Fractals and Forecasting in Earthquakes and Finance
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)
Two-fractal overlap time series: Earthquakes and market crashes
Indian Academy of Sciences (India)
203–210. Two-fractal overlap time series: Earthquakes and market crashes. BIKAS K CHAKRABARTI1,2,∗, ARNAB CHATTERJEE1,3 and. PRATIP BHATTACHARYYA1,4. 1Theoretical Condensed Matter Physics Division and Centre for Applied Mathematics and. Computational Science, Saha Institute of Nuclear Physics, ...
Fractal Nature of Earthquake Occurrence in Andaman Region
R. Samuel Selvaraj,; Gayathri,R.; B. Uma Maheswari
2010-01-01
The Andaman region (92º to 94º East Longitude and 6º to 14º North Latitude) has seen many earthquakes in past ranging from low to very high magnitude causing massive losses. Earthquakes in Andaman aremainly caused due to release of elastic strain energy created and replenished by persistent collision of the Indo- Australian plate with the Eurasian plate. In this paper the fractal analysis were done for earthquakes (mb>3) occurred during 1980 – 2007, which led to the detection of a clustering ...
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K. Gotoh
2003-01-01
Full Text Available In our recent papers we applied fractal methods to extract the earthquake precursory signatures from scaling characteristics of the ULF geomagnetic data, obtained in a seismic active region of Guam Island during the large earthquake of 8 August 1993. We found specific dynamics of their fractal characteristics (spectral exponents and fractal dimensions before the earthquake: appearance of the flicker-noise signatures and increase of the time series fractal dimension. Here we analyze ULF geomagnetic data obtained in a seismic active region of Izu Peninsula, Japan during a swarm of the strong nearby earthquakes of June–August 2000 and compare the results obtained in both regions. We apply the same methodology of data processing using the FFT procedure, Higuchi method and Burlaga-Klein approach to calculate the spectral exponents and fractal dimensions of the ULF time series. We found the common features and specific peculiarities in the behavior of fractal characteristics of the ULF time series before Izu and Guam earthquakes. As a common feature, we obtained the same increase of the ULF time series fractal dimension before the earthquakes, and as specific peculiarity – this increase appears to be sharp for Izu earthquake in comparison with gradual increase of the ULF time series fractal dimension for Guam earthquake. The results obtained in both regions are discussed on the basis of the SOC (self-organized criticality concept taking into account the differences in the depths of the earthquake focuses. On the basis of the peculiarities revealed, we advance methodology for extraction of the earthquake precursory signatures. As an adjacent step, we suggest the combined analysis of the ULF time series in the parametric space polarization ratio – fractal dimension. We reason also upon the advantage of the multifractal approach with respect to the mono-fractal analysis for study of the earthquake preparation dynamics.
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Gautam Rawat
2016-11-01
Full Text Available Ultra-low frequency (ULF geomagnetic data recorded during 1 January 2010 to 31 December 2010 at multi-parametric geophysical observatory (30.53°N, 78.74°E in Garhwal Himalaya region of Uttarakhand, India, are analyzed. From the temporal variation of polarization ratio, the presence of seismo-magnetic disturbances superposed upon background geomagnetic variations are inferred. Considering earthquake process as a self-organized critical system based on flicker noise characteristics, fractal dimension for each day is estimated using two methods namely power spectral (FFT method and Higuchi method. Variability in fractal dimension is studied in the background of local earthquakes (M ≥ 3.5 within a zone of radius 150 km from observing station multi-parametric geophysical observatory (MPGO, Ghuttu. Fractal dimension variability indicates that average fractal dimension for first half of the year is increased as compared to average fractal dimension of second half of the year and there is gradual increase in the fractal dimension before earthquakes. It is also observed that during the first half of the year, there is seismic activity within zone of 150 Km radius centred at around MPGO, Ghuttu. There are no earthquakes during the second half of the year. Gradual increase in the fractal dimension before earthquakes, observed elsewhere in the world, is considered precursory signature of seismo-electromagnetic field emissions.
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.
Fractal analysis of the spatial distribution of earthquakes along the Hellenic Subduction Zone
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
Two-fractal overlap time series: Earthquakes and market crashes
Indian Academy of Sciences (India)
We find prominent similarities in the features of the time series for the (model earthquakes or) overlap of two Cantor sets when one set moves with uniform relative velocity over the other and time series of stock prices. An anticipation method for some of the crashes have been proposed here, based on these observations.
Favela, Luis H; Coey, Charles A; Griff, Edwin R; Richardson, Michael J
2016-07-28
The present work used fractal time series analysis (detrended fluctuation analysis; DFA) to examine the spontaneous activity of single neurons in an anesthetized animal model, specifically, the mitral cells in the rat main olfactory bulb. DFA bolstered previous research in suggesting two subclasses of mitral cells. Although there was no difference in the fractal scaling of the interspike interval series at the shorter timescales, there was a significant difference at longer timescales. Neurons in Group B exhibited fractal, power-law scaled interspike intervals, whereas neurons in Group A exhibited random variation. These results raise questions about the role of these different cells within the olfactory bulb and potential explanations of their dynamics. Specifically, self-organized criticality has been proposed as an explanation of fractal scaling in many natural systems, including neural systems. However, this theory is based on certain assumptions that do not clearly hold in the case of spontaneous neural activity, which likely reflects intrinsic cell dynamics rather than activity driven by external stimulation. Moreover, it is unclear how self-organized criticality might account for the random dynamics observed in Group A, and how these random dynamics might serve some functional role when embedded in the typical activity of the olfactory bulb. These theoretical considerations provide direction for additional experimental work. Published by Elsevier Ireland Ltd.
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Bhattacharya, Pathikrit; Kamal [Department of Earth Sciences, Indian Institute of Technology, Roorkee, Uttarakhand, 247 667 (India); Chakrabarti, Bikas K, E-mail: pathikri@princeton.edu, E-mail: bikask.chakrabarti@saha.ac.in, E-mail: kamalfes@iitr.ernet.in [Theoretical Condensed Matter Physics Division and Centre for Applied Mathematics and Computational Science, Saha Institute of Nuclear Physics, Kolkata, West Bengal, 700064 (India)
2011-09-15
Our understanding of earthquakes is based on the theory of plate tectonics. Earthquake dynamics is the study of the interactions of plates (solid disjoint parts of the lithosphere) which produce seismic activity. Over the last about fifty years many models have come up which try to simulate seismic activity by mimicking plate plate interactions. The validity of a given model is subject to the compliance of the synthetic seismic activity it produces to the well known empirical laws which describe the statistical features of observed seismic activity. Here we present a review of one such, purely geometric, model of earthquake dynamics, namely The Two Fractal Overlap Model. The model tries to emulate the stick-slip dynamics of lithospheric plates with fractal surfaces by evaluating the time-evolution of overlap lengths of two identical Cantor sets sliding over each other. As we show later in the text, some statistical aspects of natural seismicity are naturally captured by this simple model. More importantly, however, this model also reveals a new statistical feature of aftershock sequences which we have verified to be present in nature as well. We show that, both in the model as well as in nature, the cumulative integral of aftershock magnitudes over time is a remarkable straight line with a characteristic slope. This slope is closely related to the fractal geometry of the fault surface that produces most of thee aftershocks. We also go on to discuss the implications that this feature may have in possible predictions of aftershock magnitudes or times of occurrence.
Fractal 1/f Dynamics Suggest Entanglement of Measurement and Human Performance
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…
Geoethical suggestions for reducing risk of next (not only strong) earthquakes
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
Fractal images induce fractal pupil dilations and constrictions.
Moon, P; Muday, J; Raynor, S; Schirillo, J; Boydston, C; Fairbanks, M S; Taylor, R P
2014-09-01
Fractals are self-similar structures or patterns that repeat at increasingly fine magnifications. Research has revealed fractal patterns in many natural and physiological processes. This article investigates pupillary size over time to determine if their oscillations demonstrate a fractal pattern. We predict that pupil size over time will fluctuate in a fractal manner and this may be due to either the fractal neuronal structure or fractal properties of the image viewed. We present evidence that low complexity fractal patterns underlie pupillary oscillations as subjects view spatial fractal patterns. We also present evidence implicating the autonomic nervous system's importance in these patterns. Using the variational method of the box-counting procedure we demonstrate that low complexity fractal patterns are found in changes within pupil size over time in millimeters (mm) and our data suggest that these pupillary oscillation patterns do not depend on the fractal properties of the image viewed. Copyright © 2014 Elsevier B.V. All rights reserved.
Tidal triggering of earthquakes suggests poroelastic behavior on the San Andreas Fault
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.
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)
Mandal, Prantik; Rodkin, Mikhail V.
2011-11-01
We use precisely located aftershocks of the 2001 Mw7.7 Bhuj earthquake (2001-2009) to explore the structure of the Kachchh seismic zone by mapping the 3-D distributions of b-value, fractal dimension (D) and seismic velocities. From frequency-magnitude analysis, we find that the catalog is complete above Mw = 3.0. Thus, we analyze 2159 aftershocks with Mw ≥ 3.0 to estimate the 3-D distribution of b-value and fractal dimensions using maximum-likelihood and spatial correlation dimension approaches, respectively. Our results show an area of high b-, D- and Vp/Vs ratio values at 15-35 km depth in the main rupture zone (MRZ), while relatively low b- and D values characterize the surrounding rigid regions and Gedi fault (GF) zone. We propose that higher material heterogeneities in the vicinity of the MRZ and/or circulation of deep aqueous fluid/volatile CO 2 is the main cause of the increased b-, D- and Vp/Vs ratio values at 15-35 km depth. Seismic velocity images also show some low velocity zones continuing in to the deep lower crust, supporting the existence of circulation of deep aqueous fluid / volatile CO 2 in the region (probably released from the eclogitasation of olivine rich lower crustal rocks). The presence of number of high and low velocity patches further reveals the heterogeneous and fractured nature of the MRZ. Interestingly, we observe that Aki (1981)'s relation (D = 2b) is not valid for the spatial b-D correlation of the events in the GF (D 2 = 1.2b) zone. However, the events in the MRZ (D 2 = 1.7b) show a fair agreement with the D = 2b relationship while the earthquakes associated with the remaining parts of the aftershock zone (D 2 = 1.95b) show a strong correlation with the Aki (1981)'s relationship. Thus, we infer that the remaining parts of the aftershock zone are probably behaving like locked un-ruptured zones, where larger stresses accumulate. We also propose that deep fluid involvement may play a key role in generating seismic activity in the
DEFF Research Database (Denmark)
Bruun Jensen, Casper
2007-01-01
. Instead, I outline a fractal approach to the study of space, society, and infrastructure. A fractal orientation requires a number of related conceptual reorientations. It has implications for thinking about scale and perspective, and (sociotechnical) relations, and for considering the role of the social...... and a fractal social theory....
... earthquake occurs in a populated area, it may cause property damage, injuries, and even deaths. If you live in a coastal area, there is the possibility of a tsunami. Damage from earthquakes can also lead to floods or fires. Although there are no guarantees of ...
Fractal and Morlet-wavelet analyses of M ≥ 6 earthquakes in the South-North Seismic Belt, China
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Jeen-Hwa Wang
2017-01-01
Full Text Available The M ≥ 6 earthquakes occurred in the South-North Seismic Belt, Mainland China (longitudes from 98 - 107°E and latitudes from 21 - 41°N during 1900 - 2016 are taken to measure the multifractal dimensionsspatial distribution and time sequence of events and the dominant periods. The multifractal dimensions, Dq, are measured from the log-log plots of Cq(r versus r and Cq(t versus t, where Cq(r and Cq(t are the generalized correlation integrals for the epicentral distribution and time sequence of events, respectively. r and t are the epicentral distance and inter-event time, respectively, at positive q. The log-log plot of Cq(r versus r shows a linear portion when log(rl ≤ log(r ≤ log(ru. The rl and ru values are, respectively, 120 and 560 km for M ≥ 6 events, 100 and 560 km for M ≥ 6.5 events, and 63 and 560 km for M ≥ 7 events. The rl value decreases with the lower-bound magnitude. Dq monotonically decreases with increasing q. The Dq values are between 1.618 and 1.426 for M ≥ 6 events, between 1.562 and 1.108 for M ≥ 6.5 events, and between 1.365 and 0.841 for M ≥ 7 events. The log-log plot Cq(t versus t show a linear distribution when log(tl ≤ log(t ≤ log(tu, where tl and tu are, respectively, 5 and 50.1 years for M ≥ 6 events, 5 and 50.1 years for M ≥ 6.5 events, and 16 and 63.1 years for M ≥ 7 event, thus suggesting that the time sequences of earthquake in the study region are multifractal. The Dq values are between 0.830 and 0.703 for M ≥ 6 events, between 0.835 and 0.820 for M ≥ 6.5 events, and between 0.786 and 0.685 for M ≥ 7 events. The Morlet wavelet technique is applied to analyze the dominant periods of temporal variations in numbers of yearly earthquakes for the three magnitude ranges, i.e., M ≥ 6, M ≥ 6.5, and M ≥ 7. The resultant dominant period is 2.94 years for M ≥ 6 events and cannot be evaluated for M ≥ 6.5 and M ≥ 7 events.
Shedlock, Kaye M.; Pakiser, Louis Charles
1998-01-01
One of the most frightening and destructive phenomena of nature is a severe earthquake and its terrible aftereffects. An earthquake is a sudden movement of the Earth, caused by the abrupt release of strain that has accumulated over a long time. For hundreds of millions of years, the forces of plate tectonics have shaped the Earth as the huge plates that form the Earth's surface slowly move over, under, and past each other. Sometimes the movement is gradual. At other times, the plates are locked together, unable to release the accumulating energy. When the accumulated energy grows strong enough, the plates break free. If the earthquake occurs in a populated area, it may cause many deaths and injuries and extensive property damage. Today we are challenging the assumption that earthquakes must present an uncontrollable and unpredictable hazard to life and property. Scientists have begun to estimate the locations and likelihoods of future damaging earthquakes. Sites of greatest hazard are being identified, and definite progress is being made in designing structures that will withstand the effects of earthquakes.
Fatemi, Omid; Panchanathan, Sethuraman
1997-01-01
Visual media processing is becoming increasingly important because of the wide variety of image and video based applications. Recently, several architectures have been reported in the literature to implement image and video processing algorithms. They range from programmable DSP processors to application specific integrated circuits (ASICs). DSPs have to be software programed to execute individual operations in image and video processing. However they are not suitable for real-time execution of highly compute intensive applications such as fractal block processing (FBP). On the other hand, dedicated architectures and ASICs are designed to implement specific functions. Since they are optimized for a specific task, they cannot be used in a wide variety of applications. In this paper, we propose a parallel and pipelined architecture called fractal engine to implement the operations in FBP. Fractal engine is simple, modular, scaleable and is optimized to execute both low level and mid level operations. We note that implementation of the basic operations by fractal engine enables efficient execution of a majority of visual computing tasks. These include spatial filtering, contrast enhancement, frequency domain operations, histogram calculation, geometric transforms, indexing, vector quantization, fractal block coding, motion estimation, etc. The individual modules of fractal engine have been implemented in VHDL (VHSIC hardware description language). We have chosen to demonstrate the real-time execution capability of fractal engine by mapping a fractal block coding (FBC) algorithm onto the proposed architecture.
Evertsz, Carl Joseph Gabriel
1989-01-01
Laplacian Fractals are physical models for the fractal properties encountered in a selected group of natural phenomena. The basis models in this class are the Dialectric Breakdown Model and the closely related Diffusion- Limited Aggregration model and Laplacian Random Walks. A full mathematical
Osler, Thomas J.
1999-01-01
Because fractal images are by nature very complex, it can be inspiring and instructive to create the code in the classroom and watch the fractal image evolve as the user slowly changes some important parameter or zooms in and out of the image. Uses programming language that permits the user to store and retrieve a graphics image as a disk file.…
Multilayer adsorption on fractal surfaces.
Vajda, Péter; Felinger, Attila
2014-01-10
Multilayer adsorption is often observed in liquid chromatography. The most frequently employed model for multilayer adsorption is the BET isotherm equation. In this study we introduce an interpretation of multilayer adsorption measured on liquid chromatographic stationary phases based on the fractal theory. The fractal BET isotherm model was successfully used to determine the apparent fractal dimension of the adsorbent surface. The nonlinear fitting of the fractal BET equation gives us the estimation of the adsorption equilibrium constants and the monolayer saturation capacity of the adsorbent as well. In our experiments, aniline and proline were used as test molecules on reversed phase and normal phase columns, respectively. Our results suggest an apparent fractal dimension 2.88-2.99 in the case of reversed phase adsorbents, in the contrast with a bare silica column with a fractal dimension of 2.54. Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved.
Madden, Elizabeth; van Zelst, Iris; Ulrich, Thomas; van Dinther, Ylona; Gabriel, Alice-Agnes
2017-04-01
A major challenge in understanding the physics of megathrust earthquakes is constraining the initial stress field. The close relationship between initial stress and friction and any variations in fault geometry make unique determination of these parameters difficult. In addition, evidence for low effective stresses (e.g. Hardebeck, 2015; Husen and Kissling, 2001) seem incompatible with the occurrence of large megathrust events. Here, we present a series of 3D dynamic ruptures along the plate interface that hosted the 2004 M 9.1-9.3 Sumatra-Andaman earthquake. The dynamic rupture models are performed with SeisSol, which solves for dynamic fault rupture and seismic wave propagation. Use of an unstructured tetrahedral mesh allows for a realistic representation of both the non-planar slab interface and the bathymetry. First, we compare earthquake models under conditions of high versus low fluid pressure. The model with a low fluid pressure (hydrostatic) produces rupture velocities and slip magnitudes that are much too high. The model with a high fluid pressure (near lithostatic) produces the observed average 2.5 km/s rupture speed and slip magnitudes that match the observed GPS surface displacements. This suggests that earthquakes along the Sumatra-Andaman subduction zone operate under the conditions of low effective principal and differential stresses that result from high fluid pressures. For a third model, we use conditions from a 2D seismo-thermo-mechanical earthquake cycle model representing long term deformation at the latitude of the 2004 earthquake's hypocenter. Slip instabilities that approximate earthquakes arise spontaneously along the subduction zone interface in this model. We use the stress and material properties at the time of nucleation for a single earthquake as initial conditions for the dynamic rupture model. In order to produce a reasonable earthquake, fluid pressure must exceed lithostatic near the hypocenter. Because the effective principal
Barnsley, Michael F
2012-01-01
""Difficult concepts are introduced in a clear fashion with excellent diagrams and graphs."" - Alan E. Wessel, Santa Clara University""The style of writing is technically excellent, informative, and entertaining."" - Robert McCartyThis new edition of a highly successful text constitutes one of the most influential books on fractal geometry. An exploration of the tools, methods, and theory of deterministic geometry, the treatment focuses on how fractal geometry can be used to model real objects in the physical world. Two sixteen-page full-color inserts contain fractal images, and a bonus CD of
Ghost quintessence in fractal gravity
Indian Academy of Sciences (India)
In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost dark energy model which was recently suggested to explain the present acceleration of the cosmic expansion. Next, we establish a connection between the quintessence scalar field and fractal ghost dark energy density.
Mishra, Jibitesh
2007-01-01
The book covers all the fundamental aspects of generating fractals through L-system. Also it provides insight to various researches in this area for generating fractals through L-system approach & estimating dimensions. Also it discusses various applications of L-system fractals. Key Features: - Fractals generated from L-System including hybrid fractals - Dimension calculation for L-system fractals - Images & codes for L-system fractals - Research directions in the area of L-system fractals - Usage of various freely downloadable tools in this area - Fractals generated from L-System including hybrid fractals- Dimension calculation for L-system fractals- Images & codes for L-system fractals- Research directions in the area of L-system fractals- Usage of various freely downloadable tools in this area
Fractals, Coherence and Brain Dynamics
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
Directory of Open Access Journals (Sweden)
Amato P
2008-01-01
Full Text Available Abstract Self-similar patterns are frequently observed in Nature. Their reproduction is possible on a length scale 102–105 nm with lithographic methods, but seems impossible on the nanometer length scale. It is shown that this goal may be achieved via a multiplicative variant of the multi-spacer patterning technology, in this way permitting the controlled preparation of fractal surfaces.
Order-fractal transitions in abstract paintings
Energy Technology Data Exchange (ETDEWEB)
Calleja, E.M. de la, E-mail: elsama79@gmail.com [Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970, Porto Alegre, RS (Brazil); Cervantes, F. [Department of Applied Physics, CINVESTAV-IPN, Carr. Antigua a Progreso km.6, Cordemex, C.P.97310, Mérida, Yucatán (Mexico); Calleja, J. de la [Department of Informatics, Universidad Politécnica de Puebla, 72640 (Mexico)
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-order 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.
Bottorff, Mark; Ferland, Gary
2001-03-01
This paper examines whether a fractal cloud geometry can reproduce the emission-line spectra of active galactic nuclei (AGNs). The nature of the emitting clouds is unknown, but many current models invoke various types of magnetohydrodynamic confinement. Recent studies have argued that a fractal distribution of clouds, in which subsets of clouds occur in self-similar hierarchies, is a consequence of such confinement. Whatever the confinement mechanism, fractal cloud geometries are found in nature and may be present in AGNs too. We first outline how a fractal geometry can apply at the center of a luminous quasar. Scaling laws are derived that establish the number of hierarchies, typical sizes, column densities, and densities. Photoionization simulations are used to predict the integrated spectrum from the ensemble. Direct comparison with observations establishes all model parameters so that the final predictions are fully constrained. Theory suggests that denser clouds might form in regions of higher turbulence and that larger turbulence results in a wider dispersion of physical gas densities. An increase in turbulence is expected deeper within the gravitational potential of the black hole, resulting in a density gradient. We mimic this density gradient by employing two sets of clouds with identical fractal structuring but different densities. The low-density clouds have a lower column density and large covering factor similar to the warm absorber. The high-density clouds have high column density and smaller covering factor similar to the broad-line region (BLR). A fractal geometry can simultaneously reproduce the covering factor, density, column density, BLR emission-line strengths, and BLR line ratios as inferred from observation. Absorption properties of the model are consistent with the integrated line-of-sight column density as determined from observations of X-ray absorption, and when scaled to a Seyfert galaxy, the model is consistent with the number of
Fractal dimensions of solar activity
Watari, Shinichi
1995-05-01
Solar activity changes in amplitude and long-term behavior irregularly. Fractal theory is used to examine the variation of solar activity, using daily solar indices (i.e., sunspot number, 10.7 cm radio flux, the SME L alpha, Fe XIV coronal emission, and the total solar irradiance measured by the Earth Radiation Budget (ERG) on the NIMBUS-7. It can handle irregular variations quantitatively. The fractal dimension of 10.7 cm radio fluxes in cycle 21 for periods of approximately 7 days or less was 1.28, 1.3 for periods longer than approximately 272 days, and 1.86 for periods between them, for example. Fractal dimensions for other solar indices show similar tendencies. These results suggest that solar activity varies more irregularly for time scales that are longer than several days and shorter than several months. Yearly values of fractal dimensions and bending points do not change in concert with the solar cycle.
Fractal and natural time analysis of geoelectrical time series
Ramirez Rojas, A.; Moreno-Torres, L. R.; Cervantes, F.
2013-05-01
In this work we show the analysis of geoelectric time series linked with two earthquakes of M=6.6 and M=7.4. That time series were monitored at the South Pacific Mexican coast, which is the most important active seismic subduction zone in México. The geolectric time series were analyzed by using two complementary methods: a fractal analysis, by means of the detrended fluctuation analysis (DFA) in the conventional time, and the power spectrum defined in natural time domain (NTD). In conventional time we found long-range correlations prior to the EQ-occurrences and simultaneously in NTD, the behavior of the power spectrum suggest the possible existence of seismo electric signals (SES) similar with the previously reported in equivalent time series monitored in Greece prior to earthquakes of relevant magnitude.
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.
Distribution of incremental static stress caused by earthquakes
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Y. Y. Kagan
1994-01-01
Full Text Available Theoretical calculations, simulations and measurements of rotation of earthquake focal mechanisms suggest that the stress in earthquake focal zones follows the Cauchy distribution which is one of the stable probability distributions (with the value of the exponent α equal to 1. We review the properties of the stable distributions and show that the Cauchy distribution is expected to approximate the stress caused by earthquakes occurring over geologically long intervals of a fault zone development. However, the stress caused by recent earthquakes recorded in instrumental catalogues, should follow symmetric stable distributions with the value of α significantly less than one. This is explained by a fractal distribution of earthquake hypocentres: the dimension of a hypocentre set, ��, is close to zero for short-term earthquake catalogues and asymptotically approaches 2¼ for long-time intervals. We use the Harvard catalogue of seismic moment tensor solutions to investigate the distribution of incremental static stress caused by earthquakes. The stress measured in the focal zone of each event is approximated by stable distributions. In agreement with theoretical considerations, the exponent value of the distribution approaches zero as the time span of an earthquake catalogue (ΔT decreases. For large stress values α increases. We surmise that it is caused by the δ increase for small inter-earthquake distances due to location errors.
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.
Thamrin, Cindy; Stern, Georgette; Frey, Urs
2010-06-01
There is increasing interest in the study of fractals in medicine. In this review, we provide an overview of fractals, of techniques available to describe fractals in physiological data, and we propose some reasons why a physician might benefit from an understanding of fractals and fractal analysis, with an emphasis on paediatric respiratory medicine where possible. Among these reasons are the ubiquity of fractal organisation in nature and in the body, and how changes in this organisation over the lifespan provide insight into development and senescence. Fractal properties have also been shown to be altered in disease and even to predict the risk of worsening of disease. Finally, implications of a fractal organisation include robustness to errors during development, ability to adapt to surroundings, and the restoration of such organisation as targets for intervention and treatment. Copyright 2010 Elsevier Ltd. All rights reserved.
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
Fractal electrodynamics via non-integer dimensional space approach
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.
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.…
Fractal electrodynamics via non-integer dimensional space approach
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru
2015-09-25
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. - Highlights: • Electrodynamics of fractal media is described by non-integer dimensional spaces. • Applications of the fractal Gauss's and Ampere's laws are suggested. • Fractal Poisson equation, equation for fractal stream of charges are considered.
Directory of Open Access Journals (Sweden)
FELICIA RAMONA BIRAU
2012-05-01
Full Text Available In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and of course, the manner in which they interpret that information may be different. Also, Fractal Market Hypothesis refers to the way that liquidity and investment horizons influence the behaviour of financial investors.
Exploring fractal behaviour of blood oxygen saturation in preterm babies
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.
Fractal dimension for fractal structures: A Hausdorff approach
Fernández-Martínez, M.; Sánchez-Granero, M. A.
2012-01-01
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a suitable discretization of the Hausdorff theory of fractal dimension. We also find some connections between our definition and the classical ones and also with fractal dimensions I & II (see http://arxiv.org/submit/0080421/pdf). Therefore, we generalize them and ...
Baryshev, Yuri
2002-01-01
This is the first book to present the fascinating new results on the largest fractal structures in the universe. It guides the reader, in a simple way, to the frontiers of astronomy, explaining how fractals appear in cosmic physics, from our solar system to the megafractals in deep space. It also offers a personal view of the history of the idea of self-similarity and of cosmological principles, from Plato's ideal architecture of the heavens to Mandelbrot's fractals in the modern physical cosmos. In addition, this invaluable book presents the great fractal debate in astronomy (after Luciano Pi
Percolation on infinitely ramified fractal networks
Balankin, Alexander S.; Martínez-Cruz, M. A.; Susarrey-Huerta, O.; Damian Adame, L.
2018-01-01
We study how fractal features of an infinitely ramified network affect its percolation properties. The fractal attributes are characterized by the Hausdorff (DH), topological Hausdorff (DtH), and spectral (ds) dimensions. Monte Carlo simulations of site percolation were performed on pre-fractal standard Sierpiński carpets with different fractal attributes. Our findings suggest that within the universality class of random percolation the values of critical percolation exponents are determined by the set of dimension numbers (DH, DtH, ds), rather than solely by the spatial dimension (d). We also argue that the relevant dimension number for the percolation threshold is the topological Hausdorff dimension DtH, whereas the hyperscaling relations between critical exponents are governed by the Hausdorff dimension DH. The effect of the network connectivity on the site percolation threshold is revealed.
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Understanding the Fractal Dimensions of Urban Forms through Spatial Entropy
Chen, Yanguang; Wang, Jiejing; Feng, Jian
2017-11-01
Spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal parameters can be employed to characterize scale-free phenomena. This paper is devoted to exploring the similarities and differences between spatial entropy and fractal dimension in urban description. Drawing an analogy between cities and growing fractals, we illustrate the definitions of fractal dimension based on different entropy concepts. Three representative fractal dimensions in the multifractal dimension set are utilized to make empirical analyses of urban form of two cities. The results show that the entropy values are not determinate, but the fractal dimension value is certain; if the linear size of boxes is small enough (e.g., fractal dimension is clear. Further empirical analysis indicates that fractal dimension is close to the characteristic values of spatial entropy. This suggests that the physical meaning of fractal dimension can be interpreted by the ideas from entropy and scales and the conclusion is revealing for future spatial analysis of cities. Key words: fractal dimension; entropy; mutlifractals; scaling; urban form; Chinese cities
Enhancement of critical temperature in fractal metamaterial superconductors
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Smolyaninov, Igor I., E-mail: smoly@umd.edu [Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742 (United States); Smolyaninova, Vera N. [Department of Physics Astronomy and Geosciences, Towson University, 8000 York Road, Towson, MD 21252 (United States)
2017-04-15
Fractal metamaterial superconductor geometry has been suggested and analyzed based on the recently developed theoretical description of critical temperature increase in epsilon near zero (ENZ) metamaterial superconductors. Considerable enhancement of critical temperature has been predicted in such materials due to appearance of large number of additional poles in the inverse dielectric response function of the fractal. Our results agree with the recent observation (Fratini et al. Nature 466, 841 (2010)) that fractal defect structure promotes superconductivity.
Enhancement of critical temperature in fractal metamaterial superconductors
Smolyaninov, Igor I.; Smolyaninova, Vera N.
2017-04-01
Fractal metamaterial superconductor geometry has been suggested and analyzed based on the recently developed theoretical description of critical temperature increase in epsilon near zero (ENZ) metamaterial superconductors. Considerable enhancement of critical temperature has been predicted in such materials due to appearance of large number of additional poles in the inverse dielectric response function of the fractal. Our results agree with the recent observation (Fratini et al. Nature 466, 841 (2010)) that fractal defect structure promotes superconductivity.
Electromagnetic fields in fractal continua
Energy Technology Data Exchange (ETDEWEB)
Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Mena, Baltasar [Instituto de Ingeniería, Universidad Nacional Autónoma de México, México D.F. (Mexico); Patiño, Julián [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Morales, Daniel [Instituto Mexicano del Petróleo, México D.F., 07730 Mexico (Mexico)
2013-04-01
Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum Φ{sub D}{sup 3}⊂E{sup 3} with a fractal metric. The generalized forms of Maxwell equations are derived employing the local fractional vector calculus related to the Hausdorff derivative. The difference between the fractal continuum electrodynamics based on the fractal metric of continua with Euclidean topology and the electrodynamics in fractional space F{sup α} accounting the fractal topology of continuum with the Euclidean metric is outlined. Some electromagnetic phenomena in fractal media associated with their fractal time and space metrics are discussed.
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
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Kyril Tintarev
2007-05-01
Full Text Available The paper studies energy functionals on quasimetric spaces, defined by quadratic measure-valued Lagrangeans. This general model of medium, known as metric fractals, includes nested fractals and sub-Riemannian manifolds. In particular, the quadratic form of the Lagrangean satisfies Sobolev inequalities with the critical exponent determined by the (quasimetric homogeneous dimension, which is also involved in the asymptotic distribution of the form's eigenvalues. This paper verifies that the axioms of the metric fractal are preserved by space products, leading thus to examples of non-differentiable media of arbitrary intrinsic dimension.
The role of the circadian system in fractal neurophysiological control.
Pittman-Polletta, Benjamin R; Scheer, Frank A J L; Butler, Matthew P; Shea, Steven A; Hu, Kun
2013-11-01
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. © 2013 The Authors. Biological Reviews © 2013 Cambridge Philosophical Society.
Fractal generalized Pascal matrices
Burlachenko, E.
2016-01-01
Set of generalized Pascal matrices whose elements are generalized binomial coefficients is considered as an integral object. The special system of generalized Pascal matrices, based on which we are building fractal generalized Pascal matrices, is introduced. Pascal matrix (Pascal triangle) is the Hadamard product of the fractal generalized Pascal matrices. The concept of zero generalized Pascal matrices, an example of which is the Pascal triangle modulo 2, arise in connection with the system ...
Spatial Dynamics of Urban Growth Based on Entropy and Fractal Dimension
Chen, Yanguang
2016-01-01
The fractal dimension growth of urban form can be described with sigmoid functions such as logistic function due to squashing effect. The sigmoid curves of fractal dimension suggest a type of spatial replacement dynamics of urban evolution. How to understand the underlying rationale of the fractal dimension curves is a pending problem. This study is based on two previous findings. First, normalized fractal dimension proved to equal normalized spatial entropy; second, a sigmoid function procee...
Fractal-Based Exponential Distribution of Urban Density and Self-Affine Fractal Forms of Cities
Chen, Yanguang
2016-01-01
Urban population density always follows the exponential distribution and can be described with Clark's model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark's model differs from the exponential function in mathematics because that urban population is distributed on the fractal support of landform and land-use form. By using mathematical transform and empirical evidence, we argue that there are self-affine scaling relations and local power laws behind the exponential distribution of urban density. The scale parameter of Clark's model indicating the characteristic radius of cities is not a real constant, but depends on the urban field we defined. So the exponential model suggests local fractal structure with two kinds of fractal parameters. The parameters can be used to characterize urban space filling, spatial correlation, self-affine properties, and self-organized evolution. The case study of the city of Hangzhou, China, is employed to ...
A New Model of Urban Population Density Indicating Latent Fractal Structure
Chen, Yanguang
2016-01-01
Fractal structure of a system suggests the optimal way in which parts arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterize fractal cities, we need the measure of fractional dimension. However, if the fractal organization is concealed in the complex spatial distributions of geographical phenomena, the common methods of evaluating fractal parameter will be disabled. In this article, a new model is proposed to describe urban density and estimate fractal dimension of urban form. If urban density takes on quasi-fractal pattern or the self-similar pattern is hidden in the negative exponential distribution, the generalized gamma function may be employed to model the urban landscape and estimate its latent fractal dimension. As a case study, the method is applied to the city of Hangzhou, China. The results show that urban form evolves from simple to complex structure with time.
The 21 May 2014 Mw 5.9 Bay of Bengal earthquake: macroseismic data suggest a high‐stress‐drop event
Martin, Stacey; Hough, Susan E.
2015-01-01
A modest but noteworthy Mw 5.9 earthquake occurred in the Bay of Bengal beneath the central Bengal fan at 21:51 Indian Standard Time (16:21 UTC) on 21 May 2014. Centered over 300 km from the eastern coastline of India (Fig. 1), it caused modest damage by virtue of its location and magnitude. However, shaking was very widely felt in parts of eastern India where earthquakes are uncommon. Media outlets reported as many as four fatalities. Although most deaths were blamed on heart attacks, the death of one woman was attributed by different sources to either a roof collapse or a stampede (see Table S1, available in the electronic supplement to this article). Across the state of Odisha, as many as 250 people were injured (see Table S1), most after jumping from balconies or terraces. Light damage was reported from a number of towns on coastal deltaic sediments, including collapsed walls and damage to pukka and thatched dwellings. Shaking was felt well inland into east‐central India and was perceptible in multistoried buildings as far as Chennai, Delhi, and Jaipur at distances of ≈1600 km (Table 1).
The fractal forest: fractal geometry and applications in forest science.
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.
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
From dendrimers to fractal polymers and beyond
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Charles N. Moorefield
2013-01-01
Full Text Available The advent of dendritic chemistry has facilitated materials research by allowing precise control of functional component placement in macromolecular architecture. The iterative synthetic protocols used for dendrimer construction were developed based on the desire to craft highly branched, high molecular weight, molecules with exact mass and tailored functionality. Arborols, inspired by trees and precursors of the utilitarian macromolecules known as dendrimers today, were the first examples to employ predesigned, 1 → 3 C-branched, building blocks; physical characteristics of the arborols, including their globular shapes, excellent solubilities, and demonstrated aggregation, combined to reveal the inherent supramolecular potential (e.g., the unimolecular micelle of these unique species. The architecture that is a characteristic of dendritic materials also exhibits fractal qualities based on self-similar, repetitive, branched frameworks. Thus, the fractal design and supramolecular aspects of these constructs are suggestive of a larger field of fractal materials that incorporates repeating geometries and are derived by complementary building block recognition and assembly. Use of terpyridine-M2+-terpyridine (where, M = Ru, Zn, Fe, etc connectivity in concert with mathematical algorithms, such as forms the basis for the Seirpinski gasket, has allowed the beginning exploration of fractal materials construction. The propensity of the fractal molecules to self-assemble into higher order architectures adds another dimension to this new arena of materials and composite construction.
Rheological and fractal hydrodynamics of aerobic granules.
Tijani, H I; Abdullah, N; Yuzir, A; Ujang, Zaini
2015-06-01
The structural and hydrodynamic features for granules were characterized using settling experiments, predefined mathematical simulations and ImageJ-particle analyses. This study describes the rheological characterization of these biologically immobilized aggregates under non-Newtonian flows. The second order dimensional analysis defined as D2=1.795 for native clusters and D2=1.099 for dewatered clusters and a characteristic three-dimensional fractal dimension of 2.46 depicts that these relatively porous and differentially permeable fractals had a structural configuration in close proximity with that described for a compact sphere formed via cluster-cluster aggregation. The three-dimensional fractal dimension calculated via settling-fractal correlation, U∝l(D) to characterize immobilized granules validates the quantitative measurements used for describing its structural integrity and aggregate complexity. These results suggest that scaling relationships based on fractal geometry are vital for quantifying the effects of different laminar conditions on the aggregates' morphology and characteristics such as density, porosity, and projected surface area. Copyright © 2015 Elsevier Ltd. All rights reserved.
Marks-Tarlow, Terry
Linear concepts of time plus the modern capacity to track history emerged out of circular conceptions characteristic of ancient and traditional cultures. A fractal concept of time lies implicitly within the analog clock, where each moment is treated as unique. With fractal geometry the best descriptor of nature, qualities of self-similarity and scale invariance easily model her endless variety and recursive patterning, both in time and across space. To better manage temporal aspects of our lives, a fractal concept of time is non-reductive, based more on the fullness of being than on fragments of doing. By using a fractal concept of time, each activity or dimension of life is multiply and vertically nested. Each nested cycle remains simultaneously present, operating according to intrinsic dynamics and time scales. By adding the vertical axis of simultaneity to the horizontal axis of length, time is already full and never needs to be filled. To attend to time's vertical dimension is to tap into the imaginary potential for infinite depth. To switch from linear to fractal time allows us to relax into each moment while keeping in mind the whole.
Fractal Electrochemical Microsupercapacitors
Hota, Mrinal Kanti
2017-08-17
The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.
Fractal geometry and stochastics IV
Bandt, Christoph
2010-01-01
Over the years fractal geometry has established itself as a substantial mathematical theory in its own right. This book collects survey articles covering many of the developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals.
Fractal design concepts for stretchable electronics.
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.
Fractal design concepts for stretchable electronics
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.
Insulator Contamination Forecasting Based on Fractal Analysis of Leakage Current
Directory of Open Access Journals (Sweden)
Bing Luo
2012-07-01
Full Text Available In this paper, an artificial pollution test is carried out to study the leakage current of porcelain insulators. Fractal theory is adopted to extract the characteristics hidden in leakage current waveforms. Fractal dimensions of the leakage current for the security, forecast and danger zones are analyzed under four types of degrees of contamination. The mean value and the standard deviation of the fractal dimension in the forecast zone are calculated to characterize the differences. The analysis reveals large differences in the fractal dimension of leakage current under different contamination discharge stages and degrees. The experimental and calculation results suggest that the fractal dimension of a leakage current waveform can be used as a new indicator of the discharge process and contamination degree of insulators. The results provide new methods and valid indicators for forecasting contamination flashovers.
