismological observations. On the other hand, catalogs of induced events when injection occurs directly onto a fault exhibit a bias toward ruptures that propagate toward the injection well. This bias is due to relatively favorable conditions for rupture that exist within the high-pressure plume. The strength of the directivity bias depends on a number of factors including the style of pressure buildup, the proximity of the fault to failure and event magnitude. For injection off a fault that triggers earthquakes, the modeled directivity bias is small and may be too weak for practical detection. For two hypothetical injection scenarios, we estimate the number of earthquake observations required to detect directivity bias.

12. Fractal Dimension Analysis of Transient Visual Evoked Potentials: Optimisation and Applications.

    PubMed

    Boon, Mei Ying; Henry, Bruce Ian; Chu, Byoung Sun; Basahi, Nour; Suttle, Catherine May; Luu, Chi; Leung, Harry; Hing, Stephen

    2016-01-01

    The visual evoked potential (VEP) provides a time series signal response to an external visual stimulus at the location of the visual cortex. The major VEP signal components, peak latency and amplitude, may be affected by disease processes. Additionally, the VEP contains fine detailed and non-periodic structure, of presently unclear relevance to normal function, which may be quantified using the fractal dimension. The purpose of this study is to provide a systematic investigation of the key parameters in the measurement of the fractal dimension of VEPs, to develop an optimal analysis protocol for application. VEP time series were mathematically transformed using delay time, τ, and embedding dimension, m, parameters. The fractal dimension of the transformed data was obtained from a scaling analysis based on straight line fits to the numbers of pairs of points with separation less than r versus log(r) in the transformed space. Optimal τ, m, and scaling analysis were obtained by comparing the consistency of results using different sampling frequencies. The optimised method was then piloted on samples of normal and abnormal VEPs. Consistent fractal dimension estimates were obtained using τ = 4 ms, designating the fractal dimension = D2 of the time series based on embedding dimension m = 7 (for 3606 Hz and 5000 Hz), m = 6 (for 1803 Hz) and m = 5 (for 1000Hz), and estimating D2 for each embedding dimension as the steepest slope of the linear scaling region in the plot of log(C(r)) vs log(r) provided the scaling region occurred within the middle third of the plot. Piloting revealed that fractal dimensions were higher from the sampled abnormal than normal achromatic VEPs in adults (p = 0.02). Variances of fractal dimension were higher from the abnormal than normal chromatic VEPs in children (p = 0.01). A useful analysis protocol to assess the fractal dimension of transformed VEPs has been developed.

13. Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors

    NASA Astrophysics Data System (ADS)

    Chen, Xiang; Li, Jingchao; Han, Hui; Ying, Yulong

    2018-05-01

    Because of the limitations of the traditional fractal box-counting dimension algorithm in subtle feature extraction of radiation source signals, a dual improved generalized fractal box-counting dimension eigenvector algorithm is proposed. First, the radiation source signal was preprocessed, and a Hilbert transform was performed to obtain the instantaneous amplitude of the signal. Then, the improved fractal box-counting dimension of the signal instantaneous amplitude was extracted as the first eigenvector. At the same time, the improved fractal box-counting dimension of the signal without the Hilbert transform was extracted as the second eigenvector. Finally, the dual improved fractal box-counting dimension eigenvectors formed the multi-dimensional eigenvectors as signal subtle features, which were used for radiation source signal recognition by the grey relation algorithm. The experimental results show that, compared with the traditional fractal box-counting dimension algorithm and the single improved fractal box-counting dimension algorithm, the proposed dual improved fractal box-counting dimension algorithm can better extract the signal subtle distribution characteristics under different reconstruction phase space, and has a better recognition effect with good real-time performance.

14. The HayWired Earthquake Scenario—Earthquake Hazards

    USGS Publications Warehouse

    Detweiler, Shane T.; Wein, Anne M.

    2017-04-24

    The HayWired scenario is a hypothetical earthquake sequence that is being used to better understand hazards for the San Francisco Bay region during and after an earthquake of magnitude 7 on the Hayward Fault. The 2014 Working Group on California Earthquake Probabilities calculated that there is a 33-percent likelihood of a large (magnitude 6.7 or greater) earthquake occurring on the Hayward Fault within three decades. A large Hayward Fault earthquake will produce strong ground shaking, permanent displacement of the Earth’s surface, landslides, liquefaction (soils becoming liquid-like during shaking), and subsequent fault slip, known as afterslip, and earthquakes, known as aftershocks. The most recent large earthquake on the Hayward Fault occurred on October 21, 1868, and it ruptured the southern part of the fault. The 1868 magnitude-6.8 earthquake occurred when the San Francisco Bay region had far fewer people, buildings, and infrastructure (roads, communication lines, and utilities) than it does today, yet the strong ground shaking from the earthquake still caused significant building damage and loss of life. The next large Hayward Fault earthquake is anticipated to affect thousands of structures and disrupt the lives of millions of people. Earthquake risk in the San Francisco Bay region has been greatly reduced as a result of previous concerted efforts; for example, tens of billions of dollars of investment in strengthening infrastructure was motivated in large part by the 1989 magnitude 6.9 Loma Prieta earthquake. To build on efforts to reduce earthquake risk in the San Francisco Bay region, the HayWired earthquake scenario comprehensively examines the earthquake hazards to help provide the crucial scientific information that the San Francisco Bay region can use to prepare for the next large earthquake, The HayWired Earthquake Scenario—Earthquake Hazards volume describes the strong ground shaking modeled in the scenario and the hazardous movements of

15. A fractal model for nuclear organization: current evidence and biological implications

    PubMed Central

    Bancaud, Aurélien; Lavelle, Christophe; Huet, Sébastien; Ellenberg, Jan

    2012-01-01

    Chromatin is a multiscale structure on which transcription, replication, recombination and repair of the genome occur. To fully understand any of these processes at the molecular level under physiological conditions, a clear picture of the polymorphic and dynamic organization of chromatin in the eukaryotic nucleus is required. Recent studies indicate that a fractal model of chromatin architecture is consistent with both the reaction-diffusion properties of chromatin interacting proteins and with structural data on chromatin interminglement. In this study, we provide a critical overview of the experimental evidence that support a fractal organization of chromatin. On this basis, we discuss the functional implications of a fractal chromatin model for biological processes and propose future experiments to probe chromatin organization further that should allow to strongly support or invalidate the fractal hypothesis. PMID:22790985

16. Terahertz response of fractal meta-atoms based on concentric rectangular square resonators

    SciTech Connect

    Song, Zhiqiang; Zhao, Zhenyu, E-mail: ; Shi, Wangzhou

    We investigate the terahertz electromagnetic responses of fractal meta-atoms (MAs) induced by different mode coupling mechanisms. Two types of MAs based on concentric rectangular square (CRS) resonators are presented: independent CRS (I-CRS) and junctional-CRS (J-CRS). In I-CRS, each resonator works as an independent dipole so as to result in the multiple resonance modes when the fractal level is above 1. In J-CRS, however, the generated layer is rotated by π/2 radius to the adjacent CRS in one MA. The multiple resonance modes are coupled into a single mode resonance. The fractal level increasing induces resonance modes redshift in I-CRS whilemore » blueshift in J-CRS. When the fractal level is below 4, the mode Q factor of J-CRS is in between the two modes of I-CRS; when the fractal level is 4 or above, the mode Q factor of J-CRS exceeds the two modes of I-CRS. Furthermore, the modulation depth (MD) decreases in I-CRS while it increases in J-CRS with the increase in fractal levels. The surface currents analysis reveals that the capacitive coupling of modes in I-CRS results in the modes redshift, while the conductive coupling of modes in J-CRS induces the mode blueshift. A high Q mode with large MD can be achieved via conductive coupling between the resonators of different scales in a fractal MA.« less

17. Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture.

    PubMed

    Pothuaud, L; Benhamou, C L; Porion, P; Lespessailles, E; Harba, R; Levitz, P

    2000-04-01

    The purpose of this work was to understand how fractal dimension of two-dimensional (2D) trabecular bone projection images could be related to three-dimensional (3D) trabecular bone properties such as porosity or connectivity. Two alteration processes were applied to trabecular bone images obtained by magnetic resonance imaging: a trabeculae dilation process and a trabeculae removal process. The trabeculae dilation process was applied from the 3D skeleton graph to the 3D initial structure with constant connectivity. The trabeculae removal process was applied from the initial structure to an altered structure having 99% of porosity, in which both porosity and connectivity were modified during this second process. Gray-level projection images of each of the altered structures were simply obtained by summation of voxels, and fractal dimension (Df) was calculated. Porosity (phi) and connectivity per unit volume (Cv) were calculated from the 3D structure. Significant relationships were found between Df, phi, and Cv. Df values increased when porosity increased (dilation and removal processes) and when connectivity decreased (only removal process). These variations were in accordance with all previous clinical studies, suggesting that fractal evaluation of trabecular bone projection has real meaning in terms of porosity and connectivity of the 3D architecture. Furthermore, there was a statistically significant linear dependence between Df and Cv when phi remained constant. Porosity is directly related to bone mineral density and fractal dimension can be easily evaluated in clinical routine. These two parameters could be associated to evaluate the connectivity of the structure.

18. On the Gompertzian growth in the fractal space-time.

    PubMed

    Molski, Marcin; Konarski, Jerzy

    2008-06-01

    An analytical approach to determination of time-dependent temporal fractal dimension b(t)(t) and scaling factor a(t)(t) for the Gompertzian growth in the fractal space-time is presented. The derived formulae take into account the proper boundary conditions and permit a calculation of the mean values b(t)(t) and a(t)(t) at any period of time. The formulae derived have been tested on experimental data obtained by Schrek for the Brown-Pearce rabbit's tumor growth. The results obtained confirm a possibility of successful mapping of the experimental Gompertz curve onto the fractal power-law scaling function y(t)=a(t)tb(t) and support a thesis that Gompertzian growth is a self-similar and allometric process of a holistic nature.

19. A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions

    NASA Astrophysics Data System (ADS)

    Zborovský, I.

    2018-04-01

    Fractal self-similarity of hadron interactions demonstrated by the z-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable z is a function of the momentum fractions x1 and x2 of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions ya and yb of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the z-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.

20. [Lithology feature extraction of CASI hyperspectral data based on fractal signal algorithm].

    PubMed

    Tang, Chao; Chen, Jian-Ping; Cui, Jing; Wen, Bo-Tao

    2014-05-01

    Hyperspectral data is characterized by combination of image and spectrum and large data volume dimension reduction is the main research direction. Band selection and feature extraction is the primary method used for this objective. In the present article, the authors tested methods applied for the lithology feature extraction from hyperspectral data. Based on the self-similarity of hyperspectral data, the authors explored the application of fractal algorithm to lithology feature extraction from CASI hyperspectral data. The "carpet method" was corrected and then applied to calculate the fractal value of every pixel in the hyperspectral data. The results show that fractal information highlights the exposed bedrock lithology better than the original hyperspectral data The fractal signal and characterized scale are influenced by the spectral curve shape, the initial scale selection and iteration step. At present, research on the fractal signal of spectral curve is rare, implying the necessity of further quantitative analysis and investigation of its physical implications.

1. Chaos, Fractals and Their Applications

   NASA Astrophysics Data System (ADS)

   Thompson, J. Michael T.

   2016-12-01

   This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton’s laws of motion to the astronomy of Poincaré and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA’s discovery and use of zero-fuel chaotic “superhighways” between the planets; erratic chaotic solutions generated by Euler’s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.

2. In the shadow of 1857-the effect of the great Ft. Tejon earthquake on subsequent earthquakes in southern California

   USGS Publications Warehouse

   Harris, R.A.; Simpson, R.W.

   1996-01-01

   The great 1857 Fort Tejon earthquake is the largest earthquake to have hit southern California during the historic period. We investigated if seismicity patterns following 1857 could be due to static stress changes generated by the 1857 earthquake. When post-1857 earthquakes with unknown focal mechanisms were assigned strike-slip mechanisms with strike and rake determined by the nearest active fault, 13 of the 13 southern California M???5.5 earthquakes between 1857 and 1907 were encouraged by the 1857 rupture. When post-1857 earthquakes in the Transverse Ranges with unknown focal mechanisms were assigned reverse mechanisms and all other events were assumed strike-slip, 11 of the 13 earthquakes were encouraged by the 1857 earthquake. These results show significant correlations between static stress changes and seismicity patterns. The correlation disappears around 1907, suggesting that tectonic loading began to overwhelm the effect of the 1857 earthquake early in the 20th century.

3. Is Fractal 1/f Scaling in Stream Chemistry Universal?

   NASA Astrophysics Data System (ADS)

   Hrachowitz, M.

   2016-12-01

   Stream water chemistry data from catchments worldwide suggest that catchments act as filters that transform white noise, i.e. random input signals such as in precipitation, into 1/fαnoise whose slope in a power spectrum typically ranges between -0.5>α> -1.5. This previously lead to the hypothesis that catchments act as fractal filters, i.e. a slope of α=-1 may be a universal and intrinsic property of catchments. That would have considerable implications on the predictability of stream water chemistry, as both, temporal short- and long-range interdependence control the system response. While short memories and thus flatter slopes with α closer to 0 indicate poor short term but good long-term predictability, steeper slopes (α <<-1) indicate the opposite. In fractal systems, i.e. α=-1, this therefore leads to inherent problems of predicting both, short and long-term response patterns. The hypothesis of catchments acting as fractal filters remains to be tested more profoundly. It is not yet clear, if observed inter-catchment variations in α need to be interpreted as noise in the signal or if the variations underlie a systematic pattern and can be explained by some characteristic of catchment function. Here we will test the hypothesis that the spectral slope of stream water chemistry is not necessarily α=-1 and that catchments therefore do not inherently act as fractal filters. Further, it will be tested if closer links between the variations in spectral slope and hydrological function of catchments can be identified. The combined data-analysis and modelling study uses hydrochemical data (i.e. Cl-) from a wide range of catchments worldwide. The study catchments are physically contrasting, from distinct climate zones, and with distinct landscapes and vegetation. To identify patterns in the variations of α, firstly the power spectra of observed stream chemistry are compared with physical catchment characteristics using methods such as cluster analysis. In a

4. Fractal planetary rings: Energy inequalities and random field model

   NASA Astrophysics Data System (ADS)

   Malyarenko, Anatoliy; Ostoja-Starzewski, Martin

   2017-12-01

   This study is motivated by a recent observation, based on photographs from the Cassini mission, that Saturn’s rings have a fractal structure in radial direction. Accordingly, two questions are considered: (1) What Newtonian mechanics argument in support of such a fractal structure of planetary rings is possible? (2) What kinematics model of such fractal rings can be formulated? Both challenges are based on taking planetary rings’ spatial structure as being statistically stationary in time and statistically isotropic in space, but statistically nonstationary in space. An answer to the first challenge is given through an energy analysis of circular rings having a self-generated, noninteger-dimensional mass distribution [V. E. Tarasov, Int. J. Mod Phys. B 19, 4103 (2005)]. The second issue is approached by taking the random field of angular velocity vector of a rotating particle of the ring as a random section of a special vector bundle. Using the theory of group representations, we prove that such a field is completely determined by a sequence of continuous positive-definite matrix-valued functions defined on the Cartesian square F2 of the radial cross-section F of the rings, where F is a fat fractal.

5. Analysis of regional deformation and strain accumulation data adjacent to the San Andreas fault

   NASA Technical Reports Server (NTRS)

   Turcotte, Donald L.

   1991-01-01

   A new approach to the understanding of crustal deformation was developed under this grant. This approach combined aspects of fractals, chaos, and self-organized criticality to provide a comprehensive theory for deformation on distributed faults. It is hypothesized that crustal deformation is an example of comminution: Deformation takes place on a fractal distribution of faults resulting in a fractal distribution of seismicity. Our primary effort under this grant was devoted to developing an understanding of distributed deformation in the continental crust. An initial effort was carried out on the fractal clustering of earthquakes in time. It was shown that earthquakes do not obey random Poisson statistics, but can be approximated in many cases by coupled, scale-invariant fractal statistics. We applied our approach to the statistics of earthquakes in the New Hebrides region of the southwest Pacific because of the very high level of seismicity there. This work was written up and published in the Bulletin of the Seismological Society of America. This approach was also applied to the statistics of the seismicity on the San Andreas fault system.

6. A common mode of origin of power laws in models of market and earthquake

   NASA Astrophysics Data System (ADS)

   Bhattacharyya, Pratip; Chatterjee, Arnab; Chakrabarti, Bikas K.

   2007-07-01

   We show that there is a common mode of origin for the power laws observed in two different models: (i) the Pareto law for the distribution of money among the agents with random-saving propensities in an ideal gas-like market model and (ii) the Gutenberg-Richter law for the distribution of overlaps in a fractal-overlap model for earthquakes. We find that the power laws appear as the asymptotic forms of ever-widening log-normal distributions for the agents’ money and the overlap magnitude, respectively. The identification of the generic origin of the power laws helps in better understanding and in developing generalized views of phenomena in such diverse areas as economics and geophysics.

7. Classical evolution of fractal measures on the lattice

   NASA Astrophysics Data System (ADS)

   Antoniou, N. G.; Diakonos, F. K.; Saridakis, E. N.; Tsolias, G. A.

   2007-04-01

   We consider the classical evolution of a lattice of nonlinear coupled oscillators for a special case of initial conditions resembling the equilibrium state of a macroscopic thermal system at the critical point. The displacements of the oscillators define initially a fractal measure on the lattice associated with the scaling properties of the order parameter fluctuations in the corresponding critical system. Assuming a sudden symmetry breaking (quench), leading to a change in the equilibrium position of each oscillator, we investigate in some detail the deformation of the initial fractal geometry as time evolves. In particular, we show that traces of the critical fractal measure can be sustained for large times, and we extract the properties of the chain that determine the associated time scales. Our analysis applies generally to critical systems for which, after a slow developing phase where equilibrium conditions are justified, a rapid evolution, induced by a sudden symmetry breaking, emerges on time scales much shorter than the corresponding relaxation or observation time. In particular, it can be used in the fireball evolution in a heavy-ion collision experiment, where the QCD critical point emerges, or in the study of evolving fractals of astrophysical and cosmological scales, and may lead to determination of the initial critical properties of the Universe through observations in the symmetry-broken phase.

8. Can fractal objects operate as efficient inline mixers?

   NASA Astrophysics Data System (ADS)

   Laizet, Sylvain; Vassilicos, John; Turbulence, Mixing; Flow Control Group Team

   2011-11-01

   Recently, Hurst & Vassilicos, PoF 2007, Seoud & Vassilicos, PoF 2007, Mazellier & Vassilicos, PoF, 2010 used different multiscale grids to generate turbulence in a wind tunnel and have shown that complex multiscale boundary/initial conditions can drastically influence the behaviour of a turbulent flow, but that the detailled specific nature of the multiscale geometry matters too. Multiscale (fractal) objects can be designed to be immersed in any fluid flow where there is a need to control and design the turbulence generated by the object. Different types of multiscale objects can be designed as different types of energy-efficient mixers with varying degrees of high turbulent intensities, small pressure drop and downstream distance from the grid where the turbulence is most vigorous. Here, we present a 3D DNS study of the stirring and mixing of a passive scalar by turbulence generated with either a fractal square grid or a regular grid in the presence of a mean scalar gradient. The results show that: (1) there is a linear increase for the passive scalar variance for both grids, (2) the passive scalar variance is ten times bigger for the fractal grid, (3) the passive scalar flux is constant after the production region for both grids, (4) the passive scalar flux is enhanced by an order of magnitude for the fractal grid. We acknowledge support from EPSRC, UK.

9. Repeating Earthquakes Following an Mw 4.4 Earthquake Near Luther, Oklahoma

   NASA Astrophysics Data System (ADS)

   Clements, T.; Keranen, K. M.; Savage, H. M.

   2015-12-01

   An Mw 4.4 earthquake on April 16, 2013 near Luther, OK was one of the earliest M4+ earthquakes in central Oklahoma, following the Prague sequence in 2011. A network of four local broadband seismometers deployed within a day of the Mw 4.4 event, along with six Oklahoma netquake stations, recorded more than 500 aftershocks in the two weeks following the Luther earthquake. Here we use HypoDD (Waldhauser & Ellsworth, 2000) and waveform cross-correlation to obtain precise aftershock locations. The location uncertainty, calculated using the SVD method in HypoDD, is ~15 m horizontally and ~ 35 m vertically. The earthquakes define a near vertical, NE-SW striking fault plane. Events occur at depths from 2 km to 3.5 km within the granitic basement, with a small fraction of events shallower, near the sediment-basement interface. Earthquakes occur within a zone of ~200 meters thickness on either side of the best-fitting fault surface. We use an equivalency class algorithm to identity clusters of repeating events, defined as event pairs with median three-component correlation > 0.97 across common stations (Aster & Scott, 1993). Repeating events occur as doublets of only two events in over 50% of cases; overall, 41% of earthquakes recorded occur as repeating events. The recurrence intervals for the repeating events range from minutes to days, with common recurrence intervals of less than two minutes. While clusters occur in tight dimensions, commonly of 80 m x 200 m, aftershocks occur in 3 distinct ~2km x 2km-sized patches along the fault. Our analysis suggests that with rapidly deployed local arrays, the plethora of ~Mw 4 earthquakes occurring in Oklahoma and Southern Kansas can be used to investigate the earthquake rupture process and the role of damage zones.

10. Earthquakes

    MedlinePlus

    ... Search Term(s): Main Content Home Be Informed Earthquakes Earthquakes An earthquake is the sudden, rapid shaking of the earth, ... by the breaking and shifting of underground rock. Earthquakes can cause buildings to collapse and cause heavy ...

