Fractal properties and small-scale structure of cosmic string networks
International Nuclear Information System (INIS)
Martins, C.J.A.P.; Shellard, E.P.S.
2006-01-01
We present results from a detailed numerical study of the small-scale and loop production properties of cosmic string networks, based on the largest and highest resolution string simulations to date. We investigate the nontrivial fractal properties of cosmic strings, in particular, the fractal dimension and renormalized string mass per unit length, and we also study velocity correlations. We demonstrate important differences between string networks in flat (Minkowski) spacetime and the two very similar expanding cases. For high resolution matter era network simulations, we provide strong evidence that small-scale structure has converged to 'scaling' on all dynamical length scales, without the need for other radiative damping mechanisms. We also discuss preliminary evidence that the dominant loop production size is also approaching scaling
Dynamical properties of fractal networks: Scaling, numerical simulations, and physical realizations
International Nuclear Information System (INIS)
Nakayama, T.; Yakubo, K.; Orbach, R.L.
1994-01-01
This article describes the advances that have been made over the past ten years on the problem of fracton excitations in fractal structures. The relevant systems to this subject are so numerous that focus is limited to a specific structure, the percolating network. Recent progress has followed three directions: scaling, numerical simulations, and experiment. In a happy coincidence, large-scale computations, especially those involving array processors, have become possible in recent years. Experimental techniques such as light- and neutron-scattering experiments have also been developed. Together, they form the basis for a review article useful as a guide to understanding these developments and for charting future research directions. In addition, new numerical simulation results for the dynamical properties of diluted antiferromagnets are presented and interpreted in terms of scaling arguments. The authors hope this article will bring the major advances and future issues facing this field into clearer focus, and will stimulate further research on the dynamical properties of random systems
Directory of Open Access Journals (Sweden)
Guang-Lei Gao
Full Text Available BACKGROUND: Biological soil crusts are common components of desert ecosystem; they cover ground surface and interact with topsoil that contribute to desertification control and degraded land restoration in arid and semiarid regions. METHODOLOGY/PRINCIPAL FINDINGS: To distinguish the changes in topsoil affected by biological soil crusts, we compared topsoil properties across three types of successional biological soil crusts (algae, lichens, and mosses crust, as well as the referenced sandland in the Mu Us Desert, Northern China. Relationships between fractal dimensions of soil particle size distribution and selected soil properties were discussed as well. The results indicated that biological soil crusts had significant positive effects on soil physical structure (P<0.05; and soil organic carbon and nutrients showed an upward trend across the successional stages of biological soil crusts. Fractal dimensions ranged from 2.1477 to 2.3032, and significantly linear correlated with selected soil properties (R(2 = 0.494∼0.955, P<0.01. CONCLUSIONS/SIGNIFICANCE: Biological soil crusts cause an important increase in soil fertility, and are beneficial to sand fixation, although the process is rather slow. Fractal dimension proves to be a sensitive and useful index for quantifying changes in soil properties that additionally implies desertification. This study will be essential to provide a firm basis for future policy-making on optimal solutions regarding desertification control and assessment, as well as degraded ecosystem restoration in arid and semiarid regions.
Dimensional analysis, scaling and fractals
International Nuclear Information System (INIS)
Timm, L.C.; Reichardt, K.; Oliveira Santos Bacchi, O.
2004-01-01
Dimensional analysis refers to the study of the dimensions that characterize physical entities, like mass, force and energy. Classical mechanics is based on three fundamental entities, with dimensions MLT, the mass M, the length L and the time T. The combination of these entities gives rise to derived entities, like volume, speed and force, of dimensions L 3 , LT -1 , MLT -2 , respectively. In other areas of physics, four other fundamental entities are defined, among them the temperature θ and the electrical current I. The parameters that characterize physical phenomena are related among themselves by laws, in general of quantitative nature, in which they appear as measures of the considered physical entities. The measure of an entity is the result of its comparison with another one, of the same type, called unit. Maps are also drawn in scale, for example, in a scale of 1:10,000, 1 cm 2 of paper can represent 10,000 m 2 in the field. Entities that differ in scale cannot be compared in a simple way. Fractal geometry, in contrast to the Euclidean geometry, admits fractional dimensions. The term fractal is defined in Mandelbrot (1982) as coming from the Latin fractus, derived from frangere which signifies to break, to form irregular fragments. The term fractal is opposite to the term algebra (from the Arabic: jabara) which means to join, to put together the parts. For Mandelbrot, fractals are non topologic objects, that is, objects which have as their dimension a real, non integer number, which exceeds the topologic dimension. For the topologic objects, or Euclidean forms, the dimension is an integer (0 for the point, 1 for a line, 2 for a surface, and 3 for a volume). The fractal dimension of Mandelbrot is a measure of the degree of irregularity of the object under consideration. It is related to the speed by which the estimate of the measure of an object increases as the measurement scale decreases. An object normally taken as uni-dimensional, like a piece of a
A Fractal Perspective on Scale in Geography
Directory of Open Access Journals (Sweden)
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.