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.
Is the co-seismic slip distribution fractal?
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
Li, Jun; Ostoja-Starzewski, Martin
2012-01-01
Over the past few decades, various conjectures were advanced that Saturn's rings are Cantor-like sets, although no convincing fractal analysis of actual images has ever appeared. We focus on the images sent by the Cassini spacecraft mission: slide #42 "Mapping Clumps in Saturn's Rings" and slide #54 "Scattered Sunshine". Using the box-counting method, we determine the fractal dimension of rings seen here (and in several other images from the same source) to be consistently about 1.6~1.7. This...
Directory of Open Access Journals (Sweden)
Deppman Airton
2017-01-01
Full Text Available The non extensive aspects of pT distributions obtained in high energy collisions are discussed in relation to possible fractal structure in hadrons, in the sense of the thermofractal structure recently introduced. The evidences of self-similarity in both theoretical and experimental works in High Energy and in Hadron Physics are discussed, to show that the idea of fractal structure of hadrons and fireballs have being under discussion for decades. The non extensive self-consistent thermodynamics and the thermofractal structure allow one to connect non extensivity to intermittence and possibly to parton distribution functions in a single theoretical framework.
Fractal elements and their applications
Gil’mutdinov, Anis Kharisovich; El-Khazali, Reyad
2017-01-01
This book describes a new type of passive electronic components, called fractal elements, from a theoretical and practical point of view. The authors discuss in detail the physical implementation and design of fractal devices for application in fractional-order signal processing and systems. The concepts of fractals and fractal signals are explained, as well as the fundamentals of fractional calculus. Several implementations of fractional impedances are discussed, along with comparison of their performance characteristics. Details of design, schematics, fundamental techniques and implementation of RC-based fractal elements are provided. .
Earnshow, R; Jones, H
1991-01-01
This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot i...
Fractal Representation of Exergy
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Yvain Canivet
2016-02-01
Full Text Available We developed a geometrical model to represent the thermodynamic concepts of exergy and anergy. The model leads to multi-scale energy lines (correlons that we characterised by fractal dimension and entropy analyses. A specific attention will be paid to overlapping points, rising interesting remarks about trans-scale dynamics of heat flows.
Fractal growth in impurity-controlled solidification in lipid monolayers
DEFF Research Database (Denmark)
Fogedby, Hans C.; Sørensen, Erik Schwartz; Mouritsen, Ole G.
1987-01-01
A simple two-dimensional microscopic model is proposed to describe solidifcation processes in systems with impurities which are miscible only in the fluid phase. Computer simulation of the model shows that the resulting solids are fractal over a wide range of impurity concentrations and impurity...... diffusional constants. A fractal-forming mechanism is suggested for impurity-controlled solidification which is consistent with recent experimental observations of fractal growth of solid phospholipid domains in monolayers. The Journal of Chemical Physics is copyrighted by The American Institute of Physics....
Fractal physiology and the fractional calculus: a perspective.
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
Complexity in earthquake sequences controlled by multi-scale heterogeneity in fault fracture energy
Aochi, H.; Ide, S.
2008-12-01
A series of dynamic rupture events under constant tectonic loading is simulated on a fault with multi-scale heterogeneity and a stochastic rupture initiation process. The fracture energy of the fault plane is assumed to have multi-scale heterogeneous distribution using fractal circular patches. The stochastic rupture initiation process with a function of the accumulated stress is introduced in order to take account for unknown smaller- scale heterogeneity and incertitude. Five realizations of a statistical spatial distribution of fracture energy (fault heterogeneity maps) are tested for the simulations of earthquake sequences during a few seismic cycles. The diversity of earthquake sequences is principally controlled by the spatial distribution of the patches. The effect of dynamic rupture appears in the residual stress after the characteristic events due to their directivity and this localizes the subsequent sequences. Although the characteristic earthquakes occur rather regularly in time and similarly in different seismic cycles, some irregular behaviors are found, based on the heterogeneity maps and the randomness of the preceding earthquake sequence, leading to a visible anomaly in the seismicity. Such anomaly is not predicable, but understandable through the analysis of the concerned earthquakes during the cycle. The similarity and the diversity simulated in this study, governed by the structure of an inherent distribution of multi-scale heterogeneity, suggests the importance of pre-existing heterogeneity field along the fault for the appearance of earthquake sequences, including those that are characteristic.
Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation.
Captur, Gabriella; Karperien, Audrey L; Li, Chunming; Zemrak, Filip; Tobon-Gomez, Catalina; Gao, Xuexin; Bluemke, David A; Elliott, Perry M; Petersen, Steffen E; Moon, James C
2015-09-07
Many of the structures and parameters that are detected, measured and reported in cardiovascular magnetic resonance (CMR) have at least some properties that are fractal, meaning complex and self-similar at different scales. To date however, there has been little use of fractal geometry in CMR; by comparison, many more applications of fractal analysis have been published in MR imaging of the brain.This review explains the fundamental principles of fractal geometry, places the fractal dimension into a meaningful context within the realms of Euclidean and topological space, and defines its role in digital image processing. It summarises the basic mathematics, highlights strengths and potential limitations of its application to biomedical imaging, shows key current examples and suggests a simple route for its successful clinical implementation by the CMR community.By simplifying some of the more abstract concepts of deterministic fractals, this review invites CMR scientists (clinicians, technologists, physicists) to experiment with fractal analysis as a means of developing the next generation of intelligent quantitative cardiac imaging tools.
Martin, Demetri
2015-03-01
Demetri Maritn prepared this palindromic poem as his project for Michael Frame's fractal geometry class at Yale. Notice the first, fourth, and seventh words in the second and next-to-second lines are palindromes, the first two and last two lines are palindromes, the middle line, "Be still if I fill its ebb" minus its last letter is a palindrome, and the entire poem is a palindrome...
Fractal physiology and the fractional calculus: a perspective
Directory of Open Access Journals (Sweden)
Bruce J West
2010-10-01
Full Text Available 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. We review the allometric aggregation approach to the processing of physiologic time series as a way of determining the fractal character of the underlying phenomena. 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. Fractional operators acting on fractal functions yield fractal functions, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine. Allometric control incorporates long-time memory, inverse power-law (IPL correlations, and long-range interactions in complex phenomena as manifest by IPL distributions. We hypothesize that allometric control, rather than homeostatic control, maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can be described using the fractional calculus to capture the dynamics of complex physiologic networks. This hypothesis is supported by a number of physiologic time series data.
Fractal differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
. Indeed, as discussed in §4 with examples, and in [32], it is possible to solve certain fractal differential equations by mapping them to ordinary differential equations and fractalizing the solutions back. The organization of the paper is as follows: ...
Vector calculus in non-integer dimensional space and its applications to fractal media
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.
Fractal dimension evolution and spatial replacement dynamics of urban growth
Chen, Yanguang
2011-01-01
This paper presents a new perspective of looking at the relation between fractals and chaos by means of cities. Especially, a principle of space filling and spatial replacement is proposed to explain the fractal dimension of urban form. The fractal dimension evolution of urban growth can be empirically modeled with Boltzmann's equation. For the normalized data, Boltzmann's equation is equivalent to the logistic function. The logistic equation can be transformed into the well-known 1-dimensional logistic map, which is based on a 2-dimensional map suggesting spatial replacement dynamics of city development. The 2-dimensional recurrence relations can be employed to generate the nonlinear dynamical behaviors such as bifurcation and chaos. A discovery is made that, for the fractal dimension growth following the logistic curve, the normalized dimension value is the ratio of space filling. If the rate of spatial replacement (urban growth) is too high, the periodic oscillations and chaos will arise, and the city syst...
The fractal heart — embracing mathematics in the cardiology clinic
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
Fractals and the Kepler equation
Kasten, Volker
1992-09-01
The application of fractal mathematics to Kepler's equation is addressed. Complex solutions to Kepler's equation are considered along with methods to determine them. The roles of regions of attraction and their boundaries, Julia quantities, Fatou quantities, and fractal quantities in these methods are discussed.
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.)
Contour fractal analysis of grains
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.
Encounters with chaos and fractals
Gulick, Denny
2012-01-01
Periodic Points Iterates of Functions Fixed Points Periodic Points Families of Functions The Quadratic Family Bifurcations Period-3 Points The Schwarzian Derivative One-Dimensional Chaos Chaos Transitivity and Strong Chaos Conjugacy Cantor Sets Two-Dimensional Chaos Review of Matrices Dynamics of Linear FunctionsNonlinear Maps The Hénon Map The Horseshoe Map Systems of Differential Equations Review of Systems of Differential Equations Almost Linearity The Pendulum The Lorenz System Introduction to Fractals Self-Similarity The Sierpiński Gasket and Other "Monsters"Space-Filling Curves Similarity and Capacity DimensionsLyapunov Dimension Calculating Fractal Dimensions of Objects Creating Fractals Sets Metric Spaces The Hausdorff Metric Contractions and Affine Functions Iterated Function SystemsAlgorithms for Drawing Fractals Complex Fractals: Julia Sets and the Mandelbrot Set Complex Numbers and Functions Julia Sets The Mandelbrot Set Computer Programs Answers to Selected Exercises References Index.
Contour fractal analysis of grains
Directory of Open Access Journals (Sweden)
Guida Giulia
2017-01-01
Full Text Available 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.
Queralt, Tomás
1997-01-01
En el presente artículo se muestra el planteamiento, justificación y la puesta en practica de algunas actividades que forman parte de un taller de fractales. Estas se han tratado en clase en grupos de segundo ciclo de ESO, y se han utilizado para iniciar el curso con un resultado satisfactorio. Con este trabajo se pretende romper con algunos estereotipos y con algunas creencias que los estudiantes tienen acerca de las matemáticas, así como crear el contexto más adecuado para que el alumno hag...
Fractal actors and infrastructures
DEFF Research Database (Denmark)
Bøge, Ask Risom
2011-01-01
-network-theory (ANT) into surveillance studies (Ball 2002, Adey 2004, Gad & Lauritsen 2009). In this paper, I further explore the potential of this connection by experimenting with Marilyn Strathern’s concept of the fractal (1991), which has been discussed in newer ANT literature (Law 2002; Law 2004; Jensen 2007). I...... argue that the concept fits nicely into the ANT-oriented situated surveillance approach (Gad & Lauritsen 2009), not because it explains surveillance, but because it brings empirical sensitivity to our efforts to understanding what comprises a surveillance actor, its network and its relations to those...
Earthquakes in British Columbia
National Research Council Canada - National Science Library
1991-01-01
This pamphlet provides information about the causes of earthquakes, where earthquakes occur, British Columbia plate techtonics, earthquake patterns, earthquake intensity, geology and earthquake impact...
Wicks, Keith R
1991-01-01
Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fracta...
Fractal Adaptive Web Service for Mobile Learning
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Ichraf Tirellil
2006-06-01
Full Text Available This paper describes our proposition for adaptive web services which is based on configurable, re-usable adaptive/personalized services. To realize our ideas, we have developed an approach for designing, implementing and maintaining personal service. This approach enables the user to accomplish an activity with a set of services answering to his preferences, his profiles and to a personalized context. In this paper, we describe the principle of our approach that we call fractal adaptation approach, and we discuss the implementation of personalization services in the context of mobile and collaborative scenario of learning. We have realized a platform in this context -a platform for mobile and collaborative learning- based on fractal adaptable web services. The platform is tested with a population of students and tutors, in order to release the gaps and the advantages of the approach suggested.
Modeling the External Structure of a Fractals
Kravchenko, Galina
2017-10-01
The article describes the main provisions of the theory of fractal geometry, two- and three-dimensional fractals. The possibility of using the fractal theory in the design of buildings and structures, as well as individual elements of the building structures is proposed. The fractal structure has been developed by parametric methods using program «3D modeling of Fractals» with the help of finite element method.
Fractal analysis of Xylella fastidiosa biofilm formation
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.
Poosapadi Arjunan, Sridhar; Kumar, Dinesh Kant
2014-01-01
This research study investigates the fractal properties of surface Electromyogram (sEMG) to estimate the force levels of contraction of three muscles with different cross-sectional areas (CSA): m. quadriceps--vastus lateralis, m. biceps brachii, andm. flexor digitorum superficialis. The fractal features were computed based on the fractal analysis of sEMG, signal recorded while performing sustained muscle contraction at different force levels. A comparison was performed between the fractal features and five other features reported in the literature. Linear regression analysis was carried out to determine the relationship between the force of contraction (20-100%) and features of sEMG. The results from the coefficients of regression r² show that the new fractal feature, maximum fractal length of the signal has highest correlation (range 0.88-0.90) when compared with other features which ranges from 0.34 to 0.74 for the three different muscles. This study suggests that the estimation of various levels of sustained contraction of muscles with varied CSA will provide a better insight into the biomechanics model that involves muscle properties and muscle activation.
The transience of virtual fractals.
Taylor, R P
2012-01-01
Artists have a long and fruitful tradition of exploiting electronic media to convert static images into dynamic images that evolve with time. Fractal patterns serve as an example: computers allow the observer to zoom in on virtual images and so experience the endless repetition of patterns in a matter that cannot be matched using static images. This year's featured cover artist, Susan Lowedermilk, instead plans to employ persistence of human vision to bring virtual fractals to life. This will be done by incorporating her prints of fractal patterns into zoetropes and phenakistoscopes.
Retinal Vascular Fractals and Cognitive Impairment
Directory of Open Access Journals (Sweden)
Yi-Ting Ong
2014-08-01
Full Text Available Background: Retinal microvascular network changes have been found in patients with age-related brain diseases such as stroke and dementia including Alzheimer's disease. We examine whether retinal microvascular network changes are also present in preclinical stages of dementia. Methods: This is a cross-sectional study of 300 Chinese participants (age: ≥60 years from the ongoing Epidemiology of Dementia in Singapore study who underwent detailed clinical examinations including retinal photography, brain imaging and neuropsychological testing. Retinal vascular parameters were assessed from optic disc-centered photographs using a semiautomated program. A comprehensive neuropsychological battery was administered, and cognitive function was summarized as composite and domain-specific Z-scores. Cognitive impairment no dementia (CIND and dementia were diagnosed according to standard diagnostic criteria. Results: Among 268 eligible nondemented participants, 78 subjects were categorized as CIND-mild and 69 as CIND-moderate. In multivariable adjusted models, reduced retinal arteriolar and venular fractal dimensions were associated with an increased risk of CIND-mild and CIND-moderate. Reduced fractal dimensions were associated with poorer cognitive performance globally and in the specific domains of verbal memory, visuoconstruction and visuomotor speed. Conclusion: A sparser retinal microvascular network, represented by reduced arteriolar and venular fractal dimensions, was associated with cognitive impairment, suggesting that early microvascular damage may be present in preclinical stages of dementia.
Eternal fractal in the universe
Winitzki, Serge
2002-04-01
Models of eternal inflation predict a stochastic self-similar geometry of the universe at very large scales and allow the existence of points that never thermalize. I explore the fractal geometry of the resulting spacetime, using coordinate-independent quantities. The formalism of stochastic inflation can be used to obtain the fractal dimension of the set of eternally inflating points (the ``eternal fractal''). I also derive a nonlinear branching diffusion equation describing global properties of the eternal set and the probability of realizing eternal inflation. I show gauge invariance of the condition for the presence of eternal inflation. Finally, I consider the question of whether all thermalized regions merge into one connected domain. The fractal dimension of the eternal set provides a (weak) sufficient condition for merging.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
Thermal transport in fractal systems
DEFF Research Database (Denmark)
Kjems, Jørgen
1992-01-01
Recent experiments on the thermal transport in systems with partial fractal geometry, silica aerogels, are reviewed. The individual contributions from phonons, fractons and particle modes, respectively, have been identified and can be described by quantitative models consistent with heat capacity...
Fractals endlessy repeated geometrical figures
Lauwerier, Hans
1991-01-01
Provides a basic mathematical introduction to fractal geometry, the mathematics that lie behind chaos theory. This book attempts to communicate the relatively simple understanding of the subject to an audience with a basic mathematical education.
Statistical validation of earthquake related observations
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
Dimension of Fractal Basin Boundaries.
Park, Bae-Sig
In many dynamical systems, multiple attractors coexist for certain parameter ranges. The set of initial conditions that asymptotically approach each attractor is its basin of attraction. These basins can be intertwined on arbitrary small scales. Basin boundary can be either smooth or fractal. Dynamical systems that have fractal basin boundary show "final state sensitivity" of the initial conditions. A measure of this sensitivity (uncertainty exponent alpha) is related to the dimension of the basin boundary d = D - alpha , where D is the dimension of the phase space and d is the dimension of the basin boundary. At metamorphosis values of the parameter, there might happen a conversion from smooth to fractal basin boundary (smooth-fractal metamorphosis) or a conversion from fractal to another fractal basin boundary characteristically different from the previous fractal one (fractal-fractal metamorphosis). The dimension changes continuously with the parameter except at the metamorphosis values where the dimension of the basin boundary jumps discontinuously. We chose the Henon map and the forced damped pendulum to investigate this. Scaling of the basin volumes near the metamorphosis values of the parameter is also being studied for the Henon map. Observations are explained analytically by using low dimensional model map. We look for universal scalings of the dimension of fractal basin boundaries near type I and type III intermittency transitions to chaos. Type I intermittency can occur as the system experiences a saddle-node (tangent) bifurcation and type III intermittency can occur as the system experiences an inverted period doubling bifurcation. At these bifurcations, multiple attractors with fractal basin boundaries can be created. It is found the dimension scales, with the parameter, according to the power law d = d_{o } - k| p - p_{c}| ^{beta} with beta = 1/2, where p is the system parameter, p _{c} is the bifurcation value, k is a scaling constant, and d_{o} is
Steady laminar flow of fractal fluids
Balankin, Alexander S.; Mena, Baltasar; Susarrey, Orlando; Samayoa, Didier
2017-02-01
We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived.
Fractal model of anomalous diffusion
Gmachowski, Lech
2015-01-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An...
Review of Fractal Heat Exchangers
Huang, Zhiwei; Hwang, Yunho; Aute, Vikrant; Radermacher, Reinhard
2016-01-01
Nature has inspired many scientists and engineers to solve problems through observation and mimicry. One such example is heat transfer enhancement. The enormous natural heat and mass transfer phenomena have led engineers to seek solutions to heat transfer enhancement problems from nature. Fractal geometries are found in respiratory and vascular systems of plants and animals, such as blood vessels, human lungs, leaves, coastlines, etc. Inspired by this, fractal heat exchangers have been develo...
Fractal dimension analysis for spike detection in low SNR extracellular signals.
Salmasi, Mehrdad; Büttner, Ulrich; Glasauer, Stefan
2016-06-01
Many algorithms have been suggested for detection and sorting of spikes in extracellular recording. Nevertheless, it is still challenging to detect spikes in low signal-to-noise ratios (SNR). We propose a spike detection algorithm that is based on the fractal properties of extracellular signals and can detect spikes in low SNR regimes. Semi-intact spikes are low-amplitude spikes whose shapes are almost preserved. The detection of these spikes can significantly enhance the performance of multi-electrode recording systems. Semi-intact spikes are simulated by adding three noise components to a spike train: thermal noise, inter-spike noise, and spike-level noise. We show that simulated signals have fractal properties which make them proper candidates for fractal analysis. Then we use fractal dimension as the main core of our spike detection algorithm and call it fractal detector. The performance of the fractal detector is compared with three frequently used spike detectors. We demonstrate that in low SNR, the fractal detector has the best performance and results in the highest detection probability. It is shown that, in contrast to the other three detectors, the performance of the fractal detector is independent of inter-spike noise power and that variations in spike shape do not alter its performance. Finally, we use the fractal detector for spike detection in experimental data and similar to simulations, it is shown that the fractal detector has the best performance in low SNR regimes. The detection of low-amplitude spikes provides more information about the neural activity in the vicinity of the recording electrodes. Our results suggest using the fractal detector as a reliable and robust method for detecting semi-intact spikes in low SNR extracellular signals.
Directory of Open Access Journals (Sweden)
Qiang Li
2013-01-01
Full Text Available Recently, research on the characteristic changes of scale invariance of seismicity before large earthquakes has received considerable attention. However, in some circumstances, it is not easy to obtain these characteristic changes because the features of seismicity in different regions are various. In this paper, we firstly introduced some important research developments of the characteristic changes of scale invariance of seismicity before large earthquakes, which are of particular importance to the researchers in earthquake forecasting and seismic activity. We secondly discussed the strengths and weaknesses of different scale invariance methods such as the local scaling property, the multifractal spectrum, the Hurst exponent analysis, and the correlation dimension. We finally came up with a constructive suggestion for the research strategy in this topic. Our suggestion is that when people try to obtain the precursory information before large earthquakes or to study the fractal property of seismicity by means of the previous scale invariance methods, the strengths and weaknesses of these methods have to be taken into consideration for the purpose of increasing research efficiency. If they do not consider the strengths and weaknesses of these methods, the efficiency of their research might greatly decrease.
Demand surge following earthquakes
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.
Rundle, J. B.; Donnellan, A.; Grant Ludwig, L.; Turcotte, D. L.; Luginbuhl, M.; Gail, G.
2016-12-01
Nowcasting is a term originating from economics and finance. It refers to the process of determining the uncertain state of the economy or markets at the current time by indirect means. We apply this idea to seismically active regions, where the goal is to determine the current state of the fault system, and its current level of progress through the earthquake cycle. In our implementation of this idea, we use the global catalog of earthquakes, using "small" earthquakes to determine the level of hazard from "large" earthquakes in the region. Our method does not involve any model other than the idea of an earthquake cycle. Rather, we define a specific region and a specific large earthquake magnitude of interest, ensuring that we have enough data to span at least 20 or more large earthquake cycles in the region. We then compute the earthquake potential score (EPS) which is defined as the cumulative probability distribution P(n
Fractal harmonic law and waterproof/dustproof
Directory of Open Access Journals (Sweden)
Kong Hai-Yan
2014-01-01
Full Text Available The fractal harmonic law admits that the friction between the pure water and the moving surface is the minimum when fractal dimensions of water in Angstrom scale are equal to fractal dimensions of the moving surface in micro scale. In the paper, the fractal harmonic law is applied to demonstrate the mechanism of waterproof/ dustproof. The waterproof phenomenon of goose feathers and lotus leaves is illustrated to verify our results and experimental results agree well with our theoretical analysis.
Fractal Structures For Fixed Mems Capacitors
Elshurafa, Amro M.
2014-08-28
An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.
Enhanced Graphene Photodetector with Fractal Metasurface
DEFF Research Database (Denmark)
Fan, Jieran; Wang, Di; DeVault, Clayton
2016-01-01
We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure.......We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure....
Steady laminar flow of fractal fluids
Energy Technology Data Exchange (ETDEWEB)
Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico); Mena, Baltasar [Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Yucatán, 97355 (Mexico); Susarrey, Orlando; Samayoa, Didier [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico)
2017-02-12
We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived. - Highlights: • Equations of Stokes flow of Newtonian fractal fluid are derived. • Pressure distribution in the Newtonian fractal fluid is derived. • Velocity distribution in Poiseuille flow of fractal fluid is found. • Velocity distribution in a steady Couette flow is established.
Fractal Structures For Mems Variable Capacitors
Elshurafa, Amro M.
2014-08-28
In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape separated by a vertical distance from a lower first metal plate with a complementary fractal shape; and a substrate above which the capacitor body is suspended.
Symmetric intersections of Rauzy fractals | Sellami | Quaestiones ...
African Journals Online (AJOL)
In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is re ection through the origin. Given an unimodular irreducible Pisot substitution, we consider the intersection of its Rauzy fractal with the Rauzy fractal of the reverse substitution. This set is ...
Fractal analysis of heart graft acute rejection microscopic images.
Pijet, M; Nozynski, J; Konecka-Mrowka, D; Zakliczynski, M; Hrapkowicz, T; Zembala, M
2014-10-01
Endomyocardial biopsy to evaluate rejection in the transplanted heart is accepted at the "gold standard." The complexity of microscopic images suggested using digital methods for precise evaluating of acute rejection episodes with numerical representation. The aim of the present was study to characterize digitally acute rejection of the transplanted heart using complexity/fractal image analysis. Biopsy samples harvested form 40 adult recipients after orthotropic heart transplantation were collected and rejection grade was evaluated according to the International Society for Heart and Lung Transplantation (0, 1a, 1b, or 3a) at transverse and longitudinal sections. Fifteen representative digital microscope images from each grade were collected and analyzed after Sobel edge detection and binarization. Only mean fractal dimension showed a progressive and significant increase and correlation based on rejection grade using longitudinal sections. Lacunarity and number of foreground pixels showed unequivocal results. Mean fractal diameter could serve as auxiliary digital parameter for grading of acute rejection in the transplanted heart.
Fractal apertures in waveguides, conducting screens and cavities analysis and design
Ghosh, Basudeb; Kartikeyan, M V
2014-01-01
This book deals with the design and analysis of fractal apertures in waveguides, conducting screens and cavities using numerical electromagnetics and field-solvers. The aim is to obtain design solutions with improved accuracy for a wide range of applications. To achieve this goal, a few diverse problems are considered. The book is organized with adequate space dedicated for the design and analysis of fractal apertures in waveguides, conducting screens, and cavities, microwave/millimeter wave applications followed by detailed case-study problems to infuse better insight and understanding of the subject. Finally, summaries and suggestions are given for future work. Fractal geometries were widely used in electromagnetics, specifically for antennas and frequency selective surfaces (FSS). The self-similarity of fractal geometry gives rise to a multiband response, whereas the space-filling nature of the fractal geometries makes it an efficient element in antenna and FSS unit cell miniaturization. Until now, no e...
Spatial Dynamics of Urban Growth Based on Entropy and Fractal Dimension
Chen, Yanguang
2016-01-01
The fractal dimension growth of urban form can be described with sigmoid functions such as logistic function due to squashing effect. The sigmoid curves of fractal dimension suggest a type of spatial replacement dynamics of urban evolution. How to understand the underlying rationale of the fractal dimension curves is a pending problem. This study is based on two previous findings. First, normalized fractal dimension proved to equal normalized spatial entropy; second, a sigmoid function proceeds from an urban-rural interaction model. Defining urban space-filling measurement by spatial entropy, and defining rural space-filling measurement by information gain, we can construct a new urban-rural interaction and coupling model. From this model, we can derive the logistic equation of fractal dimension growth strictly. This indicates that urban growth results from the unity of opposites between spatial entropy increase and information increase. In a city, an increase in spatial entropy is accompanied by a decrease i...
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
, the branching pattern of the retinal vessels demonstrated a higher structural similarity in monozygotic than in dizygotic twin pairs. The retinal vascular fractal dimension was mainly determined by genetic factors, which accounted for 54% of the variation. The genetically predetermination of the retinal......Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs......, the retinal vascular fractal dimension was measured using the box-counting method and compared within monozygotic and dizygotic twin pairs using Pearson correlation coefficients. Falconer's formula and quantitative genetic models were used to determine the genetic component of variation. Results: The mean...
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.
Synergetics and fractals in tribology
Janahmadov, Ahad Kh
2016-01-01
This book examines the theoretical and practical aspects of tribological process using synergy, fractal and multifractal methods, and the fractal and multifractal models of self-similar tribosystems developed on their basis. It provides a comprehensive analysis of their effectiveness, and also considers the method of flicker noise spectroscopy with detailed parameterization of surface roughness friction. All models, problems and solutions are taken and tested on the set of real-life examples of oil-gas industry. The book is intended for researchers, graduate students and engineers specialising in the field of tribology, and also for senior students of technical colleges.
Some recent examples of fractal music
Guerra-Torres, Cesar; Hinojosa-Rivera, Moises; Garza-Garza, Juan Angel; Elizondo-Garza, Fernando J.
2002-11-01
Since the first published studies of fractal music by Mandelbrot and Voss, the relationship between music, mathematics, and fractal geometry has been a very active field of research. It has been found that the music of classical composers can be characterized by fractal or self-affine parameters, which in turn serve as the basis for synthetic fractal music. In this work is presented a brief discussion of the state of the art as well as some recent examples of fractal music, including a live demonstration.
Quantification of the fractal nature of mycelial aggregation in Aspergillus niger submerged cultures
Directory of Open Access Journals (Sweden)
Papagianni Maria
2006-02-01
suggesting that they could be equally used as morphological descriptors. Conclusion Starting from a spore, the mycelium develops as a mass fractal and, depending on culture conditions, it either turns to a surface fractal or remains a mass fractal. Since fractal dimensions give a measure of the degree of complexity and the mass filling properties of an object, it may be possible that a large number of morphological parameters which contribute to the overall complexity of the particles, could be replaced by these indexes effectively.
Fractal ventilation enhances respiratory sinus arrhythmia
Directory of Open Access Journals (Sweden)
Girling Linda G
2005-05-01
Full Text Available Abstract Background Programming a mechanical ventilator with a biologically variable or fractal breathing pattern (an example of 1/f noise improves gas exchange and respiratory mechanics. Here we show that fractal ventilation increases respiratory sinus arrhythmia (RSA – a mechanism known to improve ventilation/perfusion matching. Methods Pigs were anaesthetised with propofol/ketamine, paralysed with doxacurium, and ventilated in either control mode (CV or in fractal mode (FV at baseline and then following infusion of oleic acid to result in lung injury. Results Mean RSA and mean positive RSA were nearly double with FV, both at baseline and following oleic acid. At baseline, mean RSA = 18.6 msec with CV and 36.8 msec with FV (n = 10; p = 0.043; post oleic acid, mean RSA = 11.1 msec with CV and 21.8 msec with FV (n = 9, p = 0.028; at baseline, mean positive RSA = 20.8 msec with CV and 38.1 msec with FV (p = 0.047; post oleic acid, mean positive RSA = 13.2 msec with CV and 24.4 msec with FV (p = 0.026. Heart rate variability was also greater with FV. At baseline the coefficient of variation for heart rate was 2.2% during CV and 4.0% during FV. Following oleic acid the variation was 2.1 vs. 5.6% respectively. Conclusion These findings suggest FV enhances physiological entrainment between respiratory, brain stem and cardiac nonlinear oscillators, further supporting the concept that RSA itself reflects cardiorespiratory interaction. In addition, these results provide another mechanism whereby FV may be superior to conventional CV.
Fractal ventilation enhances respiratory sinus arrhythmia.
Mutch, W Alan C; Graham, M Ruth; Girling, Linda G; Brewster, John F
2005-05-09
Programming a mechanical ventilator with a biologically variable or fractal breathing pattern (an example of 1/f noise) improves gas exchange and respiratory mechanics. Here we show that fractal ventilation increases respiratory sinus arrhythmia (RSA) -- a mechanism known to improve ventilation/perfusion matching. Pigs were anaesthetised with propofol/ketamine, paralysed with doxacurium, and ventilated in either control mode (CV) or in fractal mode (FV) at baseline and then following infusion of oleic acid to result in lung injury. Mean RSA and mean positive RSA were nearly double with FV, both at baseline and following oleic acid. At baseline, mean RSA = 18.6 msec with CV and 36.8 msec with FV (n = 10; p = 0.043); post oleic acid, mean RSA = 11.1 msec with CV and 21.8 msec with FV (n = 9, p = 0.028); at baseline, mean positive RSA = 20.8 msec with CV and 38.1 msec with FV (p = 0.047); post oleic acid, mean positive RSA = 13.2 msec with CV and 24.4 msec with FV (p = 0.026). Heart rate variability was also greater with FV. At baseline the coefficient of variation for heart rate was 2.2% during CV and 4.0% during FV. Following oleic acid the variation was 2.1 vs. 5.6% respectively. These findings suggest FV enhances physiological entrainment between respiratory, brain stem and cardiac nonlinear oscillators, further supporting the concept that RSA itself reflects cardiorespiratory interaction. In addition, these results provide another mechanism whereby FV may be superior to conventional CV.
Anisotropic fractal media by vector calculus in non-integer dimensional space
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.
Integration of Fractal Biosensor in a Digital Microfluidic Platform
Mashraei, Yousof
2016-06-08
The digital microfluidic (DMF) platform introduces many applications in biomedical assays. If it is to be commercially available to the public, it needs to have the essential features of smart sensing and a compact size. In this work, we report on a fractal electrode biosensor that is used for both droplet actuation and sensing C-reactive protein (CRP) concentration levels to assess cardiac disease risk. Our proposed electrode is the first two-terminal electrode design to be integrated into DMF platforms. A simulation of the electrical field distribution shows reduced peak intensities and uniform distribution of the field. When compared to a V-notch square electrode, the fractal electrode shows a superior performance in both aspects, i.e. field uniformity and intensity. These improvements are translated into a successful and responsive actuation of a water droplet with 100V. Likewise, the effective dielectric strength is improved by a 33% increase in the fractal electrode breakdown voltage. Additionally, the capability of the fractal electrode to work as a capacitive biosensor is evaluated with CRP quantification test. Selected fractal electrodes undergo a surface treatment to immobilize anti-CRP antibodies on their surface. The measurement shows a response to the added CRP in capacitance within three minutes. When the untreated electrodes were used for quantification, there was no significant change in capacitance, and this suggested that immobilization was necessary. The electrodes configuration in the fabricated DMF platform allows the fractal electrodes to be selectively used as biosensors, which means the device could be integrated into point-of-care applications.
Fractal Dimension versus Process Complexity
Directory of Open Access Journals (Sweden)
Joost J. Joosten
2016-01-01
Full Text Available We look at small Turing machines (TMs that work with just two colors (alphabet symbols and either two or three states. For any particular such machine τ and any particular input x, we consider what we call the space-time diagram which is basically the collection of consecutive tape configurations of the computation τ(x. In our setting, it makes sense to define a fractal dimension for a Turing machine as the limiting fractal dimension for the corresponding space-time diagrams. It turns out that there is a very strong relation between the fractal dimension of a Turing machine of the above-specified type and its runtime complexity. In particular, a TM with three states and two colors runs in at most linear time, if and only if its dimension is 2, and its dimension is 1, if and only if it runs in superpolynomial time and it uses polynomial space. If a TM runs in time O(xn, we have empirically verified that the corresponding dimension is (n+1/n, a result that we can only partially prove. We find the results presented here remarkable because they relate two completely different complexity measures: the geometrical fractal dimension on one side versus the time complexity of a computation on the other side.
Fractal transforms and feature invariance
B.A.M. Schouten (Ben); P.M. de Zeeuw (Paul)
2000-01-01
htmlabstractIn this paper, fractal transforms are employed with the aim of image recognition. It is known that such transforms are highly sensitive to distortions like a small shift of an image. However, by using features based on statistics kept during the actual decomposition we can derive
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…
Asymptotic Safety, Fractals, and Cosmology
Reuter, Martin; Saueressig, Frank
These lecture notes introduce the basic ideas of the asymptotic safety approach to quantum Einstein gravity (QEG). In particular they provide the background for recent work on the possibly multi-fractal structure of the QEG space-times. Implications of asymptotic safety for the cosmology of the early Universe are also discussed.
Fractal dimensions and porosities of Zoogloea ramigera and Saccharomyces cerevisae aggregates.
Logan, B E; Wilkinson, D B
1991-08-05
The fractal nature microbial aggregates is a function of the type of microorganism and mixing conditions used to develop aggregates. We determined fractal dimensions from length-projected area (D(2)) and length-number scaling (D(3)) relationships. Aggregates of Zoogloea ramigera developed in rotating test tubes were both surface and mass fractals, with fractal dimensions of D(2) = 1.69 +/- 0.11 and D(3)= 1.79 +/- 0.28 (+/-standard deviation), respectively. When we grew this bacteria in a bench-top fermentor, aggregates maintained their surface fractal characteristics (D(2) = 1.78 +/- 0.11) but lost their mass fractal characteristics (D(3) = 2.99 +/- 0.36). Yeast aggregates (Saccharomyces cerevisae) grown in rotating tests tubes had higher average fractal dimensions than bacterial aggregates grown under physically identical conditions, and were also considered fractal (D(2) = 1.92 +/- 0.08 and D(3) = 2.66 +/- 0.34). Aggregates porosity can be expressed in term of a fractal dimensions, but average porosities are higher than expected. The porosities of yeast aggregates (0.9250-0.9966) were similar to porosities of bacterial aggregates (0.9250-0.9966) cultured under the same physical conditions, although bacterial aggregates developed in the reactor had higher average porosities (0.9857-0.9980). These results suggest that that scaling relationships based on fractal geometry may be more useful than equations derived from Euclidean geometry for quantifying the effects of different fluid mechanical environments on aggregates morphology and characteristics such as density, porosity, and projected surface area.
Information entropy of earthquake populations in northeastern Italy and western Slovenia
Bressan, G.; Barnaba, C.; Gentili, S.; Rossi, G.
2017-10-01
The spatio-temporal evolution of eight seismicity populations, preceding and following moderate earthquake sequences occurred in NE-Italy and W-Slovenia, are investigated by means of the normalized Shannon entropy and the fractal dimension. Three phases are recognized in the temporal seismic series. The period preceding the mainshock is characterized by oscillations of the Shannon entropy around a nearly constant level and by fluctuations of the fractal dimension. The phase of mainshock and aftershock sequences is characterized by a significant decrease of the Shannon entropy. A simultaneous marked decrease of the fractal dimension is observed in five cases. After the sequence, the entropy recovers the nearly constant trend before the mainshock and the fractal dimension is characterized by fluctuations. We interpreted the fluctuations of the normalized Shannon entropy and the fractal dimension caused by the coupling between the stress field and the mechanical heterogeneities of the crust that results in spatial and temporal fluctuations of the strain energy.
Lung cancer-a fractal viewpoint.
Lennon, Frances E; Cianci, Gianguido C; Cipriani, Nicole A; Hensing, Thomas A; Zhang, Hannah J; Chen, Chin-Tu; Murgu, Septimiu D; Vokes, Everett E; Vannier, Michael W; Salgia, Ravi
2015-11-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.
Energy Technology Data Exchange (ETDEWEB)
Hofmann, R.B. [Center for Nuclear Waste Regulatory Analyses, San Antonio, TX (United States)
1995-09-01
Analogs are used to understand complex or poorly understood phenomena for which little data may be available at the actual repository site. Earthquakes are complex phenomena, and they can have a large number of effects on the natural system, as well as on engineered structures. Instrumental data close to the source of large earthquakes are rarely obtained. The rare events for which measurements are available may be used, with modfications, as analogs for potential large earthquakes at sites where no earthquake data are available. In the following, several examples of nuclear reactor and liquified natural gas facility siting are discussed. A potential use of analog earthquakes is proposed for a high-level nuclear waste (HLW) repository.
A Fractal Model for the Capacitance of Lunar Dust and Lunar Dust Aggregates
Collier, Michael R.; Stubbs, Timothy J.; Keller, John W.; Farrell, William M.; Marshall, John; Richard, Denis Thomas
2011-01-01
Lunar dust grains and dust aggregates exhibit clumping, with an uneven mass distribution, as well as features that span many spatial scales. It has been observed that these aggregates display an almost fractal repetition of geometry with scale. Furthermore, lunar dust grains typically have sharp protrusions and jagged features that result from the lack of aeolian weathering (as opposed to space weathering) on the Moon. A perfectly spherical geometry, frequently used as a model for lunar dust grains, has none of these characteristics (although a sphere may be a reasonable proxy for the very smallest grains and some glasses). We present a fractal model for a lunar dust grain or aggregate of grains that reproduces (1) the irregular clumpy nature of lunar dust, (2) the presence of sharp points, and (3) dust features that span multiple scale lengths. We calculate the capacitance of the fractal lunar dust analytically assuming fixed dust mass (i.e. volume) for an arbitrary number of fractal levels and compare the capacitance to that of a non-fractal object with the same volume, surface area, and characteristic width. The fractal capacitance is larger than that of the equivalent non-fractal object suggesting that for a given potential, electrostatic forces on lunar dust grains and aggregates are greater than one might infer from assuming dust grains are sphericaL Consequently, electrostatic transport of lunar dust grains, for example lofting, appears more plausible than might be inferred by calculations based on less realistic assumptions about dust shape and associated capacitance.