11. Surface Fractal Analysis for Estimating the Fracture Energy Absorption of Nanoparticle Reinforced Composites

    PubMed Central

    Pramanik, Brahmananda; Tadepalli, Tezeswi; Mantena, P. Raju

    2012-01-01

    In this study, the fractal dimensions of failure surfaces of vinyl ester based nanocomposites are estimated using two classical methods, Vertical Section Method (VSM) and Slit Island Method (SIM), based on the processing of 3D digital microscopic images. Self-affine fractal geometry has been observed in the experimentally obtained failure surfaces of graphite platelet reinforced nanocomposites subjected to quasi-static uniaxial tensile and low velocity punch-shear loading. Fracture energy and fracture toughness are estimated analytically from the surface fractal dimensionality. Sensitivity studies show an exponential dependency of fracture energy and fracture toughness on the fractal dimensionality. Contribution of fracture energy to the total energy absorption of these nanoparticle reinforced composites is demonstrated. For the graphite platelet reinforced nanocomposites investigated, surface fractal analysis has depicted the probable ductile or brittle fracture propagation mechanism, depending upon the rate of loading. PMID:28817017

12. a Fractal Analysis for Net Present Value of Multi-Stage Hydraulic Fractured Horizontal Well

    NASA Astrophysics Data System (ADS)

    Lu, Hong-Lin; Zhang, Ji-Jun; Tan, Xiao-Hua; Li, Xiao-Ping; Zhao, Jia-Hui

    Because of the low permeability, multi-stage hydraulic fractured horizontal wells (MHFHWs) occupy a dominant position among production wells in tight gas reservoir. However, net present value (NPV) estimation method for MHFHW in tight gas reservoirs often ignores the effect of heterogeneity in microscopic pore structure. Apart from that, a new fractal model is presented for NPV of MHFHW, based on the fractal expressions of formation parameters. First, with the aid of apparent permeability model, a pseudo pressure expression considering both reservoir fractal features and slippage effect is derived, contributing to establish the productivity model. Secondly, economic assessment method is built based on the fractal productivity model, in order to obtain the NPV of MHFHW. Thirdly, the type curves are illustrated and the influences of different fractal parameters are discussed. The pore fractal dimensions Df and the capillary tortuosity fractal dimensions DT have significant effects on the NPV of an MHFHW. Finally, the proposed model in this paper provides a new methodology for analyzing and predicting the NPV of an MHFHW and may be conducive to a better understanding of the optimal design of MHFHW.

13. Earthquakes of Garhwal Himalaya region of NW Himalaya, India: A study of relocated earthquakes and their seismogenic source and stress

    NASA Astrophysics Data System (ADS)

    R, A. P.; Paul, A.; Singh, S.

    2017-12-01

    suggests the presence of fluids around the chamoli region. Although the epicentral locations of these earthquakes are located near the Main Central Thrust Zone, and based on the faulting mechanisms suggest that, these earthquakes are indeed related to the detachment/Main Himalayan Thrust (MHT), hence we suggest that the detachment/MHT is seismogenic.

14. Earthquakes induced by fluid injection and explosion

    USGS Publications Warehouse

    Healy, J.H.; Hamilton, R.M.; Raleigh, C.B.

    1970-01-01

    Earthquakes generated by fluid injection near Denver, Colorado, are compared with earthquakes triggered by nuclear explosion at the Nevada Test Site. Spatial distributions of the earthquakes in both cases are compatible with the hypothesis that variation of fluid pressure in preexisting fractures controls the time distribution of the seismic events in an "aftershock" sequence. We suggest that the fluid pressure changes may also control the distribution in time and space of natural aftershock sequences and of earthquakes that have been reported near large reservoirs. ?? 1970.

15. Fractal Simulations of African Design in Pre-College Computing Education

    ERIC Educational Resources Information Center

    Eglash, Ron; Krishnamoorthy, Mukkai; Sanchez, Jason; Woodbridge, Andrew

    2011-01-01

    This article describes the use of fractal simulations of African design in a high school computing class. Fractal patterns--repetitions of shape at multiple scales--are a common feature in many aspects of African design. In African architecture we often see circular houses grouped in circular complexes, or rectangular houses in rectangular…

16. Fractality and growth of He bubbles in metals

    NASA Astrophysics Data System (ADS)

    Kajita, Shin; Ito, Atsushi M.; Ohno, Noriyasu

    2017-08-01

    Pinholes are formed on surfaces of metals by the exposure to helium plasmas, and they are regarded as the initial process of the growth of fuzzy nanostructures. In this study, number density of the pinholes is investigated in detail from the scanning electron microscope (SEM) micrographs of tungsten and tantalum exposed to the helium plasmas. A power law relation was identified between the number density and the size of pinholes. From the slope and the region where the power law was satisfied, the fractal dimension D and smin, which characterize the SEM images, are deduced. Parametric dependences and material dependence of D and smin are revealed. To explain the fractality, simple Monte-Carlo simulations including random walks of He atoms and absorption on bubble was introduced. It is shown that the initial position of the random walk is one of the key factors to deduce the fractality. The results indicated that new nucleations of bubbles are necessary to reproduce the number-density distribution of bubbles.

17. Fractal analysis on human dynamics of library loans

    NASA Astrophysics Data System (ADS)

    Fan, Chao; Guo, Jin-Li; Zha, Yi-Long

    2012-12-01

    In this paper, the fractal characteristic of human behaviors is investigated from the perspective of time series constructed with the amount of library loans. The values of the Hurst exponent and length of non-periodic cycle calculated through rescaled range analysis indicate that the time series of human behaviors and their sub-series are fractal with self-similarity and long-range dependence. Then the time series are converted into complex networks by the visibility algorithm. The topological properties of the networks such as scale-free property and small-world effect imply that there is a close relationship among the numbers of repetitious behaviors performed by people during certain periods of time. Our work implies that there is intrinsic regularity in the human collective repetitious behaviors. The conclusions may be helpful to develop some new approaches to investigate the fractal feature and mechanism of human dynamics, and provide some references for the management and forecast of human collective behaviors.

18. Electrochemical Evaluations of Fractal Microelectrodes for Energy Efficient Neurostimulation.

    PubMed

    Park, Hyunsu; Takmakov, Pavel; Lee, Hyowon

    2018-03-12

    Advancements in microfabrication has enabled manufacturing of microscopic neurostimulation electrodes with smaller footprint than ever possible. The smaller electrodes can potentially reduce tissue damage and allow better spatial resolution for neural stimulation. Although electrodes of any shape can easily be fabricated, substantial effort have been focused on identification and characterization of new materials and surface morphology for efficient charge injection, while maintaining simple circular or rectangular Euclidean electrode geometries. In this work we provide a systematic electrochemical evaluation of charge injection capacities of serpentine and fractal-shaped platinum microelectrodes and compare their performance with traditional circular microelectrodes. Our findings indicate that the increase in electrode perimeter leads to an increase in maximum charge injection capacity. Furthermore, we found that the electrode geometry can have even more significant impact on electrode performance than having a larger perimeter for a given surface area. The fractal-shaped microelectrodes, despite having smaller perimeter than other designs, demonstrated superior charge injection capacity. Our results suggest that electrode design can significantly affect both Faradaic and non-Faradaic electrochemical processes, which may be optimized to enable a more energy efficient design for neurostimulation.

19. Implications for earthquake risk reduction in the United States from the Kocaeli, Turkey, earthquake of August 17, 1999

    USGS Publications Warehouse

    ,

    2000-01-01

    This report documents implications for earthquake risk reduction in the U.S. The magnitude 7.4 earthquake caused 17,127 deaths, 43,953 injuries, and displaced more than 250,000 people from their homes. The report warns that similar disasters are possible in the United States where earthquakes of comparable size strike the heart of American urban areas. Another concern described in the report is the delayed emergency response that was caused by the inadequate seismic monitoring system in Turkey, a problem that contrasts sharply with rapid assessment and response to the September Chi-Chi earthquake in Taiwan. Additionally, the experience in Turkey suggests that techniques for forecasting earthquakes may be improving.

20. Limitation of the Predominant-Period Estimator for Earthquake Early Warning and the Initial Rupture of Earthquakes

    NASA Astrophysics Data System (ADS)

    Yamada, T.; Ide, S.

    2007-12-01

    Earthquake early warning is an important and challenging issue for the reduction of the seismic damage, especially for the mitigation of human suffering. One of the most important problems in earthquake early warning systems is how immediately we can estimate the final size of an earthquake after we observe the ground motion. It is relevant to the problem whether the initial rupture of an earthquake has some information associated with its final size. Nakamura (1988) developed the Urgent Earthquake Detection and Alarm System (UrEDAS). It calculates the predominant period of the P wave (τp) and estimates the magnitude of an earthquake immediately after the P wave arrival from the value of τpmax, or the maximum value of τp. The similar approach has been adapted by other earthquake alarm systems (e.g., Allen and Kanamori (2003)). To investigate the characteristic of the parameter τp and the effect of the length of the time window (TW) in the τpmax calculation, we analyze the high-frequency recordings of earthquakes at very close distances in the Mponeng mine in South Africa. We find that values of τpmax have upper and lower limits. For larger earthquakes whose source durations are longer than TW, the values of τpmax have an upper limit which depends on TW. On the other hand, the values for smaller earthquakes have a lower limit which is proportional to the sampling interval. For intermediate earthquakes, the values of τpmax are close to their typical source durations. These two limits and the slope for intermediate earthquakes yield an artificial final size dependence of τpmax in a wide size range. The parameter τpmax is useful for detecting large earthquakes and broadcasting earthquake early warnings. However, its dependence on the final size of earthquakes does not suggest that the earthquake rupture is deterministic. This is because τpmax does not always have a direct relation to the physical quantities of an earthquake.

1. Monte Carlo Sampling in Fractal Landscapes

   NASA Astrophysics Data System (ADS)

   Leitão, Jorge C.; Lopes, J. M. Viana Parente; Altmann, Eduardo G.

   2013-05-01

   We design a random walk to explore fractal landscapes such as those describing chaotic transients in dynamical systems. We show that the random walk moves efficiently only when its step length depends on the height of the landscape via the largest Lyapunov exponent of the chaotic system. We propose a generalization of the Wang-Landau algorithm which constructs not only the density of states (transient time distribution) but also the correct step length. As a result, we obtain a flat-histogram Monte Carlo method which samples fractal landscapes in polynomial time, a dramatic improvement over the exponential scaling of traditional uniform-sampling methods. Our results are not limited by the dimensionality of the landscape and are confirmed numerically in chaotic systems with up to 30 dimensions.

2. Fractal dimension of spatially extended systems

   NASA Astrophysics Data System (ADS)

   Torcini, A.; Politi, A.; Puccioni, G. P.; D'Alessandro, G.

   1991-10-01

   Properties of the invariant measure are numerically investigated in 1D chains of diffusively coupled maps. The coarse-grained fractal dimension is carefully computed in various embedding spaces, observing an extremely slow convergence towards the asymptotic value. This is in contrast with previous simulations, where the analysis of an insufficient number of points led the authors to underestimate the increase of fractal dimension with increasing the dimension of the embedding space. Orthogonal decomposition is also performed confirming that the slow convergence is intrinsically related to local nonlinear properties of the invariant measure. Finally, the Kaplan-Yorke conjecture is tested for short chains, showing that, despite the noninvertibility of the dynamical system, a good agreement is found between Lyapunov dimension and information dimension.

3. An application of geostatistics and fractal geometry for reservoir characterization

   SciTech Connect

   Aasum, Y.; Kelkar, M.G.; Gupta, S.P.

   1991-03-01

   This paper presents an application of geostatistics and fractal geometry concepts for 2D characterization of rock properties (k and {phi}) in a dolomitic, layered-cake reservoir. The results indicate that lack of closely spaced data yield effectively random distributions of properties. Further, incorporation of geology reduces uncertainties in fractal interpolation of wellbore properties.

4. Space-coiling fractal metamaterial with multi-bandgaps on subwavelength scale

   NASA Astrophysics Data System (ADS)

   Man, Xianfeng; Liu, Tingting; Xia, Baizhan; Luo, Zhen; Xie, Longxiang; Liu, Jian

   2018-06-01

   Acoustic metamaterials are remarkably different from conventional materials, as they can flexibly manipulate and control the propagation of sound waves. Unlike the locally resonant metamaterials introduced in earlier studies, we designed an ultraslow artificial structure with a sound speed much lower than that in air. In this paper, the space-coiling approach is proposed for achieving artificial metamaterial for extremely low-frequency airborne sound. In addition, the self-similar fractal technique is utilized for designing space-coiling Mie-resonance-based metamaterials (MRMMs) to obtain a band-dispersive spectrum. The band structures of two-dimensional (2D) acoustic metamaterials with different fractal levels are illustrated using the finite element method. The low-frequency bandgap can easily be formed, and multi-bandgap properties are observed in high-level fractals. Furthermore, the designed MRMMs with higher order fractal space coiling shows a good robustness against irregular arrangement. Besides, the proposed artificial structure was found to modify and control the radiation field arbitrarily. Thus, this work provides useful guidelines for the design of acoustic filtering devices and acoustic wavefront shaping applications on the subwavelength scale.

5. Characterization of branch complexity by fractal analyses and detect plant functional adaptations

   USGS Publications Warehouse

   Alados, C.L.; Escos, J.; Emlen, J.M.; Freeman, D.C.

   1999-01-01

   The comparison between complexity in the sense of space occupancy (box-counting fractal dimension Dc and information dimension DI ) and heterogeneity in the sense of space distribution (average evenness index and evenness variation coefficient JCV) were investigated in mathematical fractal objects and natural branch ¯ J structures. In general, increased fractal dimension was paired with low heterogeneity. Comparisons between branch architecture in Anthyllis cytisoides under different slope exposure and grazing impact revealed that branches were more complex and more homogeneously distributed for plants on northern exposures than southern, while grazing had no impact during a wet year. Developmental instability was also investigated by the statistical noise of the allometric relation between internode length and node order. In conclusion, our study demonstrated that fractal dimension of branch structure can be used to analyze the structural organization of plants, especially if we consider not only fractal dimension but also shoot distribution within the canopy (lacunarity). These indexes together with developmental instability analyses are good indicators of growth responses to the environment.

6. Continuing Megathrust Earthquake Potential in northern Chile after the 2014 Iquique Earthquake Sequence

   NASA Astrophysics Data System (ADS)

   Hayes, G. P.; Herman, M. W.; Barnhart, W. D.; Furlong, K. P.; Riquelme, S.; Benz, H.; Bergman, E.; Barrientos, S. E.; Earle, P. S.; Samsonov, S. V.

   2014-12-01

   The seismic gap theory, which identifies regions of elevated hazard based on a lack of recent seismicity in comparison to other portions of a fault, has successfully explained past earthquakes and is useful for qualitatively describing where future large earthquakes might occur. A large earthquake had been expected in the subduction zone adjacent to northern Chile, which until recently had not ruptured in a megathrust earthquake since a M~8.8 event in 1877. On April 1 2014, a M 8.2 earthquake occurred within this northern Chile seismic gap, offshore of the city of Iquique; the size and spatial extent of the rupture indicate it was not the earthquake that had been anticipated. Here, we present a rapid assessment of the seismotectonics of the March-April 2014 seismic sequence offshore northern Chile, including analyses of earthquake (fore- and aftershock) relocations, moment tensors, finite fault models, moment deficit calculations, and cumulative Coulomb stress transfer calculations over the duration of the sequence. This ensemble of information allows us to place the current sequence within the context of historic seismicity in the region, and to assess areas of remaining and/or elevated hazard. Our results indicate that while accumulated strain has been released for a portion of the northern Chile seismic gap, significant sections have not ruptured in almost 150 years. These observations suggest that large-to-great sized megathrust earthquakes will occur north and south of the 2014 Iquique sequence sooner than might be expected had the 2014 events ruptured the entire seismic gap.

7. Investigation of atmospheric anomalies associated with Kashmir and Awaran Earthquakes

   NASA Astrophysics Data System (ADS)

   Mahmood, Irfan; Iqbal, Muhammad Farooq; Shahzad, Muhammad Imran; Qaiser, Saddam

   2017-02-01

   The earthquake precursors' anomalies at diverse elevation ranges over the seismogenic region and prior to the seismic events are perceived using Satellite Remote Sensing (SRS) techniques and reanalysis datasets. In the current research, seismic precursors are obtained by analyzing anomalies in Outgoing Longwave Radiation (OLR), Air Temperature (AT), and Relative Humidity (RH) before the two strong Mw>7 earthquakes in Pakistan occurred on 8th October 2005 in Azad Jammu Kashmir with Mw 7.6, and 24th September 2013 in Awaran, Balochistan with Mw 7.7. Multi-parameter data were computed based on multi-year background data for anomalies computation. Results indicate significant transient variations in observed parameters before the main event. Detailed analysis suggests presence of pre-seismic activities one to three weeks prior to the main earthquake event that vanishes after the event. These anomalies are due to increase in temperature after release of gases and physical and chemical interactions on earth surface before the earthquake. The parameter variations behavior for both Kashmir and Awaran earthquake events are similar to other earthquakes in different regions of the world. This study suggests that energy release is not concentrated to a single fault but instead is released along the fault zone. The influence of earthquake events on lightning were also investigated and it was concluded that there is a significant atmospheric lightning activity after the earthquake suggesting a strong possibility for an earthquake induced thunderstorm. This study is valuable for identifying earthquake precursors especially in earthquake prone areas.

8. Earthquakes.

   ERIC Educational Resources Information Center

   Walter, Edward J.

   1977-01-01

   Presents an analysis of the causes of earthquakes. Topics discussed include (1) geological and seismological factors that determine the effect of a particular earthquake on a given structure; (2) description of some large earthquakes such as the San Francisco quake; and (3) prediction of earthquakes. (HM)

9. Fractal structure of sequential behaviour patterns: an indicator of stress

   USGS Publications Warehouse

   Alados, C.L.; Escos, J.M; Emlen, J.M.

   1996-01-01

   The detection of stress arising from parasitic infection bySarcoptes scabieisand from pregnancy is explored, using a fractal analysis of head lifting behaviour and feeding–non-feeding activity sequences in female Spanish ibex,Capra pyrenaica, under natural conditions. Because organisms under stress increase their metabolic rate and, in consequence, energy consumption, it follows that stress will, generally, lead to a reduction in complexity (fractal dimension) of exploratory behaviour. In the present study the fractal dimension of the three measures of complexity used declined with stress, both from pregnancy and from parasitic infection. This observation provides a new and effective way to assess the general state of animals’ health in the field, without the need for capture and handling.

10. Fractal Image Filters for Specialized Image Recognition Tasks

    DTIC Science & Technology

    2010-02-11

    butter sets of fractal geometers, such as Sierpinski triangles, twin- dragons , Koch curves, Cantor sets, fractal ferns, and so on. The geometries and...K is a centrally symmetric convex body in R m, then the function ‖x‖K defines a norm on R m. Moreover, the set K is the unit ball with respect to the...positive numbers r and R such that K contains a ball of radius r and is contained in a ball of radius R, the following proposition is clear

11. Fractal Risk Assessment of ISS Propulsion Module in Meteoroid and Orbital Debris Environments

    NASA Technical Reports Server (NTRS)

    Mog, Robert A.

    2001-01-01

    A unique and innovative risk assessment of the International Space Station (ISS) Propulsion Module is conducted using fractal modeling of the Module's response to the meteoroid and orbital debris environments. Both the environment models and structural failure modes due to the resultant hypervelocity impact phenomenology, as well as Module geometry, are investigated for fractal applicability. The fractal risk assessment methodology could produce a greatly simplified alternative to current methodologies, such as BUMPER analyses, while maintaining or increasing the number of complex scenarios that can be assessed. As a minimum, this innovative fractal approach will provide an independent assessment of existing methodologies in a unique way.

12. The Mw 7.7 Bhuj earthquake: Global lessons for earthquake hazard in intra-plate regions

    USGS Publications Warehouse

    Schweig, E.; Gomberg, J.; Petersen, M.; Ellis, M.; Bodin, P.; Mayrose, L.; Rastogi, B.K.

    2003-01-01

    The Mw 7.7 Bhuj earthquake occurred in the Kachchh District of the State of Gujarat, India on 26 January 2001, and was one of the most damaging intraplate earthquakes ever recorded. This earthquake is in many ways similar to the three great New Madrid earthquakes that occurred in the central United States in 1811-1812, An Indo-US team is studying the similarities and differences of these sequences in order to learn lessons for earthquake hazard in intraplate regions. Herein we present some preliminary conclusions from that study. Both the Kutch and New Madrid regions have rift type geotectonic setting. In both regions the strain rates are of the order of 10-9/yr and attenuation of seismic waves as inferred from observations of intensity and liquefaction are low. These strain rates predict recurrence intervals for Bhuj or New Madrid sized earthquakes of several thousand years or more. In contrast, intervals estimated from paleoseismic studies and from other independent data are significantly shorter, probably hundreds of years. All these observations together may suggest that earthquakes relax high ambient stresses that are locally concentrated by rheologic heterogeneities, rather than loading by plate-tectonic forces. The latter model generally underlies basic assumptions made in earthquake hazard assessment, that the long-term average rate of energy released by earthquakes is determined by the tectonic loading rate, which thus implies an inherent average periodicity of earthquake occurrence. Interpreting the observations in terms of the former model therefore may require re-examining the basic assumptions of hazard assessment.

13. GPS Technologies as a Tool to Detect the Pre-Earthquake Signals Associated with Strong Earthquakes

    NASA Astrophysics Data System (ADS)

    Pulinets, S. A.; Krankowski, A.; Hernandez-Pajares, M.; Liu, J. Y. G.; Hattori, K.; Davidenko, D.; Ouzounov, D.

    2015-12-01

    The existence of ionospheric anomalies before earthquakes is now widely accepted. These phenomena started to be considered by GPS community to mitigate the GPS signal degradation over the territories of the earthquake preparation. The question is still open if they could be useful for seismology and for short-term earthquake forecast. More than decade of intensive studies proved that ionospheric anomalies registered before earthquakes are initiated by processes in the boundary layer of atmosphere over earthquake preparation zone and are induced in the ionosphere by electromagnetic coupling through the Global Electric Circuit. Multiparameter approach based on the Lithosphere-Atmosphere-Ionosphere Coupling model demonstrated that earthquake forecast is possible only if we consider the final stage of earthquake preparation in the multidimensional space where every dimension is one from many precursors in ensemble, and they are synergistically connected. We demonstrate approaches developed in different countries (Russia, Taiwan, Japan, Spain, and Poland) within the framework of the ISSI and ESA projects) to identify the ionospheric precursors. They are also useful to determine the all three parameters necessary for the earthquake forecast: impending earthquake epicenter position, expectation time and magnitude. These parameters are calculated using different technologies of GPS signal processing: time series, correlation, spectral analysis, ionospheric tomography, wave propagation, etc. Obtained results from different teams demonstrate the high level of statistical significance and physical justification what gives us reason to suggest these methodologies for practical validation.

14. Temporal evolution of soil moisture statistical fractal and controls by soil texture and regional groundwater flow

    NASA Astrophysics Data System (ADS)

    Ji, Xinye; Shen, Chaopeng; Riley, William J.

    2015-12-01

    Soil moisture statistical fractal is an important tool for downscaling remotely-sensed observations and has the potential to play a key role in multi-scale hydrologic modeling. The fractal was first introduced two decades ago, but relatively little is known regarding how its scaling exponents evolve in time in response to climatic forcings. Previous studies have neglected the process of moisture re-distribution due to regional groundwater flow. In this study we used a physically-based surface-subsurface processes model and numerical experiments to elucidate the patterns and controls of fractal temporal evolution in two U.S. Midwest basins. Groundwater flow was found to introduce large-scale spatial structure, thereby reducing the scaling exponents (τ), which has implications for the transferability of calibrated parameters to predict τ. However, the groundwater effects depend on complex interactions with other physical controls such as soil texture and land use. The fractal scaling exponents, while in general showing a seasonal mode that correlates with mean moisture content, display hysteresis after storm events that can be divided into three phases, consistent with literature findings: (a) wetting, (b) re-organizing, and (c) dry-down. Modeling experiments clearly show that the hysteresis is attributed to soil texture, whose "patchiness" is the primary contributing factor. We generalized phenomenological rules for the impacts of rainfall, soil texture, groundwater flow, and land use on τ evolution. Grid resolution has a mild influence on the results and there is a strong correlation between predictions of τ from different resolutions. Overall, our results suggest that groundwater flow should be given more consideration in studies of the soil moisture statistical fractal, especially in regions with a shallow water table.

15. Exhaled Aerosol Pattern Discloses Lung Structural Abnormality: A Sensitivity Study Using Computational Modeling and Fractal Analysis

    PubMed Central

    Xi, Jinxiang; Si, Xiuhua A.; Kim, JongWon; Mckee, Edward; Lin, En-Bing

    2014-01-01

    Background Exhaled aerosol patterns, also called aerosol fingerprints, provide clues to the health of the lung and can be used to detect disease-modified airway structures. The key is how to decode the exhaled aerosol fingerprints and retrieve the lung structural information for a non-invasive identification of respiratory diseases. Objective and Methods In this study, a CFD-fractal analysis method was developed to quantify exhaled aerosol fingerprints and applied it to one benign and three malign conditions: a tracheal carina tumor, a bronchial tumor, and asthma. Respirations of tracer aerosols of 1 µm at a flow rate of 30 L/min were simulated, with exhaled distributions recorded at the mouth. Large eddy simulations and a Lagrangian tracking approach were used to simulate respiratory airflows and aerosol dynamics. Aerosol morphometric measures such as concentration disparity, spatial distributions, and fractal analysis were applied to distinguish various exhaled aerosol patterns. Findings Utilizing physiology-based modeling, we demonstrated substantial differences in exhaled aerosol distributions among normal and pathological airways, which were suggestive of the disease location and extent. With fractal analysis, we also demonstrated that exhaled aerosol patterns exhibited fractal behavior in both the entire image and selected regions of interest. Each exhaled aerosol fingerprint exhibited distinct pattern parameters such as spatial probability, fractal dimension, lacunarity, and multifractal spectrum. Furthermore, a correlation of the diseased location and exhaled aerosol spatial distribution was established for asthma. Conclusion Aerosol-fingerprint-based breath tests disclose clues about the site and severity of lung diseases and appear to be sensitive enough to be a practical tool for diagnosis and prognosis of respiratory diseases with structural abnormalities. PMID:25105680

16. Thin film growth by 3D multi-particle diffusion limited aggregation model: Anomalous roughening and fractal analysis

    NASA Astrophysics Data System (ADS)

    Nasehnejad, Maryam; Nabiyouni, G.; Gholipour Shahraki, Mehran

    2018-03-01

    In this study a 3D multi-particle diffusion limited aggregation method is employed to simulate growth of rough surfaces with fractal behavior in electrodeposition process. A deposition model is used in which the radial motion of the particles with probability P, competes with random motions with probability 1 - P. Thin films growth is simulated for different values of probability P (related to the electric field) and thickness of the layer(related to the number of deposited particles). The influence of these parameters on morphology, kinetic of roughening and the fractal dimension of the simulated surfaces has been investigated. The results show that the surface roughness increases with increasing the deposition time and scaling exponents exhibit a complex behavior which is called as anomalous scaling. It seems that in electrodeposition process, radial motion of the particles toward the growing seeds may be an important mechanism leading to anomalous scaling. The results also indicate that the larger values of probability P, results in smoother topography with more densely packed structure. We have suggested a dynamic scaling ansatz for interface width has a function of deposition time, scan length and probability. Two different methods are employed to evaluate the fractal dimension of the simulated surfaces which are "cube counting" and "roughness" methods. The results of both methods show that by increasing the probability P or decreasing the deposition time, the fractal dimension of the simulated surfaces is increased. All gained values for fractal dimensions are close to 2.5 in the diffusion limited aggregation model.

17. Nontrivial paths and periodic orbits of the T-fractal billiard table

    NASA Astrophysics Data System (ADS)

    Lapidus, Michel L.; Miller, Robyn L.; Niemeyer, Robert G.

    2016-07-01

    We introduce and prove numerous new results about the orbits of the T-fractal billiard. Specifically, in section 3, we give a variety of sufficient conditions for the existence of a sequence of compatible periodic orbits. In section 4, we examine the limiting behavior of particular sequences of compatible periodic orbits. Additionally, sufficient conditions for the existence of particular nontrivial paths are given in section 4. The proofs of two results of Lapidus and Niemeyer (2013 The current state of fractal billiards Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics (Contemporary Mathematics vol 601) ed D Carfi et al (Providence, RI: American Mathematical Society) pp 251-88 (e-print: arXiv:math.DS.1210.0282v2, 2013) appear here for the first time, as well. In section 5, an orbit with an irrational initial direction reaches an elusive point in a way that yields a nontrivial path of finite length, yet, by our convention, constitutes a singular orbit of the fractal billiard table. The existence of such an orbit seems to indicate that the classification of orbits may not be so straightforward. A discussion of our results and directions for future research is then given in section 6.

18. Effect of Fractal Dimension on the Strain Behavior of Particulate Media

    NASA Astrophysics Data System (ADS)

    Altun, Selim; Sezer, Alper; Goktepe, A. Burak

    2016-12-01

    In this study, the influence of several fractal identifiers of granular materials on dynamic behavior of a flexible pavement structure as a particulate stratum is considered. Using experimental results and numerical methods as well, 15 different grain-shaped sands obtained from 5 different sources were analyzed as pavement base course materials. Image analyses were carried out by use of a stereomicroscope on 15 different samples to obtain quantitative particle shape information. Furthermore, triaxial compression tests were conducted to determine stress-strain and shear strength parameters of sands. Additionally, the dynamic response of the particulate media to standard traffic loads was computed using finite element modeling (FEM) technique. Using area-perimeter, line divider and box counting methods, over a hundred grains for each sand type were subjected to fractal analysis. Relationships among fractal dimension descriptors and dynamic strain levels were established for assessment of importance of shape descriptors of sands at various scales on the dynamic behavior. In this context, the advantage of fractal geometry concept to describe irregular and fractured shapes was used to characterize the sands used as base course materials. Results indicated that fractal identifiers can be preferred to analyze the effect of shape properties of sands on dynamic behavior of pavement base layers.

19. Microtopographic Inspection and Fractal Analysis of Skin Neoplasia

    NASA Astrophysics Data System (ADS)

    Costa, Manuel F. M.; Hipolito, Alberto Valencia; Gutierrez, Gustavo Fidel; Chanona, Jorge; Gallegos, Eva Ramón

    2008-04-01

    Early detection of skin cancer is fundamental to a successful treatment. Changes in the shape, including the relief, of skin lesions are an indicator of a possible malignity. Optical microtopographic inspection of skin lesions can be used to identify diagnostic patterns of benign and malign skin' lesions. Statistical parameters like the mean roughness (Ra) may allow the discrimination between different types of lesions and degree of malignity. Fractal analysis of bi-dimensional and 3D images of skin lesions can validate or complement that assessment by calculation of its fractal dimensions (FD). On the study herein reported the microtopographic inspection of the skin lesions were performed using the optical triangulation based microtopographer developed at the Physics Department of the University of Minho, MICROTOP.03.MFC. The patients that participated in this research work were men and women older than 15 years with the clinical and histopathology diagnoses of: melanoma, basocellular carcinoma, epidermoide carcinoma, actinic keratosis, keratoacantosis and benign nevus. Latex impressions of the lesions were taken and microtopographically analyzed. Characteristic information for each type of studied lesion was obtained. For melanoma it was observed that on the average these tumors present an increased roughness of around 67 percent compared to the roughness of the healthy skin. This feature allows the distinction from other tumors as basocellular carcinoma (were the roughness increase was in the average of 49 percent) and benign lesions as the epidermoide cyst (37 percent) or the seborrhea keratosis (4 percent). Tumor size and roughness are directly proportional to the grade of malignality. The characterization of the fractal geometry of 2D (histological slides) and 3D images of skin lesions was performed by obtaining its FD evaluated by means of the Box counting method. Results obtained showed that the average fractal dimension of histological slide images (FDh

20. Experimental criteria for the determination of fractal parameters of premixed turbulent flames

    NASA Astrophysics Data System (ADS)

    Shepherd, I. G.; Cheng, Robert K.; Talbot, L.

    1992-10-01

    The influence of spatial resolution, digitization noise, the number of records used for averaging, and the method of analysis on the determination of the fractal parameters of a high Damköhler number, methane/air, premixed, turbulent stagnation-point flame are investigated in this paper. The flow exit velocity was 5 m/s and the turbulent Reynolds number was 70 based on a integral scale of 3 mm and a turbulent intensity of 7%. The light source was a copper vapor laser which delivered 20 nsecs, 5 mJ pulses at 4 kHz and the tomographic cross-sections of the flame were recorded by a high speed movie camera. The spatial resolution of the images is 155 × 121 μm/pixel with a field of view of 50 × 65 mm. The stepping caliper technique for obtaining the fractal parameters is found to give the clearest indication of the cutoffs and the effects of noise. It is necessary to ensemble average the results from more than 25 statistically independent images to reduce sufficiently the scatter in the fractal parameters. The effects of reduced spatial resolution on fractal plots are estimated by artificial degradation of the resolution of the digitized flame boundaries. The effect of pixel resolution, an apparent increase in flame length below the inner scale rolloff, appears in the fractal plots when the measurent scale is less than approximately twice the pixel resolution. Although a clearer determination of fractal parameters is obtained by local averaging of the flame boundaries which removes digitization noise, at low spatial resolution this technique can reduce the fractal dimension. The degree of fractal isotropy of the flame surface can have a significant effect on the estimation of the flame surface area and hence burning rate from two-dimensional images. To estimate this isotropy a determination of the outer cutoff is required and three-dimensional measurements are probably also necessary.

1. Earthquakes.

   ERIC Educational Resources Information Center

   Pakiser, Louis C.

   One of a series of general interest publications on science topics, the booklet provides those interested in earthquakes with an introduction to the subject. Following a section presenting an historical look at the world's major earthquakes, the booklet discusses earthquake-prone geographic areas, the nature and workings of earthquakes, earthquake…

2. The generalized 20/80 law using probabilistic fractals applied to petroleum field size

   USGS Publications Warehouse

   Crovelli, R.A.

   1995-01-01

   Fractal properties of the Pareto probability distribution are used to generalize "the 20/80 law." The 20/80 law is a heuristic law that has evolved over the years into the following rule of thumb for many populations: 20 percent of the population accounts for 80 percent of the total value. The general p100/q100 law in probabilistic form is defined with q as a function of p, where p is the population proportion and q is the proportion of total value. Using the Pareto distribution, the p100/q100 law in fractal form is derived with the parameter q being a fractal, where q unexpectedly possesses the scale invariance property. The 20/80 law is a special case of the p100/q100 law in fractal form. The p100/q100 law in fractal form is applied to petroleum fieldsize data to obtain p and q such that p100% of the oil fields greater than any specified scale or size in a geologic play account for q100% of the total oil of the fields. The theoretical percentages of total resources of oil using the fractal q are extremely close to the empirical percentages from the data using the statistic q. Also, the empirical scale invariance property of the statistic q for the petroleum fieldsize data is in excellent agreement with the theoretical scale invariance property of the fractal q. ?? 1995 Oxford University Press.

3. Improved visibility graph fractality with application for the diagnosis of Autism Spectrum Disorder

   NASA Astrophysics Data System (ADS)

   Ahmadlou, Mehran; Adeli, Hojjat; Adeli, Amir

   2012-10-01

   Recently, the visibility graph (VG) algorithm was proposed for mapping a time series to a graph to study complexity and fractality of the time series through investigation of the complexity of its graph. The visibility graph algorithm converts a fractal time series to a scale-free graph. VG has been used for the investigation of fractality in the dynamic behavior of both artificial and natural complex systems. However, robustness and performance of the power of scale-freeness of VG (PSVG) as an effective method for measuring fractality has not been investigated. Since noise is unavoidable in real life time series, the robustness of a fractality measure is of paramount importance. To improve the accuracy and robustness of PSVG to noise for measurement of fractality of time series in biological time-series, an improved PSVG is presented in this paper. The proposed method is evaluated using two examples: a synthetic benchmark time series and a complicated real life Electroencephalograms (EEG)-based diagnostic problem, that is distinguishing autistic children from non-autistic children. It is shown that the proposed improved PSVG is less sensitive to noise and therefore more robust compared with PSVG. Further, it is shown that using improved PSVG in the wavelet-chaos neural network model of Adeli and c-workers in place of the Katz fractality dimension results in a more accurate diagnosis of autism, a complicated neurological and psychiatric disorder.

4. Has El Salvador Fault Zone produced M ≥ 7.0 earthquakes? The 1719 El Salvador earthquake

   NASA Astrophysics Data System (ADS)

   Canora, C.; Martínez-Díaz, J.; Álvarez-Gómez, J.; Villamor, P.; Ínsua-Arévalo, J.; Alonso-Henar, J.; Capote, R.

   2013-05-01

   Historically, large earthquakes, Mw ≥ 7.0, in the Εl Salvador area have been attributed to activity in the Cocos-Caribbean subduction zone. Τhis is correct for most of the earthquakes of magnitude greater than 6.5. However, recent paleoseismic evidence points to the existence of large earthquakes associated with rupture of the Εl Salvador Fault Ζone, an Ε-W oriented strike slip fault system that extends for 150 km through central Εl Salvador. Τo calibrate our results from paleoseismic studies, we have analyzed the historical seismicity of the area. In particular, we suggest that the 1719 earthquake can be associated with paleoseismic activity evidenced in the Εl Salvador Fault Ζone. Α reinterpreted isoseismal map for this event suggests that the damage reported could have been a consequence of the rupture of Εl Salvador Fault Ζone, rather than rupture of the subduction zone. Τhe isoseismal is not different to other upper crustal earthquakes in similar tectonovolcanic environments. We thus challenge the traditional assumption that only the subduction zone is capable of generating earthquakes of magnitude greater than 7.0 in this region. Τhis result has broad implications for future risk management in the region. Τhe potential occurrence of strong ground motion, significantly higher and closer to the Salvadorian populations that those assumed to date, must be considered in seismic hazard assessment studies in this area.

5. Noteworthy fractal features and transport properties of Cantor tartans

   NASA Astrophysics Data System (ADS)

   Balankin, Alexander S.; Golmankhaneh, Alireza K.; Patiño-Ortiz, Julián; Patiño-Ortiz, Miguel

   2018-06-01

   This Letter is focused on the impact of fractal topology on the transport processes governed by different kinds of random walks on Cantor tartans. We establish that the spectral dimension of the infinitely ramified Cantor tartan ds is equal to its fractal (self-similarity) dimension D. Consequently, the random walk on the Cantor tartan leads to a normal diffusion. On the other hand, the fractal geometry of Cantor tartans allows for a natural definition of power-law distributions of the waiting times and step lengths of random walkers. These distributions are Lévy stable if D > 1.5. Accordingly, we found that the random walk with rests leads to sub-diffusion, whereas the Lévy walk leads to ballistic diffusion. The Lévy walk with rests leads to super-diffusion, if D >√{ 3 }, or sub-diffusion, if 1.5 < D <√{ 3 }.

6. Fractal modeling of fluidic leakage through metal sealing surfaces

   NASA Astrophysics Data System (ADS)

   Zhang, Qiang; Chen, Xiaoqian; Huang, Yiyong; Chen, Yong

   2018-04-01

   This paper investigates the fluidic leak rate through metal sealing surfaces by developing fractal models for the contact process and leakage process. An improved model is established to describe the seal-contact interface of two metal rough surface. The contact model divides the deformed regions by classifying the asperities of different characteristic lengths into the elastic, elastic-plastic and plastic regimes. Using the improved contact model, the leakage channel under the contact surface is mathematically modeled based on the fractal theory. The leakage model obtains the leak rate using the fluid transport theory in porous media, considering that the pores-forming percolation channels can be treated as a combination of filled tortuous capillaries. The effects of fractal structure, surface material and gasket size on the contact process and leakage process are analyzed through numerical simulations for sealed ring gaskets.

7. Earthquakes at North Atlantic passive margins

   SciTech Connect

   Gregersen, S.; Basham, P.W.

   1989-01-01

   The main focus of this volume is the earthquakes that occur at and near the continental margins on both sides of the North Atlantic. The book, which contains the proceedings of the NATO workshop on Causes and Effects of Earthquakes at Passive Margins and in Areas of Postglacial Rebound on Both Sides of the North Atlantic, draws together the fields of geophysics, geology and geodesy to address the stress and strain in the Earth's crust. The resulting earthquakes produced on ancient geological fault zones and the associated seismic hazards these pose to man are also addressed. Postglacial rebound in Northmore » America and Fennoscandia is a minor source of earthquakes today, during the interglacial period, but evidence is presented to suggest that the ice sheets suppressed earthquake strain while they were in place, and released this strain as a pulse of significant earthquakes after the ice melted about 9000 years ago.« less

8. Source properties of earthquakes near the Salton Sea triggered by the 16 October 1999 M 7.1 Hector Mine, California, earthquake

   USGS Publications Warehouse

   Hough, S.E.; Kanamori, H.

   2002-01-01

   We analyze the source properties of a sequence of triggered earthquakes that occurred near the Salton Sea in southern California in the immediate aftermath of the M 7.1 Hector Mine earthquake of 16 October 1999. The sequence produced a number of early events that were not initially located by the regional network, including two moderate earthquakes: the first within 30 sec of the P-wave arrival and a second approximately 10 minutes after the mainshock. We use available amplitude and waveform data from these events to estimate magnitudes to be approximately 4.7 and 4.4, respectively, and to obtain crude estimates of their locations. The sequence of small events following the initial M 4.7 earthquake is clustered and suggestive of a local aftershock sequence. Using both broadband TriNet data and analog data from the Southern California Seismic Network (SCSN), we also investigate the spectral characteristics of the M 4.4 event and other triggered earthquakes using empirical Green's function (EGF) analysis. We find that the source spectra of the events are consistent with expectations for tectonic (brittle shear failure) earthquakes, and infer stress drop values of 0.1 to 6 MPa for six M 2.1 to M 4.4 events. The estimated stress drop values are within the range observed for tectonic earthquakes elsewhere. They are relatively low compared to typically observed stress drop values, which is consistent with expectations for faulting in an extensional, high heat flow regime. The results therefore suggest that, at least in this case, triggered earthquakes are associated with a brittle shear failure mechanism. This further suggests that triggered earthquakes may tend to occur in geothermal-volcanic regions because shear failure occurs at, and can be triggered by, relatively low stresses in extensional regimes.

9. Fractal Stiffening

   NASA Technical Reports Server (NTRS)

   Harper, David William (Inventor)

   2017-01-01

   A structural support having fractal-stiffening and method of fabricating the support is presented where an optimized location of at least three nodes is predetermined prior to fabricating the structural support where a first set of webs is formed on one side of the support and joined to the nodes to form a first pocket region. A second set of webs is formed within the first pocket region forming a second pocket region where the height of the first set of webs extending orthogonally from the side of the support is greater than the second set of webs extending orthogonally from the support.

10. Sensing the earthquake

    NASA Astrophysics Data System (ADS)

    Bichisao, Marta; Stallone, Angela

    2017-04-01

    Making science visual plays a crucial role in the process of building knowledge. In this view, art can considerably facilitate the representation of the scientific content, by offering a different perspective on how a specific problem could be approached. Here we explore the possibility of presenting the earthquake process through visual dance. From a choreographer's point of view, the focus is always on the dynamic relationships between moving objects. The observed spatial patterns (coincidences, repetitions, double and rhythmic configurations) suggest how objects organize themselves in the environment and what are the principles underlying that organization. The identified set of rules is then implemented as a basis for the creation of a complex rhythmic and visual dance system. Recently, scientists have turned seismic waves into sound and animations, introducing the possibility of "feeling" the earthquakes. We try to implement these results into a choreographic model with the aim to convert earthquake sound to a visual dance system, which could return a transmedia representation of the earthquake process. In particular, we focus on a possible method to translate and transfer the metric language of seismic sound and animations into body language. The objective is to involve the audience into a multisensory exploration of the earthquake phenomenon, through the stimulation of the hearing, eyesight and perception of the movements (neuromotor system). In essence, the main goal of this work is to develop a method for a simultaneous visual and auditory representation of a seismic event by means of a structured choreographic model. This artistic representation could provide an original entryway into the physics of earthquakes.