Applications of fractal analysis to physiology
Glenny, Robb W.; Robertson, H. Thomas; Yamashiro, Stanley; Bassingthwaighte, James B.
2010-01-01
This review describes approaches to the analysis of fractal properties of physiological observations. Fractals are useful to describe the natural irregularity of physiological systems because their irregularity is not truly random and can be demonstrated to have spatial or temporal correlation. The concepts of fractal analysis are introduced from intuitive, visual, and mathematical perspectives. The regional heterogeneities of pulmonary and myocardial flows are discussed as applications of spatial fractal analysis, and methods for estimating a fractal dimension from physiological data are presented. Although the methods used for fractal analyses of physiological data are still under development and will require additional validation, they appear to have great potential for the study of physiology at scales of resolution ranging from the microcirculation to the intact organism. PMID:1885430
Conference on Fractals and Related Fields III
Seuret, Stéphane
2017-01-01
This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.
The Fractal Dimension of the ρ Ophiucus Molecular Cloud Complex
Lee, Yongung; Yi, Di; Kim, Y. S.; Jung, J. H.; Kang, H. W.; Lee, C. H.; Yim, I. S.; Kim, H. G.
2016-12-01
We estimate the fractal dimension of the ρ Ophiuchus Molecular Cloud Complex, associated with star forming regions. We selected a cube (v, l, b) database, obtained with J=1-0 transition lines of \\coand tco at a resolution of 22'' using a multibeam receiver system on the 14-m telescope of the Five College Radio Astronomy Observatory. Using a code developed within IRAF, we identified slice-clouds with two threshold temperatures to estimate the fractal dimension. With threshold temperatures of 2.25 K (3σ) and 3.75 K (5σ), the fractal dimension of the target cloud is estimated to be D = 1.52-1.54, where P ∝ A^{D/2} , which is larger than previous results. We suggest that the sampling rate (spatial resolution) of observed data must be an important parameter when estimating the fractal dimension, and that narrower or wider dispersion around an arbitrary fit line and the intercepts at NP = 100 should be checked whether they relate to rms noise level or characteristic structure of the target cloud. This issue could be investigated by analysing several high resolution databases with different quality (low or moderate sensitivity).
Records in fractal stochastic processes.
Aliakbari, A; Manshour, P; Salehi, M J
2017-03-01
The record statistics in stationary and non-stationary fractal time series is studied extensively. By calculating various concepts in record dynamics, we find some interesting results. In stationary fractional Gaussian noises, we observe a universal behavior for the whole range of Hurst exponents. However, for non-stationary fractional Brownian motions, the record dynamics is crucially dependent on the memory, which plays the role of a non-stationarity index, here. Indeed, the deviation from the results of the stationary case increases by increasing the Hurst exponent in fractional Brownian motions. We demonstrate that the memory governs the dynamics of the records as long as it causes non-stationarity in fractal stochastic processes; otherwise, it has no impact on the record statistics.
Fractals, malware, and data models
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.
Chaos, Fractals and Their Applications
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.
Fractal model of anomalous diffusion.
Gmachowski, Lech
2015-12-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.
The fractal dimension of architecture
Ostwald, Michael J
2016-01-01
Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along...
Fractal properties of financial markets
Budinski-Petković, Lj.; Lončarević, I.; Jakšić, Z. M.; Vrhovac, S. B.
2014-09-01
We present an analysis of the USA stock market using a simple fractal function. Financial bubbles preceding the 1987, 2000 and 2007 crashes are investigated using the Besicovitch-Ursell fractal function. Fits show a good agreement with the S&P 500 data when a complete financial growth is considered, starting at the threshold of the abrupt growth and ending at the peak. Moving the final time of the fitting interval towards earlier dates causes growing discrepancy between two curves. On the basis of a detailed analysis of the financial index behavior we propose a method for identifying the stage of the current financial growth and estimating the time in which the index value is going to reach the maximum.
The eternal fractal in the universe
Winitzki, Serge
2001-01-01
Models of eternal inflation predict a stochastic self-similar geometry of the universe at very large scales and allow existence of points that never thermalize. I explore the fractal geometry of the resulting spacetime, using coordinate-independent quantities. The formalism of stochastic inflation can be used to obtain the fractal dimension of the set of eternally inflating points (the ``eternal fractal''). I also derive a nonlinear branching diffusion equation describing global properties of...
Fractal Analysis On Internet Traffic Time Series
Chong, K. B.; Choo, K. Y.
2002-01-01
Fractal behavior and long-range dependence have been observed in tele-traffic measurement and characterization. In this paper we show results of application of the fractal analysis to internet traffic via various methods. Our result demonstrate that the internet traffic exhibits self-similarity. Time-scale analysis show to be an effective way to characterize the local irregularity. Based on the result of this study, these two Internet time series exhibit fractal characteristic with long-range...
Nonlinear fractals: applications in physiology and ophthalmology
M. V. Zueva
2014-01-01
Fractal geometry and nonlinear dynamics have applications in the field of biology and medicine. Many complex structures of living systems reveal fractal-like geometry. Among them, nonlinearity of human anatomic structures and physiologic functions are of special interest. Here, we review several multidisciplinary studies that demonstrate multi-scale nonlinear complexity of physiological functions and fractal geometry of anatomical structures of a healthy human including retina. With ageing an...
Fractal properties of nanostructured semiconductors
Energy Technology Data Exchange (ETDEWEB)
Zhanabaev, Z.Zh. [Al-Farabi Khazakh National University, Tole bi Street, 96, Almaty 050012 (Kazakhstan); Grevtseva, T.Yu. [Al-Farabi Khazakh National University, Tole bi Street, 96, Almaty 050012 (Kazakhstan)]. E-mail: kenwp@mail.ru
2007-03-15
A theory for the temperature and time dependence of current carrier concentration in semiconductors with different non-equilibrium nanocluster structure has been developed. It was shown that the scale-invariant fractal self-similar and self-affine laws can exist near by the transition point to the equilibrium state. Results of the theory have been compared to the experimental data from electrical properties of semiconductor films with nanoclusters.
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs, the reti...... vasculature may affect the retinal response to potential vascular disease in later life....
Fractal Metrology for biogeosystems analysis
Directory of Open Access Journals (Sweden)
V. Torres-Argüelles
2010-11-01
Full Text Available The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc. while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM. We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
Fractal Metrology for biogeosystems analysis
Torres-Argüelles, V.; Oleschko, K.; Tarquis, A. M.; Korvin, G.; Gaona, C.; Parrot, J.-F.; Ventura-Ramos, E.
2010-11-01
The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay) and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc.) while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM). We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
Two and Three-Phases Fractal Models Application in Soil Saturated Hydraulic Conductivity Estimation
Directory of Open Access Journals (Sweden)
ELNAZ Rezaei abajelu
2017-03-01
(porosity, fractal dimension and the intake air suction head.Some indices like RMSE, AIC and R2 were used to evaluate different fractal models. Results and Discussion: The results of the sensitivity analysis of Rawls - Huang model, showed the least sensitivity to changes in porosity and suction entry air and the most sensitivity to changes in fractal dimension. The saturated hydraulic conductivity is underestimated by increasing the fractal dimension in Rawls - Huang model. The high sensitivity of the combined model to changes in fractal dimension, is considered as one of the model limitations.In other words, fractal dimension underestimation increased the error related to the hydraulic conductivity estimation. Sensitivity analysis of Ks regression model was done among parameters like bulk density, dry density, silt, sand, fractal dimension of particle size and porosity. Results showed less sensitivity to fractal dimension and porosity. The highest RMSE was 0.018 for fractal dimension and porosity (in the range of ±30% changes. The results showed that the amount of clay in the estimation of fractal dimension is of crucial importance. Statistical analyzes indicated the high accuracy of the PSF models based on soil texture data.Error indices showed the high accuracy of Rawls and three-phase fractal (pore- solid- fractal models combination in estimating the Ks value. The results suggest that Huang and Zhang model, with the highest correlation, the least Root Mean Square Error and the least Akaike criteria among the studied fractal models for estimation of the Ks values. Fuentesand Hunt models, overestimated soil saturated hydraulic conductivity. Fuentes et al. (1996 as an experimental fractal model to estimate the saturated hydraulic conductivity indicatedvery poor results. Bird model had higher error values compared with the best model, (RMSE =0.73. This model fit well with the measured values compared to Sepaskhah and Taylor models particularly at low Ksvalues. Taylor's two
Fractal geometry mathematical foundations and applications
Falconer, Kenneth
2013-01-01
The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applica
Inkjet-Printed Ultra Wide Band Fractal Antennas
Maza, Armando Rodriguez
2012-05-01
In this work, Paper-based inkjet-printed Ultra-wide band (UWB) fractal antennas are presented. Three new designs, a combined UWB fractal monopole based on the fourth order Koch Snowflake fractal which utilizes a Sierpinski Gasket fractal for ink reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics. It is shown that fractals prove to be a successful method of reducing fabrication cost in inkjet printed antennas while retaining or enhancing printed antenna performance.
A variational principle for the Hausdorff dimension of fractal sets
DEFF Research Database (Denmark)
Olsen, Lars; Cutler, Colleen D.
1994-01-01
Matematik, fraktal (fractal), Hausdorff dimension, Renyi dimension, pakke dimension (packing dimension)......Matematik, fraktal (fractal), Hausdorff dimension, Renyi dimension, pakke dimension (packing dimension)...
New Approach to Fractal Approximation of Vector-Functions
National Research Council Canada - National Science Library
Igudesman, Konstantin; Davletbaev, Marsel; Shabernev, Gleb
2015-01-01
This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal...
Charles Darwin's earthquake reports
Galiev, Shamil
2010-05-01
As it is the 200th anniversary of Darwin's birth, 2009 has also been marked as 170 years since the publication of his book Journal of Researches. During the voyage Darwin landed at Valdivia and Concepcion, Chile, just before, during, and after a great earthquake, which demolished hundreds of buildings, killing and injuring many people. Land was waved, lifted, and cracked, volcanoes awoke and giant ocean waves attacked the coast. Darwin was the first geologist to observe and describe the effects of the great earthquake during and immediately after. These effects sometimes repeated during severe earthquakes; but great earthquakes, like Chile 1835, and giant earthquakes, like Chile 1960, are rare and remain completely unpredictable. This is one of the few areas of science, where experts remain largely in the dark. Darwin suggested that the effects were a result of ‘ …the rending of strata, at a point not very deep below the surface of the earth…' and ‘…when the crust yields to the tension, caused by its gradual elevation, there is a jar at the moment of rupture, and a greater movement...'. Darwin formulated big ideas about the earth evolution and its dynamics. These ideas set the tone for the tectonic plate theory to come. However, the plate tectonics does not completely explain why earthquakes occur within plates. Darwin emphasised that there are different kinds of earthquakes ‘...I confine the foregoing observations to the earthquakes on the coast of South America, or to similar ones, which seem generally to have been accompanied by elevation of the land. But, as we know that subsidence has gone on in other quarters of the world, fissures must there have been formed, and therefore earthquakes...' (we cite the Darwin's sentences following researchspace. auckland. ac. nz/handle/2292/4474). These thoughts agree with results of the last publications (see Nature 461, 870-872; 636-639 and 462, 42-43; 87-89). About 200 years ago Darwin gave oneself airs by the
... to the Atlantic Ocean, around Africa, Asia, and Australia, and under the Pacific Ocean to the west ... are similar to earthquakes, but occur within the ice sheet itself instead of the land underneath the ...
Fractal Stability Border in Plane Couette Flow
Schmiegel, A; Schmiegel, Armin; Eckhardt, Bruno
1997-01-01
We study the dynamics of localised perturbations in plane Couette flow with periodic lateral boundary conditions. For small Reynolds number and small amplitude of the initial state the perturbation decays on a viscous time scale $t \\propto Re$. For Reynolds number larger than about 200, chaotic transients appear with life times longer than the viscous one. Depending on the type of the perturbation isolated initial conditions with infinite life time appear for Reynolds numbers larger than about 270--320. In this third regime, the life time as a function of Reynolds number and amplitude is fractal. These results suggest that in the transition region the turbulent dynamics is characterised by a chaotic repeller rather than an attractor.
Fractal analysis of heart rate variability and mortality after an acute myocardial infarction
DEFF Research Database (Denmark)
Tapanainen, Jari M; Thomsen, Poul Erik Bloch; Køber, Lars
2002-01-01
The recently developed fractal analysis of heart rate (HR) variability has been suggested to provide prognostic information about patients with heart failure. This prospective multicenter study was designed to assess the prognostic significance of fractal and traditional HR variability parameters...... in a large, consecutive series of survivors of an acute myocardial infarction (AMI). A consecutive series of 697 patients were recruited to participate 2 to 7 days after an AMI in 3 Nordic university hospitals. The conventional time-domain and spectral parameters and the newer fractal scaling indexes of HR...... variability were analyzed from 24-hour RR interval recordings. During the mean follow-up of 18.4 +/- 6.5 months, 49 patients (7.0%) died. Of all the risk variables, a reduced short-term fractal scaling exponent (alpha(1)
Design of LTCC Based Fractal Antenna
AdbulGhaffar, Farhan
2010-09-01
The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array has been designed for the first time on Low Temperature Co-fired Ceramic (LTCC) based substrate. LTCC provides a suitable platform for the development of these antennas due to its properties of vertical stack up and embedded passives. The complete antenna concept involves integration of this fractal antenna array with a Fresnel lens antenna providing a total gain of 15dB which is appropriate for medium range radar applications. The thesis also presents a comparison between the designed fractal antenna and a conventional patch antenna outlining the advantages of fractal antenna over the later one. The fractal antenna has a bandwidth of 1.8 GHz which is 7.5% of the centre frequency (24GHz) as compared to 1.9% of the conventional patch antenna. Furthermore the fractal design exhibits a size reduction of 53% as compared to the patch antenna. In the end a sensitivity analysis is carried out for the fractal antenna design depicting the robustness of the proposed design against the typical LTCC fabrication tolerances.
Chaos and fractals an elementary introduction
Feldman, David P
2012-01-01
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.
Fractal analysis of polar bear hairs
Directory of Open Access Journals (Sweden)
Wang Qing-Li
2015-01-01
Full Text Available Hairs of a polar bear (Ursus maritimus are of superior properties such as the excellent thermal protection. Why do polar bears can resist such cold environment? The paper concludes that its fractal porosity plays an important role, and its fractal dimensions are very close to the golden mean, 1.618, revealing the possible optimal structure of polar bear hair.
Fractal basins in an ecological model
Directory of Open Access Journals (Sweden)
I. Djellit
2013-09-01
Full Text Available Complex dynamics is detected in an ecological model of host-parasitoid interaction. It illustrates fractalization of basins with self-similarity and chaotic attractors. This paper describes these dynamic behaviors, bifurcations, and chaos. Fractals basins are displayed by numerical simulations.
Undergraduate Experiment with Fractal Diffraction Gratings
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…
[Molecular structure and fractal analysis of oligosaccharide].
Liu, Wen-long; Wang, Lu-man; He, Dong-qi; Zhang, Tian-lan; Gou, Bao-di; Li, Qing
2014-10-18
To propose a calculation method of oligosaccharides' fractal dimension, and to provide a new approach to studying the drug molecular design and activity. By using the principle of energy optimization and computer simulation technology, the steady structures of oligosaccharides were found, and an effective way of oligosaccharides fractal dimension's calculation was further established by applying the theory of box dimension to the chemical compounds. By using the proposed method, 22 oligosaccharides' fractal dimensions were calculated, with the mean 1.518 8 ± 0.107 2; in addition, the fractal dimensions of the two activity multivalent oligosaccharides which were confirmed by experiments, An-2 and Gu-4, were about 1.478 8 and 1.516 0 respectively, while C-type lectin-like receptor Dectin-1's fractal dimension was about 1.541 2. The experimental and computational results were expected to help to find a class of glycoside drugs whose target receptor was Dectin-1. Fractal dimension, differing from other known macro parameters, is a useful tool to characterize the compound molecules' microscopic structure and function, which may play an important role in the molecular design and biological activity study. In the process of oligosaccharides drug screening, the fractal dimension of receptor and designed oligosaccharides or glycoclusters can be calculated respectively. The oligosaccharides with fractal dimension close to that of target receptor should then take priority compared with others, to get the drug molecules with latent activity.
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP
1994-01-01
To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We
Fractal Image Coding with Digital Watermarks
Directory of Open Access Journals (Sweden)
Z. Klenovicova
2000-12-01
Full Text Available In this paper are presented some results of implementation of digitalwatermarking methods into image coding based on fractal principles. Thepaper focuses on two possible approaches of embedding digitalwatermarks into fractal code of images - embedding digital watermarksinto parameters for position of similar blocks and coefficients ofblock similarity. Both algorithms were analyzed and verified on grayscale static images.
Fractality and Lapidus zeta functions at infinity
Radunović, Goran
2015-01-01
We study fractality of unbounded sets of finite Lebesgue measure at infinity by introducing the notions of Minkowski dimension and content at infinity. We also introduce the Lapidus zeta function at infinity, study its properties and demonstrate its use in analysis of fractal properties of unbounded sets at infinity.
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP; SCHWARZ, UJ
1991-01-01
To study the structure of interstellar clouds we used the so-called perimeter-area relation to estimate fractal dimensions. We studied the reliability of the method by applying it to artificial fractals and discuss some of the problems and pitfalls. Results for two different cloud types
... dug across a fault to learn about past earthquakes. Science Fair Projects A GPS instrument measures slow movements of the ground. Become an Earthquake Scientist Cool Earthquake Facts Today in Earthquake History ...
Earthquake Hazards Program: Earthquake Scenarios
U.S. Geological Survey, Department of the Interior — A scenario represents one realization of a potential future earthquake by assuming a particular magnitude, location, and fault-rupture geometry and estimating...
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.
Fractal organization of feline oocyte cytoplasm
Directory of Open Access Journals (Sweden)
G De Vico
2009-06-01
Full Text Available The present study aimed at verifying whether immature cat oocytes with morphologic irregular cytoplasm display selfsimilar features which can be analytically described by fractal analysis. Original images of oocytes collected by ovariectomy were acquired at a final magnification of 400 X with a CCD video camera connected to an optic microscope. After greyscale thresholding segmentation of cytoplasm, image profiles were submitted to fractal analysis using FANAL++, a program which provided an analytical standard procedure for determining the fractal dimension (FD. The presentation of the oocyte influenced the magnitude of the fractal dimension with the highest FD of 1.91 measured on grey-dark cytoplasm characterized by a highly connected network of lipid droplets and intracellular membranes. Fractal analysis provides an effective quantitative descriptor of the real cytoplasm morphology, which can influence the acquirement of in vitro developmental competence, without introducing any bias or shape approximation and thus contributes to an objective and reliable classification of feline oocytes.
Fractal Analysis of Rock Joint Profiles
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.
A random walk through fractal dimensions
Kaye, Brian H
2008-01-01
Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science.From reviews of the first edition:''...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems.'' MRS Bulletin
Designing fractal nanostructured biointerfaces for biomedical applications.
Zhang, Pengchao; Wang, Shutao
2014-06-06
Fractal structures in nature offer a unique "fractal contact mode" that guarantees the efficient working of an organism with an optimized style. Fractal nanostructured biointerfaces have shown great potential for the ultrasensitive detection of disease-relevant biomarkers from small biomolecules on the nanoscale to cancer cells on the microscale. This review will present the advantages of fractal nanostructures, the basic concept of designing fractal nanostructured biointerfaces, and their biomedical applications for the ultrasensitive detection of various disease-relevant biomarkers, such microRNA, cancer antigen 125, and breast cancer cells, from unpurified cell lysates and the blood of patients. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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.
Seismogenesis and earthquake triggering during the Van (Turkey) 2011 seismic sequence
Bayrak, Yusuf; Yadav, R. B. S.; Kalafat, Doğan; Tsapanos, T. M.; Çınar, Hakan; Singh, A. P.; Bayrak, Erdem; Yılmaz, Şeyda; Öcal, Feyza; Koravos, G.
2013-08-01
A unique and very interesting earthquake of magnitude Mw 7.2 occurred in the Van region of Turkey on October 23, 2011 that caused a heavy loss of human lives and properties. The earthquake occurred on a blind oblique thrust fault oriented towards the NE-SW direction and dipping towards NW as evidenced by focal mechanism solution and aftershock distribution. In this study, we analyzed the seismogenesis and earthquake triggering during this sequence with the help of estimated seismological parameters (b-value of frequency-magnitude relation, p-value of aftershocks temporal decay and D-value of fractal dimension), 2D mapping of b- and p-values, 3D mapping of b-value and coseismic Coulomb stress modeling. The estimated seismic b-value equal to 0.89 reveals that the mainshock occurred in a highly stressed region and sequence comprised larger magnitude aftershocks due to the presence of large size asperities within the rupture zone. The normal estimate of p-value (0.98) suggests a tectonic genesis of the aftershocks sequence. The estimated D-value equal to 1.80 reveals that rupture propagated in a two-dimensional plane filled up by fractures. The spatial 2D and 3D mapping of seismic b-value suggests that the Van earthquake originated in a highly heterogeneous fractured rock matrix with fluid intrusions into it at deeper depth beneath the mainshock hypocenter region. The estimated coseismic Coulomb stress using the variable slip model for depth range 0-30 km exhibits a 'butterfly' pattern and most of the aftershocks fall (90%) in the region of enhanced Coulomb stress. This suggests that most of the aftershock activities have been triggered by transfer of positive Coulomb stress due to coseismic slip of the mainshock. The results estimated in the present study have potential useful implications in future seismic hazard assessment and risk mitigation in Van and the surrounding regions.
Connecting slow earthquakes to huge earthquakes
Obara, Kazushige; Kato, Aitaro
2016-01-01
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 th...
Detecting Blind Fault with Fractal and Roughness Factors from High Resolution LiDAR DEM at Taiwan
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.
Pre-Service Teachers' Concept Images on Fractal Dimension
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…
Fractal gait patterns are retained after entrainment to a fractal stimulus.
Rhea, Christopher K; Kiefer, Adam W; Wittstein, Matthew W; Leonard, Kelsey B; MacPherson, Ryan P; Wright, W Geoffrey; Haran, F Jay
2014-01-01
Previous work has shown that fractal patterns in gait can be altered by entraining to a fractal stimulus. However, little is understood about how long those patterns are retained or which factors may influence stronger entrainment or retention. In experiment one, participants walked on a treadmill for 45 continuous minutes, which was separated into three phases. The first 15 minutes (pre-synchronization phase) consisted of walking without a fractal stimulus, the second 15 minutes consisted of walking while entraining to a fractal visual stimulus (synchronization phase), and the last 15 minutes (post-synchronization phase) consisted of walking without the stimulus to determine if the patterns adopted from the stimulus were retained. Fractal gait patterns were strengthened during the synchronization phase and were retained in the post-synchronization phase. In experiment two, similar methods were used to compare a continuous fractal stimulus to a discrete fractal stimulus to determine which stimulus type led to more persistent fractal gait patterns in the synchronization and post-synchronization (i.e., retention) phases. Both stimulus types led to equally persistent patterns in the synchronization phase, but only the discrete fractal stimulus led to retention of the patterns. The results add to the growing body of literature showing that fractal gait patterns can be manipulated in a predictable manner. Further, our results add to the literature by showing that the newly adopted gait patterns are retained for up to 15 minutes after entrainment and showed that a discrete visual stimulus is a better method to influence retention.
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.
Snow metamorphism: A fractal approach
Carbone, Anna; Chiaia, Bernardino M.; Frigo, Barbara; Türk, Christian
2010-09-01
Snow is a porous disordered medium consisting of air and three water phases: ice, vapor, and liquid. The ice phase consists of an assemblage of grains, ice matrix, initially arranged over a random load bearing skeleton. The quantitative relationship between density and morphological characteristics of different snow microstructures is still an open issue. In this work, a three-dimensional fractal description of density corresponding to different snow microstructure is put forward. First, snow density is simulated in terms of a generalized Menger sponge model. Then, a fully three-dimensional compact stochastic fractal model is adopted. The latter approach yields a quantitative map of the randomness of the snow texture, which is described as a three-dimensional fractional Brownian field with the Hurst exponent H varying as continuous parameters. The Hurst exponent is found to be strongly dependent on snow morphology and density. The approach might be applied to all those cases where the morphological evolution of snow cover or ice sheets should be conveniently described at a quantitative level.
Archaeon and archaeal virus diversity classification via sequence entropy and fractal dimension
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.
Correlation of optical properties with the fractal microstructure of black molybdenum coatings
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Barrera, Enrique; Gonzalez, Federico [Area de Energia, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico); Rodriguez, Eduardo [Area de Computacion y Sistemas, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico); Alvarez-Ramirez, Jose, E-mail: jjar@xanum.uam.mx [Area de Energia, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico)
2010-01-01
Coating is commonly used for improving the optical properties of surfaces for solar collector applications. The coating morphology depends on the deposition conditions, and this determines the final optical characteristics. Coating morphologies are irregular and of fractal nature, so a suitable approach for its characterization should use methods borrowed from fractal analysis. The aim of this work is to study the fractal characteristics of black molybdenum coatings on copper and to relate the fractal parameters to the optical properties. To this end, coating surfaces were prepared via immersion in a solution of ammonium paramolybdate for different deposition periods. The fractal analysis was carried out for SEM and AFM images of the coating surface and the fractal properties were obtained with a recently developed high-dimensional extension of the well-known detrended fluctuation analysis (DFA). The most salient parameter drawn from the application of the DFA is the Hurst index, a parameter related to the roughness of the coating surface, and the multifractality index, which is related to the non-linearity features of the coating morphology. The results showed that optical properties, including absorptance and emittance, are decreasing functions of the Hurst and multifractality indices. This suggests that coating surfaces with high absorptance and emittance values are related to complex coating morphologies conformed within a non-linear structure.
Predicting beauty: fractal dimension and visual complexity in art.
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.
On the ubiquitous presence of fractals and fractal concepts in pharmaceutical sciences: a review.
Pippa, Natassa; Dokoumetzidis, Aristides; Demetzos, Costas; Macheras, Panos
2013-11-18
Fractals have been very successful in quantifying nature's geometrical complexity, and have captured the imagination of scientific community. The development of fractal dimension and its applications have produced significant results across a wide variety of biomedical applications. This review deals with the application of fractals in pharmaceutical sciences and attempts to account the most important developments in the fields of pharmaceutical technology, especially of advanced Drug Delivery nano Systems and of biopharmaceutics and pharmacokinetics. Additionally, fractal kinetics, which has been applied to enzyme kinetics, drug metabolism and absorption, pharmacokinetics and pharmacodynamics are presented. This review also considers the potential benefits of using fractal analysis along with considerations of nonlinearity, scaling, and chaos as calibration tools to obtain information and more realistic description on different parts of pharmaceutical sciences. As a conclusion, the purpose of the present work is to highlight the presence of fractal geometry in almost all fields of pharmaceutical research. Copyright © 2013 Elsevier B.V. All rights reserved.
Multifractal analysis of earthquakes in Kumaun Himalaya and its surrounding region
Roy, P. N. S.; Mondal, S. K.
2012-08-01
Himalayan seismicity is related to continuing northward convergence of Indian plate against Eurasian plate. Earthquakes in this region are mainly caused due to release of elastic strain energy. The Himalayan region can be attributed to highly complex geodynamic process and therefore is best suited for multifractal seismicity analysis. Fractal analysis of earthquakes (mb ≥ 3.5) occurred during 1973-2008 led to the detection of a clustering pattern in the narrow time span. This clustering was identified in three windows of 50 events each having low spatial correlation fractal dimension ( D C ) value 0.836, 0.946 and 0.285 which were mainly during the span of 1998 to 2005. This clustering may be considered as an indication of a highly stressed region. The Guttenberg Richter b-value was determined for the same subsets considered for the D C estimation. Based on the fractal clustering pattern of events, we conclude that the clustered events are indicative of a highly stressed region of weak zone from where the rupture propagation eventually may nucleate as a strong earthquake. Multifractal analysis gave some understanding of the heterogeneity of fractal structure of the seismicity and existence of complex interconnected structure of the Himalayan thrust systems. The present analysis indicates an impending strong earthquake, which might help in better hazard mitigation for the Kumaun Himalaya and its surrounding region.
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.
Measurement Based Quantum Computation on Fractal Lattices
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Michal Hajdušek
2010-06-01
Full Text Available In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.
Heat diffusion in fractal geometry cooling surface
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Ramšak Matjaz
2012-01-01
Full Text Available In the paper the numerical simulation of heat diffusion in the fractal geometry of Koch snowflake is presented using multidomain mixed Boundary Element Method. The idea and motivation of work is to improve the cooling of small electronic devices using fractal geometry of surface similar to cooling ribs. The heat diffusion is assumed as the only principle of heat transfer. The results are compared to the heat flux of a flat surface. The limiting case of infinite small fractal element is computed using Richardson extrapolation.
Silica fractal atomic clusters saturated with OH
Olivi-Tran, N
2003-01-01
We constructed regular fractal SiOH atomic clusters which pending bonds are saturated with OH molecules. We calculated the binding energies of these clusters as well as for sp sup 2 hybridization as for sp sup 3 hybridizations. The result are the following: for the two hybridizations, the total binding energies have a linear dependence on the size of the fractal cluster, which comes directly from the scaling law of the fractal characteristic of the building of the cluster. We related by a scaling law, the number of electronic bonds and the total bonding energy.
Fractal boundaries in chaotic hamiltonian systems
Viana, R. L.; Mathias, A. C.; Marcus, F. A.; Kroetz, T.; Caldas, I. L.
2017-10-01
Fractal structures are typically present in the dynamics of chaotic orbits in non-integrable open Hamiltonian systems and result from the extremely complicated nature of the invariant manifolds of unstable periodic orbits. Exit basins, the set of initial conditions leading to orbits escaping through a given exit, have very frequently fractal boundaries. In this work we analyze exit basin boundaries in a dynamical system of physical interest, namely the motion of charged particles in a magnetized plasma subjected to electrostatic drift waves, and characterize in a quantitative way the fractality of these structures and their observable consequences, as the final-state uncertainty.
What paint can tell us: A fractal analysis of neurological changes in seven artists.
Forsythe, Alex; Williams, Tamsin; Reilly, Ronan G
2017-01-01
The notion that artistic capability increases with dementia is both novel and largely unsupported by available literature. Recent research has suggested an emergence of artistic capabilities to be a by-product of involuntary behaviour seen with dementia, as opposed to a progression in original thinking (de Souza, et al., 2010). A far more complementary explanation comes from Hannemann (2006), who suggests that art offers an outlet for dementia patients to refine and sharpen their cognitive abilities. As dementia severely impedes linguistic skills, non-verbal therapeutic methods such as painting can permit dementia patients to express themselves in a way not possible verbally. Fractal analysis has been used to determine the authenticity of major works of art. Taylor et al., (1999) found that through a fractal analysis of Jackson Pollock's paintings it was possible to distinguish authentic works from a large collection of fakes, demonstrating that when artists paint they instill within their work their own pattern of unique fractal behaviour. Can age-indexed variations in the fractal dimension of the works of artists anticipate specific cognitive deteriorations? To answer this question we analysed age-related variations in the fractal dimension of a large corpus of digital images (n = 2092) of work created by seven notable artists who experienced both normal ageing and neurodegenerative disorders. The results of our analysis showed that patterns of change in the fractal dimension of the paintings differentiated artists who suffered neurological deterioration from those of normal aging controls. These findings are of importance for two reasons. Our work adds to studies that demonstrate that fractal analysis has the potential to determine the provenance of paintings. Secondly, our work suggests that may be possible to identify a-typical changes in the structure of an artist's work; changes that may be early indicators of the onset of neurological deterioration. (Psyc
Directory of Open Access Journals (Sweden)
María Eugenia Torres
2007-01-01
Full Text Available En este trabajo comparamos tres métodos diferentes utilizados para estimar el exponente de Hurst, y analizamos su eficiencia cuando son aplicados a series de datos de diferentes longitudes. Se analizan series temporales de fBm sintetizada pura y con tendencias sinusoidales superpuestas. Mostraremos que los tres métodos aquí discutidos, DFA, basado en wavelets y de variaciones discretas, no sólo son altamente dependientes de la longitud de la señal, sino también del orden o número de los momentos (polinómico, regularidad wavelet o variaciones discretas. Para longitudes de datos suficientemente grandes (superiores a 212, los métodos basados en wavelets y de variaciones discretas mostraron ser menos sesgados y más estables para señales fBm simuladas. Mostraremos que el método de DFA, más utilizado en el ambiente biomédico, es el que proporciona peores estimaciones, arrojando resultados ambiguos cuando son aplicados a señales biológicas de diferentes longitudes o con diferentes parámetros de estimación, sin que pueda considerarse a ninguno de los otros dos como métodos confiables en el momento de desear obtener resultados de relevancia física o fisiológica. Los resultados obtenidos indican que debería procederse con más cautela cuando se trata de obtener conclusiones fisiológicas a partir de estimaciones realizadas a partir de señales reales.
Seismology: dynamic triggering of earthquakes.
Gomberg, Joan; Johnson, Paul
2005-10-06
After an earthquake, numerous smaller shocks are triggered over distances comparable to the dimensions of the mainshock fault rupture, although they are rare at larger distances. Here we analyse the scaling of dynamic deformations (the stresses and strains associated with seismic waves) with distance from, and magnitude of, their triggering earthquake, and show that they can cause further earthquakes at any distance if their amplitude exceeds several microstrain, regardless of their frequency content. These triggering requirements are remarkably similar to those measured in the laboratory for inducing dynamic elastic nonlinear behaviour, which suggests that the underlying physics is similar.
Fractal cartography of urban areas.
Encarnação, Sara; Gaudiano, Marcos; Santos, Francisco C; Tenedório, José A; Pacheco, Jorge M
2012-01-01
In a world in which the pace of cities is increasing, prompt access to relevant information is crucial to the understanding and regulation of land use and its evolution in time. In spite of this, characterization and regulation of urban areas remains a complex process, requiring expert human intervention, analysis and judgment. Here we carry out a spatio-temporal fractal analysis of a metropolitan area, based on which we develop a model which generates a cartographic representation and classification of built-up areas, identifying (and even predicting) those areas requiring the most proximate planning and regulation. Furthermore, we show how different types of urban areas identified by the model co-evolve with the city, requiring policy regulation to be flexible and adaptive, acting just in time. The algorithmic implementation of the model is applicable to any built-up area and simple enough to pave the way for the automatic classification of urban areas worldwide.
Fractal analysis reveals reduced complexity of retinal vessels in CADASIL.
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Michele Cavallari
Full Text Available The Cerebral Autosomal Dominant Arteriopathy with Subcortical Infarcts and Leukoencephalopathy (CADASIL affects mainly small cerebral arteries and leads to disability and dementia. The relationship between clinical expression of the disease and progression of the microvessel pathology is, however, uncertain as we lack tools for imaging brain vessels in vivo. Ophthalmoscopy is regarded as a window into the cerebral microcirculation. In this study we carried out an ophthalmoscopic examination in subjects with CADASIL. Specifically, we performed fractal analysis of digital retinal photographs. Data are expressed as mean fractal dimension (mean-D, a parameter that reflects complexity of the retinal vessel branching. Ten subjects with genetically confirmed diagnosis of CADASIL and 10 sex and age-matched control subjects were enrolled. Fractal analysis of retinal digital images was performed by means of a computer-based program, and the data expressed as mean-D. Brain MRI lesion volume in FLAIR and T1-weighted images was assessed using MIPAV software. Paired t-test was used to disclose differences in mean-D between CADASIL and control groups. Spearman rank analysis was performed to evaluate potential associations between mean-D values and both disease duration and disease severity, the latter expressed as brain MRI lesion volumes, in the subjects with CADASIL. The results showed that mean-D value of patients (1.42±0.05; mean±SD was lower than control (1.50±0.04; p = 0.002. Mean-D did not correlate with disease duration nor with MRI lesion volumes of the subjects with CADASIL. The findings suggest that fractal analysis is a sensitive tool to assess changes of retinal vessel branching, likely reflecting early brain microvessel alterations, in CADASIL patients.
Model of fractal aggregates induced by shear
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Wan Zhanhong
2013-01-01
Full Text Available It is an undoubted fact that particle aggregates from marine, aerosol, and engineering systems have fractal structures. In this study, fractal geometry is used to describe the morphology of irregular aggregates. The mean-field theory is employed to solve coagulation kinetic equation of aggregates. The Taylor-expansion method of moments in conjunction with the self-similar fractal characteristics is used to represent the particulate field. The effect of the target fractal dimensions on zeroth-order moment, second-order moment, and geometric standard deviation of the aggregates is explored. Results show that the developed moment method is an efficient and powerful approach to solving such evolution equations.
Fractals and Hidden Symmetries in DNA
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Carlo Cattani
2010-01-01
complex representation, together with the corresponding walks on DNA; in particular, it is shown that DNA walks are fractals. Finally, by using the wavelet analysis, the existence of symmetries is proven.
Fractal aspects of calcium binding protein structures
Energy Technology Data Exchange (ETDEWEB)
Isvoran, Adriana [West University of Timisoara, Department of Chemistry, Pestalozzi 16, 300115 Timisoara (Romania)], E-mail: aisvoran@cbg.uvt.ro; Pitulice, Laura [West University of Timisoara, Department of Chemistry, Pestalozzi 16, 300115 Timisoara (Romania); Craescu, Constantin T. [INSERM U759/Institute Curie-Recherche, Centre Universitaire Paris-Sud, Batiment 112, 91405 Orsay (France); Chiriac, Adrian [West University of Timisoara, Department of Chemistry, Pestalozzi 16, 300115 Timisoara (Romania)
2008-03-15
The structures of EF-hand calcium binding proteins may be classified into two distinct groups: extended and compact structures. In this paper we studied 20 different structures of calcium binding proteins using the fractal analysis. Nine structures show extended shapes, one is semi-compact and the other 10 have compact shapes. Our study reveals different fractal characteristics for protein backbones belonging to different structural classes and these observations may be correlated to the physicochemical forces governing the protein folding.
Pulse regime in formation of fractal fibers
Energy Technology Data Exchange (ETDEWEB)
Smirnov, B. M., E-mail: bmsmirnov@gmail.com [Joint Institute for High Temperatures (Russian Federation)
2016-11-15
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 gas 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.
The utility of fractal analysis in clinical neuroscience.
John, Ann M; Elfanagely, Omar; Ayala, Carlos A; Cohen, Michael; Prestigiacomo, Charles J
2015-01-01
Physicians and scientists can use fractal analysis as a tool to objectively quantify complex patterns found in neuroscience and neurology. Fractal analysis has the potential to allow physicians to make predictions about clinical outcomes, categorize pathological states, and eventually generate diagnoses. In this review, we categorize and analyze the applications of fractal theory in neuroscience found in the literature. We discuss how fractals are applied and what evidence exists for fractal analysis in neurodegeneration, neoplasm, neurodevelopment, neurophysiology, epilepsy, neuropharmacology, and cell morphology. The goal of this review is to introduce the medical community to the utility of applying fractal theory in clinical neuroscience.
Connecting slow earthquakes to huge earthquakes.
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.
Directory of Open Access Journals (Sweden)
Xu Jinze
2016-01-01
Full Text Available In this paper, we present the fractal complex transform via a local fractional derivative. The traveling wave solutions for the fractal Korteweg-de Vries equations within local fractional derivative are obtained based on the special functions defined on Cantor sets. The technology is a powerful tool for solving the local fractional non-linear partial differential equations.