11. Fractal analysis of the ambulation pattern of Japanese quail.

    PubMed

    Kembro, J M; Perillo, M A; Pury, P A; Satterlee, D G; Marín, R H

    2009-03-01

    1. The study examined the practicality and usefulness of fractal analyses in evaluating the temporal organisation of avian ambulatory behaviour by using female Japanese quail in their home boxes as the model system. To induce two locomotion activity levels, we tested half of the birds without disturbance (Unstimulated) and the other half when food was scattered on the floor of the home box after 3 h of feeder withdrawal (Stimulated). 2. Ambulatory activity was recorded during 40 min at a resolution of 1 s and evaluated by: (1) detrended fluctuation analyses (DFA), (2) the frequency distribution of the duration of the walking or non-walking events (FDD-W or FDD-NW, respectively), and (3) the transition probabilities between walking/non-walking states. Conventional measures of total time spent walking and average duration of the walking/non-walking events were also employed. 3. DFA showed a decreased value of the self-similarity parameter (alpha; indicative of a more complex ambulatory pattern) in Stimulated birds compared to their Unstimulated counterparts. The FDD-NW showed a more negative scaling factor in Stimulated than in Unstimulated birds. Stimulated birds also had more transitions between non-walking and walking states, consistent with stimulated exploratory activity. No differences were found between groups in the FDD-W, in percentage of total time spent walking, or in average duration of the walking events. 4. The temporal walking pattern of female Japanese quail has a fractal structure and its organisation and complexity is altered when birds are stimulated to explore. The fractal analyses detected differences between the Unstimulated and Stimulated groups that went undetected by the traditional measurements of the percentage of total time spent walking and the duration of the walking events suggesting its usefulness as a tool for behavioural studies.

12. Some statistical features of the seismic activity related to the recent M8.2 and M7.1 earthquakes in Mexico

    NASA Astrophysics Data System (ADS)

    Guzman, L.; Baeza-Blancas, E.; Reyes, I.; Angulo Brown, F.; Rudolf Navarro, A.

    2017-12-01

    By studying the magnitude earthquake catalogs, previous studies have reported evidence that some changes in the spatial and temporal organization of earthquake activity is observedbefore and after of a main-shock. These previous studies have used different approach methods for detecting clustering behavior and distance-events density in order topoint out the asymmetric behavior of before shocks and aftershocks. Here, we present a statistical analysis of the seismic activity related to the M8.2 and M7.1 earthquakes occurredon Sept. 7th and Sept. 19th, respectively. First, we calculated the interevent time and distance for the period Sept. 7th 2016 until Oct. 20th 2017 for each seismic region ( a radius of 150 km centeredat coordinates of the M8.1 and M7.1). Next, we calculated the "velocity" of the walker as the ratio between the interevent distance and interevent time, and similarly, we also constructed the"acceleration". A slider pointer is considered to estimate some statistical features within time windows of size τ for the velocity and acceleration sequences before and after the main shocks. Specifically, we applied the fractal dimension method to detect changes in the correlation (persistence) behavior of events in the period before the main events.Our preliminary results pointed out that the fractal dimension associated to the velocity and acceleration sequences exhibits changes in the persistence behavior before the mainshock, while thescaling dimension values after the main events resemble a more uncorrelated behavior. Moreover, the relationship between the standard deviation of the velocity and the local mean velocity valuefor a given time window-size τ is described by an exponent close to 1.5, and the cumulative distribution of velocity and acceleration are well described by power law functions after the crash and stretched-exponential-like distribution before the main shock. On the other hand, we present an analysis of patterns of seismicquiescence

13. Pre-earthquake magnetic pulses

    NASA Astrophysics Data System (ADS)

    Scoville, J.; Heraud, J.; Freund, F.

    2015-08-01

    A semiconductor model of rocks is shown to describe unipolar magnetic pulses, a phenomenon that has been observed prior to earthquakes. These pulses are suspected to be generated deep in the Earth's crust, in and around the hypocentral volume, days or even weeks before earthquakes. Their extremely long wavelength allows them to pass through kilometers of rock. Interestingly, when the sources of these pulses are triangulated, the locations coincide with the epicenters of future earthquakes. We couple a drift-diffusion semiconductor model to a magnetic field in order to describe the electromagnetic effects associated with electrical currents flowing within rocks. The resulting system of equations is solved numerically and it is seen that a volume of rock may act as a diode that produces transient currents when it switches bias. These unidirectional currents are expected to produce transient unipolar magnetic pulses similar in form, amplitude, and duration to those observed before earthquakes, and this suggests that the pulses could be the result of geophysical semiconductor processes.

14. Long-range (fractal) correlations in the LEDA database.

    NASA Astrophysics Data System (ADS)

    di Nella, H.; Montuori, M.; Paturel, G.; Pietronero, L.; Sylos Labini, F.

    1996-04-01

    All the recent redshift surveys show highly irregular patterns of galaxies on scales of hundreds of megaparsecs such as chains, walls and cells. One of the most powerful catalog of galaxies is represented by the LEDA database that contains more than 36,000 galaxies with redshift. We study the correlation properties of such a sample finding that galaxy distribution shows well defined fractal nature up to R_S_~150h^-1^Mpc with fractal dimension D~2. We test the consistency of these results versus the incompleteness in the sample.

15. Time Series Analysis OF SAR Image Fractal Maps: The Somma-Vesuvio Volcanic Complex Case Study

    NASA Astrophysics Data System (ADS)

    Pepe, Antonio; De Luca, Claudio; Di Martino, Gerardo; Iodice, Antonio; Manzo, Mariarosaria; Pepe, Susi; Riccio, Daniele; Ruello, Giuseppe; Sansosti, Eugenio; Zinno, Ivana

    2016-04-01

    The fractal dimension is a significant geophysical parameter describing natural surfaces representing the distribution of the roughness over different spatial scale; in case of volcanic structures, it has been related to the specific nature of materials and to the effects of active geodynamic processes. In this work, we present the analysis of the temporal behavior of the fractal dimension estimates generated from multi-pass SAR images relevant to the Somma-Vesuvio volcanic complex (South Italy). To this aim, we consider a Cosmo-SkyMed data-set of 42 stripmap images acquired from ascending orbits between October 2009 and December 2012. Starting from these images, we generate a three-dimensional stack composed by the corresponding fractal maps (ordered according to the acquisition dates), after a proper co-registration. The time-series of the pixel-by-pixel estimated fractal dimension values show that, over invariant natural areas, the fractal dimension values do not reveal significant changes; on the contrary, over urban areas, it correctly assumes values outside the natural surfaces fractality range and show strong fluctuations. As a final result of our analysis, we generate a fractal map that includes only the areas where the fractal dimension is considered reliable and stable (i.e., whose standard deviation computed over the time series is reasonably small). The so-obtained fractal dimension map is then used to identify areas that are homogeneous from a fractal viewpoint. Indeed, the analysis of this map reveals the presence of two distinctive landscape units corresponding to the Mt. Vesuvio and Gran Cono. The comparison with the (simplified) geological map clearly shows the presence in these two areas of volcanic products of different age. The presented fractal dimension map analysis demonstrates the ability to get a figure about the evolution degree of the monitored volcanic edifice and can be profitably extended in the future to other volcanic systems with

16. Fabrication of Multscale Fractal-Like Structures by Controlling Fluid Interface Instability

    PubMed Central

    Islam, Tanveer ul; Gandhi, Prasanna S.

    2016-01-01

    Nature, in quest for the best designs has shaped its vital systems into fractal geometries. Effectual way of spontaneous fabrication of scalable, ordered fractal-like structures by controlling Saffman-Taylor instability in a lifted Hele-Shaw cell is deployed here. In lifted Hele-Shaw cell uncontrolled penetration of low-viscosity fluid into its high-viscosity counterpart is known to develop irregular, non-repeatable, normally short-lived, branched patterns. We propose and characterize experimentally anisotropies in a form of spatially distributed pits on the cell plates to control initiation and further penetration of non-splitting fingers. The proposed control over shielding mechanism yields recipes for fabrication of families of ordered fractal-like patterns of multiple generations. As an example, we demonstrate and characterize fabrication of a Cayley tree fractal-like pattern. The patterns, in addition, are retained permanently by employing UV/thermally curable fluids. The proposed technique thus establishes solid foundation for bio-mimicking natural structures spanning multiple-scales for scientific and engineering use. PMID:27849003

17. Fabrication of Multscale Fractal-Like Structures by Controlling Fluid Interface Instability

    NASA Astrophysics Data System (ADS)

    Islam, Tanveer Ul; Gandhi, Prasanna S.

    2016-11-01

    Nature, in quest for the best designs has shaped its vital systems into fractal geometries. Effectual way of spontaneous fabrication of scalable, ordered fractal-like structures by controlling Saffman-Taylor instability in a lifted Hele-Shaw cell is deployed here. In lifted Hele-Shaw cell uncontrolled penetration of low-viscosity fluid into its high-viscosity counterpart is known to develop irregular, non-repeatable, normally short-lived, branched patterns. We propose and characterize experimentally anisotropies in a form of spatially distributed pits on the cell plates to control initiation and further penetration of non-splitting fingers. The proposed control over shielding mechanism yields recipes for fabrication of families of ordered fractal-like patterns of multiple generations. As an example, we demonstrate and characterize fabrication of a Cayley tree fractal-like pattern. The patterns, in addition, are retained permanently by employing UV/thermally curable fluids. The proposed technique thus establishes solid foundation for bio-mimicking natural structures spanning multiple-scales for scientific and engineering use.

18. Diagnostics of multi-fractality of magnetized plasma inside coronal holes and quiet sun areas

    NASA Astrophysics Data System (ADS)

    Abramenko, Valentyna

    Turbulent and multi-fractal properties of magnetized plasma in solar Coronal Holes (CHs) and Quiet Sun (QS) photosphere were explored using high-resolution magnetograms measured with the New Solar Telescope (NST) at the Big Bear Solar Observatory (BBSO, USA), Hinode/SOT and SDO/HMI instruments. Distribution functions of size and magnetic flux measured for small-scale magnetic elements follow the log-normal law, which implies multi-fractal organization of the magnetic field and the absence of a unique power law for all scales. The magnetograms show multi-fractality in CHs on scales 400 - 10000 km, which becomes better pronounced as the spatial resolution of data improves. Photospheric granulation measured with NST exhibits multi-fractal properties on very small scales of 50 - 600 km. While multi-fractal nature of solar active regions is well known, newly established multi-fractality of weakest magnetic fields on the solar surface, i.e., in CHs and QS, leads us to a conclusion that the entire variety of solar magnetic fields is generated by a unique nonlinear dynamical process.

19. Pitfalls in Fractal Time Series Analysis: fMRI BOLD as an Exemplary Case

    PubMed Central

    Eke, Andras; Herman, Peter; Sanganahalli, Basavaraju G.; Hyder, Fahmeed; Mukli, Peter; Nagy, Zoltan

    2012-01-01

    This article will be positioned on our previous work demonstrating the importance of adhering to a carefully selected set of criteria when choosing the suitable method from those available ensuring its adequate performance when applied to real temporal signals, such as fMRI BOLD, to evaluate one important facet of their behavior, fractality. Earlier, we have reviewed on a range of monofractal tools and evaluated their performance. Given the advance in the fractal field, in this article we will discuss the most widely used implementations of multifractal analyses, too. Our recommended flowchart for the fractal characterization of spontaneous, low frequency fluctuations in fMRI BOLD will be used as the framework for this article to make certain that it will provide a hands-on experience for the reader in handling the perplexed issues of fractal analysis. The reason why this particular signal modality and its fractal analysis has been chosen was due to its high impact on today’s neuroscience given it had powerfully emerged as a new way of interpreting the complex functioning of the brain (see “intrinsic activity”). The reader will first be presented with the basic concepts of mono and multifractal time series analyses, followed by some of the most relevant implementations, characterization by numerical approaches. The notion of the dichotomy of fractional Gaussian noise and fractional Brownian motion signal classes and their impact on fractal time series analyses will be thoroughly discussed as the central theme of our application strategy. Sources of pitfalls and way how to avoid them will be identified followed by a demonstration on fractal studies of fMRI BOLD taken from the literature and that of our own in an attempt to consolidate the best practice in fractal analysis of empirical fMRI BOLD signals mapped throughout the brain as an exemplary case of potentially wide interest. PMID:23227008

20. Dynamic triggering of deep earthquakes within a fossil slab

    NASA Astrophysics Data System (ADS)

    Cai, Chen; Wiens, Douglas A.

    2016-09-01

    The 9 November 2009 Mw 7.3 Fiji deep earthquake is the largest event in a region west of the Tonga slab defined by scattered seismicity and velocity anomalies. The main shock rupture was compact, but the aftershocks were distributed along a linear feature at distances of up to 126 km. The aftershocks and some background seismicity define a sharp northern boundary to the zone of outboard earthquakes, extending westward toward the Vitiaz deep earthquake cluster. The northern earthquake lineament is geometrically similar to tectonic reconstructions of the relict Vitiaz subduction zone at 8-10 Ma, suggesting the earthquakes are occurring in the final portion of the slab subducted at the now inactive Vitiaz trench. A Coulomb stress change calculation suggests many of the aftershocks were dynamically triggered. We propose that fossil slabs contain material that is too warm for earthquake nucleation but may be near the critical stress susceptible to dynamic triggering.

1. Fractal Tempo Fluctuation and Pulse Prediction

   PubMed Central

   Rankin, Summer K.; Large, Edward W.; Fink, Philip W.

   2010-01-01

   WE INVESTIGATED PEOPLES’ ABILITY TO ADAPT TO THE fluctuating tempi of music performance. In Experiment 1, four pieces from different musical styles were chosen, and performances were recorded from a skilled pianist who was instructed to play with natural expression. Spectral and rescaled range analyses on interbeat interval time-series revealed long-range (1/f type) serial correlations and fractal scaling in each piece. Stimuli for Experiment 2 included two of the performances from Experiment 1, with mechanical versions serving as controls. Participants tapped the beat at ¼- and ⅛-note metrical levels, successfully adapting to large tempo fluctuations in both performances. Participants predicted the structured tempo fluctuations, with superior performance at the ¼-note level. Thus, listeners may exploit long-range correlations and fractal scaling to predict tempo changes in music. PMID:25190901

2. Fractals, malware, and data models

   NASA Astrophysics Data System (ADS)

   Jaenisch, Holger M.; Potter, Andrew N.; Williams, Deborah; Handley, James W.

   2012-06-01

   We examine the hypothesis that the decision boundary between malware and non-malware is fractal. We introduce a novel encoding method derived from text mining for converting disassembled programs first into opstrings and then filter these into a reduced opcode alphabet. These opcodes are enumerated and encoded into real floating point number format and used for characterizing frequency of occurrence and distribution properties of malware functions to compare with non-malware functions. We use the concept of invariant moments to characterize the highly non-Gaussian structure of the opcode distributions. We then derive Data Model based classifiers from identified features and interpolate and extrapolate the parameter sample space for the derived Data Models. This is done to examine the nature of the parameter space classification boundary between families of malware and the general non-malware category. Preliminary results strongly support the fractal boundary hypothesis, and a summary of our methods and results are presented here.

3. Performance assessment of methods for estimation of fractal dimension from scanning electron microscope images.

   PubMed

   Risović, Dubravko; Pavlović, Zivko

   2013-01-01

   Processing of gray scale images in order to determine the corresponding fractal dimension is very important due to widespread use of imaging technologies and application of fractal analysis in many areas of science, technology, and medicine. To this end, many methods for estimation of fractal dimension from gray scale images have been developed and routinely used. Unfortunately different methods (dimension estimators) often yield significantly different results in a manner that makes interpretation difficult. Here, we report results of comparative assessment of performance of several most frequently used algorithms/methods for estimation of fractal dimension. To that purpose, we have used scanning electron microscope images of aluminum oxide surfaces with different fractal dimensions. The performance of algorithms/methods was evaluated using the statistical Z-score approach. The differences between performances of six various methods are discussed and further compared with results obtained by electrochemical impedance spectroscopy on the same samples. The analysis of results shows that the performance of investigated algorithms varies considerably and that systematically erroneous fractal dimensions could be estimated using certain methods. The differential cube counting, triangulation, and box counting algorithms showed satisfactory performance in the whole investigated range of fractal dimensions. Difference statistic is proved to be less reliable generating 4% of unsatisfactory results. The performances of the Power spectrum, Partitioning and EIS were unsatisfactory in 29%, 38%, and 75% of estimations, respectively. The results of this study should be useful and provide guidelines to researchers using/attempting fractal analysis of images obtained by scanning microscopy or atomic force microscopy. © Wiley Periodicals, Inc.

4. Proliferative diabetic retinopathy characterization based on fractal features: Evaluation on a publicly available dataset.

   PubMed

   Orlando, José Ignacio; van Keer, Karel; Barbosa Breda, João; Manterola, Hugo Luis; Blaschko, Matthew B; Clausse, Alejandro

   2017-12-01

   Diabetic retinopathy (DR) is one of the most widespread causes of preventable blindness in the world. The most dangerous stage of this condition is proliferative DR (PDR), in which the risk of vision loss is high and treatments are less effective. Fractal features of the retinal vasculature have been previously explored as potential biomarkers of DR, yet the current literature is inconclusive with respect to their correlation with PDR. In this study, we experimentally assess their discrimination ability to recognize PDR cases. A statistical analysis of the viability of using three reference fractal characterization schemes - namely box, information, and correlation dimensions - to identify patients with PDR is presented. These descriptors are also evaluated as input features for training ℓ1 and ℓ2 regularized logistic regression classifiers, to estimate their performance. Our results on MESSIDOR, a public dataset of 1200 fundus photographs, indicate that patients with PDR are more likely to exhibit a higher fractal dimension than healthy subjects or patients with mild levels of DR (P≤1.3×10-2). Moreover, a supervised classifier trained with both fractal measurements and red lesion-based features reports an area under the ROC curve of 0.93 for PDR screening and 0.96 for detecting patients with optic disc neovascularizations. The fractal dimension of the vasculature increases with the level of DR. Furthermore, PDR screening using multiscale fractal measurements is more feasible than using their derived fractal dimensions. Code and further resources are provided at https://github.com/ignaciorlando/fundus-fractal-analysis. © 2017 American Association of Physicists in Medicine.

5. A Lossless hybrid wavelet-fractal compression for welding radiographic images.

   PubMed

   Mekhalfa, Faiza; Avanaki, Mohammad R N; Berkani, Daoud

   2016-01-01

   In this work a lossless wavelet-fractal image coder is proposed. The process starts by compressing and decompressing the original image using wavelet transformation and fractal coding algorithm. The decompressed image is removed from the original one to obtain a residual image which is coded by using Huffman algorithm. Simulation results show that with the proposed scheme, we achieve an infinite peak signal to noise ratio (PSNR) with higher compression ratio compared to typical lossless method. Moreover, the use of wavelet transform speeds up the fractal compression algorithm by reducing the size of the domain pool. The compression results of several welding radiographic images using the proposed scheme are evaluated quantitatively and compared with the results of Huffman coding algorithm.

6. Dynamic evaluation of seismic hazard and risks based on the Unified Scaling Law for Earthquakes

   NASA Astrophysics Data System (ADS)

   Kossobokov, V. G.; Nekrasova, A.

   2016-12-01

   We continue applying the general concept of seismic risk analysis in a number of seismic regions worldwide by constructing seismic hazard maps based on the Unified Scaling Law for Earthquakes (USLE), i.e. log N(M,L) = A + B•(6 - M) + C•log L, where N(M,L) is the expected annual number of earthquakes of a certain magnitude M within an seismically prone area of linear dimension L, A characterizes the average annual rate of strong (M = 6) earthquakes, B determines the balance between magnitude ranges, and C estimates the fractal dimension of seismic locus in projection to the Earth surface. The parameters A, B, and C of USLE are used to assess, first, the expected maximum magnitude in a time interval at a seismically prone cell of a uniform grid that cover the region of interest, and then the corresponding expected ground shaking parameters. After a rigorous testing against the available seismic evidences in the past (e.g., the historically reported macro-seismic intensity or paleo data), such a seismic hazard map is used to generate maps of specific earthquake risks for population, cities, and infrastructures. The hazard maps for a given territory change dramatically, when the methodology is applied to a certain size moving time window, e.g. about a decade long for an intermediate-term regional assessment or exponentially increasing intervals for a daily local strong aftershock forecasting. The of dynamical seismic hazard and risks assessment is illustrated by applications to the territory of Greater Caucasus and Crimea and the two-year series of aftershocks of the 11 October 2008 Kurchaloy, Chechnya earthquake which case-history appears to be encouraging for further systematic testing as potential short-term forecasting tool.

7. Overestimation of the earthquake hazard along the Himalaya: constraints in bracketing of medieval earthquakes from paleoseismic studies

   NASA Astrophysics Data System (ADS)

   Arora, Shreya; Malik, Javed N.

   2017-12-01

   The Himalaya is one of the most seismically active regions of the world. The occurrence of several large magnitude earthquakes viz. 1905 Kangra earthquake (Mw 7.8), 1934 Bihar-Nepal earthquake (Mw 8.2), 1950 Assam earthquake (Mw 8.4), 2005 Kashmir (Mw 7.6), and 2015 Gorkha (Mw 7.8) are the testimony to ongoing tectonic activity. In the last few decades, tremendous efforts have been made along the Himalayan arc to understand the patterns of earthquake occurrences, size, extent, and return periods. Some of the large magnitude earthquakes produced surface rupture, while some remained blind. Furthermore, due to the incompleteness of the earthquake catalogue, a very few events can be correlated with medieval earthquakes. Based on the existing paleoseismic data certainly, there exists a complexity to precisely determine the extent of surface rupture of these earthquakes and also for those events, which occurred during historic times. In this paper, we have compiled the paleo-seismological data and recalibrated the radiocarbon ages from the trenches excavated by previous workers along the entire Himalaya and compared earthquake scenario with the past. Our studies suggest that there were multiple earthquake events with overlapping surface ruptures in small patches with an average rupture length of 300 km limiting Mw 7.8-8.0 for the Himalayan arc, rather than two or three giant earthquakes rupturing the whole front. It has been identified that the large magnitude Himalayan earthquakes, such as 1905 Kangra, 1934 Bihar-Nepal, and 1950 Assam, that have occurred within a time frame of 45 years. Now, if these events are dated, there is a high possibility that within the range of ±50 years, they may be considered as the remnant of one giant earthquake rupturing the entire Himalayan arc. Therefore, leading to an overestimation of seismic hazard scenario in Himalaya.

8. The Twinkling Fractal Theory of the Glass Transition: Applications to Soft Matter

   NASA Astrophysics Data System (ADS)

   Wool, Richard

   2012-02-01

   The Twinkling Fractal Theory (TFT) of the glass transition has recently been demonstrated experimentally [J.F. Stanzione et al., J. Non Cryst. Sol., (2011, 357,311]. The hard to-soft matter transition is characterized by the presence of solid fractal clusters with liquid-like pools that are dynamically interchanging via their anharmonic intermolecular potentials with Boltzmann energy populations with a characteristic temperature dependent vibrational density of states g(φ) ˜ φ^df . The twinkling fractal frequencies φ cover a range of 10^12 Hz to 10-10Hz and the fractal solid clusters of size R have a lifetime τ ˜ R^Df/df, where the fractal dimension Df 2.4 and the fracton dimension df = 4/3. Here we explore its application to a number of soft matter issues. These include (a) Confinement effects on Tg reduction in thin films of thickness h, where by virtue of large cluster exclusion, δTg ˜ 1/h^Df/df; (b) Tg gradients near bulk surfaces, where the smaller clusters on the surface have a faster relaxation time; (c) Effect of twinkling surfaces on cell growth, where at T Tg + 20 C, there exists a twinkling fractal range that leads to bell-shaped enhancement of cell growth and chemical up-regulation via the twinkling surfaces ``communicating `` with the cells through their vibrations; and (d) adhesion above and below Tg where topological fluctuations associated with g(φ) promotes the development of nano-nails at the interface.

9. Upscaling: Effective Medium Theory, Numerical Methods and the Fractal Dream

   NASA Astrophysics Data System (ADS)

   Guéguen, Y.; Ravalec, M. Le; Ricard, L.

   2006-06-01

   Upscaling is a major issue regarding mechanical and transport properties of rocks. This paper examines three issues relative to upscaling. The first one is a brief overview of Effective Medium Theory (EMT), which is a key tool to predict average rock properties at a macroscopic scale in the case of a statistically homogeneous medium. EMT is of particular interest in the calculation of elastic properties. As discussed in this paper, EMT can thus provide a possible way to perform upscaling, although it is by no means the only one, and in particular it is irrelevant if the medium does not adhere to statistical homogeneity. This last circumstance is examined in part two of the paper. We focus on the example of constructing a hydrocarbon reservoir model. Such a construction is a required step in the process of making reasonable predictions for oil production. Taking into account rock permeability, lithological units and various structural discontinuities at different scales is part of this construction. The result is that stochastic reservoir models are built that rely on various numerical upscaling methods. These methods are reviewed. They provide techniques which make it possible to deal with upscaling on a general basis. Finally, a last case in which upscaling is trivial is considered in the third part of the paper. This is the fractal case. Fractal models have become popular precisely because they are free of the assumption of statistical homogeneity and yet do not involve numerical methods. It is suggested that using a physical criterion as a means to discriminate whether fractality is a dream or reality would be more satisfactory than relying on a limited data set alone.

10. Fractal dimension of microbead assemblies used for protein detection.

    PubMed

    Hecht, Ariel; Commiskey, Patrick; Lazaridis, Filippos; Argyrakis, Panos; Kopelman, Raoul

    2014-11-10

    We use fractal analysis to calculate the protein concentration in a rotating magnetic assembly of microbeads of size 1 μm, which has optimized parameters of sedimentation, binding sites and magnetic volume. We utilize the original Forrest-Witten method, but due to the relatively small number of bead particles, which is of the order of 500, we use a large number of origins and also a large number of algorithm iterations. We find a value of the fractal dimension in the range 1.70-1.90, as a function of the thrombin concentration, which plays the role of binding the microbeads together. This is in good agreement with previous results from magnetorotation studies. The calculation of the fractal dimension using multiple points of reference can be used for any assembly with a relatively small number of particles. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

11. Fractal serpentine-shaped design for stretchable wireless strain sensors

    NASA Astrophysics Data System (ADS)

    Dong, Wentao; Cheng, Xiao; Wang, Xiaoming; Zhang, Hailiang

    2018-07-01

    Stretchable sensors have been widely applied to biological fields due to their unique capacity to integrate with soft materials and curvilinear surfaces. The article presents the fractal serpentine-shaped design for stretchable wireless strain sensor which is operating around 1.6 GHz. The wireless passive LC sensor is formed by a fractal serpentine-shaped inductor coil and a concentric coplanar capacitor. The inductance of the fractal serpentine-shaped coil varies with the deformation of the wireless sensor, and the resonance frequency also varies with the applied strain of the wireless sensor embedded in soft substrate. The 40% stretchability of wireless sensor is verified by finite element analysis (FEA). Strain response of the stretchable wireless sensor has been characterized by experiments and demonstrates high strain responsivity about 6.74 MHz/1%. The stretchable wireless sensor has the potential to be used in biological and wearable applications.

12. Excitation of Terahertz Charge Transfer Plasmons in Metallic Fractal Structures

    NASA Astrophysics Data System (ADS)

    Ahmadivand, Arash; Gerislioglu, Burak; Sinha, Raju; Vabbina, Phani Kiran; Karabiyik, Mustafa; Pala, Nezih

    2017-08-01

    There have been extensive researches on terahertz (THz) plasmonic structures supporting resonant modes to demonstrate nano and microscale devices with high efficiency and responsivity as well as frequency selectivity. Here, using antisymmetric plasmonic fractal Y-shaped (FYS) structures as building blocks, we introduce a highly tunable four-member fractal assembly to support charge transfer plasmons (CTPs) and classical dipolar resonant modes with significant absorption cross section in the THz domain. We first present that the unique geometrical nature of the FYS system and corresponding spectral response allow for supporting intensified dipolar plasmonic modes under polarised light exposure in a standalone structure. In addition to classical dipolar mode, for the very first time, we demonstrated CTPs in the THz domain due to the direct shuttling of the charges across the metallic fractal microantenna which led to sharp resonant absorption peaks. Using both numerical and experimental studies, we have investigated and confirmed the excitation of the CTP modes and highly tunable spectral response of the proposed plasmonic fractal structure. This understanding opens new and promising horizons for tightly integrated THz devices with high efficiency and functionality.

13. Down syndrome's brain dynamics: analysis of fractality in resting state.

    PubMed

    Hemmati, Sahel; Ahmadlou, Mehran; Gharib, Masoud; Vameghi, Roshanak; Sajedi, Firoozeh

    2013-08-01

    To the best knowledge of the authors there is no study on nonlinear brain dynamics of down syndrome (DS) patients, whereas brain is a highly complex and nonlinear system. In this study, fractal dimension of EEG, as a key characteristic of brain dynamics, showing irregularity and complexity of brain dynamics, was used for evaluation of the dynamical changes in the DS brain. The results showed higher fractality of the DS brain in almost all regions compared to the normal brain, which indicates less centrality and higher irregular or random functioning of the DS brain regions. Also, laterality analysis of the frontal lobe showed that the normal brain had a right frontal laterality of complexity whereas the DS brain had an inverse pattern (left frontal laterality). Furthermore, the high accuracy of 95.8 % obtained by enhanced probabilistic neural network classifier showed the potential of nonlinear dynamic analysis of the brain for diagnosis of DS patients. Moreover, the results showed that the higher EEG fractality in DS is associated with the higher fractality in the low frequencies (delta and theta), in broad regions of the brain, and the high frequencies (beta and gamma), majorly in the frontal regions.

14. Design and analysis microstrip dipole using fractal Koch for 433 MHz applications

    NASA Astrophysics Data System (ADS)

    Zulfin, M.; Rambe, A. H.; Budi, B.

    2018-02-01

    This paper discussed the dipole microstrip antenna design using fractal Koch for working on frequency of 433 MHz. The fractal Koch was used to reduce the size of the microstrip antenna. The smaller the antenna size, the lighter the equipment. AWR simulator was employed to evaluate antenna parameters such as return loss, gain and radiation pattern. The antenna was designed on a FR4 substrate with relative permittivity of 4.4 and thickness 1.6 mm. The result shows that the fractal Koch reduce antenna size about 41.2% and decrease return loss about 30%.

15. Risk Management in Earthquakes, Financial Markets, and the Game of 21: The role of Forecasting, Nowcasting, and Timecasting

    NASA Astrophysics Data System (ADS)

    Rundle, J. B.

    2017-12-01

    Earthquakes and financial markets share surprising similarities [1]. For example, the well-known VIX index, which by definition is the implied volatility of the Standard and Poors 500 index, behaves in very similar quantitative fashion to time series for earthquake rates. Both display sudden increases at the time of an earthquake or an announcement of the US Federal Reserve Open Market Committee [2], and both decay as an inverse power of time. Both can be regarded as examples of first order phase transitions [1], and display fractal and scaling behavior associated with critical transitions, such as power-law magnitude-frequency relations in the tails of the distributions. Early quantitative investors such as Edward Thorpe and John Kelly invented novel methods to mitigate or manage risk in games of chance such as blackjack, and in markets using hedging techniques that are still in widespread use today. The basic idea is the concept of proportional betting, where the gambler/investor bets a fraction of the bankroll whose size is determined by the "edge" or inside knowledge of the real (and changing) odds. For earthquake systems, the "edge" over nature can only exist in the form of a forecast (probability of a future earthquake); a nowcast (knowledge of the current state of an earthquake fault system); or a timecast (statistical estimate of the waiting time until the next major earthquake). In our terminology, a forecast is a model, while the nowcast and timecast are analysis methods using observed data only (no model). We also focus on defined geographic areas rather than on faults, thereby eliminating the need to consider specific fault data or fault interactions. Data used are online earthquake catalogs, generally since 1980. Forecasts are based on the Weibull (1952) probability law, and only a handful of parameters are needed. These methods allow the development of real time hazard and risk estimation using cloud-based technologies, and permit the application of

16. Centrality in earthquake multiplex networks

    NASA Astrophysics Data System (ADS)

    Lotfi, Nastaran; Darooneh, Amir Hossein; Rodrigues, Francisco A.

    2018-06-01

    Seismic time series has been mapped as a complex network, where a geographical region is divided into square cells that represent the nodes and connections are defined according to the sequence of earthquakes. In this paper, we map a seismic time series to a temporal network, described by a multiplex network, and characterize the evolution of the network structure in terms of the eigenvector centrality measure. We generalize previous works that considered the single layer representation of earthquake networks. Our results suggest that the multiplex representation captures better earthquake activity than methods based on single layer networks. We also verify that the regions with highest seismological activities in Iran and California can be identified from the network centrality analysis. The temporal modeling of seismic data provided here may open new possibilities for a better comprehension of the physics of earthquakes.

17. A spectrum fractal feature classification algorithm for agriculture crops with hyper spectrum image

    NASA Astrophysics Data System (ADS)

    Su, Junying

    2011-11-01

    A fractal dimension feature analysis method in spectrum domain for hyper spectrum image is proposed for agriculture crops classification. Firstly, a fractal dimension calculation algorithm in spectrum domain is presented together with the fast fractal dimension value calculation algorithm using the step measurement method. Secondly, the hyper spectrum image classification algorithm and flowchart is presented based on fractal dimension feature analysis in spectrum domain. Finally, the experiment result of the agricultural crops classification with FCL1 hyper spectrum image set with the proposed method and SAM (spectral angle mapper). The experiment results show it can obtain better classification result than the traditional SAM feature analysis which can fulfill use the spectrum information of hyper spectrum image to realize precision agricultural crops classification.

18. The fractal architecture of cytoplasmic organization: scaling, kinetics and emergence in metabolic networks.

    PubMed

    Aon, Miguel Antonio; O'Rourke, Brian; Cortassa, Sonia

    2004-01-01

    In this work, we highlight the links between fractals and scaling in cells and explore the kinetic consequences for biochemical reactions operating in fractal media. Based on the proposal that the cytoskeletal architecture is organized as a percolation lattice, with clusters emerging as fractal forms, the analysis of kinetics in percolation clusters is especially emphasized. A key consequence of this spatiotemporal cytoplasmic organization is that enzyme reactions following Michaelis-Menten or allosteric type kinetics exhibit higher rates in fractal media (for short times and at lower substrate concentrations) at the percolation threshold than in Euclidean media. As a result, considerably faster and higher amplification of enzymatic activity is obtained. Finally, we describe some of the properties bestowed by cytoskeletal organization and dynamics on metabolic networks.

19. Along-strike variations in fault frictional properties along the San Andreas Fault near Cholame, California from joint earthquake and low-frequency earthquake relocations

    USGS Publications Warehouse

    Harrington, Rebecca M.; Cochran, Elizabeth S.; Griffiths, Emily M.; Zeng, Xiangfang; Thurber, Clifford H.

    2016-01-01

    Recent observations of low‐frequency earthquakes (LFEs) and tectonic tremor along the Parkfield–Cholame segment of the San Andreas fault suggest slow‐slip earthquakes occur in a transition zone between the shallow fault, which accommodates slip by a combination of aseismic creep and earthquakes (<15 km depth), and the deep fault, which accommodates slip by stable sliding (>35 km depth). However, the spatial relationship between shallow earthquakes and LFEs remains unclear. Here, we present precise relocations of 34 earthquakes and 34 LFEs recorded during a temporary deployment of 13 broadband seismic stations from May 2010 to July 2011. We use the temporary array waveform data, along with data from permanent seismic stations and a new high‐resolution 3D velocity model, to illuminate the fine‐scale details of the seismicity distribution near Cholame and the relation to the distribution of LFEs. The depth of the boundary between earthquakes and LFE hypocenters changes along strike and roughly follows the 350°C isotherm, suggesting frictional behavior may be, in part, thermally controlled. We observe no overlap in the depth of earthquakes and LFEs, with an ∼5 km separation between the deepest earthquakes and shallowest LFEs. In addition, clustering in the relocated seismicity near the 2004 Mw 6.0 Parkfield earthquake hypocenter and near the northern boundary of the 1857 Mw 7.8 Fort Tejon rupture may highlight areas of frictional heterogeneities on the fault where earthquakes tend to nucleate.

20. Fractality of pulsatile flow in speckle images

    NASA Astrophysics Data System (ADS)

    Nemati, M.; Kenjeres, S.; Urbach, H. P.; Bhattacharya, N.

    2016-05-01

    The scattering of coherent light from a system with underlying flow can be used to yield essential information about dynamics of the process. In the case of pulsatile flow, there is a rapid change in the properties of the speckle images. This can be studied using the standard laser speckle contrast and also the fractality of images. In this paper, we report the results of experiments performed to study pulsatile flow with speckle images, under different experimental configurations to verify the robustness of the techniques for applications. In order to study flow under various levels of complexity, the measurements were done for three in-vitro phantoms and two in-vivo situations. The pumping mechanisms were varied ranging from mechanical pumps to the human heart for the in vivo case. The speckle images were analyzed using the techniques of fractal dimension and speckle contrast analysis. The results of these techniques for the various experimental scenarios were compared. The fractal dimension is a more sensitive measure to capture the complexity of the signal though it was observed that it is also extremely sensitive to the properties of the scattering medium and cannot recover the signal for thicker diffusers in comparison to speckle contrast.

1. Interfacial contact stiffness of fractal rough surfaces.

   PubMed

   Zhang, Dayi; Xia, Ying; Scarpa, Fabrizio; Hong, Jie; Ma, Yanhong

   2017-10-09

   In this work we describe a theoretical model that predicts the interfacial contact stiffness of fractal rough surfaces by considering the effects of elastic and plastic deformations of the fractal asperities. We also develop an original test rig that simulates dovetail joints for turbo machinery blades, which can fine tune the normal contact load existing between the contacting surfaces of the blade root. The interfacial contact stiffness is obtained through an inverse identification method in which finite element simulations are fitted to the experimental results. Excellent agreement is observed between the contact stiffness predicted by the theoretical model and by the analogous experimental results. We demonstrate that the contact stiffness is a power law function of the normal contact load with an exponent α within the whole range of fractal dimension D(1 < D < 2). We also show that for 1 < D < 1.5 the Pohrt-Popov behavior (α = 1/(3 - D)) is valid, however for 1.5 < D < 2, the exponent α is different and equal to 2(D - 1)/D. The diversity between the model developed in the work and the Pohrt-Popov one is explained in detail.

2. Fractal Patterns of Neural Activity Exist within the Suprachiasmatic Nucleus and Require Extrinsic Network Interactions

   PubMed Central

   Hu, Kun; Meijer, Johanna H.; Shea, Steven A.; vanderLeest, Henk Tjebbe; Pittman-Polletta, Benjamin; Houben, Thijs; van Oosterhout, Floor; Deboer, Tom; Scheer, Frank A. J. L.

   2012-01-01

   The mammalian central circadian pacemaker (the suprachiasmatic nucleus, SCN) contains thousands of neurons that are coupled through a complex network of interactions. In addition to the established role of the SCN in generating rhythms of ∼24 hours in many physiological functions, the SCN was recently shown to be necessary for normal self-similar/fractal organization of motor activity and heart rate over a wide range of time scales—from minutes to 24 hours. To test whether the neural network within the SCN is sufficient to generate such fractal patterns, we studied multi-unit neural activity of in vivo and in vitro SCNs in rodents. In vivo SCN-neural activity exhibited fractal patterns that are virtually identical in mice and rats and are similar to those in motor activity at time scales from minutes up to 10 hours. In addition, these patterns remained unchanged when the main afferent signal to the SCN, namely light, was removed. However, the fractal patterns of SCN-neural activity are not autonomous within the SCN as these patterns completely broke down in the isolated in vitro SCN despite persistence of circadian rhythmicity. Thus, SCN-neural activity is fractal in the intact organism and these fractal patterns require network interactions between the SCN and extra-SCN nodes. Such a fractal control network could underlie the fractal regulation observed in many physiological functions that involve the SCN, including motor control and heart rate regulation. PMID:23185285

3. Evidence of diffusive fractal aggregation of TiO2 nanoparticles by femtosecond laser ablation at ambient conditions

   NASA Astrophysics Data System (ADS)

   Celardo, G. L.; Archetti, D.; Ferrini, G.; Gavioli, L.; Pingue, P.; Cavaliere, E.

   2017-01-01

   The specific mechanisms which lead to the formation of fractal nanostructures by pulsed laser deposition remain elusive despite intense research efforts, motivated mainly by the technological interest in obtaining tailored nanostructures with simple and scalable production methods. Here we focus on fractal nanostructures of titanium dioxide, TiO2, a strategic material for many applications, obtained by femtosecond laser ablation at ambient conditions. We compare a theoretical model of fractal formation with experimental data. The comparison of theory and experiment confirms that fractal aggregates are formed after landing of the ablated material on the substrate surface by a simple diffusive mechanism. We model the fractal formation through extensive Monte Carlo simulations based on a set of minimal assumptions: TiO2 nanoparticles arrive already formed on the substrate, then they diffuse in a size/mass independent way and stick irreversibly upon touching, thus forming fractal clusters. Despite its simplicity, our model explains the main features of the fractal structures arising from the complex interaction of large TiO2 nanoparticles with different substrates. Indeed our model is able to reproduce both the fractal dimensions and the area distributions of the nanostructures for different densities of the ablated material. Finally we discuss the role of the thermal conductivity of the substrate and the laser fluence on the properties of the fractal nanostructures. Our results represent an advancement towards controlling the production of fractal nanostructures by pulsed laser deposition.

4. Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

   NASA Astrophysics Data System (ADS)

   Zhang, Qian; Harman, Ciaran J.; Kirchner, James W.

   2018-02-01

   River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling - in the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) - are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β = 0) to Brown noise (β = 2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb-Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among all methods for a wide range of

5. [Fractal research of neurite growth in immunofluorescent images].

   PubMed

   Tang, Min; Wang, Huinan

   2008-12-01

   Fractal dimension has been widely used in medical images processing and analysis. The neurite growth of cultured dorsal root ganglion (DRG) was detected by fluorescent immunocytochemistry treated with nerve regeneration factor (0.1, 0.5, 2.0 mg/L). A novel method based on triangular prism surface area (TPSA) was introduced and adopted to calculate the fractal dimension of the two-dimensional immunofluorescent images. Experimental results demonstrate that this method is easy to understand and convenient to operate, and the quantititve results are concordant with the observational findings under microscope. This method can be guidelines for analyzing and deciding experimental results.