Parvez, Imtiyaz A.; Nekrasova, Anastasia; Kossobokov, Vladimir
2017-03-01
The Gujarat state of India is one of the most seismically active intercontinental regions of the world. Historically, it has experienced many damaging earthquakes including the devastating 1819 Rann of Kachchh and 2001 Bhuj earthquakes. The effect of the later one is grossly underestimated by the Global Seismic Hazard Assessment Program (GSHAP). To assess a more adequate earthquake hazard for the state of Gujarat, we apply Unified Scaling Law for Earthquakes (USLE), which generalizes the Gutenberg-Richter recurrence relation taking into account naturally fractal distribution of earthquake loci. USLE has evident implications since any estimate of seismic hazard depends on the size of the territory considered and, therefore, may differ dramatically from the actual one when scaled down to the proportion of the area of interest (e.g. of a city) from the enveloping area of investigation. We cross-compare the seismic hazard maps compiled for the same standard regular grid 0.2° × 0.2° (1) in terms of design ground acceleration based on the neo-deterministic approach, (2) in terms of probabilistic exceedance of peak ground acceleration by GSHAP, and (3) the one resulted from the USLE application. Finally, we present the maps of seismic risks for the state of Gujarat integrating the obtained seismic hazard, population density based on India's Census 2011 data, and a few model assumptions of vulnerability.
Fractal Dimension in Epileptic EEG Signal Analysis
Uthayakumar, R.
Fractal Analysis is the well developed theory in the data analysis of non-linear time series. Especially Fractal Dimension is a powerful mathematical tool for modeling many physical and biological time signals with high complexity and irregularity. Fractal dimension is a suitable tool for analyzing the nonlinear behaviour and state of the many chaotic systems. Particularly in analysis of chaotic time series such as electroencephalograms (EEG), this feature has been used to identify and distinguish specific states of physiological function.Epilepsy is the main fatal neurological disorder in our brain, which is analyzed by the biomedical signal called Electroencephalogram (EEG). The detection of Epileptic seizures in the EEG Signals is an important tool in the diagnosis of epilepsy. So we made an attempt to analyze the EEG in depth for knowing the mystery of human consciousness. EEG has more fluctuations recorded from the human brain due to the spontaneous electrical activity. Hence EEG Signals are represented as Fractal Time Series.The algorithms of fractal dimension methods have weak ability to the estimation of complexity in the irregular graphs. Divider method is widely used to obtain the fractal dimension of curves embedded into a 2-dimensional space. The major problem is choosing initial and final step length of dividers. We propose a new algorithm based on the size measure relationship (SMR) method, quantifying the dimensional behaviour of irregular rectifiable graphs with minimum time complexity. The evidence for the suitability (equality with the nature of dimension) of the algorithm is illustrated graphically.We would like to demonstrate the criterion for the selection of dividers (minimum and maximum value) in the calculation of fractal dimension of the irregular curves with minimum time complexity. For that we design a new method of computing fractal dimension (FD) of biomedical waveforms. Compared to Higuchi's algorithm, advantages of this method include
Lerma, C; Martinez-Martinez, L-A; Ruiz, N; Vargas, A; Infante, O; Martinez-Lavin, M
2016-01-01
The prevailing linear reductionist medical model seems unable to explain complex multisymptomatic illnesses such as fibromyalgia (FM) and similar maladies. Paradigms derived from the complexity theory may provide a coherent framework for these elusive illnesses. Along these lines is the proposal that FM represents a degradation of our main complex adaptive system (the autonomic nervous system, ANS), in a failed effort to adjust to a hostile environment. Healthy complex systems have fractal structures. Heart rate fractal-like variability reflects resilient ANS performance. Our aim was to measure the heart rate variability (HRV) fractal scaling index in FM patients and to correlate this index with clinical symptoms. We studied 30 women with FM and 30 controls. All participants filled out questionnaires assessing the severity of FM. The HRV fractal scaling index was estimated during 24 h using detrended fluctuation analysis (DFA). The fractal scaling index alpha-1 was higher in FM patients than in controls (mean ± sd: 1.22 ± 0.10 vs. 1.16 ± 0.09; p = 0.031). There was a positive correlation between the fractal scaling index alpha-1 and the visual analogue scale (VAS) for depression (Spearman's ρ = 0.36, p = 0.04). The heart rate fractal exponent alpha-1 is altered in FM patients, suggesting a rigid ANS performance. This tangible non-linear finding supports the notion that FM may represent a degradation of our main complex adaptive system, namely the ANS.
Fractal-based analysis of optical coherence tomography data to quantify retinal tissue damage.
Somfai, Gábor Márk; Tátrai, Erika; Laurik, Lenke; Varga, Boglárka E; Ölvedy, Vera; Smiddy, William E; Tchitnga, Robert; Somogyi, Anikó; DeBuc, Delia Cabrera
2014-09-01
The sensitivity of Optical Coherence Tomography (OCT) images to identify retinal tissue morphology characterized by early neural loss from normal healthy eyes is tested by calculating structural information and fractal dimension. OCT data from 74 healthy eyes and 43 eyes with type 1 diabetes mellitus with mild diabetic retinopathy (MDR) on biomicroscopy was analyzed using a custom-built algorithm (OCTRIMA) to measure locally the intraretinal layer thickness. A power spectrum method was used to calculate the fractal dimension in intraretinal regions of interest identified in the images. ANOVA followed by Newman-Keuls post-hoc analyses were used to test for differences between pathological and normal groups. A modified p value of Fractal dimension was higher for all the layers (except the GCL + IPL and INL) in MDR eyes compared to normal healthy eyes. When comparing MDR with normal healthy eyes, the highest AUROC values estimated for the fractal dimension were observed for GCL + IPL and INL. The maximum discrimination value for fractal dimension of 0.96 (standard error =0.025) for the GCL + IPL complex was obtained at a FD ≤ 1.66 (cut off point, asymptotic 95% Confidence Interval: lower-upper bound = 0.905-1.002). Moreover, the highest AUROC values estimated for the thickness measurements were observed for the OPL, GCL + IPL and OS. Particularly, when comparing MDR eyes with control healthy eyes, we found that the fractal dimension of the GCL + IPL complex was significantly better at diagnosing early DR, compared to the standard thickness measurement. Our results suggest that the GCL + IPL complex, OPL and OS are more susceptible to initial damage when comparing MDR with control healthy eyes. Fractal analysis provided a better sensitivity, offering a potential diagnostic predictor for detecting early neurodegeneration in the retina.
Fractal gait patterns are retained after entrainment to a fractal stimulus.
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Christopher K Rhea
Full Text Available Previous work has shown that fractal patterns in gait can be altered by entraining to a fractal stimulus. However, little is understood about how long those patterns are retained or which factors may influence stronger entrainment or retention. In experiment one, participants walked on a treadmill for 45 continuous minutes, which was separated into three phases. The first 15 minutes (pre-synchronization phase consisted of walking without a fractal stimulus, the second 15 minutes consisted of walking while entraining to a fractal visual stimulus (synchronization phase, and the last 15 minutes (post-synchronization phase consisted of walking without the stimulus to determine if the patterns adopted from the stimulus were retained. Fractal gait patterns were strengthened during the synchronization phase and were retained in the post-synchronization phase. In experiment two, similar methods were used to compare a continuous fractal stimulus to a discrete fractal stimulus to determine which stimulus type led to more persistent fractal gait patterns in the synchronization and post-synchronization (i.e., retention phases. Both stimulus types led to equally persistent patterns in the synchronization phase, but only the discrete fractal stimulus led to retention of the patterns. The results add to the growing body of literature showing that fractal gait patterns can be manipulated in a predictable manner. Further, our results add to the literature by showing that the newly adopted gait patterns are retained for up to 15 minutes after entrainment and showed that a discrete visual stimulus is a better method to influence retention.
Stein, R. S.
2012-12-01
The 2004 M=9.2 Sumatra earthquake claimed what seemed an unfathomable 228,000 lives, although because of its size, we could at least assure ourselves that it was an extremely rare event. But in the short space of 8 years, the Sumatra quake no longer looks like an anomaly, and it is no longer even the worst disaster of the Century: 80,000 deaths in the 2005 M=7.6 Pakistan quake; 88,000 deaths in the 2008 M=7.9 Wenchuan, China quake; 316,000 deaths in the M=7.0 Haiti, quake. In each case, poor design and construction were unable to withstand the ferocity of the shaken earth. And this was compounded by inadequate rescue, medical care, and shelter. How could the toll continue to mount despite the advances in our understanding of quake risk? The world's population is flowing into megacities, and many of these migration magnets lie astride the plate boundaries. Caught between these opposing demographic and seismic forces are 50 cities of at least 3 million people threatened by large earthquakes, the targets of chance. What we know for certain is that no one will take protective measures unless they are convinced they are at risk. Furnishing that knowledge is the animating principle of the Global Earthquake Model, launched in 2009. At the very least, everyone should be able to learn what his or her risk is. At the very least, our community owes the world an estimate of that risk. So, first and foremost, GEM seeks to raise quake risk awareness. We have no illusions that maps or models raise awareness; instead, earthquakes do. But when a quake strikes, people need a credible place to go to answer the question, how vulnerable am I, and what can I do about it? The Global Earthquake Model is being built with GEM's new open source engine, OpenQuake. GEM is also assembling the global data sets without which we will never improve our understanding of where, how large, and how frequently earthquakes will strike, what impacts they will have, and how those impacts can be lessened by
Directory of Open Access Journals (Sweden)
Nichola eStreet
2016-05-01
Full Text Available 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 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 2-study paper aims to test preference responses to fractal dimension 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 fractal dimension 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 fractal dimension 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 paper supports the established theory that the mid-range fractal patterns appear to be a universal construct underlying
Modeling Fractal Dimension Curve of Urban Growth in Developing Countries
Chen, Yanguang
2016-01-01
The growth curve of fractal dimension of cities can be described with sigmoid function such as Boltzmann's equation and logistic function. The logistic models of fractal dimension curves have been presented for the cities in developed countries. However, these models cannot be well fitted to the observational data of fractal dimension of urban form in developing countries (e.g. China). By statistic experiments of fractal parameters, we find that the quadratic Boltzmann's equation can be used to describe fractal dimension change of Chinese cities. For the normalized fractal dimension values, the Boltzmann's equation can be reduced to a quadratic logistic function. In practice, a fractal dimension dataset of urban growth can be approximately fitted with the quadratic logistic function. Thus, a series of models of fractal dimension curve can be proposed for the cities in developing countries. The models are applied to the city of Beijing, Chinese capital, and yield satisfying trend lines of the observational dat...
Fractal scaling in bottlenose dolphin (Tursiops truncatus) echolocation: A case study
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.
Fractal Dimensions for Radioisotope Pollution Patterns by Nuclear Power Plant Accidents
Saito, K.; Ogawa, S.
2015-04-01
The radioisotope pollution shows two types of patterns: dry and wet deposits for nuclear power plant accidents. Two surface pollution patterns were analysed by fractal. In Fukushima nuclear power plant accident, surface pollution by wet deposits was estimated to occur. However, actually it was no rain and white crystals were observed on the surface. Then, fractal analysis was carried out for the spatial distribution patterns of radio isotopes on the surface to judge the types of deposits. As a reference, Chernobyl nuclear power plant accident was checked for the spatial distribution patterns of radioisotopes on the surface. The objective patterns by fractal analysis were the surface pollution maps in Fukushima and Chernobyl, Abukuma river watershed map, and NOAA/AVHRR. The calculation of fractal dimensions was carried out with the box counting for binarized images. Fractal analysis results suggested the next conclusions. The radioisotope pollution in Fukushima might occur in both dry and wet deposits. The dry deposit might make the pollution pattern similar to the watershed, while the wet deposit might make the pollution pattern similar to cloud images. Moreover, most radioisotope contaminants might flow on the road in the forest valley and deposit on forest with and without rainfall in Fukushima.
Fractal and multifractal analyses of bipartite networks
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.
Fractal nature of regional ventilation distribution.
Altemeier, W A; McKinney, S; Glenny, R W
2000-05-01
High-resolution measurements of pulmonary perfusion reveal substantial spatial heterogeneity that is fractally distributed. This observation led to the hypothesis that the vascular tree is the principal determinant of regional blood flow. Recent studies using aerosol deposition show similar ventilation heterogeneity that is closely correlated with perfusion. We hypothesize that ventilation has fractal characteristics similar to blood flow. We measured regional ventilation and perfusion with aerosolized and injected fluorescent microspheres in six anesthetized, mechanically ventilated pigs in both prone and supine postures. Adjacent regions were clustered into progressively larger groups. Coefficients of variation were calculated for each cluster size to determine fractal dimensions. At the smallest size lung piece, local ventilation and perfusion are highly correlated, with no significant difference between ventilation and perfusion heterogeneity. On average, the fractal dimension of ventilation is 1.16 in the prone posture and 1. 09 in the supine posture. Ventilation has fractal properties similar to perfusion. Efficient gas exchange is preserved, despite ventilation and perfusion heterogeneity, through close correlation. One potential explanation is the similar geometry of bronchial and vascular structures.
Radiative heat transfer in fractal structures
Nikbakht, M.
2017-09-01
The radiative properties of most structures are intimately connected to the way in which their constituents are ordered on the nanoscale. We have proposed a new representation for radiative heat transfer formalism in many-body systems. In this representation, we explain why collective effects depend on the morphology of structures, and how the arrangement of nanoparticles and their material affects the thermal properties in many-body systems. We investigated the radiative heat transfer problem in fractal (i.e., scale invariant) structures. In order to show the effect of the structure morphology on the collective properties, the radiative heat transfer and radiative cooling are studied and the results are compared for fractal and nonfractal structures. It is shown that fractal arranged nanoparticles display complex radiative behavior related to their scaling properties. We showed that, in contrast to nonfractal structures, heat flux in fractals is not of large-range character. By using the fractal dimension as a means to describe the structure morphology, we present a universal scaling behavior that quantitatively links the structure radiative cooling to the structure gyration radius.
Integration of fractal biosensor in a digital microfluidic platform
Mashraei, Yousof
2015-11-01
Fractal capacitive electrodes have been successfully integrated into a digital microfluidic open-platform. These electrodes perform actuation and withstand voltages up to 300V without insulation-layer breakdown. They were used to quantify the concentration levels of C-reactive protein (CRP) to determine the risk of cardiovascular disease. The capacitance increased sevenfold and stabilized in less than 5 minutes. The sensor shows a decreasing trend of capacitance readouts with the increase of concentrations. The same immunoassay was tested with untreated electrodes and showed no significant response, which suggests that immobilization was necessary. This configuration allows the electrodes to be used as biosensors.
Kim, S.; Saito, T.; Fukuyama, E.; Kang, T. S.
2016-12-01
Historical documents in Korea and China report abnormal waves in the sea and rivers close to the date of the 1707 Hoei earthquake, which occurred in the Nankai Trough, off southwestern Japan. This indicates that the tsunami caused by the Hoei earthquake might have reached Korea and China, which suggests a potential hazard in Korea from large earthquakes in the Nankai Trough. We conducted tsunami simulations to study the details of tsunamis in Korea caused by large earthquakes. We employed the 1707 Hoei earthquake source model and physics-based scenarios of anticipated earthquake in the Nankai subduction zone. We also considered the effect of horizontal displacement on tsunami generation. Our simulation results from the Hoei earthquake model and the anticipated earthquake models showed that the maximum tsunami height along the Korean coast was less than 0.5 m. Even though the tsunami is not life-threatening, the effect of larger earthquakes should be still considered.
Fractal analysis of rainfall occurrence observed in the synoptic ...
African Journals Online (AJOL)
Box counting method permits us to determine the fractal dimension (Dƒ) of the support. Afterward, a sensitivity analysis of the previously estimated fractal dimension is performed by varying the series length, as well as, the intensity threshold for the detection of rain. The results show that, the fractal dimension of the rainfall ...
On local fractional Volterra integral equations in fractal heat transfer
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Wu Zhong-Hua
2016-01-01
Full Text Available In the article, the fractal heat-transfer models are described by the local fractional integral equations. The local fractional linear and nonlinear Volterra integral equations are employed to present the heat transfer problems in fractal media. The local fractional integral equations are derived from the Fourier law in fractal media.
Monitoring of dry sliding wear using fractal analysis
Zhang, Jindang; Regtien, Paulus P.L.; Korsten, Maarten J.
2005-01-01
Reliable online monitoring of wear remains a challenge to tribology research as well as to the industry. This paper presents a new method for monitoring of dry sliding wear using digital imaging and fractal analysis. Fractal values, namely fractal dimension and intercept, computed from the power
New Approach to Fractal Approximation of Vector-Functions
Konstantin Igudesman; Marsel Davletbaev; Gleb Shabernev
2014-01-01
This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal interpolation functions. Best values of fractal interpolation vector-functions parameters are found. We give schemes of approximation of some sets of data and consider examples of approximation of smooth curves with different conditions.
Smitha, K A; Gupta, A K; Jayasree, R S
2015-09-07
Glioma, the heterogeneous tumors originating from glial cells, generally exhibit varied grades and are difficult to differentiate using conventional MR imaging techniques. When this differentiation is crucial in the disease prognosis and treatment, even the advanced MR imaging techniques fail to provide a higher discriminative power for the differentiation of malignant tumor from benign ones. A powerful image processing technique applied to the imaging techniques is expected to provide a better differentiation. The present study focuses on the fractal analysis of fluid attenuation inversion recovery MR images, for the differentiation of glioma. For this, we have considered the most important parameters of fractal analysis, fractal dimension and lacunarity. While fractal analysis assesses the malignancy and complexity of a fractal object, lacunarity gives an indication on the empty space and the degree of inhomogeneity in the fractal objects. Box counting method with the preprocessing steps namely binarization, dilation and outlining was used to obtain the fractal dimension and lacunarity in glioma. Statistical analysis such as one-way analysis of variance and receiver operating characteristic (ROC) curve analysis helped to compare the mean and to find discriminative sensitivity of the results. It was found that the lacunarity of low and high grade gliomas vary significantly. ROC curve analysis between low and high grade glioma for fractal dimension and lacunarity yielded 70.3% sensitivity and 66.7% specificity and 70.3% sensitivity and 88.9% specificity, respectively. The study observes that fractal dimension and lacunarity increases with an increase in the grade of glioma and lacunarity is helpful in identifying most malignant grades.
Levy dusts, Mittag-Leffler statistics, mass fractal lacunarity, and perceived dimension
Energy Technology Data Exchange (ETDEWEB)
Blumenfeld, R. [Theoretical Division and CNLS, Mail Stop B262, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Mandelbrot, B.B. [Mathematics Department, Yale University, New Haven, Connecticut 06520-8283 (United States)
1997-07-01
We study the Levy dusts on the line on two accounts: the fluctuations around the average power law that characterizes the mass-radius relation for self-similar fractals, and the statistics of the intervals between strides along the logarithmic axis (their tail distribution is related to the dust`s fractal dimension). The Levy dusts are suggested as a yardstick of neutral lacunarity, against which non-neutral lacunarity can be measured objectively. A notion of perceived dimension is introduced. We conclude with an application of the Mittag-Leffler statistics to a nonlinear electrical network. {copyright} {ital 1997} {ital The American Physical Society}
Computer Security: The dilemma of fractal defence
Stefan Lueders, Computer Security Team
2015-01-01
Aren’t mathematical fractals just beautiful? The Mandelbrot set and the Julia set, the Sierpinski gasket, the Menger sponge, the Koch curve (see here)… Based on very simple mathematical rules, they quickly develop into a mosaic of facets slightly different from each other. More and more features appear the closer you zoom into a fractal and expose similar but not identical features of the overall picture. Computer security is like these fractals, only much less pretty: simple at first glance, but increasingly complex and complicated when you look more closely at the details. The deeper you dig, the more and more possibilities open up for malicious people as the attack surface grows, just like that of “Koch’s snowflakes”, where the border length grows exponentially. Consequently, the defensive perimeter also increases when we follow the bits and bytes layer by layer from their processing in the CPU, trickling up the software stack thro...
Edges of Saturn's rings are fractal.
Li, Jun; Ostoja-Starzewski, Martin
2015-01-01
The images recently sent by the Cassini spacecraft mission (on the NASA website http://saturn.jpl.nasa.gov/photos/halloffame/) show the complex and beautiful rings of Saturn. Over the past few decades, various conjectures were advanced that Saturn's rings are Cantor-like sets, although no convincing fractal analysis of actual images has ever appeared. Here we focus on four images sent by the Cassini spacecraft mission (slide #42 "Mapping Clumps in Saturn's Rings", slide #54 "Scattered Sunshine", slide #66 taken two weeks before the planet's Augus't 200'9 equinox, and slide #68 showing edge waves raised by Daphnis on the Keeler Gap) and one image from the Voyager 2' mission in 1981. Using three box-counting methods, we determine the fractal dimension of edges of rings seen here to be consistently about 1.63 ~ 1.78. This clarifies in what sense Saturn's rings are fractal.
``the Human BRAIN & Fractal quantum mechanics''
Rosary-Oyong, Se, Glory
In mtDNA ever retrieved from Iman Tuassoly, et.al:Multifractal analysis of chaos game representation images of mtDNA''.Enhances the price & valuetales of HE. Prof. Dr-Ing. B.J. HABIBIE's N-219, in J. Bacteriology, Nov 1973 sought:'' 219 exist as separate plasmidDNA species in E.coli & Salmonella panama'' related to ``the brain 2 distinct molecular forms of the (Na,K)-ATPase..'' & ``neuron maintains different concentration of ions(charged atoms'' thorough Rabi & Heisenber Hamiltonian. Further, after ``fractal space time are geometric analogue of relativistic quantum mechanics''[Ord], sought L.Marek Crnjac: ``Chaotic fractals at the root of relativistic quantum physics''& from famous Nottale: ``Scale relativity & fractal space-time:''Application to Quantum Physics , Cosmology & Chaotic systems'',1995. Acknowledgements to HE. Mr. H. TUK SETYOHADI, Jl. Sriwijaya Raya 3, South-Jakarta, INDONESIA.
A fractal-based image encryption system
Abd-El-Hafiz, S. K.
2014-12-01
This study introduces a novel image encryption system based on diffusion and confusion processes in which the image information is hidden inside the complex details of fractal images. A simplified encryption technique is, first, presented using a single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved through several parameters: feedback delay, multiplexing and independent horizontal or vertical shifts. The effect of each parameter is studied separately and, then, they are combined to illustrate their influence on the encryption quality. The encryption quality is evaluated using different analysis techniques such as correlation coefficients, differential attack measures, histogram distributions, key sensitivity analysis and the National Institute of Standards and Technology (NIST) statistical test suite. The obtained results show great potential compared to other techniques.
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.
Directory of Open Access Journals (Sweden)
Potapov A. A.
2008-10-01
Full Text Available Main results of theoretical and experimental investigations since eighties of XX that led to formation and developing of new fundamental science discipline: “Fractal Radio Physics and Fractal Radio Electronics: Fractal Radio Systems Designing” are briefly classified in the paper.
Estimation of fractal dimensions from transect data
Energy Technology Data Exchange (ETDEWEB)
Loehle, C. [Argonne National Lab., IL (United States)
1994-04-01
Fractals are a useful tool for analyzing the topology of objects such as coral reefs, forest canopies, and landscapes. Transects are often studied in these contexts, and fractal dimensions computed from them. An open question is how representative a single transect is. Transects may also be used to estimate the dimensionality of a surface. Again the question of representativeness of the transect arises. These two issues are related. This note qualifies the conditions under which transect data may be considered to be representative or may be extrapolated, based on both theoretical and empirical results.
The virtual education fractality: nature and organization
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Osbaldo Turpo Gebera
2013-04-01
Full Text Available The potential generated by ICT in education raises reflect on the underlying frameworks. In this sense, the fractal is an opportunity to explain how it organizes and manages virtual education.This approach recognizes that educational dynamics are recursive and iterative processes instituted as progressive sequences, by way of fractals. This understanding enables becoming as mediated and articulated successive levels. In each dimension are embodied own activities and in turn, involves the recurrence of subsequent levels as possible solving of problem situations. Thus, the knowledge built in response to a collaborative action, participation in networks, ranging from autonomous to the cultural level or conversely.
Wei, Ben-Yong; Nie, Gao-Zhong; Su, Gui-Wu; Sun, Lei
2017-04-01
China is one of the most earthquake prone countries in the world. The priority during earthquake emergency response is saving lives and minimizing casualties. Rapid judgment of the trapped location is the important basis for government to reasonable arrange the emergency rescue forces and resources after the earthquake. Through analyzing the key factors resulting in people trapped, we constructed an assessment model of personal trapped (PTED)in collapsed buildings caused by earthquake disaster. Then taking the 2014 Ludian Earthquake as a case, this study evaluated the distribution of trapped personal during this earthquake using the assessment model based on km grid data. Results showed that, there are two prerequisites for people might be trapped by the collapse of buildings in earthquake: earthquake caused buildings collapse and there are people in building when building collapsing; the PTED model could be suitable to assess the trapped people in collapsed buildings caused by earthquake. The distribution of people trapped by the collapse of buildings in the Ludian earthquake assessed by the model is basically the same as that obtained by the actual survey. Assessment of people trapped in earthquake based on km grid can meet the requirements of search-and-rescue zone identification and rescue forces allocation in the early stage of the earthquake emergency. In future, as the basic data become more complete, assessment of people trapped in earthquake based on km grid should provide more accurate and valid suggestions for earthquake emergency search and rescue.
Generalized statistical mechanics approaches to earthquakes and tectonics.
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.
Generalized statistical mechanics approaches to earthquakes and tectonics
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
Fault lubrication during earthquakes.
Di Toro, G; Han, R; Hirose, T; De Paola, N; Nielsen, S; Mizoguchi, K; Ferri, F; Cocco, M; Shimamoto, T
2011-03-24
The determination of rock friction at seismic slip rates (about 1 m s(-1)) is of paramount importance in earthquake mechanics, as fault friction controls the stress drop, the mechanical work and the frictional heat generated during slip. Given the difficulty in determining friction by seismological methods, elucidating constraints are derived from experimental studies. Here we review a large set of published and unpublished experiments (∼300) performed in rotary shear apparatus at slip rates of 0.1-2.6 m s(-1). The experiments indicate a significant decrease in friction (of up to one order of magnitude), which we term fault lubrication, both for cohesive (silicate-built, quartz-built and carbonate-built) rocks and non-cohesive rocks (clay-rich, anhydrite, gypsum and dolomite gouges) typical of crustal seismogenic sources. The available mechanical work and the associated temperature rise in the slipping zone trigger a number of physicochemical processes (gelification, decarbonation and dehydration reactions, melting and so on) whose products are responsible for fault lubrication. The similarity between (1) experimental and natural fault products and (2) mechanical work measures resulting from these laboratory experiments and seismological estimates suggests that it is reasonable to extrapolate experimental data to conditions typical of earthquake nucleation depths (7-15 km). It seems that faults are lubricated during earthquakes, irrespective of the fault rock composition and of the specific weakening mechanism involved.
The 2007 Bengkulu earthquake, its rupture model and implications ...
Indian Academy of Sciences (India)
Thus, despite its great magnitude, this earthquake did not generate a major tsunami. Further, we suggest that the occurrence of great earthquakes in the subduction zone on either side of the Siberut Island region, might have led to the increase in static stress in the region, where the last great earthquake occurred in 1797 ...
Statistical physics approach to earthquake occurrence and forecasting
Energy Technology Data Exchange (ETDEWEB)
Arcangelis, Lucilla de [Department of Industrial and Information Engineering, Second University of Naples, Aversa (CE) (Italy); Godano, Cataldo [Department of Mathematics and Physics, Second University of Naples, Caserta (Italy); Grasso, Jean Robert [ISTerre, IRD-CNRS-OSUG, University of Grenoble, Saint Martin d’Héres (France); Lippiello, Eugenio, E-mail: eugenio.lippiello@unina2.it [Department of Mathematics and Physics, Second University of Naples, Caserta (Italy)
2016-04-25
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
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1, 2, and 3 of Eric Hammel's Fractal Dimensions, Volume 4 is
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1 and 2 of Eric Hammel's Fractal Dimensions, Volume 3 is fil
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volume 1 of Eric Hammel's Fractal Dimensions, Volume 2 is filled wit
FRACTAL DIMENSIONING OF SAND GRAINS USING IMAGE ANALYSIS SYSTEM
Directory of Open Access Journals (Sweden)
Suat AKBULUT
2002-03-01
Full Text Available Engineers and earth scientists have successfully used the concept of fractal theory to better analyze the roughness of soil and/or rock particles, and how it affects the permeability, structure and distribution of pores in sedimentary rocks and their influence on strength. Use of fractals as a way to describe irregular or rough objects has been highlighted in articles by researchers working in fields such as powder mechanics, rock and soil mechanics, sedimentary petrography and geoenvironmental applications. Fractal scaling has been found appropriate to express such scale independence for collection of soil particles and aggregates. In many aspects, soil is a fractal medium and fractal models are available for the fragmentation of aggregates with fractal pore space, and with fractal surface. Applications of fractal concepts encompass description of soil physical properties such as pore-size distribution, pore surface area, and grain-size distribution. The roughness of particulate soils is an important characteristic that affects the mass behavior of the soil. The area-perimeter technique was used to predict the fractal dimension using image analysis system. This paper presents the effects of the roughness and sorting of the sand patterns with different shapes on fractal dimension. Results confirmed the significance of the roughness effect on fractal dimension.
Fractal Structure and Entropy Production within the Central Nervous System
Directory of Open Access Journals (Sweden)
Andrew J. E. Seely
2014-08-01
Full Text Available Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS. Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer’s and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.
The fractal harmonic law and its application to swimming suit
Directory of Open Access Journals (Sweden)
Kong Hai-Yan
2012-01-01
Full Text Available Decreasing friction force between a swimming suit and water is the key factor to design swimming suits. Water continuum mechanics forbids discontinuous fluids, but in angstrom scale water is indeed discontinuous. Swimming suit is smooth on large scale, but it is discontinuous when the scale becomes smaller. If fractal dimensions of swimming suit and water are the same, a minimum of friction force is predicted, which means fractal harmonization. In the paper, fractal harmonic law is introduced to design a swimsuit whose surface fractal dimensions on a macroscopic scale should be equal to or closed to the water's fractal dimensions on an Angstrom scale. Various possible microstructures of fabric are analyzed and a method to obtain perfect fractal structure of fabric is proposed by spraying nanofibers to its surface. The fractal harmonic law can be used to design a moving surface with a minimal friction.
Fractals and spectra related to fourier analysis and function spaces
Triebel, Hans
1997-01-01
Fractals and Spectra Hans Triebel This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Atomic and quarkonial (subatomic) decompositions in scalar and vector valued function spaces on the euclidean n-space pave the way to study properties (compact embeddings, entropy numbers) of function spaces on and of fractals. On this basis, distributions of eigenvalues of fractal (pseudo)differential operators are investigated. Diverse versions of fractal drums are played. The book is directed to mathematicians interested in functional analysis, the theory of function spaces, fractal geometry, partial and pseudodifferential operators, and, in particular, in how these domains are interrelated. ------ It is worth mentioning that there is virtually no literature on this topic and hence the most of the presented material is published here the first time. - Zentralblatt MATH (…) ...
Fractal analysis of spontaneous fluctuations of the BOLD signal in the human brain networks.
Li, Yi-Chia; Huang, Yun-An
2014-05-01
To investigate what extent brain regions are continuously interacting during resting-state, independent component analyses (ICA) was applied to analyze resting-state functional MRI (RS-fMRI) data. According to the analyzed results, it was surprisingly found that low frequency fluctuations (LFFs), which belong to the 1/f signal (a signal with power spectrum whose power spectral density is inversely proportional to the frequency), have been classified into groups using ICA; furthermore, the spatial distributions of these groups within the brain were found to resemble the spatial distributions of different networks, which manifests that the signal characteristics of RS LFFs are distinct across networks. In our work, we applied the 1/f model in the fractal analyses to further investigate this distinction. Twenty healthy participants got involved in this study. They were scanned to acquire the RS-fMRI data. The acquired data were first processed with ICA to obtain the networks of the resting brain. Afterward, the blood-oxygenation level dependent (BOLD) signals of these networks were processed with the fractal analyses for obtaining the fractal parameter α. α was found to significantly vary across networks, which reveals that the fractal characteristic of LFFs differs across networks. According to prior literatures, this difference could be brought by the discrepancy of hemodynamic response amplitude (HRA) between networks. Hence, in our work, we also performed the computational simulation to discover the relationship between α and HRA. Based on the simulation results, HRA is highly linear-correlated with the fractal characteristics of LFFs which is revealed by α. Our results support that the origin of RS-fMRI signals contains arterial fluctuations. Hence, in addition to the commonly used method such as synchrony analysis and power spectral analysis, another approach, the fractal analysis, is suggested for acquiring the information of hemodynamic responses by means
Energy Technology Data Exchange (ETDEWEB)
Vasylkivska, Veronika S. [National Energy Technology Lab. (NETL), Albany, OR (United States); Oak Ridge Inst. for Science and Education (ORISE), Oak Ridge, TN (United States); Huerta, Nicolas J. [National Energy Technology Lab. (NETL), Albany, OR (United States)
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 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.
DEFF Research Database (Denmark)
Teisbæk, Henrik Bjørn; Jakobsen, Kaj Bjarne
2009-01-01
A Yagi-Uda antenna constructed of three Koch fractal elements is presented. Simulated and measured characteristics of the antenna shows a half-power beam-width of 64◦ achieved with dimensions below a third of a wavelength. Furthermore, the Koch dipole and its size miniaturization capabilities...
Fractal Image Editing with PhotoFrac
Directory of Open Access Journals (Sweden)
Tim McGraw
2016-12-01
Full Text Available In this paper, we describe the development and use of PhotoFrac, an application that allows artists and designers to turn digital images into fractal patterns interactively. Fractal equations are a rich source of procedural texture and detail, but controlling the patterns and incorporating traditional media has been difficult. Additionally, the iterative nature of fractal calculations makes implementation of interactive techniques on mobile devices and web apps challenging. We overcome these problems by using an image coordinate based orbit trapping technique that permits a user-selected image to be embedded into the fractal. Performance challenges are addressed by exploiting the processing power of graphic processing unit (GPU and precomputing some intermediate results for use on mobile devices. This paper presents results and qualitative analyses of the tool by four artists (the authors who used the PhotoFrac application to create new artworks from original digital images. The final results demonstrate a fusion of traditional media with algorithmic art.
1000 Fractal Dimension and the Cantor Set
Indian Academy of Sciences (India)
IAS Admin
974. RESONANCE ⎜ November 2014. Resonance journal of science education. November 2014 Volume 19 Number 11. GENERALARTICLES. 977 How did Cantor Discover Set Theory and Topology? S M Srivastava. 1000 Fractal Dimension and the Cantor Set. Shailesh A Shirali. 1005 Biofilms: Community Behavior by ...
Geological mapping using fractal technique | Lawal | Nigerian ...
African Journals Online (AJOL)
... in Nigeria) showed good correlation with the geological maps of the areas. The results also indicated that basement rocks can generally be represented by scaling exponents with values ranging between -3.0 and -2.0. Keywords: Fractal, dimension, susceptibility, spectra, scaling exponent. Nigerian Journal of Physics Vol.
Geological mapping using fractal technique | Lawal | Nigerian ...
African Journals Online (AJOL)
In this work the use of fractal scaling exponents for geological mapping was first investigated using theoretical models, and results from the analysis showed that the scaling exponents mapped isolated bodies but did not properly resolve bodies close to each other. However application on real data (the Mamfe basin, the ...
Fractal turbulence enhancing low-swirl combustion
Verbeek, Antonie Alex; Bouten, Thijs W.F.M.; Stoffels, Genie G.M.; Geurts, Bernardus J.; van der Meer, Theodorus H.
The use of fractal grids in a low-swirl burner can significantly increase the turbulent combustion rate, realizing a higher power density in these flames. The standard turbulence generating blocking grid has been replaced by one consisting of a pattern of cruciform structures of different sizes,
Flames in fractal grid generated turbulence
Energy Technology Data Exchange (ETDEWEB)
Goh, K H H; Hampp, F; Lindstedt, R P [Department of Mechanical Engineering, Imperial College, London SW7 2AZ (United Kingdom); Geipel, P, E-mail: p.lindstedt@imperial.ac.uk [Siemens Industrial Turbomachinery AB, SE-612 83 Finspong (Sweden)
2013-12-15
Twin premixed turbulent opposed jet flames were stabilized for lean mixtures of air with methane and propane in fractal grid generated turbulence. A density segregation method was applied alongside particle image velocimetry to obtain velocity and scalar statistics. It is shown that the current fractal grids increase the turbulence levels by around a factor of 2. Proper orthogonal decomposition (POD) was applied to show that the fractal grids produce slightly larger turbulent structures that decay at a slower rate as compared to conventional perforated plates. Conditional POD (CPOD) was also implemented using the density segregation technique and the results show that CPOD is essential to segregate the relative structures and turbulent kinetic energy distributions in each stream. The Kolmogorov length scales were also estimated providing values {approx}0.1 and {approx}0.5 mm in the reactants and products, respectively. Resolved profiles of flame surface density indicate that a thin flame assumption leading to bimodal statistics is not perfectly valid under the current conditions and it is expected that the data obtained will be of significant value to the development of computational methods that can provide information on the conditional structure of turbulence. It is concluded that the increase in the turbulent Reynolds number is without any negative impact on other parameters and that fractal grids provide a route towards removing the classical problem of a relatively low ratio of turbulent to bulk strain associated with the opposed jet configuration. (paper)
FRACTAL DIMENSIONALITY ANALYSIS OF MAMMARY GLAND THERMOGRAMS
Yu. E. Lyah; V. G. Guryanov; E. A. Yakobson
2016-01-01
Thermography may enable early detection of a cancer tumour within a mammary gland at an early, treatable stage of the illness, but thermogram analysis methods must be developed to achieve this goal. This study analyses the feasibility of applying the Hurst exponent readings algorithm for evaluation of the high dimensionality fractals to reveal any possible difference between normal thermograms (NT) and malignant thermograms (MT).
Do-It-Yourself Fractal Functions
Shriver, Janet; Willard, Teri; McDaniel, Mandy
2017-01-01
In the set of fractal activities described in this article, students will accomplish much more than just creating a fun set of cards that simply resemble an art project. Goals of this activity, designed for an algebra 1 class, are to encourage students to generate data, look for and analyze patterns, and create their own models--all from a set of…
Fractal analysis of the Navassa Island seascape
Zawada, David G.
2011-01-01
This release provides the numerical results of the fractal analyses discussed in Zawada and others (2010) for the Navassa Island reefscape. The project represents the continuation of a U.S. Geological Survey (USGS) research effort begun in 2006 (Zawada and others, 2006) to understand the patterns and scalability of roughness and topographic complexity from individual corals to complete reefscapes.
Design of silicon-based fractal antennas
Ghaffar, Farhan A.
2012-11-20
This article presents Sierpinski carpet fractal antennas implemented in conventional low resistivity (Ï =10 Ω cm) as well as high resistivity (Ï =1500 Ω cm) silicon mediums. The fractal antenna is 36% smaller as compared with a typical patch antenna at 24 GHz and provides 13% bandwidth on high resistivity silicon, suitable for high data rate applications. For the first time, an on-chip fractal antenna array is demonstrated in this work which provides double the gain of a single fractal element as well as enhanced bandwidth. A custom test fixture is utilized to measure the radiation pattern and gain of these probe-fed antennas. In addition to gain and impedance characterization, measurements have also been made to study intrachip communication through these antennas. The comparison between the low resistivity and high resistivity antennas indicate that the former is not a suitable medium for array implementation and is only suitable for short range communication whereas the latter is appropriate for short and medium range wireless communication. The design is well-suited for compact, high data rate System-on-Chip (SoC) applications as well as for intrachip communication such as wireless global clock distribution in synchronous systems. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:180-186, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27245 Copyright © 2012 Wiley Periodicals, Inc.
Generalized Fragmentation Functions for Fractal Jet Observables
Elder, B.T.; Procura, M.; Thaler, J.; Waalewijn, W.J.; Zhou, K.
We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation functions, which are important objects in QCD for calculating
Solar Cycle Phase Dependence of Supergranular Fractal ...