6. Super Water-Repellent Fractal Surfaces of a Photochromic Diarylethene Induced by UV Light

   NASA Astrophysics Data System (ADS)

   Izumi, Norikazu; Minami, Takayuki; Mayama, Hiroyuki; Takata, Atsushi; Nakamura, Shinichiro; Yokojima, Satoshi; Tsujii, Kaoru; Uchida, Kingo

   2008-09-01

   Photochromic diarylethene forms super water-repellent surfaces upon irradiation with UV light. Microfibril-like crystals grow on the solid diarylethene surface after UV irradiation, and the contact angle of water on the surface becomes larger with increasing surface roughness with time. The fractal analysis was made by the box-counting method for the rough surfaces. There are three regions in the roughness size having the fractal dimension of ca. 2.4 (size of roughness smaller than 5 µm), of ca. 2.2 (size of roughness between 5-40 µm), and of ca. 2.0 (size of roughness larger than 40 µm). The fractal dimension of ca. 2.4 was due to the fibril-like structures generated gradually by UV irradiation on diarylethene surfaces accompanied with an increase in the contact angle. The surface structure with larger fractal dimension mainly contributes to realizing the super water-repellency of the diarylethene surfaces. This mechanism of spontaneous formation of fractal surfaces is similar to that for triglyceride and alkylketene dimer waxes.

7. The 2004 Parkfield, CA Earthquake: A Teachable Moment for Exploring Earthquake Processes, Probability, and Earthquake Prediction

   NASA Astrophysics Data System (ADS)

   Kafka, A.; Barnett, M.; Ebel, J.; Bellegarde, H.; Campbell, L.

   2004-12-01

   The occurrence of the 2004 Parkfield earthquake provided a unique "teachable moment" for students in our science course for teacher education majors. The course uses seismology as a medium for teaching a wide variety of science topics appropriate for future teachers. The 2004 Parkfield earthquake occurred just 15 minutes after our students completed a lab on earthquake processes and earthquake prediction. That lab included a discussion of the Parkfield Earthquake Prediction Experiment as a motivation for the exercises they were working on that day. Furthermore, this earthquake was recorded on an AS1 seismograph right in their lab, just minutes after the students left. About an hour after we recorded the earthquake, the students were able to see their own seismogram of the event in the lecture part of the course, which provided an excellent teachable moment for a lecture/discussion on how the occurrence of the 2004 Parkfield earthquake might affect seismologists' ideas about earthquake prediction. The specific lab exercise that the students were working on just before we recorded this earthquake was a "sliding block" experiment that simulates earthquakes in the classroom. The experimental apparatus includes a flat board on top of which are blocks of wood attached to a bungee cord and a string wrapped around a hand crank. Plate motion is modeled by slowly turning the crank, and earthquakes are modeled as events in which the block slips ("blockquakes"). We scaled the earthquake data and the blockquake data (using how much the string moved as a proxy for time) so that we could compare blockquakes and earthquakes. This provided an opportunity to use interevent-time histograms to teach about earthquake processes, probability, and earthquake prediction, and to compare earthquake sequences with blockquake sequences. We were able to show the students, using data obtained directly from their own lab, how global earthquake data fit a Poisson exponential distribution better

8. Earthquake geology of the Bulnay Fault (Mongolia)

   USGS Publications Warehouse

   Rizza, Magali; Ritz, Jean-Franciois; Prentice, Carol S.; Vassallo, Ricardo; Braucher, Regis; Larroque, Christophe; Arzhannikova, A.; Arzhanikov, S.; Mahan, Shannon; Massault, M.; Michelot, J-L.; Todbileg, M.

   2015-01-01

   The Bulnay earthquake of July 23, 1905 (Mw 8.3-8.5), in north-central Mongolia, is one of the world's largest recorded intracontinental earthquakes and one of four great earthquakes that occurred in the region during the 20th century. The 375-km-long surface rupture of the left-lateral, strike-slip, N095°E trending Bulnay Fault associated with this earthquake is remarkable for its pronounced expression across the landscape and for the size of features produced by previous earthquakes. Our field observations suggest that in many areas the width and geometry of the rupture zone is the result of repeated earthquakes; however, in those areas where it is possible to determine that the geomorphic features are the result of the 1905 surface rupture alone, the size of the features produced by this single earthquake are singular in comparison to most other historical strike-slip surface ruptures worldwide. Along the 80 km stretch, between 97.18°E and 98.33°E, the fault zone is characterized by several meters width and the mean left-lateral 1905 offset is 8.9 ± 0.6 m with two measured cumulative offsets that are twice the 1905 slip. These observations suggest that the displacement produced during the penultimate event was similar to the 1905 slip. Morphotectonic analyses carried out at three sites along the eastern part of the Bulnay fault, allow us to estimate a mean horizontal slip rate of 3.1 ± 1.7 mm/yr over the Late Pleistocene-Holocene period. In parallel, paleoseismological investigations show evidence for two earthquakes prior to the 1905 event with recurrence intervals of ~2700-4000 years.

9. Possible scenarios for occurrence of M ~ 7 interplate earthquakes prior to and following the 2011 Tohoku-Oki earthquake based on numerical simulation.

   PubMed

   Nakata, Ryoko; Hori, Takane; Hyodo, Mamoru; Ariyoshi, Keisuke

   2016-05-10

   We show possible scenarios for the occurrence of M ~ 7 interplate earthquakes prior to and following the M ~ 9 earthquake along the Japan Trench, such as the 2011 Tohoku-Oki earthquake. One such M ~ 7 earthquake is so-called the Miyagi-ken-Oki earthquake, for which we conducted numerical simulations of earthquake generation cycles by using realistic three-dimensional (3D) geometry of the subducting Pacific Plate. In a number of scenarios, the time interval between the M ~ 9 earthquake and the subsequent Miyagi-ken-Oki earthquake was equal to or shorter than the average recurrence interval during the later stage of the M ~ 9 earthquake cycle. The scenarios successfully reproduced important characteristics such as the recurrence of M ~ 7 earthquakes, coseismic slip distribution, afterslip distribution, the largest foreshock, and the largest aftershock of the 2011 earthquake. Thus, these results suggest that we should prepare for future M ~ 7 earthquakes in the Miyagi-ken-Oki segment even though this segment recently experienced large coseismic slip in 2011.

10. Possible scenarios for occurrence of M ~ 7 interplate earthquakes prior to and following the 2011 Tohoku-Oki earthquake based on numerical simulation

    PubMed Central

    Nakata, Ryoko; Hori, Takane; Hyodo, Mamoru; Ariyoshi, Keisuke

    2016-01-01

    We show possible scenarios for the occurrence of M ~ 7 interplate earthquakes prior to and following the M ~ 9 earthquake along the Japan Trench, such as the 2011 Tohoku-Oki earthquake. One such M ~ 7 earthquake is so-called the Miyagi-ken-Oki earthquake, for which we conducted numerical simulations of earthquake generation cycles by using realistic three-dimensional (3D) geometry of the subducting Pacific Plate. In a number of scenarios, the time interval between the M ~ 9 earthquake and the subsequent Miyagi-ken-Oki earthquake was equal to or shorter than the average recurrence interval during the later stage of the M ~ 9 earthquake cycle. The scenarios successfully reproduced important characteristics such as the recurrence of M ~ 7 earthquakes, coseismic slip distribution, afterslip distribution, the largest foreshock, and the largest aftershock of the 2011 earthquake. Thus, these results suggest that we should prepare for future M ~ 7 earthquakes in the Miyagi-ken-Oki segment even though this segment recently experienced large coseismic slip in 2011. PMID:27161897

11. An Evaluation of Fractal Surface Measurement Methods for Characterizing Landscape Complexity from Remote-Sensing Imagery

    NASA Technical Reports Server (NTRS)

    Lam, Nina Siu-Ngan; Qiu, Hong-Lie; Quattrochi, Dale A.; Emerson, Charles W.; Arnold, James E. (Technical Monitor)

    2001-01-01

    The rapid increase in digital data volumes from new and existing sensors necessitates the need for efficient analytical tools for extracting information. We developed an integrated software package called ICAMS (Image Characterization and Modeling System) to provide specialized spatial analytical functions for interpreting remote sensing data. This paper evaluates the three fractal dimension measurement methods: isarithm, variogram, and triangular prism, along with the spatial autocorrelation measurement methods Moran's I and Geary's C, that have been implemented in ICAMS. A modified triangular prism method was proposed and implemented. Results from analyzing 25 simulated surfaces having known fractal dimensions show that both the isarithm and triangular prism methods can accurately measure a range of fractal surfaces. The triangular prism method is most accurate at estimating the fractal dimension of higher spatial complexity, but it is sensitive to contrast stretching. The variogram method is a comparatively poor estimator for all of the surfaces, particularly those with higher fractal dimensions. Similar to the fractal techniques, the spatial autocorrelation techniques are found to be useful to measure complex images but not images with low dimensionality. These fractal measurement methods can be applied directly to unclassified images and could serve as a tool for change detection and data mining.

12. Simultaneous estimation of deterministic and fractal stochastic components in non-stationary time series

    NASA Astrophysics Data System (ADS)

    García, Constantino A.; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G.

    2018-07-01

    In the past few decades, it has been recognized that 1 / f fluctuations are ubiquitous in nature. The most widely used mathematical models to capture the long-term memory properties of 1 / f fluctuations have been stochastic fractal models. However, physical systems do not usually consist of just stochastic fractal dynamics, but they often also show some degree of deterministic behavior. The present paper proposes a model based on fractal stochastic and deterministic components that can provide a valuable basis for the study of complex systems with long-term correlations. The fractal stochastic component is assumed to be a fractional Brownian motion process and the deterministic component is assumed to be a band-limited signal. We also provide a method that, under the assumptions of this model, is able to characterize the fractal stochastic component and to provide an estimate of the deterministic components present in a given time series. The method is based on a Bayesian wavelet shrinkage procedure that exploits the self-similar properties of the fractal processes in the wavelet domain. This method has been validated over simulated signals and over real signals with economical and biological origin. Real examples illustrate how our model may be useful for exploring the deterministic-stochastic duality of complex systems, and uncovering interesting patterns present in time series.

13. Sierpinski triangles as a tool to introduce fractal geometry to children and their parents

    NASA Astrophysics Data System (ADS)

    Gires, Auguste; Schertzer, Daniel

    2017-04-01

    There are currently two somehow contradictory trends in the public debates involving scientific issues. On the one hand there is a need to address topics of increasing complexity, while on the other hand simple(istic) solutions are suggested by numerous people (including high level ones). Meanwhile there seems to be growing defiance towards science findings. Such problems are faced in numerous fields including geosciences where famous examples are the debates dealing with climate change, or water / air contamination. Such unfortunate trends means that the input of scientists in the society and public debates is strongly required. Although it not actually their job, scientists should get involved as a citizens. They should try to explain the complexity of the issues at stake, and take the necessary time to achieve this; not all problems can be explained with the help of a 140 characters tweet! Rather than hiding the uncertainties, they should try to explain this notion often not well understood, and admit the current limitations of knowledge. In the meantime it would be positive if this dialogue could help children and their parents to get familiarized with science and scientists, show that science is not obscure and actually present in everyday life. Scientists obviously also have the hope of fostering a desire for understanding, enhancing scientific culture and even promoting careers in this field. Fractals and fractal geometry are actually a rather good tool to achieve this. Indeed through numerous iterations of a simple process, one can easily obtain a rather complex shape, exhibiting some of the features observed in the nature. Fractal shapes are scale invariant, i.e. the more you zoom in, the more details you see; a portion of the shape is similar to the full one. This paper aims at presenting a series of activities presenting fractals to young people developed primarily around the famous Sierpinski triangles. Two types of activities were carefully designed

14. [A method to estimate the short-term fractal dimension of heart rate variability based on wavelet transform].

    PubMed

    Zhonggang, Liang; Hong, Yan

    2006-10-01

    A new method of calculating fractal dimension of short-term heart rate variability signals is presented. The method is based on wavelet transform and filter banks. The implementation of the method is: First of all we pick-up the fractal component from HRV signals using wavelet transform. Next, we estimate the power spectrum distribution of fractal component using auto-regressive model, and we estimate parameter 7 using the least square method. Finally according to formula D = 2- (gamma-1)/2 estimate fractal dimension of HRV signal. To validate the stability and reliability of the proposed method, using fractional brown movement simulate 24 fractal signals that fractal value is 1.6 to validate, the result shows that the method has stability and reliability.

15. Are seismic hazard assessment errors and earthquake surprises unavoidable?

    NASA Astrophysics Data System (ADS)

    Kossobokov, Vladimir

    2013-04-01

    Why earthquake occurrences bring us so many surprises? The answer seems evident if we review the relationships that are commonly used to assess seismic hazard. The time-span of physically reliable Seismic History is yet a small portion of a rupture recurrence cycle at an earthquake-prone site, which makes premature any kind of reliable probabilistic statements about narrowly localized seismic hazard. Moreover, seismic evidences accumulated to-date demonstrate clearly that most of the empirical relations commonly accepted in the early history of instrumental seismology can be proved erroneous when testing statistical significance is applied. Seismic events, including mega-earthquakes, cluster displaying behaviors that are far from independent or periodic. Their distribution in space is possibly fractal, definitely, far from uniform even in a single segment of a fault zone. Such a situation contradicts generally accepted assumptions used for analytically tractable or computer simulations and complicates design of reliable methodologies for realistic earthquake hazard assessment, as well as search and definition of precursory behaviors to be used for forecast/prediction purposes. As a result, the conclusions drawn from such simulations and analyses can MISLEAD TO SCIENTIFICALLY GROUNDLESS APPLICATION, which is unwise and extremely dangerous in assessing expected societal risks and losses. For example, a systematic comparison of the GSHAP peak ground acceleration estimates with those related to actual strong earthquakes, unfortunately, discloses gross inadequacy of this "probabilistic" product, which appears UNACCEPTABLE FOR ANY KIND OF RESPONSIBLE SEISMIC RISK EVALUATION AND KNOWLEDGEABLE DISASTER PREVENTION. The self-evident shortcomings and failures of GSHAP appeals to all earthquake scientists and engineers for an urgent revision of the global seismic hazard maps from the first principles including background methodologies involved, such that there becomes: (a) a

16. Fractal feature of sEMG from Flexor digitorum superficialis muscle correlated with levels of contraction during low-level finger flexions.

    PubMed

    Arjunan, Sridhar P; Kumar, Dinesh K; Naik, Ganesh R

    2010-01-01

    This research paper reports an experimental study on identification of the changes in fractal properties of surface Electromyogram (sEMG) with the changes in the force levels during low-level finger flexions. In the previous study, the authors have identified a novel fractal feature, Maximum fractal length (MFL) as a measure of strength of low-level contractions and has used this feature to identify various wrist and finger movements. This study has tested the relationship between the MFL and force of contraction. The results suggest that changes in MFL is correlated with the changes in contraction levels (20%, 50% and 80% maximum voluntary contraction (MVC)) during low-level muscle activation such as finger flexions. From the statistical analysis and by visualisation using box-plot, it is observed that MFL (p ≈ 0.001) is a more correlated to force of contraction compared to RMS (p≈0.05), even when the muscle contraction is less than 50% MVC during low-level finger flexions. This work has established that this fractal feature will be useful in providing information about changes in levels of force during low-level finger movements for prosthetic control or human computer interface.

17. Fractal spectral triples on Kellendonk's C∗-algebra of a substitution tiling

    NASA Astrophysics Data System (ADS)

    Mampusti, Michael; Whittaker, Michael F.

    2017-02-01

    We introduce a new class of noncommutative spectral triples on Kellendonk's C∗-algebra associated with a nonperiodic substitution tiling. These spectral triples are constructed from fractal trees on tilings, which define a geodesic distance between any two tiles in the tiling. Since fractals typically have infinite Euclidean length, the geodesic distance is defined using Perron-Frobenius theory, and is self-similar with scaling factor given by the Perron-Frobenius eigenvalue. We show that each spectral triple is θ-summable, and respects the hierarchy of the substitution system. To elucidate our results, we construct a fractal tree on the Penrose tiling, and explicitly show how it gives rise to a collection of spectral triples.

18. Fractal dynamics of heartbeat time series of young persons with metabolic syndrome

    NASA Astrophysics Data System (ADS)

    Muñoz-Diosdado, A.; Alonso-Martínez, A.; Ramírez-Hernández, L.; Martínez-Hernández, G.

    2012-10-01

    Many physiological systems have been in recent years quantitatively characterized using fractal analysis. We applied it to study heart variability of young subjects with metabolic syndrome (MS); we examined the RR time series (time between two R waves in ECG) with the detrended fluctuation analysis (DFA) method, the Higuchi's fractal dimension method and the multifractal analysis to detect the possible presence of heart problems. The results show that although the young persons have MS, the majority do not present alterations in the heart dynamics. However, there were cases where the fractal parameter values differed significantly from the healthy people values.

19. Earthquakes

    MedlinePlus

    An earthquake happens when two blocks of the earth suddenly slip past one another. Earthquakes strike suddenly, violently, and without warning at any time of the day or night. If an earthquake occurs in a populated area, it may cause ...

20. What Googling Trends Tell Us About Public Interest in Earthquakes

    NASA Astrophysics Data System (ADS)

    Tan, Y. J.; Maharjan, R.

    2017-12-01

    Previous studies have shown that immediately after large earthquakes, there is a period of increased public interest. This represents a window of opportunity for science communication and disaster relief fundraising efforts to reach more people. However, how public interest varies for different earthquakes has not been quantified systematically on a global scale. We analyze how global search interest for the term "earthquake" on Google varies following earthquakes of magnitude ≥ 5.5 from 2004 to 2016. We find that there is a spike in search interest after large earthquakes followed by an exponential temporal decay. Preliminary results suggest that the period of increased search interest scales with death toll and correlates with the period of increased media coverage. This suggests that the relationship between the period of increased public interest in earthquakes and death toll might be an effect of differences in media coverage. However, public interest never remains elevated for more than three weeks. Therefore, to take advantage of this short period of increased public interest, science communication and disaster relief fundraising efforts have to act promptly following devastating earthquakes.

1. Study of Fractal Features of Geomagnetic Activity Through an MHD Shell Model

   NASA Astrophysics Data System (ADS)

   Dominguez, M.; Nigro, G.; Munoz, V.; Carbone, V.

   2013-12-01

   Studies on complexity have been of great interest in plasma physics, because they provide new insights and reveal possible universalities on issues such as geomagnetic activity, turbulence in laboratory plasmas, physics of the solar wind, etc. [1, 2]. In particular, various studies have discussed the relationship between the fractal dimension, as a measure of complexity, and physical processes in magnetized plasmas such as the Sun's surface, the solar wind and the Earth's magnetosphere, including the possibility of forecasting geomagnetic activity [3, 4, 5]. Shell models are low dimensional dynamical models describing the main statistical properties of magnetohydrodynamic (MHD) turbulence [6]. These models allow us to describe extreme parameter conditions hence reaching very high Reynolds (Re) numbers. In this work a MHD shell model is used to describe the dissipative events which are taking place in the Earth's magnetosphere and causing geomagnetic storms. The box-counting fractal dimension (D) [7] is calculated for the time series of the magnetic energy dissipation rate obtained in this MHD shell model. We analyze the correlation between D and the energy dissipation rate in order to make a comparison with the same analysis made on the geomagnetic data. We show that, depending on the values of the viscosity and the diffusivity, the fractal dimension and the occurrence of bursts exhibit correlations similar as those observed in geomagnetic and solar data, [8] suggesting that the latter parameters could play a fundamental role in these processes. References [1] R. O. Dendy, S. C. Chapman, and M. Paczuski, Plasma Phys. Controlled Fusion 49, A95 (2007). [2] T. Chang and C. C. Wu, Phys. Rev. E 77, 045401 (2008). [3] R. T. J. McAteer, P. T. Gallagher, and J. Ireland, Astrophys. J. 631, 628 (2005). [4] V. M. Uritsky, A. J. Klimas, and D. Vassiliadis, Adv. Space Res. 37, 539 (2006). [5] S. C. Chapman, B. Hnat, and K. Kiyani, Nonlinear Proc. Geophys. 15, 445 (2008). [6] G

2. "Storms of crustal stress" and AE earthquake precursors

   NASA Astrophysics Data System (ADS)

   Gregori, G. P.; Poscolieri, M.; Paparo, G.; de Simone, S.; Rafanelli, C.; Ventrice, G.

   2010-02-01

   "storm", started in 2008, the l'Aquila earthquake occurred. Additional logical analysis envisages the possibility of distinguishing some kind of "elementary" constituents of a "crustal storm", which can be briefly called "crustal substorms". The concept of "storm" and "substorm" is a common logical aspect, which is shared by several phenomena, depending on their common intrinsic and primary logical properties that can be called lognormality and fractality. Compared to a "crustal storm", a "crustal substorm" is likely to be reckoned to some specific seismic event. Owing to brevity purposes, however, the discussion of "substorms" is given elsewhere. AE is an effective tool for monitoring these phenomena, and other processes that are ongoing within the crust. Eventually they result to be precursors of some more or less violent earthquake. It should be stressed, however, that the target of AE monitoring is diagnosing the Earth's crust. In contrast, earthquake prediction implies a much different perspective, which makes sense only by means of more detailed multiparametric monitoring. An AE array can provide real physical information only about the processes that are objectively ongoing inside different and contiguous large slabs of the crust. The purpose is to monitor the stress propagation that crosses different regions, in order to envisage where and when it can eventually trigger a catastrophe of the system. The conclusion is that continental - or planetary - scale arrays of AE monitoring stations, which record a few different AE frequencies, appear to be the likely first step for diagnosing the evolution of local structures preceding an earthquake. On the other hand, as it is well known, the magnitude of the shock is to be related to the elastic energy stored in the focal volume, rather than to the trigger that starts it.

3. Earthquake impact scale

   USGS Publications Warehouse

   Wald, D.J.; Jaiswal, K.S.; Marano, K.D.; Bausch, D.

   2011-01-01

   also be both specific (although allowably uncertain) and actionable. In this analysis, an attempt is made at both simple and intuitive color-coded alerting criteria; yet the necessary uncertainty measures by which one can gauge the likelihood for the alert to be over- or underestimated are preserved. The essence of the proposed impact scale and alerting is that actionable loss information is now available in the immediate aftermath of significant earthquakes worldwide on the basis of quantifiable loss estimates. Utilizing EIS, PAGER's rapid loss estimates can adequately recommend alert levels and suggest appropriate response protocols, despite the uncertainties; demanding or awaiting observations or loss estimates with a high level of accuracy may increase the losses. ?? 2011 American Society of Civil Engineers.

4. Ocean manganese nodules as stromatolite with a fractal like-signature

   NASA Astrophysics Data System (ADS)

   Akai, Junji; Akiyama, Shigeki; Tsuchiyama, Akira; Akai, Kurumi

   Deep-sea manganese (Mn) nodules are problematic in terms of factors such as their characteristic form and genesis. There are many reports of bacterial species from manganese nodules. However, the genesis of these nodules has not been fully confirmed. Samples, mainly from the Clarion Clipperton Fracture zone in the Pacific Ocean, were examined by mineralogical methods and X-ray CT. Thin sections of these samples showed columnar stromatolite structures with rhythmic bands. Mineralized bacteria were observed by SEM and TEM. Surface morphology could be described as having a fractal-like nature. The fractal characteristics of spherical to dome-like forms were fundamentally composed of at least four ranks. The 4th order form corresponds to the stromatolite dome top shapes. Similar granular domain units and porous characteristics in manganese nodules were clearly observed by X-ray CT sections. Mathematical simulation based on fractal models reproduced similar morphological characteristics to the natural samples. So, we arrived at the concluding hypothesis that manganese nodules are aggregated stromatolite with fractal-like characteristics. Furthermore, we discussed the possibility that the nature of the layer manganese oxide minerals as the major component of the nodule and associated Fe-oxyhydroxide minerals may become an absorber/scavenger of strategic heavy metals and also toxic metals in the environments.

5. Synthesis of the advances in and application of fractal characteristic of traffic flow.

   DOT National Transportation Integrated Search

   2013-07-01

   Fractals are irregular geometric objects that exhibit finite details at all scales, and once magnified, their basic structures remain the same regardless of the scale of magnification. Fractal theory has been successfully applied in different fields ...

6. Synthesis of the advance in and application of fractal characteristics of traffic flow.

   DOT National Transportation Integrated Search

   2013-07-01

   Fractals are irregular geometric objects that exhibit finite details at all scales, and once magnified, their basic structures remain the same regardless of the scale of magnification. Fractal theory has been successfully applied in different fields ...

7. Characterization of Atrophic Changes in the Cerebral Cortex Using Fractal Dimensional Analysis

   PubMed Central

   George, Anuh T.; Jeon, Tina; Hynan, Linda S.; Youn, Teddy S.; Kennedy, David N.; Dickerson, Bradford

   2010-01-01

   The purpose of this project is to apply a modified fractal analysis technique to high-resolution T1 weighted magnetic resonance images in order to quantify the alterations in the shape of the cerebral cortex that occur in patients with Alzheimer’s disease. Images were selected from the Alzheimer’s Disease Neuroimaging Initiative database (Control N=15, Mild-Moderate AD N=15). The images were segmented using a semi-automated analysis program. Four coronal and three axial profiles of the cerebral cortical ribbon were created. The fractal dimensions (Df) of the cortical ribbons were then computed using a box-counting algorithm. The mean Df of the cortical ribbons from AD patients were lower than age-matched controls on six of seven profiles. The fractal measure has regional variability which reflects local differences in brain structure. Fractal dimension is complementary to volumetric measures and may assist in identifying disease state or disease progression. PMID:20740072

8. Fractal based modelling and analysis of electromyography (EMG) to identify subtle actions.

   PubMed

   Arjunan, Sridhar P; Kumar, Dinesh K

   2007-01-01

   The paper reports the use of fractal theory and fractal dimension to study the non-linear properties of surface electromyogram (sEMG) and to use these properties to classify subtle hand actions. The paper reports identifying a new feature of the fractal dimension, the bias that has been found to be useful in modelling the muscle activity and of sEMG. Experimental results demonstrate that the feature set consisting of bias values and fractal dimension of the recordings is suitable for classification of sEMG against the different hand gestures. The scatter plots demonstrate the presence of simple relationships of these features against the four hand gestures. The results indicate that there is small inter-experimental variation but large inter-subject variation. This may be due to differences in the size and shape of muscles for different subjects. The possible applications of this research include use in developing prosthetic hands, controlling machines and computers.

9. The Fractal Self at Play

   ERIC Educational Resources Information Center

   Marks-Tarlow, Terry

   2010-01-01

   In this article, the author draws on contemporary science to illuminate the relationship between early play experiences, processes of self-development, and the later emergence of the fractal self. She argues that orientation within social space is a primary function of early play and developmentally a two-step process. With other people and with…

10. Triggered earthquakes and the 1811-1812 New Madrid, central United States, earthquake sequence

    USGS Publications Warehouse

    Hough, S.E.

    2001-01-01

    The 1811-1812 New Madrid, central United States, earthquake sequence included at least three events with magnitudes estimated at well above M 7.0. I discuss evidence that the sequence also produced at least three substantial triggered events well outside the New Madrid Seismic Zone, most likely in the vicinity of Cincinnati, Ohio. The largest of these events is estimated to have a magnitude in the low to mid M 5 range. Events of this size are large enough to cause damage, especially in regions with low levels of preparedness. Remotely triggered earthquakes have been observed in tectonically active regions in recent years, but not previously in stable continental regions. The results of this study suggest, however, that potentially damaging triggered earthquakes may be common following large mainshocks in stable continental regions. Thus, in areas of low seismic activity such as central/ eastern North America, the hazard associated with localized source zones might be more far reaching than previously recognized. The results also provide additional evidence that intraplate crust is critically stressed, such that small stress changes are especially effective at triggering earthquakes.

11. Aggregates and Superaggregates of Soot with Four Distinct Fractal Morphologies

    NASA Technical Reports Server (NTRS)

    Sorensen, C. M.; Kim, W.; Fry, D.; Chakrabarti, A.

    2004-01-01

    Soot formed in laminar diffusion flames of heavily sooting fuels evolves through four distinct growth stages which give rise to four distinct aggregate fractal morphologies. These results were inferred from large and small angle static light scattering from the flames, microphotography of the flames, and analysis of soot sampled from the flames. The growth stages occur approximately over four successive orders of magnitude in aggregate size. Comparison to computer simulations suggests that these four growth stages involve either diffusion limited cluster aggregation or percolation in either three or two dimensions.

12. High resolution strain sensor for earthquake precursor observation and earthquake monitoring

    NASA Astrophysics Data System (ADS)

    Zhang, Wentao; Huang, Wenzhu; Li, Li; Liu, Wenyi; Li, Fang

    2016-05-01

    We propose a high-resolution static-strain sensor based on a FBG Fabry-Perot interferometer (FBG-FP) and a wavelet domain cross-correlation algorithm. This sensor is used for crust deformation measurement, which plays an important role in earthquake precursor observation. The Pound-Drever-Hall (PDH) technique based on a narrow-linewidth tunable fiber laser is used to interrogate the FBG-FPs. A demodulation algorithm based on wavelet domain cross-correlation is used to calculate the wavelength difference. The FBG-FP sensor head is fixed on the two steel alloy rods which are installed in the bedrock. The reference FBG-FP is placed in a strain-free state closely to compensate the environment temperature fluctuation. A static-strain resolution of 1.6 n(epsilon) can be achieved. As a result, clear solid tide signals and seismic signals can be recorded, which suggests that the proposed strain sensor can be applied to earthquake precursor observation and earthquake monitoring.

13. Widespread Triggering of Earthquakes in the Central US by the 2011 M9.0 Tohoku-Oki Earthquake

    NASA Astrophysics Data System (ADS)

    Rubinstein, J. L.; Savage, H. M.

    2011-12-01

    The strong shaking of the 2011 M9.0 off-Tohoku earthquake triggered tectonic tremor and earthquakes in many locations around the world. We analyze broadband records from the USARRAY to identify triggered seismicity in more than 10 different locations in the Central United States. We identify triggered events in many states including: Kansas, Nebraska, Arkansas, Minnesota, and Iowa. The locally triggered earthquakes are obscured in broadband records by the Tohoku-Oki mainshock but can be revealed with high-pass filtering. With the exception of one location (central Arkansas), the triggered seismicity occurred in regions that are seismically quiet. The coincidence of this seismicity with the Tohoku-Oki event suggests that these earthquakes were triggered. The triggered seismicity in Arkansas occurred in a region where there has been an active swarm of seismicity since August 2010. There are two lines of evidence to indicate that the seismicity in Arkansas is triggered instead of part of the swarm: (1) we observe two earthquakes that initiate coincident with the arrival of shear wave and Love wave; (2) the seismicity rate increased dramatically following the Tohoku-Oki mainshock. Our observations of widespread earthquake triggering in regions thought to be seismically quiet remind us that earthquakes can occur in most any location. Studying additional teleseismic events has the potential to reveal regions with a propensity for earthquake triggering.

14. Interactive Effects of Dorsomedial Hypothalamic Nucleus and Time-Restricted Feeding on Fractal Motor Activity Regulation.

    PubMed

    Lo, Men-Tzung; Chiang, Wei-Yin; Hsieh, Wan-Hsin; Escobar, Carolina; Buijs, Ruud M; Hu, Kun

    2016-01-01

    differential impacts of food restriction on fractal activity control in intact and DMH-lesioned animals suggest that the DMH plays a crucial role in integrating these different time cues to the circadian network for multiscale regulation of motor activity.

15. Physics of Earthquake Rupture Propagation

    NASA Astrophysics Data System (ADS)

    Xu, Shiqing; Fukuyama, Eiichi; Sagy, Amir; Doan, Mai-Linh

    2018-05-01

    A comprehensive understanding of earthquake rupture propagation requires the study of not only the sudden release of elastic strain energy during co-seismic slip, but also of other processes that operate at a variety of spatiotemporal scales. For example, the accumulation of the elastic strain energy usually takes decades to hundreds of years, and rupture propagation and termination modify the bulk properties of the surrounding medium that can influence the behavior of future earthquakes. To share recent findings in the multiscale investigation of earthquake rupture propagation, we held a session entitled "Physics of Earthquake Rupture Propagation" during the 2016 American Geophysical Union (AGU) Fall Meeting in San Francisco. The session included 46 poster and 32 oral presentations, reporting observations of natural earthquakes, numerical and experimental simulations of earthquake ruptures, and studies of earthquake fault friction. These presentations and discussions during and after the session suggested a need to document more formally the research findings, particularly new observations and views different from conventional ones, complexities in fault zone properties and loading conditions, the diversity of fault slip modes and their interactions, the evaluation of observational and model uncertainties, and comparison between empirical and physics-based models. Therefore, we organize this Special Issue (SI) of Tectonophysics under the same title as our AGU session, hoping to inspire future investigations. Eighteen articles (marked with "this issue") are included in this SI and grouped into the following six categories.

16. The repetition of large-earthquake ruptures.

    PubMed Central

    Sieh, K

    1996-01-01

    This survey of well-documented repeated fault rupture confirms that some faults have exhibited a "characteristic" behavior during repeated large earthquakes--that is, the magnitude, distribution, and style of slip on the fault has repeated during two or more consecutive events. In two cases faults exhibit slip functions that vary little from earthquake to earthquake. In one other well-documented case, however, fault lengths contrast markedly for two consecutive ruptures, but the amount of offset at individual sites was similar. Adjacent individual patches, 10 km or more in length, failed singly during one event and in tandem during the other. More complex cases of repetition may also represent the failure of several distinct patches. The faults of the 1992 Landers earthquake provide an instructive example of such complexity. Together, these examples suggest that large earthquakes commonly result from the failure of one or more patches, each characterized by a slip function that is roughly invariant through consecutive earthquake cycles. The persistence of these slip-patches through two or more large earthquakes indicates that some quasi-invariant physical property controls the pattern and magnitude of slip. These data seem incompatible with theoretical models that produce slip distributions that are highly variable in consecutive large events. Images Fig. 3 Fig. 7 Fig. 9 PMID:11607662

17. Dynamics of Fractal Cluster Gels with Embedded Active Colloids

    NASA Astrophysics Data System (ADS)

    Szakasits, Megan E.; Zhang, Wenxuan; Solomon, Michael J.

    2017-08-01

    We find that embedded active colloids increase the ensemble-averaged mean squared displacement of particles in otherwise passively fluctuating fractal cluster gels. The enhancement in dynamics occurs by a mechanism in which the active colloids contribute to the average dynamics both directly through their own active motion and indirectly through their excitation of neighboring passive colloids in the fractal network. Fractal cluster gels are synthesized by addition of magnesium chloride to an initially stable suspension of 1.0 μ m polystyrene colloids in which a dilute concentration of platinum coated Janus colloids has been dispersed. The Janus colloids are thereby incorporated into the fractal network. We measure the ensemble-averaged mean squared displacement of all colloids in the gel before and after the addition of hydrogen peroxide, a fuel that drives diffusiophoretic motion of the Janus particles. The gel mean squared displacement increases by up to a factor of 3 for an active to passive particle ratio of 1 ∶20 and inputted active energy—defined based on the hydrogen peroxide's effect on colloid swim speed and run length—that is up to 9.5 times thermal energy, on a per particle basis. We model the enhancement in gel particle dynamics as the sum of a direct contribution from the displacement of the Janus particles themselves and an indirect contribution from the strain field that the active colloids induce in the surrounding passive particles.

18. Bifurcation and Fractal of the Coupled Logistic Map

    NASA Astrophysics Data System (ADS)

    Wang, Xingyuan; Luo, Chao

    The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot-Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.

19. Collisions of ideal gas molecules with a rough/fractal surface. A computational study.

    PubMed

    Panczyk, Tomasz

    2007-02-01

    The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using random deposition technique. By applying various depositions, the roughness of the surface was controlled and, as a measure of the irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in argon (under pressures 2 x 10(3) to 2 x 10(5) Pa) and the numbers of collisions with these surfaces were counted. The calculations were carried out using a simplified molecular dynamics simulation technique (only hard core repulsions were assumed). As a result, it was stated that the frequency of collisions is a linear function of pressure for all fractal dimensions studied (D = 2, ..., 2.5). The frequency per unit pressure is quite complex function of the fractal dimension; however, the changes of that frequency with the fractal dimension are not strong. It was found that the frequency of collisions is controlled by the number of weakly folded sites on the surfaces and there is some mapping between the shape of adsorption energy distribution functions and this number of weakly folded sites. The results for the rough/fractal surfaces were compared with the prediction given by the Langmuir-Hertz equation (valid for smooth surface), generally the departure from the Langmuir-Hertz equation is not higher than 48% for the studied systems (i.e. for the surfaces created using the random deposition technique).

20. Fractal mechanisms in the electrophysiology of the heart

    NASA Technical Reports Server (NTRS)

    Goldberger, A. L.

    1992-01-01

    The mathematical concept of fractals provides insights into complex anatomic branching structures that lack a characteristic (single) length scale, and certain complex physiologic processes, such as heart rate regulation, that lack a single time scale. Heart rate control is perturbed by alterations in neuro-autonomic function in a number of important clinical syndromes, including sudden cardiac death, congestive failure, cocaine intoxication, fetal distress, space sickness and physiologic aging. These conditions are associated with a loss of the normal fractal complexity of interbeat interval dynamics. Such changes, which may not be detectable using conventional statistics, can be quantified using new methods derived from "chaos theory.".

1. Limits on great earthquake size at subduction zones

   NASA Astrophysics Data System (ADS)

   McCaffrey, R.

   2012-12-01

   Subduction zones are where the world's greatest earthquakes occur due to the large fault area available to slip. Yet some subduction zones are thought to be immune from these massive events, where quake size is limited by some physical processes or properties. Accordingly, the size of the 2011 Tohoku-oki Mw 9.0 earthquake caught some in the earthquake research community by surprise. The expectations of these massive quakes have been driven in the past by reliance on our short, incomplete history of earthquakes and causal relationships derived from it. The logic applied is that if a great earthquake has not happened in the past, that we know of, one cannot happen in the future. Using the ~100-year global earthquake seismological history, and in some cases extended with geologic observations, relationships between maximum earthquake sizes and other properties of subduction zones are suggested, leading to the notion that some subduction zones, like the Japan Trench, would never produce a magnitude ~9 event. Empirical correlations of earthquake behavior with other subduction parameters can give false positive results when the data are incomplete or incorrect, of small numbers and numerous attributes are examined. Given multi-century return times of the greatest earthquakes, ignorance of those return times and our relatively limited temporal observation span (in most places), I suggest that we cannot yet rule out great earthquakes at any subduction zones. Alternatively, using the length of a subduction zone that is available for slip as the predominant factor in determining maximum earthquake size, we cannot rule out that any subduction zone of a few hundred kilometers or more in length may be capable of producing a magnitude 9 or larger earthquake. Based on this method, the expected maximum size for the Japan Trench was 9.0 (McCaffrey, Geology, p. 263, 2008). The same approach indicates that a M > 9 off Java, with twice the population density as Honshu and much lower

2. Assessment of the spatial pattern of colorectal tumour perfusion estimated at perfusion CT using two-dimensional fractal analysis.

   PubMed

   Goh, Vicky; Sanghera, Bal; Wellsted, David M; Sundin, Josefin; Halligan, Steve

   2009-06-01

   The aim was to evaluate the feasibility of fractal analysis for assessing the spatial pattern of colorectal tumour perfusion at dynamic contrast-enhanced CT (perfusion CT). Twenty patients with colorectal adenocarcinoma underwent a 65-s perfusion CT study from which a perfusion parametric map was generated using validated commercial software. The tumour was identified by an experienced radiologist, segmented via thresholding and fractal analysis applied using in-house software: fractal dimension, abundance and lacunarity were assessed for the entire outlined tumour and for selected representative areas within the tumour of low and high perfusion. Comparison was made with ten patients with normal colons, processed in a similar manner, using two-way mixed analysis of variance with statistical significance at the 5% level. Fractal values were higher in cancer than normal colon (p < or = 0.001): mean (SD) 1.71 (0.07) versus 1.61 (0.07) for fractal dimension and 7.82 (0.62) and 6.89 (0.47) for fractal abundance. Fractal values were lower in 'high' than 'low' perfusion areas. Lacunarity curves were shifted to the right for cancer compared with normal colon. In conclusion, colorectal cancer mapped by perfusion CT demonstrates fractal properties. Fractal analysis is feasible, potentially providing a quantitative measure of the spatial pattern of tumour perfusion.

3. Growing surfaces with anomalous diffusion: Results for the fractal Kardar-Parisi-Zhang equation

   NASA Astrophysics Data System (ADS)

   Katzav, Eytan

   2003-09-01

   In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that surface transport is caused by a hopping mechanism of a Levy flight. It is shown that for a specific choice of parameters of the FKPZ equation, the equation can be solved exactly in one dimension, so that all the critical exponents, which describe the surface that grows under FKPZ, can be derived for that case. Afterwards, the self-consistent expansion (SCE) is used to predict the critical exponents for the FKPZ model for any choice of the parameters and any spatial dimension. It is then verified that the results obtained using SCE recover the exact result in one dimension. At the end a simple picture for the behavior of the fractal KPZ equation is suggested and the upper critical dimension of this model is discussed.

4. The Generalization of Rook Number r2 for the Fractal Chessboard

   NASA Astrophysics Data System (ADS)

   Sangeetha, R.; Jayalalitha, G.

   2018-04-01

   In this paper we develop a generalized formula of r 2, the number of ways of placing two non-attacking Rooks for the Fractal Chessboard which is defined as a board that grows progressively in a consistent manner using a 2 × 2 chessboard to its sides and corners. The board is disintegrated into small sub boards based on their position in the whole Fractal Chessboard (FC). The board is disintegrated into sub boards based on their position in the whole board FC. By finding the value of r 2 for each of these sub boards and adding them, the r 2 value of the whole board FC is obtained. Finally the r 2 value is generalized the Fractal Chessboard at any iteration I ≥ 4 .

5. Describing soil surface microrelief by crossover length and fractal dimension

   NASA Astrophysics Data System (ADS)

   Vidal Vázquez, E.; Miranda, J. G. V.; Paz González, A.

   2007-05-01

   Accurate description of soil surface topography is essential because different tillage tools produce different soil surface roughness conditions, which in turn affects many processes across the soil surface boundary. Advantages of fractal analysis in soil microrelief assessment have been recognised but the use of fractal indices in practice remains challenging. There is also little information on how soil surface roughness decays under natural rainfall conditions. The objectives of this work were to investigate the decay of initial surface roughness induced by natural rainfall under different soil tillage systems and to compare the performances of a classical statistical index and fractal microrelief indices. Field experiments were performed on an Oxisol at Campinas, São Paulo State (Brazil). Six tillage treatments, namely, disc harrow, disc plow, chisel plow, disc harrow + disc level, disc plow + disc level and chisel plow + disc level were tested. Measurements were made four times, firstly just after tillage and subsequently with increasing amounts of natural rainfall. Duplicated measurements were taken per treatment and date, yielding a total of 48 experimental surfaces. The sampling scheme was a square grid with 25×25 mm point spacing and the plot size was 1350×1350 mm, so that each data set consisted of 3025 individual elevation points. Statistical and fractal indices were calculated both for oriented and random roughness conditions, i.e. after height reading have been corrected for slope and for slope and tillage tool marks. The main drawback of the standard statistical index random roughness, RR, lies in its no spatial nature. The fractal approach requires two indices, fractal dimension, D, which describes how roughness changes with scale, and crossover length, l, specifying the variance of surface microrelief at a reference scale. Fractal parameters D and l, were estimated by two independent self-affine models, semivariogram (SMV) and local root mean

6. Prospective Validation of Pre-earthquake Atmospheric Signals and Their Potential for Short–term Earthquake Forecasting

   NASA Astrophysics Data System (ADS)

   Ouzounov, Dimitar; Pulinets, Sergey; Hattori, Katsumi; Lee, Lou; Liu, Tiger; Kafatos, Menas

   2015-04-01

   We are presenting the latest development in multi-sensors observations of short-term pre-earthquake phenomena preceding major earthquakes. Our challenge question is: "Whether such pre-earthquake atmospheric/ionospheric signals are significant and could be useful for early warning of large earthquakes?" To check the predictive potential of atmospheric pre-earthquake signals we have started to validate anomalous ionospheric / atmospheric signals in retrospective and prospective modes. The integrated satellite and terrestrial framework (ISTF) is our method for validation and is based on a joint analysis of several physical and environmental parameters (Satellite thermal infrared radiation (STIR), electron concentration in the ionosphere (GPS/TEC), radon/ion activities, air temperature and seismicity patterns) that were found to be associated with earthquakes. The science rationale for multidisciplinary analysis is based on concept Lithosphere-Atmosphere-Ionosphere Coupling (LAIC) [Pulinets and Ouzounov, 2011], which explains the synergy of different geospace processes and anomalous variations, usually named short-term pre-earthquake anomalies. Our validation processes consist in two steps: (1) A continuous retrospective analysis preformed over two different regions with high seismicity- Taiwan and Japan for 2003-2009 (2) Prospective testing of STIR anomalies with potential for M5.5+ events. The retrospective tests (100+ major earthquakes, M>5.9, Taiwan and Japan) show STIR anomalous behavior before all of these events with false negatives close to zero. False alarm ratio for false positives is less then 25%. The initial prospective testing for STIR shows systematic appearance of anomalies in advance (1-30 days) to the M5.5+ events for Taiwan, Kamchatka-Sakhalin (Russia) and Japan. Our initial prospective results suggest that our approach show a systematic appearance of atmospheric anomalies, one to several days prior to the largest earthquakes That feature could be

7. Shallow moonquakes - How they compare with earthquakes

   NASA Technical Reports Server (NTRS)

   Nakamura, Y.