Indian Academy of Sciences (India)
1a). Regions that were not unequivocally quiescent or active were avoided for simplicity. 2. Data processing and results. The area and perimeter data were obtained by obtaining profile scans (Fig. 1b), details of which can be found in our earlier paper (Paniveni et al. 2005). The main results pertaining to fractal dimension is ...
Fractality in selfsimilar minimal mass structures
De Tommasi, D.; Maddalena, F.; Puglisi, G.; Trentadue, F.
2017-10-01
In this paper we study the diffusely observed occurrence of Fractality and Self-organized Criticality in mechanical systems. We analytically show, based on a prototypical compressed tensegrity structure, that these phenomena can be viewed as the result of the contemporary attainment of mass minimization and global stability in elastic systems.
Tohoku earthquake: a surprise?
Kagan, Yan Y
2011-01-01
We consider three issues related to the 2011 Tohoku mega-earthquake: (1) how to evaluate the earthquake maximum size in subduction zones, (2) what is the repeat time for the largest earthquakes in Tohoku area, and (3) what are the possibilities of short-term forecasts during the 2011 sequence. There are two quantitative methods which can be applied to estimate the maximum earthquake size: a statistical analysis of the available earthquake record and the moment conservation principle. The latter technique studies how much of the tectonic deformation rate is released by earthquakes. For the subduction zones, the seismic or historical record is not sufficient to provide a reliable statistical measure of the maximum earthquake. The moment conservation principle yields consistent estimates of maximum earthquake size: for all the subduction zones the magnitude is of the order 9.0--9.7, and for major subduction zones the maximum earthquake size is statistically indistinguishable. Starting in 1999 we have carried out...
Clinical characteristics of patients seizure following the 2016 Kumamoto earthquake.
Inatomi, Yuichiro; Nakajima, Makoto; Yonehara, Toshiro; Ando, Yukio
2017-06-01
To investigate the clinical characteristics of patients with seizure following the 2016 Kumamoto earthquake. We retrospectively studied patients with seizure admitted to our hospital for 12weeks following the earthquake. We compared the clinical backgrounds and characteristics of the patients: before (the same period from the previous 3years) and after the earthquake; and the early (first 2weeks) and late (subsequent 10weeks) phases. A total of 60 patients with seizure were admitted to the emergency room after the earthquake, and 175 (58.3/year) patients were admitted before the earthquake. Of them, 35 patients with seizure were hospitalized in the Department of Neurology after the earthquake, and 96 (32/year) patients were hospitalized before the earthquake. In patients after the earthquake, males and non-cerebrovascular diseases as an epileptogenic disease were seen more frequently than before the earthquake. During the early phase after the earthquake, female, first-attack, and non-focal-type patients were seen more frequently than during the late phase after the earthquake. These characteristics of patients with seizure during the early phase after the earthquake suggest that many patients had non-epileptic seizures. To prevent seizures following earthquakes, mental stress and physical status of evacuees must be assessed. Copyright © 2017. Published by Elsevier Ltd.
Shedding light on fractals: exploration of the Sierpinski carpet optical antenna
Chen, T.L.
2015-01-01
We describe experimental and theoretical investigations of the properties of a fractal optical antenna-the Sierpinski carpet optical antenna. Fractal optical antennas are inspired by fractal antennas designed in radio frequency (RF) region. Shrinking the size of fractal optical antennas from fractal
Rodkin, Mikhail V.; Mandal, Prantik
2012-04-01
The 2001 Bhuj earthquake took place in a region away from the active plate boundaries, which qualifies this earthquake to be a typical intraplate event that claimed a death toll of 20,000 people. The aftershock sequence of this earthquake is still continuing for the last eleven years, which makes this aftershock sequence as a unique intraplate earthquake sequence in the world. This sequence is being monitored by a close digital seismic network consisting of 5-12 three-component broadband seismographs and 10-20 accelerographs that led to a homogeneous earthquake catalog consisting of precise and accurate estimates of hypocentral and source parameters. This catalog enabled us to examine the evolution of this earthquake sequence. Our study reveals a few interconnected regularities in the rate of earthquake occurrence, b-values, fractal dimensions, stress drops, and the mean earthquake depth values. We observe that a slow decrease in background seismic activity and a number of bursts in seismic activity characterize the 2001 Bhuj earthquake sequence. We also notice that the background seismic activity is associated with a monotonic decrease in the mean earthquake depth values while the bursts in seismic activity are found to be associated with a decrease in fractal dimension, b-value and mean earthquake depth estimates, and an increase in stress drop values. We propose that these bursts in seismic activity are related to the episodes of break in deep fluid circulation in the direction of the Earth's surface. The effective background permeability of the mid-crust in the 2001 Bhuj earthquake region is evaluated to be about k ≈ 10- 13 m2 based on the estimates of changes in mean earthquake depth. Thus, we infer that seismogenesis of the 2001 Bhuj earthquake sequence is probably connected with active deep fluid circulation underlying the Kachchh seismic zone.
Roth, Eric J; Gilbert, Benjamin; Mays, David C
2015-10-20
Experiments reveal a wide discrepancy between the permeability of porous media containing colloid deposits and the available predictive equations. Evidence suggests that this discrepancy results, in part, from the predictive equations failing to account for colloid deposit morphology. This article reports a series of experiments using static light scattering (SLS) to characterize colloid deposit morphology within refractive index matched (RIM) porous media during flow through a column. Real time measurements of permeability, specific deposit, deposit fractal dimension, and deposit radius of gyration, at different vertical positions, were conducted with initially clean porous media at various ionic strengths and fluid velocities. Decreased permeability (i.e., increased clogging) corresponded with higher specific deposit, lower fractal dimension, and smaller radius of gyration. During deposition, fractal dimension, radius of gyration, and permeability decreased with increasing specific deposit. During flushing with colloid-free fluid, these trends reversed, with increased fractal dimension, radius of gyration, and permeability. These observations suggest a deposition scenario in which large and uniform aggregates become deposits, which reduce porosity, lead to higher fluid shear forces, which then decompose the deposits, filling the pore space with small and dendritic fragments of aggregate.
Fractal dimensions: A new paradigm to assess spatial memory and learning using Morris water maze.
Singh, Surjeet; Kaur, Harpreet; Sandhir, Rajat
2016-02-15
Morris water maze has been widely used for analysis of cognitive functions and relies on the time taken by animal to find the platform i.e. escape latency as a parameter to quantify spatial memory and learning. However, escape latency is confounded by swimming speed which is not necessarily a cognitive factor. Rather, path length may be a more appropriate and reliable parameter to assess spatial learning. This paper presents fractal dimension as a new paradigm to assess spatial memory and learning in animals. Male wistar rats were administrated with pentylenetetrazole and scopolamine to induce chronic epilepsy and dementia respectively. Fractal dimension of the random path followed by the animals on Morris water maze was analyzed and statistically compared among different experimental groups; the results suggest that fractal dimension is more reliable and accurate parameter to assess cognitive deficits compared to escape latency. Thus, the present study suggests that fractal dimensions could be used as an independent parameter to assess spatial memory and learning in animals using Morris water maze. Copyright © 2015 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Edgardo Jonathan Suárez Dominguez
2013-09-01
Full Text Available Poured earth is a sustainable construction and economically feasible technique to develop in Tamaulipas, by the materials availability and traditional manufacturing procedures uses. There are several variables to be considered in these elements for their properties, among them it can be found roughness and porosity analysis which are important because they are related to material mechanical resistance and durability. This study aimed to characterize solid surfaces using fractal dimension to know its uniformity and porosity, compared with a concrete surface. Solids were obtained from poured earth of two combinations of soils stabilized with cement from the state of Tamaulipas. We found that a surface of a sample, obtained with ground, is more uniform than poured concrete surface, and that fractal dimension is higher while porosity increases; results suggest that this is because of the presence of clay in the poured earth mixtures. La tierra vertida es una técnica constructiva sustentable y económicamente viable para desarrollarse en Tamaulipas, por la disponibilidad de materiales y procedimientos de fabricación similares a los tradicionales. Son diversas las variables que deben estudiarse en estos elementos para conocer sus propiedades, entre las que se encuentran la rugosidad y la porosidad, las cuales son importantes debido a su estrecha relación con la resistencia mecánica y durabilidad del material estudiado. El presente trabajo tuvo por objetivo caracterizar superficies sólidas a partir de la dimensión fractal para conocer su uniformidad y porosidad, comparándola con una superficie de concreto. Los sólidos fueron obtenidos a partir de tierra vertida conformada de dos combinaciones de suelos estabilizadas con cemento provenientes del estado de Tamaulipas. Se encontró que una superficie de tierra vertida es menos irregular que una superficie de concreto además de tener una menor porosidad reflejada en una menor dimensión fractal
Hierarchical fractal structure of perfect single-layer grapheme
Zhang, T.; Ding, K.
2013-12-01
The atomic lattice structure of perfect singlelayer graphene that can actually be regarded as a kind of hierarchical fractal structure from the perspective of fractal geometry was studied for the first time. Three novel and special discoveries on hierarchical fractal structure and sets were unveiled upon examination of the regular crystal lattices of the single-layer graphene. The interior fractaltype structure was discovered to be the fifth space-filling curve from physical realm. Two efficient methods for calculating the fractal dimension of this fresh member was also provided. The outer boundary curve had a fractal dimension equal to one, and a multi-fractal structure from a naturally existing material was found for the first time. A series of strict self-similar hexagons comprised a rotating fractal set. These hexagons slewed at a constant counterclockwise angle α of 19.1° when observed from one level to the next higher level. From the perspective of fractal geometry, these pioneering discoveries added three new members to the existing regular fractal structures and sets. A fundamental example of a multi-fractal structure was also presented.
FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY
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Ian Parkinson
2011-05-01
Full Text Available A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge. The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals, with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.
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.
Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics.
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.
Evolution of fractal structures in dislocation ensembles during plastic deformation.
Vinogradov, A; Yasnikov, I S; Estrin, Y
2012-05-18
Based on the irreversible thermodynamics approach to dislocation plasticity of metals, a simple description of the dislocation density evolution and strain hardening was suggested. An analytical expression for the fractal dimension (FD) of a cellular (or tangled) dislocation structure evolving in the course of plastic deformation was obtained on the basis of the dislocation model proposed. This makes it possible to trace the variation of FD of the dislocation cell structure with strain by just measuring the macroscopic stress-strain curve. The FD behavior predicted in this way showed good agreement with the experimentally measured FD evolution at different stages of deformation of a Ni single crystal and a Cu polycrystal. One new result following from the present model is that the FD of the bulk dislocation structure in a deforming metal peaks at a certain strain close to the onset of necking. The significance of fractal analysis as an informative index to follow the spatial evolution of dislocation structures approaching the critical state is highlighted.
Multispectral image fusion based on fractal features
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
The hidden simplicity of subduction megathrust earthquakes
Meier, M.-A.; Ampuero, J. P.; Heaton, T. H.
2017-09-01
The largest observed earthquakes occur on subduction interfaces and frequently cause widespread damage and loss of life. Understanding the rupture behavior of megathrust events is crucial for earthquake rupture physics, as well as for earthquake early-warning systems. However, the large variability in behavior between individual events seemingly defies a description with a simple unifying model. Here we use three source time function (STF) data sets for subduction zone earthquakes, with moment magnitude Mw ≥ 7, and show that such large ruptures share a typical universal behavior. The median STF is scalable between events with different sizes, grows linearly, and is nearly triangular. The deviations from the median behavior are multiplicative and Gaussian—that is, they are proportionally larger for larger events. Our observations suggest that earthquake magnitudes cannot be predicted from the characteristics of rupture onsets.
Scaling relation of earthquake seismic data
Liu, Gang; Li, Ru; He, Jing; Li, Weile; Lu, Jiayan; Long, Wen; Gao, Peichao; Cai, Guolin; Tang, Min
2018-02-01
We study the spatio-temporal characteristics of earthquakes, and find that power laws and allometric growth laws are both statistically significant in the seismic dataset. For further analyzing the complexity of earthquake sequence, an approach of weighted earthquake networks modeling is presented with using the seismic and rock mass datasets. The rock masses covering the entire region are used to divide the region into a lot of small areas. It is shown that the distributions of connectivities and link weights both follow power law decay forms. The discovery of allometric growth laws is important for studying the dynamics of massive earthquakes. The suggested earthquake network is helpful to study the interactions between rock masses and expand a research prototype for modeling seismicity on complex networks.
Earthquakes: hydrogeochemical precursors
Ingebritsen, Steven E.; Manga, Michael
2014-01-01
Earthquake prediction is a long-sought goal. Changes in groundwater chemistry before earthquakes in Iceland highlight a potential hydrogeochemical precursor, but such signals must be evaluated in the context of long-term, multiparametric data sets.
National Oceanic and Atmospheric Administration, Department of Commerce — An earthquake is the motion or trembling of the ground produced by sudden displacement of rock in the Earth's crust. Earthquakes result from crustal strain,...
Earthquakes in Southern California
National Oceanic and Atmospheric Administration, Department of Commerce — There have been many earthquake occurrences in Southern California. This set of slides shows earthquake damage from the following events: Imperial Valley, 1979,...
Earthquake Notification Service
U.S. Geological Survey, Department of the Interior — The Earthquake Notification Service (ENS) is a free service that sends you automated notifications to your email or cell phone when earthquakes happen.
Unified scaling law for earthquakes in Crimea and Northern Caucasus
Nekrasova, A. K.; Kossobokov, V. G.
2016-10-01
This study continues detailed investigations on the construction of regional charts of the parameters of the generalized Guttenberg-Richter Law, which takes into account the properties of the spatiotemporal seismic energy scaling. We analyzed the parameters of the law in the vicinity of the intersections of morphostructural lineaments in Crimea and Greater Caucasus. It was shown that ignoring the fractal character of the spatial distribution of earthquakes in the southern part of the Russian Federation can lead to significant underestimation of the seismic hazard in the largest cities of the region.
Fractal zeta functions and fractal drums higher-dimensional theory of complex dimensions
Lapidus, Michel L; Žubrinić, Darko
2017-01-01
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the f...
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SARI BAHAGIARTI KUSUMAYUDHA
2011-12-01
Full Text Available Almost all of the Indonesian territories are high potential of geologic disaster, such as earthquake, tsunami, volcanic eruptions and landslides, because the country belongs to tectonically active areas of the world. There are three big lithosperic plates interacting one with one another and influencing the tectonic setting of Indonesia. The plates are Indo-Australia plate, Eurasia plate and Pacific plate. Indo-Australia plate moves relatively northward by about 9 cm/year, Eurasia plate creeps south eastward with approximately 7 cm/year speed, and Pacific plate moves to the west with around 11 cm/year velocity. In the meeting line of the plates, about 300 km to the south of Indonesian islands, there is the subduction zone that become places, where earthquake focuses are generated. Earthquakes from submarine source with more than 6.5 magnitude have the potential to generate tsunami. Areas situated along the south coast of Indonesia islands are vulnerable to tsunami, because directly facing the boundary lines between Eurasia plate and Indo-Australia plate. This study verified that there is positive correlation between coastal line geometry and the tsunami impact, based on fractal analysis. The case study is Maumere, Flores island, East Nusa Tenggara, Indonesia. Result of the study is expected to be used for predicting the tsunami impact intensiveness at other areas.
Spatial Entropy and Fractal Dimension of Urban Form
Chen, Yanguang; Feng, Jian
2016-01-01
Entropy is an important concept in the studies on complex systems such as cities. Spatial patterns and processes can be described with varied entropy functions. However, spatial entropy always depends on the scale of measurement, and we cannot find a characteristic value for it. In contrast, entropy-based fractal parameters can be employed to characterize scale-free phenomena. This paper is devoted to exploring the similarities and differences between spatial entropy and fractal dimension in urban description. Drawing an analogy between cities and growing fractals, we illustrate the definitions of fractal dimension based on several entropy formulae. Three representative fractal dimensions in the multifractal dimension set, capacity dimension, information dimension, and correlation dimension, are utilized to make an empirical analysis of Beijing's and Hangzhou's urban form using functional box-counting method. The results show that the entropy values are not determinate, but the fractal dimension value is cert...
Evaluation of 3D Printer Accuracy in Producing Fractal Structure.
Kikegawa, Kana; Takamatsu, Kyuuichirou; Kawakami, Masaru; Furukawa, Hidemitsu; Mayama, Hiroyuki; Nonomura, Yoshimune
2017-01-01
Hierarchical structures, also known as fractal structures, exhibit advantageous material properties, such as water- and oil-repellency as well as other useful optical characteristics, owing to its self-similarity. Various methods have been developed for producing hierarchical geometrical structures. Recently, fractal structures have been manufactured using a 3D printing technique that involves computer-aided design data. In this study, we confirmed the accuracy of geometrical structures when Koch curve-like fractal structures with zero to three generations were printed using a 3D printer. The fractal dimension was analyzed using a box-counting method. This analysis indicated that the fractal dimension of the third generation hierarchical structure was approximately the same as that of the ideal Koch curve. These findings demonstrate that the design and production of fractal structures can be controlled using a 3D printer. Although the interior angle deviated from the ideal value, the side length could be precisely controlled.
Automatic detection of microcalcifications with multi-fractal spectrum.
Ding, Yong; Dai, Hang; Zhang, Hang
2014-01-01
For improving the detection of micro-calcifications (MCs), this paper proposes an automatic detection of MC system making use of multi-fractal spectrum in digitized mammograms. The approach of automatic detection system is based on the principle that normal tissues possess certain fractal properties which change along with the presence of MCs. In this system, multi-fractal spectrum is applied to reveal such fractal properties. By quantifying the deviations of multi-fractal spectrums between normal tissues and MCs, the system can identify MCs altering the fractal properties and finally locate the position of MCs. The performance of the proposed system is compared with the leading automatic detection systems in a mammographic image database. Experimental results demonstrate that the proposed system is statistically superior to most of the compared systems and delivers a superior performance.
The coastline and lake shores on a fractal island
Energy Technology Data Exchange (ETDEWEB)
Blaudeck, Peter [Institut fuer Physik, Technische Universitaet, 09107 Chemnitz (Germany); Seeger, Steffen [Institut fuer Physik, Technische Universitaet, 09107 Chemnitz (Germany); Schulzky, Christian [Institut fuer Physik, Technische Universitaet, 09107 Chemnitz (Germany); Hoffmann, Karl Heinz [Institut fuer Physik, Technische Universitaet, 09107 Chemnitz (Germany); Dutta, Tapati [Physics Department, St Xavier' s College, Kolkata 700 016 (India); Tarafdar, Sujata [Condensed Matter Physics Research Centre, Jadavpur University, Kolkata 700 032 (India)
2006-02-17
We compute the fractal dimensions of the 'hulls' or external boundary and the boundaries of the internal cavities in several deterministic as well as random fractal structures. Our conclusion is that the two fractal dimensions are in fact identical. The deterministic fractals we study are Sierpinski carpets (SC) in a two-dimensional space and the random fractals are percolation clusters at criticality. As an intermediate case, we present results on some randomized SC. In the random structures, statistics of the area and perimeters of all internal cavities or holes are taken and the fractal dimension of the hull borderline is computed. Two different definitions of the borderline are used, considering nearest neighbours as well as nearest and second nearest neighbours as connected. The conclusion is valid for both cases.
Fractal dimension analysis of complexity in Ligeti piano pieces
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.
A model of characteristic earthquakes and its implications for regional seismicity
DEFF Research Database (Denmark)
López-Ruiz, R.; Vázquez-Prada, M.; Pacheco, A.F.
2004-01-01
Regional seismicity (i.e. that averaged over large enough areas over long enough periods of time) has a size-frequency relationship, the Gutenberg-Richter law, which differs from that found for some seismic faults, the Characteristic Earthquake relationship. But all seismicity comes in the end from...... active faults, so the question arises of how one seismicity pattern could emerge from the other. The recently introduced Minimalist Model of Vázquez-Prada et al. of characteristic earthquakes provides a simple representation of the seismicity originating from a single fault. Here, we show...... that a Characteristic Earthquake relationship together with a fractal distribution of fault lengths can accurately describe the total seismicity produced in a region. The resulting earthquake catalogue accounts for the addition of both all the characteristic and all the non-characteristic events triggered in the faults...
Redefining Earthquakes and the Earthquake Machine
Hubenthal, Michael; Braile, Larry; Taber, John
2008-01-01
The Earthquake Machine (EML), a mechanical model of stick-slip fault systems, can increase student engagement and facilitate opportunities to participate in the scientific process. This article introduces the EML model and an activity that challenges ninth-grade students' misconceptions about earthquakes. The activity emphasizes the role of models…
Children's Ideas about Earthquakes
Simsek, Canan Lacin
2007-01-01
Earthquake, a natural disaster, is among the fundamental problems of many countries. If people know how to protect themselves from earthquake and arrange their life styles in compliance with this, damage they will suffer will reduce to that extent. In particular, a good training regarding earthquake to be received in primary schools is considered…
Estimation of Fractal Dimension in Differential Diagnosis of Pigmented Skin Lesions
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.
Fractal dimension of chromatin: potential molecular diagnostic applications for cancer prognosis
Metze, Konradin
2013-01-01
Fractal characteristics of chromatin, revealed by light or electron microscopy, have been reported during the last 20 years. Fractal features can easily be estimated in digitalized microscopic images and are helpful for diagnosis and prognosis of neoplasias. During carcinogenesis and tumor progression, an increase of the fractal dimension (FD) of stained nuclei has been shown in intraepithelial lesions of the uterine cervix and the anus, oral squamous cell carcinomas or adenocarcinomas of the pancreas. Furthermore, an increased FD of chromatin is an unfavorable prognostic factor in squamous cell carcinomas of the oral cavity and the larynx, melanomas and multiple myelomas. High goodness-of-fit of the regression line of the FD is a favorable prognostic factor in acute leukemias and multiple myelomas. The nucleus has fractal and power-law organization in several different levels, which might in part be interrelated. Some possible relations between modifications of the chromatin organization during carcinogenesis and tumor progression and an increase of the FD of stained chromatin are suggested. Furthermore, increased complexity of the chromatin structure, loss of heterochromatin and a less-perfect self-organization of the nucleus in aggressive neoplasias are discussed. PMID:24063399
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Mahnaz Etehad Tavakol
2010-01-01
Full Text Available Early detection of breast cancer by means of thermal imaging has a long and extremely controversial history. Recently, the availability of highly sensitive infrared (IR cameras which can produce high-resolution diagnostic images of the temperature and vascular changes of breasts, as well as a better knowledge of advanced image processing techniques, has generated a renewed interest. The objective of this study is to investigate fractal analysis of breast thermal images and to develop an algorithm for detecting benignity and malignancy of breast diseases. The study is based on IR images captured by thermal camera, in which the resolution of the results is within the state of the art of IR camera. A total of 7 malignant cases and 8 benign cases have been considered. The breast images were first segmented by fuzzy c-means clustering. Then the first hottest regions for each image were identified and the fractal dimension of those regions was computed. It is shown that the fractal dimension results significantly differ between malignant and benign patterns, suggesting that fractal analysis may potentially improve the reliability of thermography in breast tumor detection.
Scale invariance of shallow seismicity and the prognostic signatures of earthquakes
Stakhovsky, I. R.
2017-08-01
The results of seismic investigations based on methods of the theory of nonequilibrium processes and self-similarity theory have shown that a shallow earthquake can be treated as a critical transition that occurs during the evolution of a non-equilibrium seismogenic system and is preceded by phenomena such as the scale invariance of spatiotemporal seismic structures. The implication is that seismicity can be interpreted as a purely multifractal process. Modeling the focal domain as a fractal cluster of microcracks allows formulating the prognostic signatures of earthquakes actually observed in seismic data. Seismic scaling permits monitoring the state of a seismogenic system as it approaches instability.
Enhanced Graphene Photodetector with Fractal Metasurface
DEFF Research Database (Denmark)
Fang, Jieran; Wang, Di; DeVault, Clayton T
2017-01-01
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...
Power spectra of the angular fractals
Zhong, Xihua; Zhu, Yafen; Zhou, Yueming
1993-09-01
Based on the angular backbone taken from the triangular Sierpinski gasket, several seLf-similar structures are disigned, corresponding diffraction screens are made, and the Fraunhofer patterns as power spectra of them are given. Based upon a viewpoint of generative production and by means of the ui-branched displacement operation, we have found the recurrence formulae of spectral structure factor for these angular fractals. As a example, the recurrence formulae of power spectra for a coherent point group is given, corresponding a series of curves as well as an isogram are plotted. The analysis of result shows that the power spectra of this fractal point group has a rotation symmetry and a mirror symmetry, and appears a period doubling phenomenon which follows the process of generative production.
A TUTORIAL INTRODUCTION TO ADAPTIVE FRACTAL ANALYSIS
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Michael A Riley
2012-09-01
Full Text Available The authors present a tutorial description of adaptive fractal analysis (AFA. AFA utilizes an adaptive detrending algorithm to extract globally smooth trend signals from the data and then analyzes the scaling of the residuals to the fit as a function of the time scale at which the fit is computed. The authors present applications to synthetic mathematical signals to verify the accuracy of AFA and demonstrate the basic steps of the analysis. The authors then present results from applying AFA to time series from a cognitive psychology experiment on repeated estimation of durations of time to illustrate some of the complexities of real-world data. AFA shows promise in dealing with many types of signals, but like any fractal analysis method there are special challenges and considerations to take into account, such as determining the presence of linear scaling regions.
On the permeability of fractal tube bundles
Zinovik, I
2011-01-01
The permeability of a porous medium is strongly affected by its local geometry and connectivity, the size distribution of the solid inclusions and the pores available for flow. Since direct measurements of the permeability are time consuming and require experiments that are not always possible, the reliable theoretical assessment of the permeability based on the medium structural characteristics alone is of importance. When the porosity approaches unity, the permeability-porosity relationships represented by the Kozeny-Carman equations and Archie's law predict that permeability tends to infinity and thus they yield unrealistic results if specific area of the porous media does not tend to zero. The goal of this paper is an evaluation of the relationships between porosity and permeability for a set of fractal models with porosity approaching unity and a finite permeability. It is shown that the two-dimensional foams generated by finite iterations of the corresponding geometric fractals can be used to model poro...
Fractal properties of LED avalanche breakdown
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Antonina S. Shashkina
2016-12-01
Full Text Available The conventional model of the processes occurring in the course of a p–n-junction's partial avalanche breakdown has been analyzed in this paper. Microplasma noise spectra of industrially produced LEDs were compared with those predicted by the model. It was established that the data obtained experimentally on reverse-biased LEDs could not be described in terms of this model. The degree to which the fractal properties were pronounced was shown to be variable by changing the reverse voltage. The discovered fractal properties of microplasma noise can serve as the basis for further studies which are bound to explain the breakdown characteristics of real LEDs and to correct the conventional model of p–n-junction's avalanche breakdown.
Fractal structures in centrifugal flywheel governor system
Rao, Xiao-Bo; Chu, Yan-Dong; Lu-Xu; Chang, Ying-Xiang; Zhang, Jian-Gang
2017-09-01
The global structure of nonlinear response of mechanical centrifugal governor, forming in two-dimensional parameter space, is studied in this paper. By using three kinds of phases, we describe how responses of periodicity, quasi-periodicity and chaos organize some self-similarity structures with parameters varying. For several parameter combinations, the regular vibration shows fractal characteristic, that is, the comb-shaped self-similarity structure is generated by alternating periodic response with intermittent chaos, and Arnold's tongues embedded in quasi-periodic response are organized according to Stern-Brocot tree. In particular, a new type of mixed-mode oscillations (MMOs) is found in the periodic response. These unique structures reveal the natural connection of various responses between part and part, part and the whole in parameter space based on self-similarity of fractal. Meanwhile, the remarkable and unexpected results are to contribute a valid dynamic reference for practical applications with respect to mechanical centrifugal governor.
Toward a new “Fractals-General Science”
Dorrah, Hassen Taher
2014-01-01
A recent study has shown that everywhere real systems follow common “fractals-general stacking behavior” during their change pathways (or evolutionary life cycles). This fact leads to the emergence of the new discipline “Fractals-General Science” as a mother-discipline (and acting as upper umbrella) of existing natural and applied sciences to commonly handle their fractals-general change behavior. It is, therefore, the main targets of this short communication are to present the motives, objec...
Fractal analysis of pharmaceutical particles by atomic force microscopy.
Li, T; Park, K
1998-08-01
Reliable methods are needed to characterize the surface roughness of pharmaceutical solid particles for quality control and for finding the correlations with other properties. In this study, we used fractal analysis to describe the surface roughness. Atomic force microscopy (AFM) was used to obtain three-dimensional surface profiles. The variation method was used to calculate fractal dimensions. We have measured fractal dimensions of four granule samples, four powders, and two freeze-dried powders. A computer-program was written to implement the variation method. The implementation was verified using the model surfaces generated by fractional Brownian motion. The fractal dimensions of most particles and granules were between 2.1 and 2.2, and were independent of the scan size we measured. The freeze-dried samples, however showed wide variation in the values of fractal dimension, which were dependent on the scan size. As scan size increased, the fractal dimension also increased up to 2.5. Fractal analysis can be used to describe surface roughness of pharmaceutical particles. The variation method allows calculation of reliable fractal dimensions of surface profiles obtained by AFM. Careful analysis is required for the estimation of fractal dimension, since the estimates are dependent on the algorithm and the digitized model size (i.e., number of data points of the measured surface profile) used. The fractal dimension of pharmaceutical materials is also a function of the observation scale i.e., the scan size) used in the profile measurement. The multi-fractal features and the scale-dependency of fractal dimension result from the artificial processes controlling the surface morphology.
A Fractal Perspective on Scale in Geography
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Bin Jiang
2016-06-01
Full Text Available Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information science, because of scale-related issues such as image resolution and the modifiable areal unit problem (MAUP. This paper argues that the confusion and frustration arise from traditional Euclidean geometric thinking, in which locations, directions, and sizes are considered absolute, and it is now time to revise this conventional thinking. Hence, we review fractal geometry, together with its underlying way of thinking, and compare it to Euclidean geometry. Under the paradigm of Euclidean geometry, everything is measurable, no matter how big or small. However, most geographic features, due to their fractal nature, are essentially unmeasurable or their sizes depend on scale. For example, the length of a coastline, the area of a lake, and the slope of a topographic surface are all scale-dependent. Seen from the perspective of fractal geometry, many scale issues, such as the MAUP, are inevitable. They appear unsolvable, but can be dealt with. To effectively deal with scale-related issues, we present topological and scaling analyses illustrated by street-related concepts such as natural streets, street blocks, and natural cities. We further contend that one of the two spatial properties, spatial heterogeneity, is de facto the fractal nature of geographic features, and it should be considered the first effect among the two, because it is global and universal across all scales, which should receive more attention from practitioners of geography.
An Introduction to Fractals and Chaos
1989-06-01
fractals) on a scale of about 10 km on down. More recently, from satellite photographs, it was found that they’re actually self-similar on a scale of 1000 km...8217’ kJ". ’u.z - S’la way Our world changes with time" a o f.. Ivrick, ry -c 1.i- Firzcrals are nivel in so many .Ahe- toip. t,c~h.~’.~- ways that it is
FRACTAL DIMENSIONALITY ANALYSIS OF MAMMARY GLAND THERMOGRAMS
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Yu. E. Lyah
2016-06-01
Full Text Available Thermography may enable early detection of a cancer tumour within a mammary gland at an early, treatable stage of the illness, but thermogram analysis methods must be developed to achieve this goal. This study analyses the feasibility of applying the Hurst exponent readings algorithm for evaluation of the high dimensionality fractals to reveal any possible difference between normal thermograms (NT and malignant thermograms (MT.
Fractal dimension of down fibre assemblies
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Gao, J; Yu, W [College of Textiles, Donghua University, West Yan' an Road 1882, Shanghai 200051 (China); Pan, N [Biological and Agricultural Engineering Department, University of California at Davis California 95616 (United States)], E-mail: gao2001jing@dhu.edu.cn
2008-02-15
As porous media materials, down fiber assemblies have excellent heat insulating and are widely used in the thermal products. The internal microstructures and fibers arrangement strongly influence heat conduction in down fiber assembly. This work presents a unified treatment using the tool of ''local fractal dimensions'' to describe the geometric complexity of the relative fibers arrangement in the down fiber assembly.
Box fractal dimension in speckle images
Rabal, Héctor; Grumel, Eduardo; Cap, Nelly; Buffarini, Leandro; Trivi, Marcelo
2017-06-01
In this paper, we propose a generalization of the box fractal dimension in images by considering the curve obtained from its value as a function of the binarization threshold. This curve can be used to describe speckle patterns. We show some examples of both objective simulated and experimental and subjective speckle in some cases of interest. The concept can be extended for all types of images.
Password Authentication Based on Fractal Coding Scheme
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Nadia M. G. Al-Saidi
2012-01-01
Full Text Available Password authentication is a mechanism used to authenticate user identity over insecure communication channel. In this paper, a new method to improve the security of password authentication is proposed. It is based on the compression capability of the fractal image coding to provide an authorized user a secure access to registration and login process. In the proposed scheme, a hashed password string is generated and encrypted to be captured together with the user identity using text to image mechanisms. The advantage of fractal image coding is to be used to securely send the compressed image data through a nonsecured communication channel to the server. The verification of client information with the database system is achieved in the server to authenticate the legal user. The encrypted hashed password in the decoded fractal image is recognized using optical character recognition. The authentication process is performed after a successful verification of the client identity by comparing the decrypted hashed password with those which was stored in the database system. The system is analyzed and discussed from the attacker’s viewpoint. A security comparison is performed to show that the proposed scheme provides an essential security requirement, while their efficiency makes it easier to be applied alone or in hybrid with other security methods. Computer simulation and statistical analysis are presented.
Stochastic Fractal Based Multiobjective Fruit Fly Optimization
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Zuo Cili
2017-06-01
Full Text Available The fruit fly optimization algorithm (FOA is a global optimization algorithm inspired by the foraging behavior of a fruit fly swarm. In this study, a novel stochastic fractal model based fruit fly optimization algorithm is proposed for multiobjective optimization. A food source generating method based on a stochastic fractal with an adaptive parameter updating strategy is introduced to improve the convergence performance of the fruit fly optimization algorithm. To deal with multiobjective optimization problems, the Pareto domination concept is integrated into the selection process of fruit fly optimization and a novel multiobjective fruit fly optimization algorithm is then developed. Similarly to most of other multiobjective evolutionary algorithms (MOEAs, an external elitist archive is utilized to preserve the nondominated solutions found so far during the evolution, and a normalized nearest neighbor distance based density estimation strategy is adopted to keep the diversity of the external elitist archive. Eighteen benchmarks are used to test the performance of the stochastic fractal based multiobjective fruit fly optimization algorithm (SFMOFOA. Numerical results show that the SFMOFOA is able to well converge to the Pareto fronts of the test benchmarks with good distributions. Compared with four state-of-the-art methods, namely, the non-dominated sorting generic algorithm (NSGA-II, the strength Pareto evolutionary algorithm (SPEA2, multi-objective particle swarm optimization (MOPSO, and multiobjective self-adaptive differential evolution (MOSADE, the proposed SFMOFOA has better or competitive multiobjective optimization performance.
New Derivatives on the Fractal Subset of Real-Line
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Alireza Khalili Golmankhaneh
2016-01-01
Full Text Available In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on the fractals subset of real-line lies in the fact that they are better at modeling processes with memory effect.
Fractal analysis for osteoporosis: a likelihood ratio approach
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Jessica B. Lepschy
2010-01-01
Full Text Available Based on the traditional fractal theory and on the paper of Stehlík, (2009 the range of fractal dimension of osteoporosis vertebras is analysed. First we give an insight into the field of fractals and the usage of fractals in medicine. After this we show how the analytical tool of Stehlík, (2009 may be applied to the osteoporosis vertebras. It turns out that the used method can be applied very well and that it could help with medical diagnosis. Real data example illustrates the methods discussed.
Fractal analysis of electroviscous effect in charged porous media
Liang, Mingchao; Yang, Shanshan; Cui, Xiaomin; Li, Yongfeng
2017-04-01
An electroviscous effect is an important phenomenon making flow resistance larger in electrically charged capillaries or porous media. Thus, the study of this phenomenon is very meaningful in various scientific and engineering fields. In this work, based on the fractal characteristics of porous media, a theoretical apparent viscosity model is expressed in terms of the solid surface zeta potential, physical properties (viscosity, dielectric constant, and conductivity) of the electrolyte solution, maximum pore radius, pore fractal dimension, and tortuosity fractal dimension of porous media. A reasonably good match is found between the results from the fractal model and the available experimental data reported in the literature.
Adhesion and Disintegration Phenomena on Fractal Agar Gel Surfaces.
Kudo, Ayano; Sato, Marika; Sawaguchi, Haruna; Hotta, Jun-Ichi; Mayama, Hiroyuki; Nonomura, Yoshimune
2016-11-01
In the present study, mechanical phenomena on fractal agar gel were analyzed to understand the interfacial properties of hydrophilic biosurfaces. The evaluation of adhesion strength between the fractal agar gel surfaces showed that the fractal structure inhibits the adhesion between the agar gel surfaces. In addition, when the disintegration behavior of an agar gel block was observed between fractal agar gel substrates, the rough structure prevented the sliding of an agar gel block. These findings are useful for understanding the biological significance of rough structure on the biological surfaces.
International Conference on Advances of Fractals and Related Topics
Lau, Ka-Sing
2014-01-01
This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.
Lu, Xiao-long; Zheng, Qin; Yin, Xian-zhen; Xiao, Guang-qing; Liao, Zu-hua; Yang, Ming; Zhang, Ji-wen
2015-06-01
The shape and structure of granules are controlled by the granulation process, which is one of the main factors to determine the nature of the solid dosage forms. In this article, three kinds of granules of a traditional Chinese medicine for improving appetite and promoting digestion, namely, Jianwei Granules, were prepared using granulation technologies as pendular granulation, high speed stirring granulation, and fluidized bed granulation and the powder properties of them were investigated. Meanwhile, synchrotron radiation X-ray computed micro tomography (SR-µCT) was applied to quantitatively determine the irregular internal structures of the granules. The three-dimensional (3D) structure models were obtained by 3D reconstruction, which were more accurately to characterize the three-dimensional structures of the particles through the quantitative data. The models were also used to quantitatively compare the structural differences of granules prepared by different granulation processes with the same formula, so as to characterize how the production process plays a role in the pharmaceutical behaviors of the granules. To focus on the irregularity of the particle structure, the box counting method was used to calculate the fractal dimensions of the granules. The results showed that the fractal dimension is more sensitive to reflect the minor differences in the structure features than the conventional parameters, and capable to specifically distinct granules in structure. It is proved that the fractal dimension could quantitatively characterize the structural information of irregular granules. It is the first time suggested by our research that the fractal dimension difference (Df,c) between two fractal dimension parameters, namely, the volume matrix fractal dimension and the surface matrix fractal dimension, is a new index to characterize granules with irregular structures and evaluate the effects of production processes on the structures of granules as a new
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
2013-12-01
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 gray 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
Crowdsourced earthquake early warning
Minson, Sarah E.; Brooks, Benjamin A.; Glennie, Craig L.; Murray, Jessica R.; Langbein, John O.; Owen, Susan E.; Heaton, Thomas H.; Iannucci, Robert A.; Hauser, Darren L.
2015-01-01
Earthquake early warning (EEW) can reduce harm to people and infrastructure from earthquakes and tsunamis, but it has not been implemented in most high earthquake-risk regions because of prohibitive cost. Common consumer devices such as smartphones contain low-cost versions of the sensors used in EEW. Although less accurate than scientific-grade instruments, these sensors are globally ubiquitous. Through controlled tests of consumer devices, simulation of an Mw (moment magnitude) 7 earthquake on California’s Hayward fault, and real data from the Mw 9 Tohoku-oki earthquake, we demonstrate that EEW could be achieved via crowdsourcing.
Lowen, S. B.; Teich, M. C.
1993-08-01
Hair-cell ion channels, which provide a crucial link in the transformation of incoming acoustic information to neural action-potential trains, switch between open and closed states with power-law-distributed (fractal) dwell times. Trains of action potentials recorded from auditory nerves in mammals always exhibit fractal behavior, including a 1/f-type spectrum, for long time scales. We provide a mathematical model linking these two fractal behaviors within a common framework.
Incubation of Chile's 1960 Earthquake
Atwater, B. F.; Cisternas, M.; Salgado, I.; Machuca, G.; Lagos, M.; Eipert, A.; Shishikura, M.
2003-12-01
trees. We sampled 45 such trees, some of them completely dead and the rest surviving only from shoots near the ground. One-third of these trees lived through the 1837 earthquake; they contain over 180 annual rings. Five of the trees also contain rings earlier than 1737. From this evidence, we tentatively infer that the islands underwent more subsidence in 1960 than they did in 1737 or 1837. Comparisons with old Chilean documents for the estuary further suggest that subsidence in 1837 did not approach that of 1960. In their depiction and description of the Misquihue islands in 1874, surveyor Francisco Vidal and botanist Carlos Juliet show nothing like the ghost forests seen today. Twice in the first 37 years after the 1837 earthquake, surveyors mapped as emergent several islands that the 1960 earthquake would lower into tidal water. Today, 43 years after they subsided in 1960, these islands remain submerged as barren intertidal flats. Research supported by Fondecyt 1020224.
Are fractal dimensions of the spatial distribution of mineral deposits meaningful?
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.
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Francis Lopes Pacagnelli
2016-01-01
Full Text Available Abstract Background: Right-sided heart failure has high morbidity and mortality, and may be caused by pulmonary arterial hypertension. Fractal dimension is a differentiated and innovative method used in histological evaluations that allows the characterization of irregular and complex structures and the quantification of structural tissue changes. Objective: To assess the use of fractal dimension in cardiomyocytes of rats with monocrotaline-induced pulmonary arterial hypertension, in addition to providing histological and functional analysis. Methods: Male Wistar rats were divided into 2 groups: control (C; n = 8 and monocrotaline-induced pulmonary arterial hypertension (M; n = 8. Five weeks after pulmonary arterial hypertension induction with monocrotaline, echocardiography was performed and the animals were euthanized. The heart was dissected, the ventricles weighed to assess anatomical parameters, and histological slides were prepared and stained with hematoxylin/eosin for fractal dimension analysis, performed using box-counting method. Data normality was tested (Shapiro-Wilk test, and the groups were compared with non-paired Student t test or Mann Whitney test (p < 0.05. Results: Higher fractal dimension values were observed in group M as compared to group C (1.39 ± 0.05 vs. 1.37 ± 0.04; p < 0.05. Echocardiography showed lower pulmonary artery flow velocity, pulmonary acceleration time and ejection time values in group M, suggesting function worsening in those animals. Conclusion: The changes observed confirm pulmonary-arterial-hypertension-induced cardiac dysfunction, and point to fractal dimension as an effective method to evaluate cardiac morphological changes induced by ventricular dysfunction.
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Jinxiang Xi
Full Text Available 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.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.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.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.
Assessment of seismic hazard of the Japanese islands based on fractal analysis of GPS time series
Filatov, D. M.; Lyubushin, A. A.
2017-07-01
Based on the fractal analysis of the time series of the Earth's surface vertical displacements in the region of the Japanese Archipelago, the maps of the estimates of seismic activity in the region over 2015 are constructed. The analysis of the maps revealed several segments of the territory which are prone to the emergence of significant earthquakes. The characteristic peculiarity is noted in the change of the behavior of the geophysical dynamic system—the Earth's crust—before the occurrence of seismic events: the mechanism of transition to the critical state demonstrates the energy preservation of the low frequencies with the simultaneous energy decay of the middle and high frequencies, which differs from the behavior of the other dynamical systems.
Changes in Dimensionality and Fractal Scaling Suggest Soft-Assembled Dynamics in Human EEG
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Wiltshire, Travis; Euler, Matthew J.; McKinney, Ty
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...
No unitary bootstrap for the fractal Ising model
Golden, John
2015-01-01
We consider the conformal bootstrap for spacetime dimension $1
Fractal Dimension and Universality in Avascular Tumor Growth
Ribeiro, Fabiano L; Mata, Angélica S
2016-01-01
The comprehension of tumor growth is a intriguing subject for scientists. New researches has been constantly required to better understand the complexity of this phenomenon. In this paper, we pursue a physical description that account for some experimental facts involving avascular tumor growth. We have proposed an explanation of some phenomenological (macroscopic) aspects of tumor, as the spatial form and the way it growths, from a individual-level (microscopic) formulation. The model proposed here is based on a simple principle: competitive interaction between the cells dependent on their mutual distances. As a result, we reproduce many empirical evidences observed in real tumors, as exponential growth in their early stages followed by a power law growth. The model also reproduces the fractal space distribution of tumor cells and the universal behavior presented in animals and tumor growth, conform reported by West, Guiot {\\it et. al.}\\cite{West2001,Guiot2003}. The results suggest that the universal similar...
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.
Fractal And Multi-fractal Analysis Of The Hydraulic Property Variations Of Karst Aquifers
Majone, B.; Bellin, A.; Borsato, A.
Karst aquifers are very heterogeneous systems with hydraulic property variations acting at several continuous and discrete scales, as a result of the fact that macro- structural elements, such as faults and karst channels, and fractures are intertwined in a complex, and largely unknown, manner. Many experimental studies on karst springs showed that the recession limb of the typical storm hydrograph can be divided into several regions with different decreasing rate, suggesting that the discharge is com- posed of contributions experiencing different travel times. Despite the importance of karst aquifers as a source of fresh water for most Mediterranean countries fostered the attention of scientists and practitioners, the mechanisms controlling runoff production in such a complex subsurface environment need to be further explored. A detailed sur- vey, lasting for one year and conducted by the Museo Tridentino di Scienze Naturali of Trento, represents a unique opportunity to analyze the imprint of hydraulic prop- erty variations on the hydrological signal recorded at the spring of Prese Val, located in the Dolomiti group near Trento. Data include water discharge (Q), temperature (T) and electric conductivity of water (E). Analysis of the data revealed that the power spectrum of E scales as 1/f, with slightly, but significantly, smaller than 1. The scaling nature of the E-signal has been confirmed by rescaled range analysis of the time series. Since the electric conductivity is proportional to the concentration of ions in the spring water, which increases with the residence time, one may conclude that the fractal structure of the E signal is the consequence of a similar structure in the hydraulic property variations. This finding confirms previous results of Kirchner et al. (2000), who reported a similar behavior for chloride concentration in the streamflow of three small Welsh catchments. A more detailed analysis revealed that E and T are both multifractal signals
Definition of fractal topography to essential understanding of scale-invariance
Jin, Yi; Wu, Ying; Li, Hui; Zhao, Mengyu; Pan, Jienan
2017-01-01
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. PMID:28436450
Kamer, Yavor; Ouillon, Guy; Sornette, Didier; Wössner, Jochen
2015-08-01
We present the "condensation" method that exploits the heterogeneity of the probability distribution functions (PDFs) of event locations to improve the spatial information content of seismic catalogs. As its name indicates, the condensation method reduces the size of seismic catalogs while improving the access to the spatial information content of seismic catalogs. The PDFs of events are first ranked by decreasing location errors and then successively condensed onto better located and lower variance event PDFs. The obtained condensed catalog differs from the initial catalog by attributing different weights to each event, the set of weights providing an optimal spatial representation with respect to the spatially varying location capability of the seismic network. Synthetic tests on fractal distributions perturbed with realistic location errors show that condensation improves spatial information content of the original catalog, which is quantified by the likelihood gain per event. Applied to Southern California seismicity, the new condensed catalog highlights major mapped fault traces and reveals possible additional structures while reducing the catalog length by ∼25%. The condensation method allows us to account for location error information within a point based spatial analysis. We demonstrate this by comparing the multifractal properties of the condensed catalog locations with those of the original catalog. We evidence different spatial scaling regimes characterized by distinct multifractal spectra and separated by transition scales. We interpret the upper scale as to agree with the thickness of the brittle crust, while the lower scale (2.5 km) might depend on the relocation procedure. Accounting for these new results, the epidemic type aftershock model formulation suggests that, contrary to previous studies, large earthquakes dominate the earthquake triggering process. This implies that the limited capability of detecting small magnitude events cannot be used
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Alexander J. Bies
2016-07-01
Full Text Available Two measures are commonly used to describe scale-invariant complexity in images: fractal dimension (D and power spectrum decay rate (β. Although a relationship between these measures has been derived mathematically, empirical validation across measurements is lacking. Here, we determine the relationship between D and β for 1- and 2-dimensional fractals. We find that for 1-dimensional fractals, measurements of D and β obey the derived relationship. Similarly, in 2-dimensional fractals, measurements along any straight-line path across the fractal’s surface obey the mathematically derived relationship. However, the standard approach of vision researchers is to measure β of the surface after 2-dimensional Fourier decomposition rather than along a straight-line path. This surface technique provides measurements of β that do not obey the mathematically derived relationship with D. Instead, this method produces values of β that imply that the fractal’s surface is much smoother than the measurements along the straight lines indicate. To facilitate communication across disciplines, we provide empirically derived equations for relating each measure of β to D. Finally, we discuss implications for future research on topics including stress reduction and the perception of motion in the context of a generalized equation relating β to D.
Universal fractality of morphological transitions in stochastic growth processes.
Nicolás-Carlock, J R; Carrillo-Estrada, J L; Dossetti, V
2017-06-14
Stochastic growth processes give rise to diverse and intricate structures everywhere in nature, often referred to as fractals. In general, these complex structures reflect the non-trivial competition among the interactions that generate them. In particular, the paradigmatic Laplacian-growth model exhibits a characteristic fractal to non-fractal morphological transition as the non-linear effects of its growth dynamics increase. So far, a complete scaling theory for this type of transitions, as well as a general analytical description for their fractal dimensions have been lacking. In this work, we show that despite the enormous variety of shapes, these morphological transitions have clear universal scaling characteristics. Using a statistical approach to fundamental particle-cluster aggregation, we introduce two non-trivial fractal to non-fractal transitions that capture all the main features of fractal growth. By analyzing the respective clusters, in addition to constructing a dynamical model for their fractal dimension, we show that they are well described by a general dimensionality function regardless of their space symmetry-breaking mechanism, including the Laplacian case itself. Moreover, under the appropriate variable transformation this description is universal, i.e., independent of the transition dynamics, the initial cluster configuration, and the embedding Euclidean space.
Fractal Modeling and Scaling in Natural Systems - Editorial
The special issue of Ecological complexity journal on Fractal Modeling and Scaling in Natural Systems contains representative examples of the status and evolution of data-driven research into fractals and scaling in complex natural systems. The editorial discusses contributions to understanding rela...
Clear and fuzzy fractal models of spreading dangerous environmental phenomena
Directory of Open Access Journals (Sweden)
A.E. Guy
2006-04-01
Full Text Available This article is devoted to investigation of possibility of widening models of spreading dangerous environmental phenomena, in particular Grassberger’s models, on the base of notion of fuzzy fractal sets introduced by one of the authors. Basic concepts from the theory of fuzzy fractals are considered.
Extended fractal analysis method and its application for linear rivers
Wang, Liqin; Long, Yi; Cui, Shilin
2008-10-01
Extended fractal analysis method can analyze the fractal character (i.e. self-similarity) objectively, especially the difference and change of the shape and the structure in different observation scale intervals. As one of the common fractal objects, river on the map can be surveyed its length and quantified the complexity of its shape and structure as well as its partial details with Extended Fractal Dimension Analysis method (abbreviated as EFDA). Compared to the traditional method, EFDA has unparalleled advantages. Considering the extended fractal character with scaling variance, and based on its simulating function adopting the Inverse Logistic Model, the paper gained the extended fractal function for quantifying the length of the river depending on the different observing scales. Furthermore, based on the mathematical derivation of its simulating function and fractal analysis, the paper obtained the relevant parameter for establishing Meta Fractal Dimension (abbreviated as MFD) Model to quantify the local complexity of the river on the map. Several experiments based on the China's seven major rivers done indicate that this method is easy to operate and has a relatively high calculation precision and a logical result of spatial analysis.
Usefulness of fractal analysis for the diagnosis of periodontitis
Energy Technology Data Exchange (ETDEWEB)
Cha, Sang Yun; Han, Won Jeong; Kim, Eun Kyung [Dankook Univ. School of Dentistry, Seoul (Korea, Republic of)
2001-03-15
To evaluate the usefulness of fractal analysis for diagnosis of periodontitis. Each 30 cases of periapical films of male mandibular molar were selected in normal group and patient group which had complete furcation involvement. They were digitized at 300 dpi, 256 gray levels and saved with gif format. Rectangular ROIs (10 X 20 pixel) were selected at furcation, interdental crest, and interdental middle 1/3 area. Fractal dimensions were calculated three times at each area by mass radius method and were determined using a mean of three measurements. We computed fractal dimensions at furcation and interdental crest area of normal group with those of patient group. And then we compared ratio of fractal dimensions at furcation area, interdental crest area to interdental middle 1/3 area. Fractal dimension at interdental crest area of normal group was 1.979{+-}0.018 (p<0.05). The radio of fractal dimension at furcation area to interdental middle 1/3 of normal group was 1.006{+-}0.018 and that of patient group 0.9940.018 (p<0.05). The radio of fractal dimension at interdental crest and furcation area to interdental middle 1/3 area showed a statistically significant difference between normal and patient group. In conclusion, it is thought that fractal analysis might be useful for the diagnosis of periodontitis.
Fractal and Multifractal Models Applied to Porous Media - Editorial
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 ...
Fractal and euclidean interaction in some transmission problems
Directory of Open Access Journals (Sweden)
Maria Agostina Vivaldi
2007-12-01
Full Text Available In this talk some model examples of second order elliptic transmission problems with highly conductive layers will be described. Regularity and numerical results for solutions of transmission problems across fractal layers imbedded in Euclidean domains will be presented in the aim of better understanding the analytical problems which arise when fractal and Euclidean structures mutually interact.
Bouguer correction density determination from fractal analysis using ...
African Journals Online (AJOL)
In this work, Bouguer density is determined using the fractal approach. This technique was applied to the gravity data of the Kwello area of the Basement Complex, north-western Nigeria. The density obtained using the fractal approach is 2500 kgm which is lower than the conventional value of 2670 kgm used for average ...
Earthquake prediction from China's mobile gravity data
Directory of Open Access Journals (Sweden)
Yiqing Zhu
2015-03-01
Full Text Available The relation between plate tectonics and earthquake evolution is analyzed systematically on the basis of 1998–2010 absolute and relative gravity data from the Crustal Movement Observation Network of China. Most earthquakes originated in the plate boundary or within the fault zone. Tectonic deformation was most intense and exhibited discontinuity within the tectonically active fault zone because of the differential movement; the stress accumulation produced an abrupt gravity change, which was further enhanced by the earthquake. The gravity data from mainland China since 2000 obviously reflected five major earthquakes (Ms > 7, all of which were better reflected than before 2000. Regional gravity anomalies and a gravity gradient change were observed in the area around the epicenter about 2 or 3 years before the earthquake occurred, suggesting that gravity change may be a seismic precursor. Furthermore, in this study, the medium-term predictions of the Ms7.3 Yutian, Ms8.0 Wenchuan, and Ms7.0 Lushan earthquakes are analytically presented and evaluated, especially to estimate location of earthquake.
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.
Hypnosis, suggestion, and suggestibility: an integrative model.
Lynn, Steven Jay; Laurence, Jean-Roch; Kirsch, Irving
2015-01-01
This article elucidates an integrative model of hypnosis that integrates social, cultural, cognitive, and neurophysiological variables at play both in and out of hypnosis and considers their dynamic interaction as determinants of the multifaceted experience of hypnosis. The roles of these variables are examined in the induction and suggestion stages of hypnosis, including how they are related to the experience of involuntariness, one of the hallmarks of hypnosis. It is suggested that studies of the modification of hypnotic suggestibility; cognitive flexibility; response sets and expectancies; the default-mode network; and the search for the neurophysiological correlates of hypnosis, more broadly, in conjunction with research on social psychological variables, hold much promise to further understanding of hypnosis.
Kim, SatByul; Saito, Tatsuhiko; Fukuyama, Eiichi; Kang, Tae-Seob
2016-04-01
Historical documents in Korea and China report abnormal waves in the sea and rivers close to the date of the 1707 Hoei earthquake, which occurred in the Nankai Trough, off southwestern Japan. This indicates that the tsunami caused by the Hoei earthquake might have reached Korea and China, which suggests a potential hazard in Korea from large earthquakes in the Nankai Trough. We conducted tsunami simulations to study the details of tsunamis in Korea caused by large earthquakes. Our results showed that the Hoei earthquake (Mw 8.8) tsunami reached the Korean Peninsula about 200 min after the earthquake occurred. The maximum tsunami height was ~0.5 m along the Korean coast. The model of the Hoei earthquake predicted a long-lasting tsunami whose highest peak arrived 600 min later after the first arrival near the coastline of Jeju Island. In addition, we conducted tsunami simulations using physics-based scenarios of anticipated earthquakes in the Nankai subduction zone. The maximum tsunami height in the scenarios (Mw 8.5-8.6) was ~0.4 m along the Korean coast. As a simple evaluation of larger possible tsunamis, we increased the amount of stress released by the earthquake by a factor of two and three, resulting in scenarios for Mw 8.8 and 8.9 earthquakes, respectively. The tsunami height increased by 0.1-0.4 m compared to that estimated by the Hoei earthquake.
Perceptual and physiological responses to Jackson Pollock’s fractals
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Richard eTaylor
2011-06-01
Full Text Available 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 ten 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.
Physics, Perception, and Physiological of Jackson Pollock's Fractals
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Richard P. Taylor
2011-05-01
Full Text Available Fractals have experienced considerable success 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 ten 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, EEG and preliminary fMRI measurement techniques. We discuss the artistic implications of the positive perceptual, physiological, and neurological responses to fractal patterns.
Multi-Scale Fractal Analysis of Image Texture and Pattern
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.
International Conference and Workshop on Fractals and Wavelets
Barnsley, Michael; Devaney, Robert; Falconer, Kenneth; Kannan, V; PB, Vinod
2014-01-01
Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.
Intergranular area microalloyed aluminium-silicate ceramics fractal analysis
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Purenović J.
2013-01-01
Full Text Available Porous aluminium-silicate ceramics, modified by alloying with magnesium and microalloying with alluminium belongs to a group of advanced multifunctional ceramics materials. This multiphase solid-solid system has predominantly amorphous microstructure and micro morphology. Intergranular and interphase areas are very complex, because they represent areas, where numbered processes and interactions take place, making new boundaries and regions with fractal nature. Fractal analysis of intergranular microstructure has included determination of ceramic grain fractal dimension by using Richardson method. Considering the fractal nature of intergranular contacts, it is possible to establish correlation between material electrical properties and fractal analysis, as a tool for future correlation with microstructure characterization. [Projekat Ministarstva nauke Republike Srbije, br. ON 172057 i br. III 45012
Permeability and porosity models of bi-fractal porous media
Tan, Xiao-Hua; Kui, Ming-Qing; Li, Xiao-Ping; Mao, Zheng-Lin; Xiao, Heng
2017-11-01
In previous studies, it is found that the frame and pore in porous media both possess the fractal geometric character. So the permeability and porosity models of bi-fractal porous media are derived based on the assumption that a porous media consists of fractal solid clusters and capillary bundles. The expressions of presented models are constituted by the fractal parameters of solid cluster and those of capillary bundle. Good agreement between model predictions and experimental data is obtained. This verifies the validity of the permeability and porosity models for bi-fractal porous media. The sensitive parameters that influence the permeability and porosity are specified, and their effects on the relationship between permeability and porosity are discussed.
Determination of fish gender using fractal analysis of ultrasound images
DEFF Research Database (Denmark)
McEvoy, Fintan J.; Tomkiewicz, Jonna; Støttrup, Josianne
2009-01-01
The gender of cod Gadus morhua can be determined by considering the complexity in their gonadal ultrasonographic appearance. The fractal dimension (DB) can be used to describe this feature in images. B-mode gonadal ultrasound images in 32 cod, where gender was known, were collected. Fractal...... by subjective analysis alone. The mean (and standard deviation) of the fractal dimension DB for male fish was 1.554 (0.073) while for female fish it was 1.468 (0.061); the difference was statistically significant (P=0.001). The area under the ROC curve was 0.84 indicating the value of fractal analysis in gender...... result. Fractal analysis is useful for gender determination in cod. This or a similar form of analysis may have wide application in veterinary imaging as a tool for quantification of complexity in images...
Enhancement of dielectrophoresis using fractal gold nanostructured electrodes.
Koklu, Anil; Sabuncu, Ahmet C; Beskok, Ali
2017-06-01
Dielectrophoretic motions of Saccharomyces cerevisiae (yeast) cells and colloidal gold are investigated using electrochemically modified electrodes exhibiting fractal topology. Electrodeposition of gold on electrodes generated repeated patterns with a fern-leaf type self-similarity. A particle tracking algorithm is used to extract dielectrophoretic particle velocities using fractal and planar electrodes in two different medium conductivities. The results show increased dielectrophoretic force when using fractal electrodes. Strong negative dielectrophoresis of yeast cells in high-conductivity media (1.5 S/m) is observed using fractal electrodes, while no significant motion is present using planar electrodes. Electrical impedance at the electrode/electrolyte interface is measured using impedance spectroscopy technique. Stronger electrode polarization (EP) effects are reported for planar electrodes. Decreased EP in fractal electrodes is considered as a reason for enhanced dielectrophoretic response. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Band structures in Sierpinski triangle fractal porous phononic crystals
Energy Technology Data Exchange (ETDEWEB)
Wang, Kai; Liu, Ying, E-mail: yliu5@bjtu.edu.cn; Liang, Tianshu
2016-10-01
In this paper, the band structures in Sierpinski triangle fractal porous phononic crystals (FPPCs) are studied with the aim to clarify the effect of fractal hierarchy on the band structures. Firstly, one kind of FPPCs based on Sierpinski triangle routine is proposed. Then the influence of the porosity on the elastic wave dispersion in Sierpinski triangle FPPCs is investigated. The sensitivity of the band structures to the fractal hierarchy is discussed in detail. The results show that the increase of the hierarchy increases the sensitivity of ABG (Absolute band gap) central frequency to the porosity. But further increase of the fractal hierarchy weakens this sensitivity. On the same hierarchy, wider ABGs could be opened in Sierpinski equilateral triangle FPPC; whilst, a lower ABG could be opened at lower porosity in Sierpinski right-angled isosceles FPPCs. These results will provide a meaningful guidance in tuning band structures in porous phononic crystals by fractal design.
DEFF Research Database (Denmark)
Holm, Isak Winkel
2012-01-01
In the vocabulary of modern disaster research, Heinrich von Kleist's seminal short story "The Earthquake in Chile" from 1806 is a tale of disaster vulnerability. The story is not just about a natural disaster destroying the innocent city of Santiago but also about the ensuing social disaster...... orchestrated by the citizens of Santiago themselves. Three cognitive schemes play a role for the way Kleist – and his fictional characters – imagine the vulnerability of human society: the theodicy, the sublime, and the state of exception. These three symbolic forms are part of the surprisingly small...... and surprisingly stable repertoire of cultural concepts and images that, for several centuries now, govern the way we think about disasters and the way we act when they strike. The task of a cultural disaster research, the essay suggests, is to study the deep grammar of our common imagination of disaster surfacing...
Encyclopedia of earthquake engineering
Kougioumtzoglou, Ioannis; Patelli, Edoardo; Au, Siu-Kui
2015-01-01
The Encyclopedia of Earthquake Engineering is designed to be the authoritative and comprehensive reference covering all major aspects of the science of earthquake engineering, specifically focusing on the interaction between earthquakes and infrastructure. The encyclopedia comprises approximately 265 contributions. Since earthquake engineering deals with the interaction between earthquake disturbances and the built infrastructure, the emphasis is on basic design processes important to both non-specialists and engineers so that readers become suitably well-informed without needing to deal with the details of specialist understanding. The content of this encyclopedia provides technically inclined and informed readers about the ways in which earthquakes can affect our infrastructure and how engineers would go about designing against, mitigating and remediating these effects. The coverage ranges from buildings, foundations, underground construction, lifelines and bridges, roads, embankments and slopes. The encycl...
The fractal theory of the Saturn Ring
Zelikin, Mikhail
2015-01-01
The true reason for partition of the Saturn ring as well as rings of other planets into great many of sub-rings is found. This reason is the theorem of Zelikin-Lokutsievskiy-Hildebrand about fractal structure of solutions to generic piece-wise smooth Hamiltonian systems. The instability of two-dimensional model of rings with continues surface density of particles distribution is proved both for Newtonian and for Boltzmann equations. We do not claim that we have solved the problem of stability...
Fractal-Flows and Time's Arrow
Susskind, Leonard
2012-01-01
This is the written version of a lecture at the KITP workshop on Bits, Branes, and Black Holes. In it I describe work with D. Harlow, S. Shenker, D. Stanford which explains how the tree-like structure of eternal inflation, together with the existence of terminal vacua, leads to an arrow-of-time. Conformal symmetry of the dS/CFT type is inconsistent with an arrow-of-time and must be broken. The presence in the landscape of terminal vacua leads to a new kind of attractor called a fractal-flow, ...
Chaotic Maps Dynamics, Fractals, and Rapid Fluctuations
Chen, Goong
2011-01-01
This book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include one-dimensional dynamical systems (interval maps), bifurcations, general topological, symbolic dynamical systems, fractals and a class of infinite-dimensional dynamical systems which are induced by interval maps, plus rapid fluctuations of chaotic maps as a
Trabecular Bone Mechanical Properties and Fractal Dimension
Hogan, Harry A.
1996-01-01
Countermeasures for reducing bone loss and muscle atrophy due to extended exposure to the microgravity environment of space are continuing to be developed and improved. An important component of this effort is finite element modeling of the lower extremity and spinal column. These models will permit analysis and evaluation specific to each individual and thereby provide more efficient and effective exercise protocols. Inflight countermeasures and post-flight rehabilitation can then be customized and targeted on a case-by-case basis. Recent Summer Faculty Fellowship participants have focused upon finite element mesh generation, muscle force estimation, and fractal calculations of trabecular bone microstructure. Methods have been developed for generating the three-dimensional geometry of the femur from serial section magnetic resonance images (MRI). The use of MRI as an imaging modality avoids excessive exposure to radiation associated with X-ray based methods. These images can also detect trabecular bone microstructure and architecture. The goal of the current research is to determine the degree to which the fractal dimension of trabecular architecture can be used to predict the mechanical properties of trabecular bone tissue. The elastic modulus and the ultimate strength (or strain) can then be estimated from non-invasive, non-radiating imaging and incorporated into the finite element models to more accurately represent the bone tissue of each individual of interest. Trabecular bone specimens from the proximal tibia are being studied in this first phase of the work. Detailed protocols and procedures have been developed for carrying test specimens through all of the steps of a multi-faceted test program. The test program begins with MRI and X-ray imaging of the whole bones before excising a smaller workpiece from the proximal tibia region. High resolution MRI scans are then made and the piece further cut into slabs (roughly 1 cm thick). The slabs are X-rayed again
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.
Earthquake Prognosis With Applied Microseism.
Ahmedov, N.; Nagiyev, A.
Earthquakes are the most dangerous natural catastrophy in terms of numerous casualties, amount of damages, areal coverage and difficulties associated with a need to provide secure measures. Inability to forecast these events makes the situation worse due to the following circumstances:-their buried focuses are invisible in the subsurface, they occur suddenly as a thunder, and some tens of the seconds later they leave devastated areas and casualties of tens of thousands of people. Currently earthquake forecausting is actually absolutely inefficient. Microseism application is one of the possible ways to forecast earthquakes. These small oscillation of up-going low-ampitude, irregular wawes observed on seismograms are refered to as microseism. Having been different from earhquakes itself, they are continuous, that is, have no origin coordinate on time axis. Their occurence is associated with breakers observed along shorelines, strong wind and hurricane patterns and so on. J.J.Linch has discovered a new tool to monitor hurricane motion trend over the seas with applied microseism recorded at ad hocstations. Similar to these observations it became possible to monitor the formation of the earthquake focuses based on correlation between low-frequency horizontal ahannels'N-S and E-W components. Microseism field and preceding abnormal variations monitoring data derived from "Cherepaha" 3M and 6/12 device enable to draw out some systematic trend in amplitude/frecuency domain. This relationship observed in a certain frequency range made it possible to define the generation of earthquake focuses with regard to the monitoring station. This variation trend was observed while Turkish and Iranian events happened during 1990,1992, and 1997. It is suggested to be useful to verify these effects in other regions to further correlate available data and work out common forecausting criteria.
Multifractal analysis of 2001 Mw 7 . 7 Bhuj earthquake sequence in Gujarat, Western India
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.
Subduction zone earthquakes and stress in slabs
Vassiliou, M. S.; Hager, B. H.
1988-01-01
Simple viscous fluid models of subducting slabs are used to explain observations of the distribution of earthquakes as a function of depth and the orientation of stress axes of deep (greater than 300 km) and intermediate (70-300 km) earthquakes. Results suggest the following features in the distribution of earthquakes with depth: (1) an exponential decrease from shallow depths down to 250 to 300 km, (2) a minimum near 250 to 300 km, and (3) a deep peak below 300 km. Many shallow subducting slabs show only the first characteristic, while deeper extending regions tend to show all three features, with the deep peak varying in position and intensity. These data, combined with the results on the stress orientations of various-depth earthquakes, are consistent with the existence of a barrier of some sort at 670-km depth and a uniform viscosity mantle above this barrier.
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.
Drawing conformal diagrams for a fractal landscape
Winitzki, Sergei
2005-06-01
Generic models of cosmological inflation and the recently proposed scenarios of a recycling universe and the string theory landscape predict spacetimes whose global geometry is a stochastic, self-similar fractal. To visualize the complicated causal structure of such a universe, one usually draws a conformal (Carter-Penrose) diagram. I develop a new method for drawing conformal diagrams, applicable to arbitrary 1+1-dimensional spacetimes. This method is based on a qualitative analysis of intersecting lightrays and thus avoids the need for explicit transformations of the spacetime metric. To demonstrate the power and simplicity of this method, I present derivations of diagrams for spacetimes of varying complication. I then apply the lightray method to three different models of an eternally inflating universe (scalar-field inflation, recycling universe, and string theory landscape) involving the nucleation of nested asymptotically flat, de Sitter and/or anti-de Sitter bubbles. I show that the resulting diagrams contain a characteristic fractal arrangement of lines.
Wireless Fractal Ultra-Dense Cellular Networks
Hao, Yixue; Chen, Min; Hu, Long; Song, Jeungeun; Volk, Mojca; Humar, Iztok
2017-01-01
With the ever-growing number of mobile devices, there is an explosive expansion in mobile data services. This represents a challenge for the traditional cellular network architecture to cope with the massive wireless traffic generated by mobile media applications. To meet this challenge, research is currently focused on the introduction of a small cell base station (BS) due to its low transmit power consumption and flexibility of deployment. However, due to a complex deployment environment and low transmit power of small cell BSs, the coverage boundary of small cell BSs will not have a traditional regular shape. Therefore, in this paper, we discuss the coverage boundary of an ultra-dense small cell network and give its main features: aeolotropy of path loss fading and fractal coverage boundary. Simple performance analysis is given, including coverage probability and transmission rate, etc., based on stochastic geometry theory and fractal theory. Finally, we present an application scene and discuss challenges in the ultra-dense small cell network. PMID:28417927
Fractal-based image sequence compression scheme
Li, Haibo; Novak, Mirek; Forchheimer, Robert
1993-07-01
The dominant image transformation used in the existing fractal coding schemes is the affine function. Although an affine transformation is easy to compute and understand, its linear approximation ability limits the employment of larger range blocks, that is, it limits further improvement in compression efficiency. We generalize the image transformation from the usual affine form to the more general quadratic form, and provide theoretical requirements for the generalized transformation to be contractive. Based on the self-transformation system (STS) model, an image sequence coding scheme--fractal-based image sequence coding--is proposed. In this coding scheme, our generalized transformation is used to model the self- transformation is used to model the self-transformation from the domain block to its range blocks. Experimental results on a real image sequence show that for the same size of blocks, the SNR can be improved by 10 dB, or, for the same SNR of the decoded image sequence, the compression ratio is raised twofold when the new generalized transformation is used to replace the usual affine transformation. In addition, due to the utilization of the STS model, the computational complexity is only linearly related to the size of the 3-D blocks. This provides for fast encoding and decoding.
Fractal avalanche ruptures in biological membranes
Gözen, Irep; Dommersnes, Paul; Czolkos, Ilja; Jesorka, Aldo; Lobovkina, Tatsiana; Orwar, Owe
2010-11-01
Bilayer membranes envelope cells as well as organelles, and constitute the most ubiquitous biological material found in all branches of the phylogenetic tree. Cell membrane rupture is an important biological process, and substantial rupture rates are found in skeletal and cardiac muscle cells under a mechanical load. Rupture can also be induced by processes such as cell death, and active cell membrane repair mechanisms are essential to preserve cell integrity. Pore formation in cell membranes is also at the heart of many biomedical applications such as in drug, gene and short interfering RNA delivery. Membrane rupture dynamics has been studied in bilayer vesicles under tensile stress, which consistently produce circular pores. We observed very different rupture mechanics in bilayer membranes spreading on solid supports: in one instance fingering instabilities were seen resulting in floral-like pores and in another, the rupture proceeded in a series of rapid avalanches causing fractal membrane fragmentation. The intermittent character of rupture evolution and the broad distribution in avalanche sizes is consistent with crackling-noise dynamics. Such noisy dynamics appear in fracture of solid disordered materials, in dislocation avalanches in plastic deformations and domain wall magnetization avalanches. We also observed similar fractal rupture mechanics in spreading cell membranes.
Fractal profit landscape of the stock market.
Grönlund, Andreas; Yi, Il Gu; Kim, Beom Jun
2012-01-01
We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.
Wireless Fractal Ultra-Dense Cellular Networks.
Hao, Yixue; Chen, Min; Hu, Long; Song, Jeungeun; Volk, Mojca; Humar, Iztok
2017-04-12
With the ever-growing number of mobile devices, there is an explosive expansion in mobile data services. This represents a challenge for the traditional cellular network architecture to cope with the massive wireless traffic generated by mobile media applications. To meet this challenge, research is currently focused on the introduction of a small cell base station (BS) due to its low transmit power consumption and flexibility of deployment. However, due to a complex deployment environment and low transmit power of small cell BSs, the coverage boundary of small cell BSs will not have a traditional regular shape. Therefore, in this paper, we discuss the coverage boundary of an ultra-dense small cell network and give its main features: aeolotropy of path loss fading and fractal coverage boundary. Simple performance analysis is given, including coverage probability and transmission rate, etc., based on stochastic geometry theory and fractal theory. Finally, we present an application scene and discuss challenges in the ultra-dense small cell network.
Fractal Time Series—A Tutorial Review
Directory of Open Access Journals (Sweden)
Ming Li
2010-01-01
Full Text Available Fractal time series substantially differs from conventional one in its statistic properties. For instance, it may have a heavy-tailed probability distribution function (PDF, a slowly decayed autocorrelation function (ACF, and a power spectrum function (PSD of 1/f type. It may have the statistical dependence, either long-range dependence (LRD or short-range dependence (SRD, and global or local self-similarity. This article will give a tutorial review about those concepts. Note that a conventional time series can be regarded as the solution to a differential equation of integer order with the excitation of white noise in mathematics. In engineering, such as mechanical engineering or electronics engineering, engineers may usually consider it as the output or response of a differential system or filter of integer order under the excitation of white noise. In this paper, a fractal time series is taken as the solution to a differential equation of fractional order or a response of a fractional system or a fractional filter driven with a white noise in the domain of stochastic processes.
Sierpinski triangles as a tool to introduce fractal geometry to children and their parents
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
Fractal analysis of electrical trees in a cross-linked synthetic resin
Irurzun, I. M.; Vicente, J. L.; Cordero, M. C.; Mola, E. E.
2001-01-01
A statistical picture of dielectric breakdown in cross-linked polyester resins for a two-dimensional geometry is presented and discussed in this paper. A connection is established between the dielectric breakdown model (DBM) and the physical properties of the resin. Distribution propagation times of simulated trees obey a Weibull statistics, as was experimentally found. This adjustment is achieved by a redefinition of the unit of time, which is different from the one employed up to date. The experimental dependence of characteristic propagation times on the fractal dimension D can be reproduced in the range 1.2
A fractal analysis of skin pigmented lesions using the novel tool of the variogram technique
Energy Technology Data Exchange (ETDEWEB)
Mastrolonardo, Mario [Department of Medical and Occupational Sciences, Unit of Dermatology, Azienda Ospedaliero-Universitaria ' Ospedali Riuniti' di Foggia (Italy)]. E-mail: mariomastrolonardo@libero.it; Conte, Elio [Department of Medical and Occupational Sciences, Unit of Dermatology, Azienda Ospedaliero-Universitaria ' Ospedali Riuniti' di Foggia (Italy); Department of Pharmacology and Human Physiology, TIRES-Center for Innovative Technology for Signal Detection and Processing, Bari University, 70100 Bari (Italy); Zbilut, Joseph P. [Department of Molecular Biophysics and Physiology, Rush University, Chicago, IL 60612 (United States)
2006-06-15
The incidence of the cutaneous malignant melanoma is increasing rapidly in the world [Ferlay J, Bray F, Pisani P, et al. GLOBOCAN 2000: Cancer incidence, mortality and prevalence worldwide, Version 1.0 IARC Cancer Base no. 5. Lyon: IARC Press, 2001]. The therapeutic address requires a method having high sensitivity and capability to diagnose such disease at an early stage. We introduce a new diagnostic method based on non-linear methodologies. In detail we suggest that fractal as well as noise and chaos dynamics are the most important components responsible for genetic instability of melanocytes. As consequence we introduce the new technique of the variogram and of fractal analysis extended to the whole regions of interest of skin in order to obtain parameters able to identify the malignant lesion. In a preliminary analysis, satisfactory results are reached.
Noda, Masahiro; Demura, Shin-Ichi
2006-04-01
To examine the influence of muscle fatigue on center of pressure displacement during quiet standing using quantitative and fractal analyses, 12 healthy young men and women did the exercise stress test on the triceps surae muscle until fatigued. Subjects were measured for body stability for 60 sec. before and after the exercise. Quantitative analysis showed that center-of-pressure parameters for distance, velocity, amplitude distribution, and mean vector length of sway in the anterior/posterior direction changed significantly after muscle fatigue but not on the periodic parameters. This result suggested that quantitative analysis may identify the effects of muscle fatigue on the parameters that show displacement in the anterior/posterior direction of center of pressure. Fractal analysis indicated the value of critical point coordinates increased after muscle fatigue. This analysis can clarify the fundamental postural control strategy and time-series characteristics of postural sway which cannot be identified by spectral analysis.
ABC of multi-fractal spacetimes and fractional sea turtles
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.
ABC of multi-fractal spacetimes and fractional sea turtles
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)
2016-04-15
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. (orig.)
Insights on the fractal-fracture behaviour relationship
Directory of Open Access Journals (Sweden)
Rodrigues José de Anchieta
1998-01-01
Full Text Available The fractals theory has been increasingly applied in the field of materials science and engineering. Models of fractal lines and surfaces have been generated to describe the microstructural features of materials. Special interest is placed upon a description of the fracture surface based on a fractal geometry in order to understand the crack path in materials. Several papers have demonstrated the relationship between the fractal dimension of a fracture surface and the values of roughness and fracture toughness. In this work an extension of the theory of fractals for ceramic materials is proposed, to which the crack deflection toughening mechanism is thought to be related. In order to accomplish this objective, a review describing the concept of fractals and its relationship with the fracture toughness is presented. In the following part, a correlation between fractal dimension, total energy of fracture and the average resistance to crack propagation is proposed; all these parameters being dependent on the history and on the complexity of crack propagation path.