   1980-01-01

   Of three types of moonquakes strong enough to be detectable at large distances - deep moonquakes, meteoroid impacts and shallow moonquakes - only shallow moonquakes are similar in nature to earthquakes. A comparison of various characteristics of moonquakes with those of earthquakes indeed shows a remarkable similarity between shallow moonquakes and intraplate earthquakes: (1) their occurrences are not controlled by tides; (2) they appear to occur in locations where there is evidence of structural weaknesses; (3) the relative abundances of small and large quakes (b-values) are similar, suggesting similar mechanisms; and (4) even the levels of activity may be close. The shallow moonquakes may be quite comparable in nature to intraplate earthquakes, and they may be of similar origin.

8. Earthquake behavior along the Levant fault from paleoseismology (Invited)

   NASA Astrophysics Data System (ADS)

   Klinger, Y.; Le Beon, M.; Wechsler, N.; Rockwell, T. K.

   2013-12-01

   The Levant fault is a major continental structure 1200 km-long that bounds the Arabian plate to the west. The finite offset of this left-lateral strike-slip fault is estimated to be 105 km for the section located south of the restraining bend corresponding roughly to Lebanon. Along this southern section the slip-rate has been estimated over a large range of time scales, from few years to few hundreds thousands of years. Over these different time scales, studies agree for the slip-rate to be 5mm/yr × 2 mm/yr. The southern section of the Levant fault is particularly attractive to study earthquake behavior through time for several reasons: 1/ The fault geometry is simple and well constrained. 2/ The fault system is isolated and does not interact with obvious neighbor fault systems. 3/ The Middle-East, where the Levant fault is located, is the region in the world where one finds the longest and most complete historical record of past earthquakes. About 30 km north of the city of Aqaba, we opened a trench in the southern part of the Yotvata playa, along the Wadi Araba fault segment. The stratigraphy presents silty sand playa units alternating with coarser sand sediments from alluvial fans flowing westwards from the Jordan plateau. Two fault zones can be recognized in the trench and a minimum of 8 earthquakes can be identified, based on upward terminations of ground ruptures. Dense 14C dating through the entire exposure allows matching the 4 most recent events with historical events in AD1458, AD1212, AD1068 and AD748. Size of the ground rupture suggests a bi-modal distribution of earthquakes with earthquakes rupturing the entire Wadi Araba segment and earthquakes ending in the extensional jog forming the playa. Timing of earthquakes shows that no earthquakes occurred at this site since about 600 years, suggesting earthquake clustering along this section of the fault and potential for a large earthquake in the near future. 3D paleoseismological trenches at the Beteiha

9. Critical behavior in earthquake energy dissipation

   NASA Astrophysics Data System (ADS)

   Wanliss, James; Muñoz, Víctor; Pastén, Denisse; Toledo, Benjamín; Valdivia, Juan Alejandro

   2017-09-01

   We explore bursty multiscale energy dissipation from earthquakes flanked by latitudes 29° S and 35.5° S, and longitudes 69.501° W and 73.944° W (in the Chilean central zone). Our work compares the predictions of a theory of nonequilibrium phase transitions with nonstandard statistical signatures of earthquake complex scaling behaviors. For temporal scales less than 84 hours, time development of earthquake radiated energy activity follows an algebraic arrangement consistent with estimates from the theory of nonequilibrium phase transitions. There are no characteristic scales for probability distributions of sizes and lifetimes of the activity bursts in the scaling region. The power-law exponents describing the probability distributions suggest that the main energy dissipation takes place due to largest bursts of activity, such as major earthquakes, as opposed to smaller activations which contribute less significantly though they have greater relative occurrence. The results obtained provide statistical evidence that earthquake energy dissipation mechanisms are essentially "scale-free", displaying statistical and dynamical self-similarity. Our results provide some evidence that earthquake radiated energy and directed percolation belong to a similar universality class.

10. Earthquakes and depleted gas reservoirs: which comes first?

    NASA Astrophysics Data System (ADS)

    Mucciarelli, M.; Donda, F.; Valensise, G.

    2015-10-01

    While scientists are paying increasing attention to the seismicity potentially induced by hydrocarbon exploitation, so far, little is known about the reverse problem, i.e. the impact of active faulting and earthquakes on hydrocarbon reservoirs. The 20 and 29 May 2012 earthquakes in Emilia, northern Italy (Mw 6.1 and 6.0), raised concerns among the public for being possibly human-induced, but also shed light on the possible use of gas wells as a marker of the seismogenic potential of an active fold and thrust belt. We compared the location, depth and production history of 455 gas wells drilled along the Ferrara-Romagna arc, a large hydrocarbon reserve in the southeastern Po Plain (northern Italy), with the location of the inferred surface projection of the causative faults of the 2012 Emilia earthquakes and of two pre-instrumental damaging earthquakes. We found that these earthquake sources fall within a cluster of sterile wells, surrounded by productive wells at a few kilometres' distance. Since the geology of the productive and sterile areas is quite similar, we suggest that past earthquakes caused the loss of all natural gas from the potential reservoirs lying above their causative faults. To validate our hypothesis we performed two different statistical tests (binomial and Monte Carlo) on the relative distribution of productive and sterile wells, with respect to seismogenic faults. Our findings have important practical implications: (1) they may allow major seismogenic sources to be singled out within large active thrust systems; (2) they suggest that reservoirs hosted in smaller anticlines are more likely to be intact; and (3) they also suggest that in order to minimize the hazard of triggering significant earthquakes, all new gas storage facilities should use exploited reservoirs rather than sterile hydrocarbon traps or aquifers.

11. The 1868 Hayward Earthquake Alliance: A Case Study - Using an Earthquake Anniversary to Promote Earthquake Preparedness

    NASA Astrophysics Data System (ADS)

    Brocher, T. M.; Garcia, S.; Aagaard, B. T.; Boatwright, J. J.; Dawson, T.; Hellweg, M.; Knudsen, K. L.; Perkins, J.; Schwartz, D. P.; Stoffer, P. W.; Zoback, M.

    2008-12-01

    Last October 21st marked the 140th anniversary of the M6.8 1868 Hayward Earthquake, the last damaging earthquake on the southern Hayward Fault. This anniversary was used to help publicize the seismic hazards associated with the fault because: (1) the past five such earthquakes on the Hayward Fault occurred about 140 years apart on average, and (2) the Hayward-Rodgers Creek Fault system is the most likely (with a 31 percent probability) fault in the Bay Area to produce a M6.7 or greater earthquake in the next 30 years. To promote earthquake awareness and preparedness, over 140 public and private agencies and companies and many individual joined the public-private nonprofit 1868 Hayward Earthquake Alliance (1868alliance.org). The Alliance sponsored many activities including a public commemoration at Mission San Jose in Fremont, which survived the 1868 earthquake. This event was followed by an earthquake drill at Bay Area schools involving more than 70,000 students. The anniversary prompted the Silver Sentinel, an earthquake response exercise based on the scenario of an earthquake on the Hayward Fault conducted by Bay Area County Offices of Emergency Services. 60 other public and private agencies also participated in this exercise. The California Seismic Safety Commission and KPIX (CBS affiliate) produced professional videos designed forschool classrooms promoting Drop, Cover, and Hold On. Starting in October 2007, the Alliance and the U.S. Geological Survey held a sequence of press conferences to announce the release of new research on the Hayward Fault as well as new loss estimates for a Hayward Fault earthquake. These included: (1) a ShakeMap for the 1868 Hayward earthquake, (2) a report by the U. S. Bureau of Labor Statistics forecasting the number of employees, employers, and wages predicted to be within areas most strongly shaken by a Hayward Fault earthquake, (3) new estimates of the losses associated with a Hayward Fault earthquake, (4) new ground motion

12. Fractal lacunarity of trabecular bone and magnetic resonance imaging: New perspectives for osteoporotic fracture risk assessment

    PubMed Central

    Zaia, Annamaria

    2015-01-01

    Osteoporosis represents one major health condition for our growing elderly population. It accounts for severe morbidity and increased mortality in postmenopausal women and it is becoming an emerging health concern even in aging men. Screening of the population at risk for bone degeneration and treatment assessment of osteoporotic patients to prevent bone fragility fractures represent useful tools to improve quality of life in the elderly and to lighten the related socio-economic impact. Bone mineral density (BMD) estimate by means of dual-energy X-ray absorptiometry is normally used in clinical practice for osteoporosis diagnosis. Nevertheless, BMD alone does not represent a good predictor of fracture risk. From a clinical point of view, bone microarchitecture seems to be an intriguing aspect to characterize bone alteration patterns in aging and pathology. The widening into clinical practice of medical imaging techniques and the impressive advances in information technologies together with enhanced capacity of power calculation have promoted proliferation of new methods to assess changes of trabecular bone architecture (TBA) during aging and osteoporosis. Magnetic resonance imaging (MRI) has recently arisen as a useful tool to measure bone structure in vivo. In particular, high-resolution MRI techniques have introduced new perspectives for TBA characterization by non-invasive non-ionizing methods. However, texture analysis methods have not found favor with clinicians as they produce quite a few parameters whose interpretation is difficult. The introduction in biomedical field of paradigms, such as theory of complexity, chaos, and fractals, suggests new approaches and provides innovative tools to develop computerized methods that, by producing a limited number of parameters sensitive to pathology onset and progression, would speed up their application into clinical practice. Complexity of living beings and fractality of several physio-anatomic structures suggest

13. Triggering of repeating earthquakes in central California

    USGS Publications Warehouse

    Wu, Chunquan; Gomberg, Joan; Ben-Naim, Eli; Johnson, Paul

    2014-01-01

    Dynamic stresses carried by transient seismic waves have been found capable of triggering earthquakes instantly in various tectonic settings. Delayed triggering may be even more common, but the mechanisms are not well understood. Catalogs of repeating earthquakes, earthquakes that recur repeatedly at the same location, provide ideal data sets to test the effects of transient dynamic perturbations on the timing of earthquake occurrence. Here we employ a catalog of 165 families containing ~2500 total repeating earthquakes to test whether dynamic perturbations from local, regional, and teleseismic earthquakes change recurrence intervals. The distance to the earthquake generating the perturbing waves is a proxy for the relative potential contributions of static and dynamic deformations, because static deformations decay more rapidly with distance. Clear changes followed the nearby 2004 Mw6 Parkfield earthquake, so we study only repeaters prior to its origin time. We apply a Monte Carlo approach to compare the observed number of shortened recurrence intervals following dynamic perturbations with the distribution of this number estimated for randomized perturbation times. We examine the comparison for a series of dynamic stress peak amplitude and distance thresholds. The results suggest a weak correlation between dynamic perturbations in excess of ~20 kPa and shortened recurrence intervals, for both nearby and remote perturbations.

14. Effect of fractal silver electrodes on charge collection and light distribution in semiconducting organic polymer films

    DOE PAGES

    Chamousis, Rachel L.; Chang, Lilian; Watterson, William J.; ...

    2014-08-21

    Living organisms use fractal structures to optimize material and energy transport across regions of differing size scales. Here we test the effect of fractal silver electrodes on light distribution and charge collection in organic semiconducting polymer films made of P3HT and PCBM. The semiconducting polymers were deposited onto electrochemically grown fractal silver structures (5000 nm × 500 nm; fractal dimension of 1.71) with PEDOT:PSS as hole-selective interlayer. The fractal silver electrodes appear black due to increased horizontal light scattering, which is shown to improve light absorption in the polymer. According to surface photovoltage spectroscopy, fractal silver electrodes outperform the flatmore » electrodes when the BHJ film thickness is large (>400 nm, 0.4 V photovoltage). Photocurrents of up to 200 microamperes cm -2 are generated from the bulk heterojunction (BHJ) photoelectrodes under 435 nm LED (10–20 mW cm -2) illumination in acetonitrile solution containing 0.005 M ferrocenium hexafluorophosphate as the electron acceptor. In conclusion, the low IPCE values (0.3–0.7%) are due to slow electron transfer to ferrocenium ion and due to shunting along the large metal–polymer interface. Overall, this work provides an initial assessment of the potential of fractal electrodes for organic photovoltaic cells.« less

15. Inverse Proportional Relationship Between Switching-Time Length and Fractal-Like Structure for Continuous Tracking Movement

    NASA Astrophysics Data System (ADS)

    Hirakawa, Takehito; Suzuki, Hiroo; Gohara, Kazutoshi; Yamamoto, Yuji

    We investigate the relationship between the switching-time length T and the fractal-like feature that characterizes the behavior of dissipative dynamical systems excited by external temporal inputs for tracking movement. Seven healthy right-handed male participants were asked to continuously track light-emitting diodes that were located on the right and left sides in front of them. These movements were performed under two conditions: when the same input pattern was repeated (the periodic-input condition) and when two different input patterns were switched stochastically (the switching-input condition). The repeated time lengths of input patterns during these conditions were 2.00, 1.00, 0.75, 0.50, 0.35, and 0.25s. The movements of a lever held between a participant’s thumb and index finger were measured by a motion-capture system and were analyzed with respect to position and velocity. The condition in which the same input was repeated revealed that two different stable trajectories existed in a cylindrical state space, while the condition in which the inputs were switched induced transitions between these two trajectories. These two different trajectories were considered as excited attractors. The transitions between the two excited attractors produced eight trajectories; they were then characterized by a fractal-like feature as a third-order sequence effect. Moreover, correlation dimensions, which are typically used to evaluate fractal-like features, calculated from the set on the Poincaré section increased as the switching-time length T decreased. These results suggest that an inverse proportional relationship exists between the switching-time length T and the fractal-like feature of human movement.

16. An "ASYMPTOTIC FRACTAL" Approach to the Morphology of Malignant Cell Nuclei

    NASA Astrophysics Data System (ADS)

    Landini, Gabriel; Rippin, John W.

    To investigate quantitatively nuclear membrane irregularity, 672 nuclei from 10 cases of oral cancer (squamous cell carcinoma) and normal cells from oral mucosa were studied in transmission electron micrographs. The nuclei were photographed at ×1400 magnification and transferred to computer memory (1 pixel = 35 nm). The perimeter of the profiles was analysed using the "yardstick method" of fractal dimension estimation, and the log-log plot of ruler size vs. boundary length demonstrated that there exists a significant effect of resolution on length measurement. However, this effect seems to disappear at higher resolutions. As this observation is compatible with the concept of asymptotic fractal, we estimated the parameters c, L and Bm from the asymptotic fractal formula Br = Bm {1 + (r / L)c}-1 , where Br is the boundary length measured with a ruler of size r, Bm is the maximum boundary for r → 0, L is a constant, and c = asymptotic fractal dimension minus topological dimension (D - Dt) for r → ∞. Analyses of variance showed c to be significantly higher in the normal than malignant cases (P < 0.001), but log(L) and Bm to be significantly higher in the malignant cases (P < 0.001). A multivariate linear discrimination analysis on c, log(L) and Bm re-classified 76.6% of the cells correctly (84.8% of the normal and 67.5% of the tumor). Furthermore, this shows that asymptotic fractal analysis applied to nuclear profiles has great potential for shape quantification in diagnosis of oral cancer.

17. Evolutionary and Cognitive Motivations for Fractal Art in Art and Design Education

    ERIC Educational Resources Information Center

    Joye, Yannick

    2005-01-01

    Humans are endowed with cognitive modules specialised in processing information about the class of natural things. Due to their naturalness, fractal art and design can contribute to developing these modules, and trigger affective responses that are associated with certain natural objects. It is argued that exposure to fractals in an art and design…

18. Detection and classification of Breast Cancer in Wavelet Sub-bands of Fractal Segmented Cancerous Zones.

    PubMed

    Shirazinodeh, Alireza; Noubari, Hossein Ahmadi; Rabbani, Hossein; Dehnavi, Alireza Mehri

    2015-01-01

    Recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. It is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. In this paper, for fractal modeling, the original image is first segmented into appropriate fractal boxes followed by identifying the fractal dimension of each windowed section using a computationally efficient two-dimensional box-counting algorithm. Furthermore, using appropriate wavelet sub-bands and image Reconstruction based on modified wavelet coefficients, it is shown that it is possible to arrive at enhanced features for detection of cancerous zones. In this paper, we have attempted to benefit from the advantages of both fractals and wavelets by introducing a new algorithm. By using a new algorithm named F1W2, the original image is first segmented into appropriate fractal boxes, and the fractal dimension of each windowed section is extracted. Following from that, by applying a maximum level threshold on fractal dimensions matrix, the best-segmented boxes are selected. In the next step, the segmented Cancerous zones which are candidates are then decomposed by utilizing standard orthogonal wavelet transform and db2 wavelet in three different resolution levels, and after nullifying wavelet coefficients of the image at the first scale and low frequency band of the third scale, the modified reconstructed image is successfully utilized for detection of breast cancer regions by applying an appropriate threshold. For detection of cancerous zones, our simulations indicate the accuracy of 90.9% for masses and 88.99% for microcalcifications detection results using the F1W2 method. For classification of detected mictocalcification into benign and malignant cases, eight features are identified and

19. The correlation of fractal structures in the photospheric and the coronal magnetic field

    NASA Astrophysics Data System (ADS)

    Dimitropoulou, M.; Georgoulis, M.; Isliker, H.; Vlahos, L.; Anastasiadis, A.; Strintzi, D.; Moussas, X.

    2009-10-01

    Context: This work examines the relation between the fractal properties of the photospheric magnetic patterns and those of the coronal magnetic fields in solar active regions. Aims: We investigate whether there is any correlation between the fractal dimensions of the photospheric structures and the magnetic discontinuities formed in the corona. Methods: To investigate the connection between the photospheric and coronal complexity, we used a nonlinear force-free extrapolation method that reconstructs the 3d magnetic fields using 2d observed vector magnetograms as boundary conditions. We then located the magnetic discontinuities, which are considered as spatial proxies of reconnection-related instabilities. These discontinuities form well-defined volumes, called here unstable volumes. We calculated the fractal dimensions of these unstable volumes and compared them to the fractal dimensions of the boundary vector magnetograms. Results: Our results show no correlation between the fractal dimensions of the observed 2d photospheric structures and the extrapolated unstable volumes in the corona, when nonlinear force-free extrapolation is used. This result is independent of efforts to (1) bring the photospheric magnetic fields closer to a nonlinear force-free equilibrium and (2) omit the lower part of the modeled magnetic field volume that is almost completely filled by unstable volumes. A significant correlation between the fractal dimensions of the photospheric and coronal magnetic features is only observed at the zero level (lower limit) of approximation of a current-free (potential) magnetic field extrapolation. Conclusions: We conclude that the complicated transition from photospheric non-force-free fields to coronal force-free ones hampers any direct correlation between the fractal dimensions of the 2d photospheric patterns and their 3d counterparts in the corona at the nonlinear force-free limit, which can be considered as a second level of approximation in this

20. Evaluating spatial and temporal relationships between an earthquake cluster near Entiat, central Washington, and the large December 1872 Entiat earthquake

    USGS Publications Warehouse

    Brocher, Thomas M.; Blakely, Richard J.; Sherrod, Brian

    2017-01-01

    We investigate spatial and temporal relations between an ongoing and prolific seismicity cluster in central Washington, near Entiat, and the 14 December 1872 Entiat earthquake, the largest historic crustal earthquake in Washington. A fault scarp produced by the 1872 earthquake lies within the Entiat cluster; the locations and areas of both the cluster and the estimated 1872 rupture surface are comparable. Seismic intensities and the 1–2 m of coseismic displacement suggest a magnitude range between 6.5 and 7.0 for the 1872 earthquake. Aftershock forecast models for (1) the first several hours following the 1872 earthquake, (2) the largest felt earthquakes from 1900 to 1974, and (3) the seismicity within the Entiat cluster from 1976 through 2016 are also consistent with this magnitude range. Based on this aftershock modeling, most of the current seismicity in the Entiat cluster could represent aftershocks of the 1872 earthquake. Other earthquakes, especially those with long recurrence intervals, have long‐lived aftershock sequences, including the Mw">MwMw 7.5 1891 Nobi earthquake in Japan, with aftershocks continuing 100 yrs after the mainshock. Although we do not rule out ongoing tectonic deformation in this region, a long‐lived aftershock sequence can account for these observations.

What element of art is being described by roughness and smoothness of the visual impact of an artwork?

What is an element of art that is determined by the roughness or smoothness?

What is rough texture in art?

What is the element of visual arts that refers to quality of the surface of an art object?