Fractal dimension determination of sol-gel powders using transmission electron microscopy images
Energy Technology Data Exchange (ETDEWEB)
Dobrescu, Gianina; Crisan, Maria; Zaharescu, Maria; Ionescu, N.I
2004-09-15
SiO{sub 2}, TiO{sub 2} and AlO(OH) powders obtained by the sol-gel method were investigated by transmission electron microscopy. The mass-radius relation was used to determine the fractal dimensions from the images. These fractal dimensions were corrected in order to obtain the powder fractal dimensions. The results indicate a good fractal behavior and high fractal dimensions.
High Attenuation Rate for Shallow, Small Earthquakes in Japan
Si, Hongjun; Koketsu, Kazuki; Miyake, Hiroe
2017-09-01
We compared the attenuation characteristics of peak ground accelerations (PGAs) and velocities (PGVs) of strong motion from shallow, small earthquakes that occurred in Japan with those predicted by the equations of Si and Midorikawa (J Struct Constr Eng 523:63-70, 1999). The observed PGAs and PGVs at stations far from the seismic source decayed more rapidly than the predicted ones. The same tendencies have been reported for deep, moderate, and large earthquakes, but not for shallow, moderate, and large earthquakes. This indicates that the peak values of ground motion from shallow, small earthquakes attenuate more steeply than those from shallow, moderate or large earthquakes. To investigate the reason for this difference, we numerically simulated strong ground motion for point sources of M w 4 and 6 earthquakes using a 2D finite difference method. The analyses of the synthetic waveforms suggested that the above differences are caused by surface waves, which are predominant at stations far from the seismic source for shallow, moderate earthquakes but not for shallow, small earthquakes. Thus, although loss due to reflection at the boundaries of the discontinuous Earth structure occurs in all shallow earthquakes, the apparent attenuation rate for a moderate or large earthquake is essentially the same as that of body waves propagating in a homogeneous medium due to the dominance of surface waves.
Stress drops of induced and tectonic earthquakes in the central United States are indistinguishable.
Huang, Yihe; Ellsworth, William L; Beroza, Gregory C
2017-08-01
Induced earthquakes currently pose a significant hazard in the central United States, but there is considerable uncertainty about the severity of their ground motions. We measure stress drops of 39 moderate-magnitude induced and tectonic earthquakes in the central United States and eastern North America. Induced earthquakes, more than half of which are shallower than 5 km, show a comparable median stress drop to tectonic earthquakes in the central United States that are dominantly strike-slip but a lower median stress drop than that of tectonic earthquakes in the eastern North America that are dominantly reverse-faulting. This suggests that ground motion prediction equations developed for tectonic earthquakes can be applied to induced earthquakes if the effects of depth and faulting style are properly considered. Our observation leads to the notion that, similar to tectonic earthquakes, induced earthquakes are driven by tectonic stresses.
National Clearinghouse for Educational Facilities, 2008
2008-01-01
Earthquakes are low-probability, high-consequence events. Though they may occur only once in the life of a school, they can have devastating, irreversible consequences. Moderate earthquakes can cause serious damage to building contents and non-structural building systems, serious injury to students and staff, and disruption of building operations.…
2004-01-01
Following their request for help from members of international organisations, the permanent Mission of the Islamic Republic of Iran has given the following bank account number, where you can donate money to help the victims of the Bam earthquake. Re: Bam earthquake 235 - UBS 311264.35L Bubenberg Platz 3001 BERN
Particle Swarm Optimization for Multiband Metamaterial Fractal Antenna
Directory of Open Access Journals (Sweden)
Balamati Choudhury
2013-01-01
Full Text Available The property of self-similarity, recursive irregularity, and space filling capability of fractal antennas makes it useful for various applications in wireless communication, including multiband miniaturized antenna designs. In this paper, an effort has been made to use the metamaterial structures in conjunction with the fractal patch antenna, which resonates at six different frequencies covering both C and X band. Two different types of square SRR are loaded on the fractal antenna for this purpose. Particle swarm optimization (PSO is used for optimization of these metamaterial structures. The optimized metamaterial structures, after loading upon, show significant increase in performance parameters such as bandwidth, gain, and directivity.
Polygon-based fractals from compressed iterated function systems.
Van Loocke, Philip
2010-01-01
This paper addresses the equivalence between iterative function systems (IFS). It also explains how to classify and reduce the parameter space for a particular class of IFS.The proposed method generates various fractal textures for regular polygons and allows the creation of polygon-based fractal flakes, polygon-based spirals, and many other forms. It employs sth-order restriction, a new version of recurrent iterated function systems. Level-specified symmetry in the fractals is controlled through rth-level symmetrization.
Fractal aspects and convergence of Newton`s method
Energy Technology Data Exchange (ETDEWEB)
Drexler, M. [Oxford Univ. Computing Lab. (United Kingdom)
1996-12-31
Newton`s Method is a widely established iterative algorithm for solving non-linear systems. Its appeal lies in its great simplicity, easy generalization to multiple dimensions and a quadratic local convergence rate. Despite these features, little is known about its global behavior. In this paper, we will explain a seemingly random global convergence pattern using fractal concepts and show that the behavior of the residual is entirely explicable. We will also establish quantitative results for the convergence rates. Knowing the mechanism of fractal generation, we present a stabilization to the orthodox Newton method that remedies the fractal behavior and improves convergence.
The Application of Fractal Theory in Image Recognition
Directory of Open Access Journals (Sweden)
Qiu Li
2014-04-01
Full Text Available At present, technicians are constantly exploring how to do effective managements and convenient and efficient queries on the large number of images in database. This article puts forward a new idea that doing the image retrieval with the similarity characteristics of fractal theory. It makes image similarity verification with the method of Opency image histogram and makes explanations by using the application of fractal theory in image pattern recognition. Fractal theory has provided a new method for the methods of image pattern recognition, the recognition research on related images and the classification of huge image database.
Generalized Fractals for Computer Generated Art: Preliminary Results
Babbs, Charles F
2017-01-01
This paper explores new types of fractals created by iteration of the functions xn+1 = f1(xn, yn) and yn+1 = f2(xn, yn) in a general plane, rather than in the complex plane. Iteration of such functions generates orbits with novel fractal patterns. Especially interesting are N-th order polynomials, raised to a positive or negative integer power, p. Such functions create novel fractal patterns, including budding, spiked, striped, dragon head, and bat-like forms. The present faculty working p...
FRACTAL IMAGE FEATURE VECTORS WITH APPLICATIONS IN FRACTOGRAPHY
Directory of Open Access Journals (Sweden)
Hynek Lauschmann
2011-05-01
Full Text Available The morphology of fatigue fracture surface (caused by constant cycle loading is strictly related to crack growth rate. This relation may be expressed, among other methods, by means of fractal analysis. Fractal dimension as a single numerical value is not sufficient. Two types of fractal feature vectors are discussed: multifractal and multiparametric. For analysis of images, the box-counting method for 3D is applied with respect to the non-homogeneity of dimensions (two in space, one in brightness. Examples of application are shown: images of several fracture surfaces are analyzed and related to crack growth rate.
Moisture diffusivity in structure of random fractal fiber bed
Energy Technology Data Exchange (ETDEWEB)
Zhu, Fanglong, E-mail: zhufanglong_168@163.com [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); The Chinese People' s Armed Police Forces Academy, Langfan City (China); Zhou, Yu; Feng, Qianqian [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); Xia, Dehong [School of Mechanical Engineering, University of Science and Technology, Beijing (China)
2013-11-08
A theoretical expression related to effective moisture diffusivity to random fiber bed is derived by using fractal theory and considering both parallel and perpendicular channels to diffusion flow direction. In this Letter, macroporous structure of hydrophobic nonwoven material is investigated, and Knudsen diffusion and surface diffusion are neglected. The effective moisture diffusivity predicted by the present fractal model are compared with water vapor transfer rate (WVTR) experiment data and calculated values obtained from other theoretical models. This verifies the validity of the present fractal diffusivity of fibrous structural beds.
Sandwich type plasmonic platform for MEF using silver fractals
DEFF Research Database (Denmark)
Raut, Sangram L.; Rich, Ryan; Shtoyko, Tanya
2015-01-01
In this report, we describe a plasmonic platform with silver fractals for metal enhanced fluorescence (MEF) measurements. When a dye containing surface was brought into contact with silver fractals, a significantly enhanced fluorescence signal from the dye was observed. Fluorescence enhancement...... was studied with the N-methyl-azadioxatriangulenium chloride salt (Me-ADOTA·Cl) in PVA films made from 0.2% PVA (w/v) solution spin-coated on a clean glass coverslip. The Plasmonic Platforms (PP) were assembled by pressing together silver fractals on one glass slide and a separate glass coverslip spin...
Journal of Reading, 1987
1987-01-01
Offers (1) suggestions for improving college students' study skills; (2) a system for keeping track of parent, teacher, and community contacts; (3) suggestions for motivating students using tic tac toe; (4) suggestions for using etymology to improve word retention; (5) a word search grid; and (6) suggestions for using postcards in remedial reading…
Modelling the elements of country vulnerability to earthquake disasters.
Asef, M R
2008-09-01
Earthquakes have probably been the most deadly form of natural disaster in the past century. Diversity of earthquake specifications in terms of magnitude, intensity and frequency at the semicontinental scale has initiated various kinds of disasters at a regional scale. Additionally, diverse characteristics of countries in terms of population size, disaster preparedness, economic strength and building construction development often causes an earthquake of a certain characteristic to have different impacts on the affected region. This research focuses on the appropriate criteria for identifying the severity of major earthquake disasters based on some key observed symptoms. Accordingly, the article presents a methodology for identification and relative quantification of severity of earthquake disasters. This has led to an earthquake disaster vulnerability model at the country scale. Data analysis based on this model suggested a quantitative, comparative and meaningful interpretation of the vulnerability of concerned countries, and successfully explained which countries are more vulnerable to major disasters.
Geoelectric Anomalies Preceding the Aug. 24 2016 Amatrice, Italy Earthquake
Scoville, J.; Bobrovskiy, V.; Freund, F. T.
2016-12-01
We report on geoelectric measurements taken at 70 and 120 km from the epicenter of the M6.2 Amatrice Central Italy Earthquake Aug. 24, 2016. Two stations, each consisting of 12 buried electrodes at depths of 1 to 3 meters, recorded ground EMF values once per second for approximately one year prior to the earthquake. Several geoelectric anomalies suggest the incidence of seismic electric signals in the weeks leading up to the earthquake. Notably, EMF values in the DC regime deviated progressively farther from baseline levels and AC components exhibited episodes of significant nonstationarity in their frequency spectra as the earthquake approached.
A fractal model of the Universe
Gottlieb, Ioan
The book represents a revisioned, extended, completed and translated version of the book "Superposed Universes. A scientific novel and a SF story" (1995). The book contains a hypothesis by the author concerning the complexity of the Nature. An introduction to the theories of numbers, manyfolds and topology is given. The possible connection with the theory of evolution of the Universe is discussed. The book contains also in the last chapter a SF story based on the hypothesis presented. A connection with fractals theory is given. A part of his earlier studies (1955-1956) were subsequently published without citation by Ali Kyrala (Phys. Rev. vol.117, No.5, march 1, 1960). The book contains as an important appendix the early papers (some of which are published in the coauthoprship with his scientific advisors): 1) T.T. Vescan, A. Weiszmann and I.Gottlieb, Contributii la studiul problemelor geometrice ale teoriei relativitatii restranse. Academia R.P.R. Baza Timisoara. Lucrarile consfatuirii de geometrie diferentiala din 9-12 iunie 1955. In this paper the authors show a new method of the calculation of the metrics. 2) Jean Gottlieb, L'hyphotese d'un modele de la structure de la matiere, Revista Matematica y Fisica Teorica, Serie A, Volumen XY, No.1, y.2, 1964 3) I. Gottlieb, Some hypotheses on space, time and gravitation, Studies in Gravitation Theory, CIP Press, Bucharest, 1988, pp.227-234 as well as some recent papers (published in the coauthorship with his disciples): 4)M. Agop, Gottlieb speace-time. A fractal axiomatic model of the Universe. in Particles and Fields, Editors: M.Agop and P.D. Ioannou, Athens University Press, 2005, pp. 59-141 5) I. Gottlieb, M.Agop and V.Enache, Games with Cantor's dust. Chaos, Solitons and Fractals, vol.40 (2009) pp. 940-945 6) I. Gottlieb, My picture over the World, Bull. of the Polytechnic Institute of Iasi. Tom LVI)LX, Fasc. 1, 2010, pp. 1-18. The book contains also a dedication to father Vasile Gottlieb and wife Cleopatra
Do weak global stresses synchronize earthquakes?
Bendick, R.; Bilham, R.
2017-08-01
Insofar as slip in an earthquake is related to the strain accumulated near a fault since a previous earthquake, and this process repeats many times, the earthquake cycle approximates an autonomous oscillator. Its asymmetric slow accumulation of strain and rapid release is quite unlike the harmonic motion of a pendulum and need not be time predictable, but still resembles a class of repeating systems known as integrate-and-fire oscillators, whose behavior has been shown to demonstrate a remarkable ability to synchronize to either external or self-organized forcing. Given sufficient time and even very weak physical coupling, the phases of sets of such oscillators, with similar though not necessarily identical period, approach each other. Topological and time series analyses presented here demonstrate that earthquakes worldwide show evidence of such synchronization. Though numerous studies demonstrate that the composite temporal distribution of major earthquakes in the instrumental record is indistinguishable from random, the additional consideration of event renewal interval serves to identify earthquake groupings suggestive of synchronization that are absent in synthetic catalogs. We envisage the weak forces responsible for clustering originate from lithospheric strain induced by seismicity itself, by finite strains over teleseismic distances, or by other sources of lithospheric loading such as Earth's variable rotation. For example, quasi-periodic maxima in rotational deceleration are accompanied by increased global seismicity at multidecadal intervals.
Earthquakes trigger the loss of groundwater biodiversity
Galassi, Diana M. P.; Lombardo, Paola; Fiasca, Barbara; di Cioccio, Alessia; di Lorenzo, Tiziana; Petitta, Marco; di Carlo, Piero
2014-09-01
Earthquakes are among the most destructive natural events. The 6 April 2009, 6.3-Mw earthquake in L'Aquila (Italy) markedly altered the karstic Gran Sasso Aquifer (GSA) hydrogeology and geochemistry. The GSA groundwater invertebrate community is mainly comprised of small-bodied, colourless, blind microcrustaceans. We compared abiotic and biotic data from two pre-earthquake and one post-earthquake complete but non-contiguous hydrological years to investigate the effects of the 2009 earthquake on the dominant copepod component of the obligate groundwater fauna. Our results suggest that the massive earthquake-induced aquifer strain biotriggered a flushing of groundwater fauna, with a dramatic decrease in subterranean species abundance. Population turnover rates appeared to have crashed, no longer replenishing the long-standing communities from aquifer fractures, and the aquifer became almost totally deprived of animal life. Groundwater communities are notorious for their low resilience. Therefore, any major disturbance that negatively impacts survival or reproduction may lead to local extinction of species, most of them being the only survivors of phylogenetic lineages extinct at the Earth surface. Given the ecological key role played by the subterranean fauna as decomposers of organic matter and ``ecosystem engineers'', we urge more detailed, long-term studies on the effect of major disturbances to groundwater ecosystems.
Earthquakes trigger the loss of groundwater biodiversity
Galassi, Diana M. P.; Lombardo, Paola; Fiasca, Barbara; Di Cioccio, Alessia; Di Lorenzo, Tiziana; Petitta, Marco; Di Carlo, Piero
2014-01-01
Earthquakes are among the most destructive natural events. The 6 April 2009, 6.3-Mw earthquake in L'Aquila (Italy) markedly altered the karstic Gran Sasso Aquifer (GSA) hydrogeology and geochemistry. The GSA groundwater invertebrate community is mainly comprised of small-bodied, colourless, blind microcrustaceans. We compared abiotic and biotic data from two pre-earthquake and one post-earthquake complete but non-contiguous hydrological years to investigate the effects of the 2009 earthquake on the dominant copepod component of the obligate groundwater fauna. Our results suggest that the massive earthquake-induced aquifer strain biotriggered a flushing of groundwater fauna, with a dramatic decrease in subterranean species abundance. Population turnover rates appeared to have crashed, no longer replenishing the long-standing communities from aquifer fractures, and the aquifer became almost totally deprived of animal life. Groundwater communities are notorious for their low resilience. Therefore, any major disturbance that negatively impacts survival or reproduction may lead to local extinction of species, most of them being the only survivors of phylogenetic lineages extinct at the Earth surface. Given the ecological key role played by the subterranean fauna as decomposers of organic matter and “ecosystem engineers”, we urge more detailed, long-term studies on the effect of major disturbances to groundwater ecosystems. PMID:25182013
The Christchurch earthquake stroke incidence study.
Wu, Teddy Y; Cheung, Jeanette; Cole, David; Fink, John N
2014-03-01
We examined the impact of major earthquakes on acute stroke admissions by a retrospective review of stroke admissions in the 6 weeks following the 4 September 2010 and 22 February 2011 earthquakes. The control period was the corresponding 6 weeks in the previous year. In the 6 weeks following the September 2010 earthquake there were 97 acute stroke admissions, with 79 (81.4%) ischaemic infarctions. This was similar to the 2009 control period which had 104 acute stroke admissions, of whom 80 (76.9%) had ischaemic infarction. In the 6 weeks following the February 2011 earthquake, there were 71 stroke admissions, and 61 (79.2%) were ischaemic infarction. This was less than the 96 strokes (72 [75%] ischaemic infarction) in the corresponding control period. None of the comparisons were statistically significant. There was also no difference in the rate of cardioembolic infarction from atrial fibrillation between the study periods. Patients admitted during the February 2011 earthquake period were less likely to be discharged directly home when compared to the control period (31.2% versus 46.9%, p=0.036). There was no observable trend in the number of weekly stroke admissions between the 2 weeks leading to and 6 weeks following the earthquakes. Our results suggest that severe psychological stress from earthquakes did not influence the subsequent short term risk of acute stroke, but the severity of the earthquake in February 2011 and associated civil structural damages may have influenced the pattern of discharge for stroke patients. Copyright © 2013 Elsevier Ltd. All rights reserved.
Transient effects in friction fractal asperity creep
Goedecke, Andreas
2013-01-01
Transient friction effects determine the behavior of a wide class of mechatronic systems. Classic examples are squealing brakes, stiction in robotic arms, or stick-slip in linear drives. To properly design and understand mechatronic systems of this type, good quantitative models of transient friction effects are of primary interest. The theory developed in this book approaches this problem bottom-up, by deriving the behavior of macroscopic friction surfaces from the microscopic surface physics. The model is based on two assumptions: First, rough surfaces are inherently fractal, exhibiting roughness on a wide range of scales. Second, transient friction effects are caused by creep enlargement of the real area of contact between two bodies. This work demonstrates the results of extensive Finite Element analyses of the creep behavior of surface asperities, and proposes a generalized multi-scale area iteration for calculating the time-dependent real contact between two bodies. The toolset is then demonstrated both...
Multifractal analysis of earthquakes in Kumaun Himalaya and its ...
Indian Academy of Sciences (India)
Earthquakes in this region are mainly caused due to release of elastic strain energy. The Himalayan region can be attributed to .... the Himalayas and the aseismic slip rate simu- lated below the Higher Himalayas suggests that ..... observed power-law build-up of intermediate events before a great earthquake represent the ...
Fractal based curves in musical creativity: A critical annotation
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.
Heritability of retinal vascular fractals: a twin study
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50-degree, disc-centred fundus photographs from 59 monozygotic and 55 dizygotic, same-sex twin pairs aged 20-46 years....... The retinal vascular fractal dimension was measured using the box-counting method and compared within monozygotic and dizygotic twin pairs using Pearson correlation coefficents. Falconer´s formula and quantitative genetic models were used to determine the genetic component of variation. Results: The retinal...... vascular fractal dimensions were measurable for both twins in 50 monozygotic and 49 dizygotic twin pairs. The mean fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, p=0.06), supporting that the study population was suitable...
Exact solutions for the differential equations in fractal heat transfer
Directory of Open Access Journals (Sweden)
Yang Chun-Yu
2016-01-01
Full Text Available In this article we consider the boundary value problems for differential equations in fractal heat transfer. The exact solutions of non-differentiable type are obtained by using the local fractional differential transform method.
A Stacked Microstrip Antenna Array with Fractal Patches
National Research Council Canada - National Science Library
Xueyao Ren; Xing Chen; Yufeng Liu; Wei Jin; Kama Huang
2014-01-01
A novel microstrip antenna array, which utilizes Giuseppe Peano fractal shaped patches as its radiation elements and adopts a two-layer stacked structure for achieving both wideband and high-gain...
Modelling, fabrication and characterisation of THz fractal meta-materials
DEFF Research Database (Denmark)
Xiao, S.; Zhou, L.; Malureanu, Radu
2011-01-01
We present theoretical predictions, fabrication procedure and characterisation results of fractal metamaterials for the THz frequency range. The characterisation results match well the predicted response thus validating both the fabrication procedure as well as the simulation one. Such systems show...
Fractal analysis of circulating platelets in type 2 diabetic patients.
Bianciardi, G; Tanganelli, I
2015-01-01
This paper investigates the use of computerized fractal analysis for objective characterization by means of transmission electron microscopy of the complexity of circulating platelets collected from healthy individuals and from type 2 diabetic patients, a pathologic condition in which platelet hyperreactivity has been described. Platelet boundaries were extracted by means of automatically image analysis. Local fractal dimension by box counting (measure of geometric complexity) was automatically calculated. The results showed that the platelet boundary observed by electron microscopy is fractal and that the shape of the circulating platelets is significantly more complex in the diabetic patients in comparison to healthy subjects (p fractal analysis of platelet shape by transmission electron microscopy can provide accurate, quantitative, data to study platelet activation in diabetes mellitus.
Improved Fourier-based characterization of intracellular fractal features
Xylas, Joanna; Quinn, Kyle P.; Hunter, Martin; Georgakoudi, Irene
2012-01-01
A novel Fourier-based image analysis method for measuring fractal features is presented which can significantly reduce artifacts due to non-fractal edge effects. The technique is broadly applicable to the quantitative characterization of internal morphology (texture) of image features with well-defined borders. In this study, we explore the capacity of this method for quantitative assessment of intracellular fractal morphology of mitochondrial networks in images of normal and diseased (precancerous) epithelial tissues. Using a combination of simulated fractal images and endogenous two-photon excited fluorescence (TPEF) microscopy, our method is shown to more accurately characterize the exponent of the high-frequency power spectral density (PSD) of these images in the presence of artifacts that arise due to cellular and nuclear borders. PMID:23188308
Transmission and reflection properties of terahertz fractal metamaterials
DEFF Research Database (Denmark)
Malureanu, Radu; Lavrinenko, Andrei; Cooke, David
2010-01-01
We use THz time-domain spectroscopy to investigate transmission and reflection properties of metallic fractal metamaterial structures. We observe loss of free-space energy at certain resonance frequencies, indicating excitation of surface modes of the metamaterial....
Nonlinear interpolation fractal classifier for multiple cardiac arrhythmias recognition
Energy Technology Data Exchange (ETDEWEB)
Lin, C.-H. [Department of Electrical Engineering, Kao-Yuan University, No. 1821, Jhongshan Rd., Lujhu Township, Kaohsiung County 821, Taiwan (China); Institute of Biomedical Engineering, National Cheng-Kung University, Tainan 70101, Taiwan (China)], E-mail: eechl53@cc.kyu.edu.tw; Du, Y.-C.; Chen Tainsong [Institute of Biomedical Engineering, National Cheng-Kung University, Tainan 70101, Taiwan (China)
2009-11-30
This paper proposes a method for cardiac arrhythmias recognition using the nonlinear interpolation fractal classifier. A typical electrocardiogram (ECG) consists of P-wave, QRS-complexes, and T-wave. Iterated function system (IFS) uses the nonlinear interpolation in the map and uses similarity maps to construct various data sequences including the fractal patterns of supraventricular ectopic beat, bundle branch ectopic beat, and ventricular ectopic beat. Grey relational analysis (GRA) is proposed to recognize normal heartbeat and cardiac arrhythmias. The nonlinear interpolation terms produce family functions with fractal dimension (FD), the so-called nonlinear interpolation function (NIF), and make fractal patterns more distinguishing between normal and ill subjects. The proposed QRS classifier is tested using the Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database. Compared with other methods, the proposed hybrid methods demonstrate greater efficiency and higher accuracy in recognizing ECG signals.
Two Dimensional Drug Diffusion Between Nanoparticles and Fractal Tumors
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.
The colours of infinity the beauty and power of fractals
Lesmoir-Gordon, Nigel
2010-01-01
The groundbreaking documentary (accompanying this book) has been shown in over 50 countries around the world. The contributors to the film are joined in this comprehensive survey of fractal theory and practice by leading experts in the field.
Fractality in nonequilibrium steady states of quasiperiodic systems
Varma, Vipin Kerala; de Mulatier, Clélia; Žnidarič, Marko
2017-09-01
We investigate the nonequilibrium response of quasiperiodic systems to boundary driving. In particular, we focus on the Aubry-André-Harper model at its metal-insulator transition and the diagonal Fibonacci model. We find that opening the system at the boundaries provides a viable experimental technique to probe its underlying fractality, which is reflected in the fractal spatial dependence of simple observables (such as magnetization) in the nonequilibrium steady state. We also find that the dynamics in the nonequilibrium steady state depends on the length of the chain chosen: generic length chains harbour qualitatively slower transport (different scaling exponent) than Fibonacci length chains, which is in turn slower than in the closed system. We conjecture that such fractal nonequilibrium steady states should arise in generic driven critical systems that have fractal properties.
A variable-order fractal derivative model for anomalous diffusion
Directory of Open Access Journals (Sweden)
Liu Xiaoting
2017-01-01
Full Text Available This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.
Mapping physical problems on fractals onto boundary value problems within continuum framework
Balankin, Alexander S.
2018-01-01
In this Letter, we emphasize that methods of fractal homogenization should take into account a loop structure of the fractal, as well as its connectivity and geodesic metric. The fractal attributes can be quantified by a set of dimension numbers. Accordingly, physical problems on fractals can be mapped onto the boundary values problems in the fractional-dimensional space with metric induced by the fractal topology. The solutions of these problems represent analytical envelopes of non-analytical functions defined on the fractal. Some examples are briefly discussed. The interplay between effects of fractal connectivity, loop structure, and mass distributions on electromagnetic fields in fractal media is highlighted. The effects of fractal connectivity, geodesic metric, and loop structure are outlined.
FRACTAL DIMENSIONING OF SAND GRAINS USING IMAGE ANALYSIS SYSTEM
Suat AKBULUT
2002-01-01
Engineers and earth scientists have successfully used the concept of fractal theory to better analyze the roughness of soil and/or rock particles, and how it affects the permeability, structure and distribution of pores in sedimentary rocks and their influence on strength. Use of fractals as a way to describe irregular or rough objects has been highlighted in articles by researchers working in fields such as powder mechanics, rock and soil mechanics, sedimentary petrography and geoenvironm...
The Fractal Universe: From the Planck to the Hubble Scale
Sidharth, B. G.
1999-01-01
We examine the fractal structure of the physical universe from the large scale to the smallest scale, including the phenomenon of fractal scaling. This is explained in terms of a stochastic underpinning for the laws of physics. A picture in pleasing agreement with experiment and observation at all scales emerges, very much in the spirit of Wheeler's "Law Without Law". It is argued that our depiction of the universe is akin to a broad brush delineation of a jagged coastline, the Compton wavele...
Slim Fractals: The Geometry of Doubly Transient Chaos
Directory of Open Access Journals (Sweden)
Xiaowen Chen
2017-06-01
Full Text Available Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between geometry and dynamics in undriven dissipative systems. These systems can exhibit a prevalent form of complex dynamics, dubbed doubly transient chaos because not only typical trajectories but also the (otherwise invariant chaotic saddles are transient. This property, along with a manifest lack of scale invariance, has hindered the study of the geometric properties of basin boundaries in these systems—most remarkably, the very question of whether they are fractal across all scales has yet to be answered. Here, we derive a general dynamical condition that answers this question, which we use to demonstrate that the basin boundaries can indeed form a true fractal; in fact, they do so generically in a broad class of transiently chaotic undriven dissipative systems. Using physical examples, we demonstrate that the boundaries typically form a slim fractal, which we define as a set whose dimension at a given resolution decreases when the resolution is increased. To properly characterize such sets, we introduce the notion of equivalent dimension for quantifying their relation with sensitive dependence on initial conditions at all scales. We show that slim fractal boundaries can exhibit complex geometry even when they do not form a true fractal and fractal scaling is observed only above a certain length scale at each boundary point. Thus, our results reveal slim fractals as a geometrical hallmark of transient chaos in undriven dissipative systems.
Structure of attractors and estimates of their fractal dimension
Matheus Cheque Bortolan
2013-01-01
This work is dedicated to the study of the structure of attractors of dynamical systems with the objective of estimating their fractal dimension. First we study the case of exponential global attractors of some generalized gradient-like semigroups in a general Banach space, and estimate their fractal dimension in terms of themaximumof the dimension of the local unstablemanifolds of the isolated invariant sets, Lipschitz properties of the semigroup and rate of exponential attraction. We also g...
Earthquake engineering in Peru
Vargas, N.J
1983-01-01
During the last decade, earthquake engineering research in Peru has been carried out at the Catholic University of Peru and at the Universidad Nacional de Ingeniera (UNI). The Geophysical Institute (IGP) under the auspices of the Organization of American States (OAS) has initiated in Peru other efforts in regional seismic hazard assessment programs with direct impact to the earthquake engineering program. Further details on these programs have been reported by L. Ocola in the Earthquake Information Bulletin, January-February 1982, vol. 14, no. 1, pp. 33-38.
Creating a fractal-based quality management infrastructure.
Pronovost, Peter J; Marsteller, Jill A
2014-01-01
The purpose of this paper is to describe how a fractal-based quality management infrastructure could benefit quality improvement (QI) and patient safety efforts in health care. The premise for this infrastructure comes from the QI work with health care professionals and organizations. The authors used the fractal structure system in a health system initiative, a statewide collaborative, and several countrywide efforts to improve quality of care. It is responsive to coordination theory and this infrastructure is responsive to coordination theory and repeats specific characteristics at every level of an organization, with vertical and horizontal connections among these levels to establish system-wide interdependence. The fractal system infrastructure helped a health system achieve 96 percent compliance on national core measures, and helped intensive care units across the USA, Spain, and England to reduce central line-associated bloodstream infections. The fractal system approach organizes workers around common goals, links all hospital levels and, supports peer learning and accountability, grounds solutions in local wisdom, and effectively uses available resources. The fractal structure helps health care organizations meet their social and ethical obligations as learning organizations to provide the highest possible quality of care and safety for patients using their services. The concept of deliberately creating an infrastructure to manage QI and patient safety work and support organizational learning is new to health care. This paper clearly describes how to create a fractal infrastructure that can scale up or down to a department, hospital, health system, state, or country.
Fractal continuum model for tracer transport in a porous medium.
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.
Generating one-column grids with fractal flow dimension
Doughty, Christine
2017-11-01
The grid generation capability built into the numerical simulator TOUGH for multi-phase fluid and heat flow through geologic media can create one-column grids with linear or radial geometry, corresponding to one-dimensional or two-dimensional radial flow, respectively. The integral-finite-difference-method that TOUGH employs for spatial discretization makes it very simple to generalize the grid-generation algorithm from integer to non-integer (fractal) flow dimension. Here the grid-generation algorithm is generalized to create one-column grids with fractal flow dimension ranging from less than 1 to 3. The fractal grid generation method is verified by comparing numerical simulation results to an analytical solution for a generalized Theis solution for integer and non-integer flow dimensions between 0.4 and 3. It is then applied to examine gas production decline curves from hydraulically fractured shale that is modeled as a fractal-dimensioned fracture network with flow dimensions between 0.25 and 3. Grids with fractal flow dimension are useful for representing flow through fracture networks or highly heterogeneous geologic media with fractal geometry, and may be particularly useful for inverse methods.
Intrinsic half-metallicity in fractal carbon nitride honeycomb lattices.
Wang, Aizhu; Zhao, Mingwen
2015-09-14
Fractals are natural phenomena that exhibit a repeating pattern "exactly the same at every scale or nearly the same at different scales". Defect-free molecular fractals were assembled successfully in a recent work [Shang et al., Nature Chem., 2015, 7, 389-393]. Here, we adopted the feature of a repeating pattern in searching two-dimensional (2D) materials with intrinsic half-metallicity and high stability that are desirable for spintronics applications. Using first-principles calculations, we demonstrate that the electronic properties of fractal frameworks of carbon nitrides have stable ferromagnetism accompanied by half-metallicity, which are highly dependent on the fractal structure. The ferromagnetism increases gradually with the increase of fractal order. The Curie temperature of these metal-free systems estimated from Monte Carlo simulations is considerably higher than room temperature. The stable ferromagnetism, intrinsic half-metallicity, and fractal characteristics of spin distribution in the carbon nitride frameworks open an avenue for the design of metal-free magnetic materials with exotic properties.
Experimental control of scaling behavior: what is not fractal?
Likens, Aaron D; Fine, Justin M; Amazeen, Eric L; Amazeen, Polemnia G
2015-10-01
The list of psychological processes thought to exhibit fractal behavior is growing. Although some might argue that the seeming ubiquity of fractal patterns illustrates their significance, unchecked growth of that list jeopardizes their relevance. It is important to identify when a single behavior is and is not fractal in order to make meaningful conclusions about the processes underlying those patterns. The hypothesis tested in the present experiment is that fractal patterns reflect the enactment of control. Participants performed two steering tasks: steering on a straight track and steering on a circular track. Although each task could be accomplished by holding the steering wheel at a constant angle, steering around a curve may require more constant control, at least from a psychological standpoint. Results showed that evidence for fractal behavior was strongest for the circular track; straight tracks showed evidence of two scaling regions. We argue from those results that, going forward, the goal of the fractal literature should be to bring scaling behavior under experimental control.
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
Manufacturer's Suggested Retail Prices
Rosenkranz, S.|info:eu-repo/dai/nl/157222241
2003-01-01
Based on arguments of the `reference- dependent' theory of consumer choice we assume that a retailer's discount of a manufacturer's suggested retail price changes consumers' demand. We can show that the producer benefits from suggesting a retail price. If consumers are additionally sufficiently
Inverted fractal analysis of TiO{sub x} thin layers grown by inverse pulsed laser deposition
Energy Technology Data Exchange (ETDEWEB)
Égerházi, L., E-mail: egerhazi.laszlo@gmail.com [University of Szeged, Faculty of Medicine, Department of Medical Physics and Informatics, Korányi fasor 9., H-6720 Szeged (Hungary); Smausz, T. [University of Szeged, Faculty of Science, Department of Optics and Quantum Electronics, Dóm tér 9., H-6720 Szeged (Hungary); Bari, F. [University of Szeged, Faculty of Medicine, Department of Medical Physics and Informatics, Korányi fasor 9., H-6720 Szeged (Hungary)
2013-08-01
Inverted fractal analysis (IFA), a method developed for fractal analysis of scanning electron microscopy images of cauliflower-like thin films is presented through the example of layers grown by inverse pulsed laser deposition (IPLD). IFA uses the integrated fractal analysis module (FracLac) of the image processing software ImageJ, and an objective thresholding routine that preserves the characteristic features of the images, independently of their brightness and contrast. IFA revealed f{sub D} = 1.83 ± 0.01 for TiO{sub x} layers grown at 5–50 Pa background pressures. For a series of images, this result was verified by evaluating the scaling of the number of still resolved features on the film, counted manually. The value of f{sub D} not only confirms the fractal structure of TiO{sub x} IPLD thin films, but also suggests that the aggregation of plasma species in the gas atmosphere may have only limited contribution to the deposition.
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.
Fractional Calculus of Fractal Interpolation Function on [0,b](b>0
Directory of Open Access Journals (Sweden)
XueZai Pan
2014-01-01
Full Text Available The paper researches the continuity of fractal interpolation function’s fractional order integral on [0,+∞ and judges whether fractional order integral of fractal interpolation function is still a fractal interpolation function on [0,b](b>0 or not. Relevant theorems of iterated function system and Riemann-Liouville fractional order calculus are used to prove the above researched content. The conclusion indicates that fractional order integral of fractal interpolation function is a continuous function on [0,+∞ and fractional order integral of fractal interpolation is still a fractal interpolation function on the interval [0,b].
National Research Council Canada - National Science Library
Ellsworth, William L
2013-01-01
...s. It has long been understood that earthquakes can be induced by impoundment of reservoirs, surface and underground mining, withdrawal of fluids and gas from the subsurface, and injection of fluids...
1988 Spitak Earthquake Database
National Oceanic and Atmospheric Administration, Department of Commerce — The 1988 Spitak Earthquake database is an extensive collection of geophysical and geological data, maps, charts, images and descriptive text pertaining to the...
Earthquakes and plate tectonics
Spall, H.
1977-01-01
The world's earthquakes are not randomly distributed over the Earth's surface. They tend to be concentrated in narrow zones. Why is this? And why are volcanoes and mountain ranges also found in these zones too?
Tweet Earthquake Dispatch (TED)
U.S. Geological Survey, Department of the Interior — The USGS is offering earthquake alerts via two twitter accounts: @USGSted and @USGSBigQuakes. On average, @USGSted and @USGSBigQuakes will produce about one tweet...
National Oceanic and Atmospheric Administration, Department of Commerce — This set of slides graphically illustrates the potential danger that major earthquakes pose to school structures and to the children and adults who happen to be...
Earthquake Ground Motion Selection
2012-05-01
Nonlinear analyses of soils, structures, and soil-structure systems offer the potential for more accurate characterization of geotechnical and structural response under strong earthquake shaking. The increasing use of advanced performance-based desig...
Dynamic rupture process of the great 1668 Anatolian earthquake
Kase, Yuko; Kondo, Hisao; Emre, Ömer
2010-05-01
al., 2009). We use a finite-difference method with a conventional grid formulated by Kase and Day (2006). Under the stress condition mentioned in the previous paragraph, a rupture initiating on the Erbaa segment propagates on the Niksar segment, but cannot jump across the 11-km-wide discontinuity between the Niksar and Resadiye segments. The result shows that the discontinuity acts as a geometrical barrier during ‘usual' earthquakes like ones in the 20th century earthquake sequence. In the Niksar segments, paleoslips of up to 8 m are observed as the 1668 earthquake. The paleoseismological data also show that the last earthquake before the 1668 earthquake was during the 6th century; thus, the interval between these was much longer than the 274 years between the 1942 and 1668 earthquakes. The 1668 earthquake following a long quiescent period had the capability for accumulating large strain. We thus assume larger values of stress drop for the Niksar and Erbaa segments, and simulate dynamic ruptures. When the stress drop is twice as large as in the 1942 earthquake, a rupture can jump across the 11-km-wide discontinuity and propagates onto the Resadiye segment. The maximum surface slip on the Niksar segment is 6.65 m. Although the simulated slip is less than the observed one, the rupture jump succeeds. The numerical result shows the possibility that the 1668 earthquake was a single multi-segment earthquake, therefore, it suggests that the 11 km-width jump in the 1668 earthquake was caused by large stress drop releasing the vast accumulation of strain during the preceding long quiescence.
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.
Pre-Earthquake Unipolar Electromagnetic Pulses
Scoville, J.; Freund, F.
2013-12-01
Transient ultralow frequency (ULF) electromagnetic (EM) emissions have been reported to occur before earthquakes [1,2]. They suggest powerful transient electric currents flowing deep in the crust [3,4]. Prior to the M=5.4 Alum Rock earthquake of Oct. 21, 2007 in California a QuakeFinder triaxial search-coil magnetometer located about 2 km from the epicenter recorded unusual unipolar pulses with the approximate shape of a half-cycle of a sine wave, reaching amplitudes up to 30 nT. The number of these unipolar pulses increased as the day of the earthquake approached. These pulses clearly originated around the hypocenter. The same pulses have since been recorded prior to several medium to moderate earthquakes in Peru, where they have been used to triangulate the location of the impending earthquakes [5]. To understand the mechanism of the unipolar pulses, we first have to address the question how single current pulses can be generated deep in the Earth's crust. Key to this question appears to be the break-up of peroxy defects in the rocks in the hypocenter as a result of the increase in tectonic stresses prior to an earthquake. We investigate the mechanism of the unipolar pulses by coupling the drift-diffusion model of semiconductor theory to Maxwell's equations, thereby producing a model describing the rock volume that generates the pulses in terms of electromagnetism and semiconductor physics. The system of equations is then solved numerically to explore the electromagnetic radiation associated with drift-diffusion currents of electron-hole pairs. [1] Sharma, A. K., P. A. V., and R. N. Haridas (2011), Investigation of ULF magnetic anomaly before moderate earthquakes, Exploration Geophysics 43, 36-46. [2] Hayakawa, M., Y. Hobara, K. Ohta, and K. Hattori (2011), The ultra-low-frequency magnetic disturbances associated with earthquakes, Earthquake Science, 24, 523-534. [3] Bortnik, J., T. E. Bleier, C. Dunson, and F. Freund (2010), Estimating the seismotelluric current
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
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.
Naturaleza fractal en redes de cristales de grasas
Directory of Open Access Journals (Sweden)
Gómez Herrera, C.
2004-06-01
Full Text Available The determination of the mechanical and rheological characterisÂtics of several plastic fats requires a detailed understanding of the microstructure of the fat crystal network aggregates. The (or A fractal approach is useful for the characterization of this microsÂtructure. This review begins with information on fractality and statistical self-similar structure. Estimations for fractal dimension by means of equations relating the volume fraction of solid fat to shear elastic modulus G' in linear region are described. The influence of interesterification on fractal dimension decrease (from 2, 46 to 2 ,15 for butterfat-canola oil blends is notable . This influence is not significant for fat blends without butterfat. The need for an increase in research concerning the relationship between fractality and rheology in plastic fats is emphasized.La determinación de las características mecánicas y reológicas de ciertas grasas plásticas requiere conocimientos detallados sobre las microestructuras de los agregados que forman la red de cristales grasos. El estudio de la naturaleza fractal de estas microestructuras resulta útil para su caracÂterización. Este artículo de información se inicia con descripciones de la dimensión fractal y de la "autosimilitud estadística". A continuación se describe el cálculo de la dimensión fractal mediante ecuaciones que relacionan la fracción en volumen de grasa sólida con el módulo de recuperación (G' dentro de un comportamiento viscoelástico lineal. Se destaca la influencia que la interesterificación ejerce sobre la dimensión fractal de una mezcla de grasa láctea y aceite de canola (que pasa de 2,64 a 2,15. Esta influencia no se presenta en mezclas sin grasa láctea. Se insiste sobre la necesidad de incrementar las investiÂgaciones sobre la relación entre reología y estructura fractal en grasas plásticas.
DEFF Research Database (Denmark)
Ratner, Helene Gad
2009-01-01
In Western secular societies, spiritual life is no longer limited to classical religious institutions but can also be found at workplace organizations. While spirituality is conventionally understood as a subjective and internal process, this paper proposes the concept of ‘suggestive objects’, co...... scaffolding. This has deep implications for our understanding of the sacred, including a better appreciation of the way that suggestive objects make the sacred durable, the way they organize it....
Suggestive techniques in advertising
Sora, Olena
2011-01-01
In my thesis I focused on a detailed analysis of suggestive techniques that appear in contemporary advertising. The issue of the effects of advertising has existed for many years and still staying timely. On the one side there are entrepreneurs and advertising agencies that are trying to influence opinions and suggest motivation for consuming. On the other side there is a potential customer, who is trying to obtain information about the product he needs and at the same time not letting anybod...
[Psychoanalysis and suggestion].
Thomä, H
1977-01-01
In the history of psychoanalysis the problem of suggestion has been a central one. At first it involved the necessity to establish the psychoanalytic technique as independent scientific paradigm in contrast to persuasion and hypnosis. However, it was not only the symptom-oriented suggestion that had to be given up for scientific reasons and reasons of treatment technique. Since professional and human factors as well could have influenced the psychoanalytic situation to revert to the traditional "suggestion", Freud has given some technical considerations (e.g. the mirror-analogy), that were meant to counteract the confusion of the psychoanalytic technique with the persuasive one that had to come up to late. The discovery of the transference phenomena has further complicated the problem. It became obvious that the capacity of the analyst to exert an influence and to have impact, originated in very basic human categories and their specific psychogenetic developments and distortions. This understanding contributed to the development of psychoanalytic theories of suggestibility. Until the present day the discovery of the transference phenomena has determined the discussions of psychoanalytic technique in term of the relationship between the special and general therapeutic factors (i.e. interpretation versus relationship). The departure from the therapeutic mode of persuasive suggestion and the introduction of psychoanalytic technique signaled the revolutionary paradigm of Sigmund Freud, i.e. the active participation of the patient and the process of observation. Often scientific problems related to this pradigm and suggestion are discussed concurrently.
Fractal analysis of sound signals in SAMPO 3065 combine harvester
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F Mahdiyeh Broujeni
2017-05-01
Full Text Available Introduction Nowadays, many studies were performed about noise source and its type and effects related to duration of sound emission. Most of these researches just report sound pressure level in frequency or time domain. These researches should be continued in order to find better absorber material in noise pollution. Use of fractal geometry is a new method in this filed. Wave fractal dimension value is a strong tool for diagnosis of signal instability and fractal analysis is a good method to finding sound signal characteristics. Therefore the aim of this study is on the fractal geometry of SAMPO 3065 combine harvester signals and determine the fractal dimension value of these signals in different operational conditions by Katz, Sevcik, Higuchi and MRBC methods. Materials and Methods In this research, sound signals of SAMPO 3065 harvester combine that were recorded by Maleki and Lashgari (2014, were analyzed. Engine speed (high and low, gear ratio (neutral, 1st, 2nd, 3rd gear, type of operation (traveling and harvesting and microphone position (in and out of the cabin were the main factors of this research. For determining signal fractal dimension value in time domain, wave shape supposed as a geometrical shape and for calculation of fractal dimension value of these signals, total area of wave shape was divided into boxes in 50, 100, 200 milliseconds with an interval 25 millisecond box. Then Fractal dimension value of these boxes was calculated by Katz, Sevcik, Higuchi and MRBC methods using MATLAB (2010a software. SPSS (Ver.20 software was used for further analysis. Results and Discussion Results showed mean effects of engine speed, microphone position, gear ratio, type of operation, box length, calculation method and all of two way interaction effects were significant. Means of Fractal Dimension in the road and field position were 1.4 and 1.28 respectively. The Maximum growth ratio of fractal dimension value during engine speed levels was
Holtkamp, S.; Brudzinski, M. R.
2011-12-01
For each Mw≥8.5 earthquake with a publicly available finite fault rupture model, we find slip is closely bounded along-strike by earthquake swarms, either prior or subsequent. These earthquake swarms tend to have much larger spatial extents than their cumulative moment would suggest, arguing against a static stress triggering mechanism. In Japan, Chile, Sumatra, and Alaska, earthquake swarms correlate with regions of the plate interface that exhibit low interseismic strain accumulation. This low fault coupling could be a result of aseismic slip during swarms or stress heterogeneity that leads to both swarm occurrence and great earthquake termination. Geodetic studies of earthquake swarms are limited but show several cases with no evidence for aseismic slip during swarms. Moreover, the 1964 Alaska and 2010 Maule earthquakes ruptured through regions with lower coupling than where they terminated, arguing that a factor other than small pre-stress controls where large earthquakes terminate. Large variations in coupling over small spatial scales could produce a fragmented set of small asperities conducive for generating a swarm of smaller earthquakes (Figure). Great earthquakes would be unlikely to rupture through that region as homogeneity of fault zone properties seems to be conducive for generating the largest megathrust earthquakes. Earthquake swarms are one of the better proxies for along-strike segmentation of subduction megathrusts, thereby potentially providing an new method for finding margins with the potential for devastating Mw~9 scale earthquakes. Figure: Cartoon illustrating our preferred hypothesis that increased stress heterogeneity causes earthquake swarm activity and stops large earthquake rupture propagation. Stress on the fault is in grayscale with black being high fault pre-stress. In this model, the heterogeneous stress distribution fosters swarm activity by limiting the size to which an earthquake can grow (leading to a high b
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A. O. Öncel
1995-01-01
Full Text Available Seismically-active fault zones are complex natural systems exhibiting scale-invariant or fractal correlation between earthquakes in space and time, and a power-law scaling of fault length or earthquake source dimension consistent with the exponent b of the Gutenberg-Richter frequency-magnitude relation. The fractal dimension of seismicity is a measure of the degree of both the heterogeneity of the process (whether fixed or self-generated and the clustering of seismic activity. Temporal variations of the b-value and the two-point fractal (correlation dimension Dc have been related to the preparation process for natural earthquakes and rock fracture in the laboratory These statistical scaling properties of seismicity may therefore have the potential at least to be sensitive short- term predictors of major earthquakes. The North Anatolian Fault Zone (NAFZ is a seismicallyactive dextral strike slip fault zone which forms the northern boundary of the westward moving Anatolian plate. It is splayed into three branches at about 31oE and continues westward toward the northern Aegean sea. In this study, we investigate the temporal variation of Dc and the Gutenberg-Richter b-value for seismicity in the western part of the NAFZ (including the northern Aegean sea for earthquakes of Ms > 4.5 occurring in the period between 1900 and 1992. b ranges from 0.6-1.6 and Dc from 0.6 to 1.4. The b-value is found to be weakly negatively correlated with Dc (r=-0.56. However the (log of event rate N is positively correlated with b, with a similar degree of statistical significance (r=0.42, and negatively correlated with Dc (r=-0.48. Since N increases dramatically with improved station coverage since 1970, the observed negative correlation between b and Dc is therefore more likely to be due to this effect than any underlying physical process in this case. We present this as an example of how man-made artefacts of recording can have similar statistical effects to
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.
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Men-Tzung eLo
2016-05-01
-entrained circadian rhythm of the SCN. The 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.
Bony change of apical lesion healing process using fractal analysis
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Lee, Ji Min; Park, Hyok; Jeong, Ho Gul; Kim, Kee Deog; Park, Chang Seo [Yonsei University College of Medicine, Seoul (Korea, Republic of)
2005-06-15
To investigate the change of bone healing process after endodontic treatment of the tooth with an apical lesion by fractal analysis. Radiographic images of 35 teeth from 33 patients taken on first diagnosis, 6 months, and 1 year after endodontic treatment were selected. Radiographic images were taken by JUPITER computerized Dental X-ray System. Fractal dimensions were calculated three times at each area by Scion Image PC program. Rectangular region of interest (30 x 30) were selected at apical lesion and normal apex of each image. The fractal dimension at apical lesion of first diagnosis (L{sub 0}) is 0.940 {+-} 0.361 and that of normal area (N{sub 0}) is 1.186 {+-} 0.727 (p<0.05). Fractal dimension at apical lesion of 6 months after endodontic treatment (L{sub 1}) is 1.076 {+-} 0.069 and that of normal area (N{sub 1}) is 1.192 {+-} 0.055 (p<0.05). Fractal dimension at apical lesion of 1 year after endodontic treatment (L{sub 2}) is 1.163 {+-} 0.074 and that of normal area (N{sub 2}) is 1.225 {+-} 0.079 (p<0.05). After endodontic treatment, the fractal dimensions at each apical lesions depending on time showed statistically significant difference. And there are statistically significant different between normal area and apical lesion on first diagnosis, 6 months after, 1 year after. But the differences were grow smaller as time flows. The evaluation of the prognosis after the endodontic treatment of the apical lesion was estimated by bone regeneration in apical region. Fractal analysis was attempted to overcome the limit of subjective reading, and as a result the change of the bone during the healing process was able to be detected objectively and quantitatively.
Persistent fluctuations in stride intervals under fractal auditory stimulation.
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.
Fractal dimension and universality in avascular tumor growth
Ribeiro, Fabiano L.; dos Santos, Renato Vieira; Mata, Angélica S.
2017-04-01
For years, the comprehension of the tumor growth process has been intriguing scientists. New research has been constantly required to better understand the complexity of this phenomenon. In this paper, we propose a mathematical model that describes the properties, already known empirically, of avascular tumor growth. We present, from an individual-level (microscopic) framework, an explanation of some phenomenological (macroscopic) aspects of tumors, such as their spatial form and the way they develop. Our approach is based on competitive interaction between the cells. This simple rule makes the model able to reproduce evidence observed in real tumors, such as exponential growth in their early stage followed by power-law growth. The model also reproduces (i) the fractal-space distribution of tumor cells and (ii) the universal growth behavior observed in both animals and tumors. Our analyses suggest that the universal similarity between tumor and animal growth comes from the fact that both can be described by the same dynamic equation—the Bertalanffy-Richards model—even if they do not necessarily share the same biological properties.
Mixing and the fractal geometry of piecewise isometries
Park, Paul P.; Lynn, Thomas F.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.
2017-04-01
Mathematical concepts often have applicability in areas that may have surprised their original developers. This is the case with piecewise isometries (PWIs), which transform an object by cutting it into pieces that are then rearranged to reconstruct the original object, and which also provide a paradigm to study mixing via cutting and shuffling in physical sciences and engineering. Every PWI is characterized by a geometric structure called the exceptional set, E , whose complement comprises nonmixing regions in the domain. Varying the parameters that define the PWI changes both the structure of E as well as the degree of mixing the PWI produces, which begs the question of how to determine which parameters produce the best mixing. Motivated by mixing of yield stress materials, for example granular media, in physical systems, we use numerical simulations of PWIs on a hemispherical shell and examine how the fat fractal properties of E relate to the degree of mixing for any particular PWI. We present numerical evidence that the fractional coverage of E negatively correlates with the intensity of segregation, a standard measure for the degree of mixing, which suggests that fundamental properties of E such as fractional coverage can be used to predict the effectiveness of a particular PWI as a mixing mechanism.
Journal of Reading, 1986
1986-01-01
Offers (1) suggestions on how to teach students the importance of regular study habits for learning to spell, (2) story ideas to help students get started with creative writing, and (3) a model of a daily record assignment book to help students organize and remember their homework assignments. (SRT)
A Deterministic Approach to Earthquake Prediction
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Vittorio Sgrigna
2012-01-01
Full Text Available The paper aims at giving suggestions for a deterministic approach to investigate possible earthquake prediction and warning. A fundamental contribution can come by observations and physical modeling of earthquake precursors aiming at seeing in perspective the phenomenon earthquake within the framework of a unified theory able to explain the causes of its genesis, and the dynamics, rheology, and microphysics of its preparation, occurrence, postseismic relaxation, and interseismic phases. Studies based on combined ground and space observations of earthquake precursors are essential to address the issue. Unfortunately, up to now, what is lacking is the demonstration of a causal relationship (with explained physical processes and looking for a correlation between data gathered simultaneously and continuously by space observations and ground-based measurements. In doing this, modern and/or new methods and technologies have to be adopted to try to solve the problem. Coordinated space- and ground-based observations imply available test sites on the Earth surface to correlate ground data, collected by appropriate networks of instruments, with space ones detected on board of Low-Earth-Orbit (LEO satellites. Moreover, a new strong theoretical scientific effort is necessary to try to understand the physics of the earthquake.
Earthquake Coverage by the Western Press.
Gaddy, Gary D.; Tanjong, Enoh
1986-01-01
Describes a study to determine the type and quantity of Western news coverage of Third World earthquakes. Finds little evidence of geographical bias in coverage studied, and suggests that care must be taken to examine the underlying news events before bias is alleged. (MS)
Bioinspired fractal electrodes for solar energy storages.
Thekkekara, Litty V; Gu, Min
2017-03-31
Solar energy storage is an emerging technology which can promote the solar energy as the primary source of electricity. Recent development of laser scribed graphene electrodes exhibiting a high electrical conductivity have enabled a green technology platform for supercapacitor-based energy storage, resulting in cost-effective, environment-friendly features, and consequent readiness for on-chip integration. Due to the limitation of the ion-accessible active porous surface area, the energy densities of these supercapacitors are restricted below ~3 × 10-3 Whcm-3. In this paper, we demonstrate a new design of biomimetic laser scribed graphene electrodes for solar energy storage, which embraces the structure of Fern leaves characterized by the geometric family of space filling curves of fractals. This new conceptual design removes the limit of the conventional planar supercapacitors by significantly increasing the ratio of active surface area to volume of the new electrodes and reducing the electrolyte ionic path. The attained energy density is thus significantly increased to ~10-1 Whcm-3- more than 30 times higher than that achievable by the planar electrodes with ~95% coulombic efficiency of the solar energy storage. The energy storages with these novel electrodes open the prospects of efficient self-powered and solar-powered wearable, flexible and portable applications.
Analysis of Texture Using the Fractal Model
Navas, William; Espinosa, Ramon Vasquez
1997-01-01
Properties such as the fractal dimension (FD) can be used for feature extraction and classification of regions within an image. The FD measures the degree of roughness of a surface, so this number is used to characterize a particular region, in order to differentiate it from another. There are two basic approaches discussed in the literature to measure FD: the blanket method, and the box counting method. Both attempt to measure FD by estimating the change in surface area with respect to the change in resolution. We tested both methods but box counting resulted computationally faster and gave better results. Differential Box Counting (DBC) was used to segment a collage containing three textures. The FD is independent of directionality and brightness so five features were used derived from the original image to account for directionality and gray level biases. FD can not be measured on a point, so we use a window that slides across the image giving values of FD to the pixel on the center of the window. Windowing blurs the boundaries of adjacent classes, so an edge-preserving, feature-smoothing algorithm is used to improve classification within segments and to make the boundaries sharper. Segmentation using DBC was 90.8910 accurate.
Bioinspired fractal electrodes for solar energy storages
Thekkekara, Litty V.; Gu, Min
2017-03-01
Solar energy storage is an emerging technology which can promote the solar energy as the primary source of electricity. Recent development of laser scribed graphene electrodes exhibiting a high electrical conductivity have enabled a green technology platform for supercapacitor-based energy storage, resulting in cost-effective, environment-friendly features, and consequent readiness for on-chip integration. Due to the limitation of the ion-accessible active porous surface area, the energy densities of these supercapacitors are restricted below ~3 × 10-3 Whcm-3. In this paper, we demonstrate a new design of biomimetic laser scribed graphene electrodes for solar energy storage, which embraces the structure of Fern leaves characterized by the geometric family of space filling curves of fractals. This new conceptual design removes the limit of the conventional planar supercapacitors by significantly increasing the ratio of active surface area to volume of the new electrodes and reducing the electrolyte ionic path. The attained energy density is thus significantly increased to ~10-1 Whcm-3- more than 30 times higher than that achievable by the planar electrodes with ~95% coulombic efficiency of the solar energy storage. The energy storages with these novel electrodes open the prospects of efficient self-powered and solar-powered wearable, flexible and portable applications.
Synthesis of the advance in and application of fractal characteristics of traffic flow.
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 ...
Synthesis of the advances in and application of fractal characteristic of traffic flow.
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 ...
Synthesis of the advances in and application of fractal characteristic of traffic flow : [summary].
2013-07-01
Fractals are geometric objects that are self-similar, meaning that their basic structure remains the same regardless of the scale of magnification. Self-similarity is readily seen in nature, for example, in trees, coastlines, clouds, etc. fractal...
Formation of fractals by the self-assembly of interpolymer adducts of ...
Indian Academy of Sciences (India)
vinylpyrrolidone) in presence of sodium chloride or potassium chloride form highly ordered fractal patterns in films on glass surface on drying at ambient temperature. The structure, morphology and the conditions under which the formation of fractal patterns ...
Earthquake triggering in southeast Africa following the 2012 Indian Ocean earthquake
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.
First Results of the Regional Earthquake Likelihood Models Experiment
Schorlemmer, Danijel; Zechar, J. Douglas; Werner, Maximilian J.; Field, Edward H.; Jackson, David D.; Jordan, Thomas H.
2010-08-01
The ability to successfully predict the future behavior of a system is a strong indication that the system is well understood. Certainly many details of the earthquake system remain obscure, but several hypotheses related to earthquake occurrence and seismic hazard have been proffered, and predicting earthquake behavior is a worthy goal and demanded by society. Along these lines, one of the primary objectives of the Regional Earthquake Likelihood Models (RELM) working group was to formalize earthquake occurrence hypotheses in the form of prospective earthquake rate forecasts in California. RELM members, working in small research groups, developed more than a dozen 5-year forecasts; they also outlined a performance evaluation method and provided a conceptual description of a Testing Center in which to perform predictability experiments. Subsequently, researchers working within the Collaboratory for the Study of Earthquake Predictability (CSEP) have begun implementing Testing Centers in different locations worldwide, and the RELM predictability experiment—a truly prospective earthquake prediction effort—is underway within the U.S. branch of CSEP. The experiment, designed to compare time-invariant 5-year earthquake rate forecasts, is now approximately halfway to its completion. In this paper, we describe the models under evaluation and present, for the first time, preliminary results of this unique experiment. While these results are preliminary—the forecasts were meant for an application of 5 years—we find interesting results: most of the models are consistent with the observation and one model forecasts the distribution of earthquakes best. We discuss the observed sample of target earthquakes in the context of historical seismicity within the testing region, highlight potential pitfalls of the current tests, and suggest plans for future revisions to experiments such as this one.
Fractal symmetry of protein interior: what have we learned?
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
Geometria fractal em física do solo Fractal geometry in soil physics
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O.O.S. Bacchi
1993-09-01
Full Text Available A geometria fractal tem sido aplicada nos mais diversos ramos da ciencia, mostrando grande potencial na descrição de estruturas altamente complexas. A sua aplicação em ciência do solo tem despertado grande interesse e vem se intensificando nos últimos anos. Apesar da sua divulgação através da literatura científica internacional, de conhecido acesso por parte dos pesquisadores brasileiros, o assunto parece não ter merecido ainda a nossa atenção, a contar pela ausência do tema em nossas revistas especializadas. Tratamos aqui da conceituação básica dessa nova abordagem e de algumas aplicações em física do solo.Fractal geometry has been applied on different branches of science, showing high potential in describing complex structures. Its applications in soil science have received large attention and have been intensified in the last few years. Inspite of the large number of internationally published papers, the subject seems not having received the same attention by Brazilian soil scientists, as verified by the absence of the subject in our scientific journals. This paper presents the basic concepts of this new tool and some of its applications in soil physics.
Fractal geometry in an expanding, one-dimensional, Newtonian universe.
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.
Towards Video Quality Metrics Based on Colour Fractal Geometry
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Richard Noël
2010-01-01
Full Text Available Vision is a complex process that integrates multiple aspects of an image: spatial frequencies, topology and colour. Unfortunately, so far, all these elements were independently took into consideration for the development of image and video quality metrics, therefore we propose an approach that blends together all of them. Our approach allows for the analysis of the complexity of colour images in the RGB colour space, based on the probabilistic algorithm for calculating the fractal dimension and lacunarity. Given that all the existing fractal approaches are defined only for gray-scale images, we extend them to the colour domain. We show how these two colour fractal features capture the multiple aspects that characterize the degradation of the video signal, based on the hypothesis that the quality degradation perceived by the user is directly proportional to the modification of the fractal complexity. We claim that the two colour fractal measures can objectively assess the quality of the video signal and they can be used as metrics for the user-perceived video quality degradation and we validated them through experimental results obtained for an MPEG-4 video streaming application; finally, the results are compared against the ones given by unanimously-accepted metrics and subjective tests.
The fractal nature materials microstructure influence on electrochemical energy sources
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Mitić V.V.
2015-01-01
Full Text Available With increasing of the world energy crisis, research for new, renewable and alternative energy sources are in growth. The focus is on research areas, sometimes of minor importance and applications, where the different synthesis methods and microstructure properties optimization, performed significant improvement of output materials’ and components’ electro-physical properties, which is important for higher energy efficiency and in the electricity production (batteries and battery systems, fuel cells and hydrogen energy contribution. Also, the storage tanks capacity improvement, for the energy produced on such way, which is one of the most important development issues in the energy sphere, represents a very promising research and application area. Having in mind, the results achieved in the electrochemical energy sources field, especially electrolyte development, these energy sources, materials fractal nature optimization analysis contribution, have been investigated. Based on materials fractal structure research field, particularly electronic materials, we have performed microstructure influence parameters research in electrochemistry area. We have investigated the Ho2O3 concentration influence (from 0.01wt% to 1wt% and sintering temperature (from 1320°C to 1380°C, as consolidation parameters, and thus, also open the electrochemical function fractalization door and in the basic thermodynamic parameters the fractal correction introduced. The fractal dimension dependence on additive concentration is also investigated. [Projekat Ministarstva nauke Republike Srbije, br. 172057: Directed synthesis, structure and properties of multifunctional materials
Wideband Fractal Antennas for Holographic Imaging and Rectenna Applications
Energy Technology Data Exchange (ETDEWEB)
Bunch, Kyle J.; McMakin, Douglas L.; Sheen, David M.
2008-04-18
At Pacific Northwest National Laboratory, wideband antenna arrays have been successfully used to reconstruct three-dimensional images at microwave and millimeter-wave frequencies. Applications of this technology have included portal monitoring, through-wall imaging, and weapons detection. Fractal antennas have been shown to have wideband characteristics due to their self-similar nature (that is, their geometry is replicated at different scales). They further have advantages in providing good characteristics in a compact configuration. We discuss the application of fractal antennas for holographic imaging. Simulation results will be presented. Rectennas are a specific class of antennas in which a received signal drives a nonlinear junction and is retransmitted at either a harmonic frequency or a demodulated frequency. Applications include tagging and tracking objects with a uniquely-responding antenna. It is of interest to consider fractal rectenna because the self-similarity of fractal antennas tends to make them have similar resonance behavior at multiples of the primary resonance. Thus, fractal antennas can be suited for applications in which a signal is reradiated at a harmonic frequency. Simulations will be discussed with this application in mind.
Enhanced Fluorescent Immunoassays on Silver Fractal-like Structures
Shtoyko, Tanya; Matveeva, Evgenia G.; Chang, I-Fen; Gryczynski, Zygmunt; Goldys, Ewa; Gryczynski, Ignacy
2009-01-01
Using the effect of the fluorescence enhancement in close proximity to metal nanostructures, we have been able to demonstrate ultrasensitive immunoassays suitable for the detection of biomarkers. Silver fractal-like structures have been grown by electrochemical reduction of silver on the surface of glass slides. A model immunoassay was performed on the slide surface with rabbit IgG (antigen) non-covalently immobilized on the slide, and Rhodamine Red-X labeled anti-rabbit IgG conjugate subsequently bound to the immobilized antigen. The fluorescence signal was measured from the glass-fractals surface using a confocal microscope, and the images were compared to the images from the same surface not coated with fractals. Our results showed significant enhancement (more than 100-fold) of the signal detected on fractals compared to bare glass. We thus demonstrate that such fractal-like structures can assist in improving the signals from assays used in medical diagnostics, especially those for analytes with molecular weight under 100 kD. PMID:18288816
Fractal image perception provides novel insights into hierarchical cognition.
Martins, M J; Fischmeister, F P; Puig-Waldmüller, E; Oh, J; Geissler, A; Robinson, S; Fitch, W T; Beisteiner, R
2014-08-01
Hierarchical structures play a central role in many aspects of human cognition, prominently including both language and music. In this study we addressed hierarchy in the visual domain, using a novel paradigm based on fractal images. Fractals are self-similar patterns generated by repeating the same simple rule at multiple hierarchical levels. Our hypothesis was that the brain uses different resources for processing hierarchies depending on whether it applies a "fractal" or a "non-fractal" cognitive strategy. We analyzed the neural circuits activated by these complex hierarchical patterns in an event-related fMRI study of 40 healthy subjects. Brain activation was compared across three different tasks: a similarity task, and two hierarchical tasks in which subjects were asked to recognize the repetition of a rule operating transformations either within an existing hierarchical level, or generating new hierarchical levels. Similar hierarchical images were generated by both rules and target images were identical. We found that when processing visual hierarchies, engagement in both hierarchical tasks activated the visual dorsal stream (occipito-parietal cortex, intraparietal sulcus and dorsolateral prefrontal cortex). In addition, the level-generating task specifically activated circuits related to the integration of spatial and categorical information, and with the integration of items in contexts (posterior cingulate cortex, retrosplenial cortex, and medial, ventral and anterior regions of temporal cortex). These findings provide interesting new clues about the cognitive mechanisms involved in the generation of new hierarchical levels as required for fractals. Copyright © 2014 Elsevier Inc. All rights reserved.
Fractal Dimensions of Umbral and Penumbral Regions of Sunspots
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.
Gene essentiality prediction based on fractal features and machine learning.
Yu, Yongming; Yang, Licai; Liu, Zhiping; Zhu, Chuansheng
2017-02-28
Essential genes are required for the viability of an organism. Accurate and rapid identification of new essential genes is of substantial theoretical interest to synthetic biology and has practical applications in biomedicine. Fractals provide facilitated access to genetic structure analysis on a different scale. In this study, machine learning-based methods using solely fractal features are presented and the problem of predicting essential genes in bacterial genomes is evaluated. Six fractal features were investigated to learn the parameters of five supervised classification methods for the binary classification task. The optimal parameters of these classifiers are determined via grid-based searching technique. All the currently available identified genes from the database of essential genes were utilized to build the classifiers. The fractal features were proven to be more robust and powerful in the prediction performance. In a statistical sense, the ELM method shows superiority in predicting the essential genes. Non-parameter tests of the average AUC and ACC showed that the fractal feature is much better than other five compared features sets. Our approach is promising and convenient to identify new bacterial essential genes.
Analysis of fractal electrodes for efficient neural stimulation.
Golestanirad, Laleh; Elahi, Behzad; Molina, Alberto; Mosig, Juan R; Pollo, Claudio; Chen, Robert; Graham, Simon J
2013-01-01
Planar electrodes are increasingly used in therapeutic neural stimulation techniques such as functional electrical stimulation, epidural spinal cord stimulation (ESCS), and cortical stimulation. Recently, optimized electrode geometries have been shown to increase the efficiency of neural stimulation by increasing the variation of current density on the electrode surface. In the present work, a new family of modified fractal electrode geometries is developed to enhance the efficiency of neural stimulation. It is shown that a promising approach in increasing the neural activation function is to increase the "edginess" of the electrode surface, a concept that is explained and quantified by fractal mathematics. Rigorous finite element simulations were performed to compute electric potential produced by proposed modified fractal geometries. The activation of 256 model axons positioned around the electrodes was then quantified, showing that modified fractal geometries required a 22% less input power while maintaining the same level of neural activation. Preliminary in vivo experiments investigating muscle evoked potentials due to median nerve stimulation showed encouraging results, supporting the feasibility of increasing neural stimulation efficiency using modified fractal geometries.
Earthquake number forecasts testing
Kagan, Yan Y.
2017-10-01
We study the distributions of earthquake numbers in two global earthquake catalogues: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. The properties of these distributions are especially required to develop the number test for our forecasts of future seismic activity rate, tested by the Collaboratory for Study of Earthquake Predictability (CSEP). A common assumption, as used in the CSEP tests, is that the numbers are described by the Poisson distribution. It is clear, however, that the Poisson assumption for the earthquake number distribution is incorrect, especially for the catalogues with a lower magnitude threshold. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrences, the negative-binomial distribution (NBD) has two parameters. The second parameter can be used to characterize the clustering or overdispersion of a process. We also introduce and study a more complex three-parameter beta negative-binomial distribution. We investigate the dependence of parameters for both Poisson and NBD distributions on the catalogue magnitude threshold and on temporal subdivision of catalogue duration. First, we study whether the Poisson law can be statistically rejected for various catalogue subdivisions. We find that for most cases of interest, the Poisson distribution can be shown to be rejected statistically at a high significance level in favour of the NBD. Thereafter, we investigate whether these distributions fit the observed distributions of seismicity. For this purpose, we study upper statistical moments of earthquake numbers (skewness and kurtosis) and compare them to the theoretical values for both distributions. Empirical values for the skewness and the kurtosis increase for the smaller magnitude threshold and increase with even greater intensity for small temporal subdivision of catalogues. The Poisson distribution for large rate values approaches the Gaussian law, therefore its skewness
Synthesis of Cobalt Oxides Thin Films Fractal Structures by Laser Chemical Vapor Deposition
Directory of Open Access Journals (Sweden)
P. Haniam
2014-01-01
Full Text Available Thin films of cobalt oxides (CoO and Co3O4 fractal structures have been synthesized by using laser chemical vapor deposition at room temperature and atmospheric pressure. Various factors which affect the density and crystallization of cobalt oxides fractal shapes have been examined. We show that the fractal structures can be described by diffusion-limited aggregation model and discuss a new possibility to control the fractal structures.
Induced seismicity provides insight into why earthquake ruptures stop
Galis, Martin
2017-12-21
Injection-induced earthquakes pose a serious seismic hazard but also offer an opportunity to gain insight into earthquake physics. Currently used models relating the maximum magnitude of injection-induced earthquakes to injection parameters do not incorporate rupture physics. We develop theoretical estimates, validated by simulations, of the size of ruptures induced by localized pore-pressure perturbations and propagating on prestressed faults. Our model accounts for ruptures growing beyond the perturbed area and distinguishes self-arrested from runaway ruptures. We develop a theoretical scaling relation between the largest magnitude of self-arrested earthquakes and the injected volume and find it consistent with observed maximum magnitudes of injection-induced earthquakes over a broad range of injected volumes, suggesting that, although runaway ruptures are possible, most injection-induced events so far have been self-arrested ruptures.
Precursory seismicity pattern before strong earthquakes in Greece
Directory of Open Access Journals (Sweden)
Ioannis Baskoutas
2014-05-01
Full Text Available The temporal variation of seismicity, based on the retrospective analyses of three seismic parameters i.e., number of earthquakes, bvalue and energy released, have shown significant changes. Their remarkable relation with strong earthquakes occurrence was formulated as a qualitative character precursory seismicity pattern, which were interpreted in terms of a strong earthquakes occurrence preparation phases. The main characteristic of this pattern is that permits the identification of two period of low and high probability for an earthquake occurrence, suggesting its utility in the current seismic hazard assessment, by the continuous monitoring of the temporal variation of the seismic parameters in a given area. This paper investigates the qualitative and quantitative characteristics of the proposed precursory seismicity pattern, before al strong earthquakes occurrence in Greece the time period 2000-2008.
Effects of the 2010 Haiti Earthquake on Women's Reproductive Health.
Behrman, Julia Andrea; Weitzman, Abigail
2016-03-01
This article explores the effects of the 2010 Haiti earthquake on women's reproductive health, using geocoded data from the 2005 and 2012 Haiti Demographic and Health Surveys. We use geographic variation in the destructiveness of the earthquake to conduct a difference-in-difference analysis. Results indicate that heightened earthquake intensity reduced use of injectables-the most widely used modern contraceptive method in Haiti-and increased current pregnancy and current unwanted pregnancy. Analysis of impact pathways suggests that severe earthquake intensity significantly increased women's unmet need for family planning and reduced their access to condoms. The earthquake also affected other factors that influence reproductive health, including women's ability to negotiate condom use in their partnerships. Our findings highlight how disruptions to health care services following a natural disaster can have negative consequences for women's reproductive health. © 2016 The Population Council, Inc.
Rupture, waves and earthquakes
UENISHI, Koji
2017-01-01
Normally, an earthquake is considered as a phenomenon of wave energy radiation by rupture (fracture) of solid Earth. However, the physics of dynamic process around seismic sources, which may play a crucial role in the occurrence of earthquakes and generation of strong waves, has not been fully understood yet. Instead, much of former investigation in seismology evaluated earthquake characteristics in terms of kinematics that does not directly treat such dynamic aspects and usually excludes the influence of high-frequency wave components over 1 Hz. There are countless valuable research outcomes obtained through this kinematics-based approach, but “extraordinary” phenomena that are difficult to be explained by this conventional description have been found, for instance, on the occasion of the 1995 Hyogo-ken Nanbu, Japan, earthquake, and more detailed study on rupture and wave dynamics, namely, possible mechanical characteristics of (1) rupture development around seismic sources, (2) earthquake-induced structural failures and (3) wave interaction that connects rupture (1) and failures (2), would be indispensable. PMID:28077808
Rupture, waves and earthquakes.
Uenishi, Koji
2017-01-01
Normally, an earthquake is considered as a phenomenon of wave energy radiation by rupture (fracture) of solid Earth. However, the physics of dynamic process around seismic sources, which may play a crucial role in the occurrence of earthquakes and generation of strong waves, has not been fully understood yet. Instead, much of former investigation in seismology evaluated earthquake characteristics in terms of kinematics that does not directly treat such dynamic aspects and usually excludes the influence of high-frequency wave components over 1 Hz. There are countless valuable research outcomes obtained through this kinematics-based approach, but "extraordinary" phenomena that are difficult to be explained by this conventional description have been found, for instance, on the occasion of the 1995 Hyogo-ken Nanbu, Japan, earthquake, and more detailed study on rupture and wave dynamics, namely, possible mechanical characteristics of (1) rupture development around seismic sources, (2) earthquake-induced structural failures and (3) wave interaction that connects rupture (1) and failures (2), would be indispensable.
Earthquake Damage to Transportation Systems
National Oceanic and Atmospheric Administration, Department of Commerce — Earthquakes represent one of the most destructive natural hazards known to man. A serious result of large-magnitude earthquakes is the disruption of transportation...
Scale relativity and fractal space-time a new approach to unifying relativity and quantum mechanics
Nottale, Laurent
2011-01-01
This book provides a comprehensive survey of the development of the theory of scale relativity and fractal space-time. It suggests an original solution to the disunified nature of the classical-quantum transition in physical systems, enabling the basis of quantum mechanics on the principle of relativity, provided this principle is extended to scale transformations of the reference system. In the framework of such a newly generalized relativity theory (including position, orientation, motion and now scale transformations), the fundamental laws of physics may be given a general form that unifies
Seeing shapes in seemingly random spatial patterns: Fractal analysis of Rorschach inkblots
Taylor, R. P.; Martin, T. P.; Montgomery, R. D.; Smith, J. H.; Micolich, A. P.; Boydston, C.; Scannell, B. C.; Fairbanks, M. S.; Spehar, B.
2017-01-01
Rorschach inkblots have had a striking impact on the worlds of art and science because of the remarkable variety of associations with recognizable and namable objects they induce. Originally adopted as a projective psychological tool to probe mental health, psychologists and artists have more recently interpreted the variety of induced images simply as a signature of the observers’ creativity. Here we analyze the relationship between the spatial scaling parameters of the inkblot patterns and the number of induced associations, and suggest that the perceived images are induced by the fractal characteristics of the blot edges. We discuss how this relationship explains the frequent observation of images in natural scenery. PMID:28196082
Characterizing Aftershock Sequences of the Recent Strong Earthquakes in Central Italy
Kossobokov, Vladimir G.; Nekrasova, Anastasia K.
2017-10-01
The recent strong earthquakes in Central Italy allow for a comparative analysis of their aftershocks from the viewpoint of 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. In particular, we consider aftershocks as a sequence of avalanches in self-organized system of blocks-and-faults of the Earth lithosphere, each aftershock series characterized with the distribution of the USLE control parameter, η. We found the existence, in a long-term, of different, intermittent levels of rather steady seismic activity characterized with a near constant value of η, which switch, in mid-term, at times of transition associated with catastrophic events. On such a transition, seismic activity 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 as observed in the case of the ongoing one associated with the three strong earthquakes in 2016. Evidently, our results do not support the presence of universality of seismic energy release, while providing constraints on modelling seismic sequences for earthquake physicists and supplying decision makers with information for improving local seismic hazard assessments.