Fractal scale-free networks resistant to disease spread
International Nuclear Information System (INIS)
Zhang, Zhongzhi; Zhou, Shuigeng; Zou, Tao; Chen, Guisheng
2008-01-01
The conventional wisdom is that scale-free networks are prone to epidemic propagation; in the paper we demonstrate that, on the contrary, disease spreading is inhibited in fractal scale-free networks. We first propose a novel network model and show that it simultaneously has the following rich topological properties: scale-free degree distribution, tunable clustering coefficient, 'large-world' behavior, and fractal scaling. Existing network models do not display these characteristics. Then, we investigate the susceptible–infected–removed (SIR) model of the propagation of diseases in our fractal scale-free networks by mapping it to the bond percolation process. We establish the existence of non-zero tunable epidemic thresholds by making use of the renormalization group technique, which implies that power law degree distribution does not suffice to characterize the epidemic dynamics on top of scale-free networks. We argue that the epidemic dynamics are determined by the topological properties, especially the fractality and its accompanying 'large-world' behavior
Fractal and mechanical micro- and nanorange properties of sylvite and halite crystals
Directory of Open Access Journals (Sweden)
Valery N. Aptukov
2017-09-01
Full Text Available This article involves the treatment of micro- and nanorange scanning and indentation data for salt rock crystals obtained with help of the scanning microscope Dimension Icon using the mathematical models. It also describes the basic methods of fractal analysis. It shows the effectiveness of the method of minimal covering which is chosen to research the fractal properties of salt rock crystal surfaces. The article includes the algorithm of this method and the description of its generalization for the two-dimensional case. The values of fractal index and multifractal parameters have been calculated on the basis of the minimal covering method. The article also involves the anisotropy effects for fractal properties, comparison of fractal behavior on different scale levels. It gives the values of hardness for different parts of the crystals and studies the correlation between hardness and fractal index and describes the character of the influence of fractal dimension on roughness.
Generating hierarchial scale-free graphs from fractals
Energy Technology Data Exchange (ETDEWEB)
Komjathy, Julia, E-mail: komyju@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary); Simon, Karoly, E-mail: simonk@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary)
2011-08-15
Highlights: > We generate deterministic scale-free networks using graph-directed self similar IFS. > Our model exhibits similar clustering, power law decay properties to real networks. > The average length of shortest path and the diameter of the graph are determined. > Using this model, we generate random graphs with prescribed power law exponent. - Abstract: Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal {Lambda}. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal {Lambda} we generate random graph sequence sharing similar properties.
Fractals as objects with nontrivial structures at all scales
International Nuclear Information System (INIS)
Lacan, Francis; Tresser, Charles
2015-01-01
Toward the middle of 2001, the authors started arguing that fractals are important when discussing the operational resilience of information systems and related computer sciences issues such as artificial intelligence. But in order to argue along these lines it turned out to be indispensable to define fractals so as to let one recognize as fractals some sets that are very far from being self similar in the (usual) metric sense. This paper is devoted to define (in a loose sense at least) fractals in ways that allow for instance all the Cantor sets to be fractals and that permit to recognize fractality (the property of being fractal) in the context of the information technology issues that we had tried to comprehend. Starting from the meta-definition of a fractal as an “object with non-trivial structure at all scales” that we had used for long, we ended up taking these words seriously. Accordingly we define fractals in manners that depend both on the structures that the fractals are endowed with and the chosen sets of structure compatible maps, i.e., we approach fractals in a category-dependent manner. We expect that this new approach to fractals will contribute to the understanding of more of the fractals that appear in exact and other sciences than what can be handled presently
Mitered fractal trees: constructions and properties
Verhoeff, T.; Verhoeff, K.; Bosch, R.; McKenna, D.; Sarhangi, R.
2012-01-01
Tree-like structures, that is, branching structures without cycles, are attractive for artful expression. Especially interesting are fractal trees, where each subtree is a scaled and possibly otherwise transformed version of the entire tree. Such trees can be rendered in 3D by using beams with a
Transport properties of electrons in fractal magnetic-barrier structures
Sun, Lifeng; Fang, Chao; Guo, Yong
2010-09-01
Quantum transport properties in fractal magnetically modulated structures are studied by the transfer-matrix method. It is found that the transmission spectra depend sensitively not only on the incident energy and the direction of the wave vector but also on the stage of the fractal structures. Resonance splitting, enhancement, and position shift of the resonance peaks under different magnetic modulation are observed at four different fractal stages, and the relationship between the conductance in the fractal structure and magnetic modulation is also revealed. The results indicate the spectra of the transmission can be considered as fingerprints for the fractal structures, which show the subtle correspondence between magnetic structures and transport behaviors.
Turbulence Enhancement by Fractal Square Grids: Effects of the Number of Fractal Scales
Omilion, Alexis; Ibrahim, Mounir; Zhang, Wei
2017-11-01
Fractal square grids offer a unique solution for passive flow control as they can produce wakes with a distinct turbulence intensity peak and a prolonged turbulence decay region at the expense of only minimal pressure drop. While previous studies have solidified this characteristic of fractal square grids, how the number of scales (or fractal iterations N) affect turbulence production and decay of the induced wake is still not well understood. The focus of this research is to determine the relationship between the fractal iteration N and the turbulence produced in the wake flow using well-controlled water-tunnel experiments. Particle Image Velocimetry (PIV) is used to measure the instantaneous velocity fields downstream of four different fractal grids with increasing number of scales (N = 1, 2, 3, and 4) and a conventional single-scale grid. By comparing the turbulent scales and statistics of the wake, we are able to determine how each iteration affects the peak turbulence intensity and the production/decay of turbulence from the grid. In light of the ability of these fractal grids to increase turbulence intensity with low pressure drop, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.
Emergence of fractal scale-free networks from stochastic evolution on the Cayley tree
Energy Technology Data Exchange (ETDEWEB)
Chełminiak, Przemysław, E-mail: geronimo@amu.edu.pl
2013-11-29
An unexpected recognition of fractal topology in some real-world scale-free networks has evoked again an interest in the mechanisms stimulating their evolution. To explain this phenomenon a few models of a deterministic construction as well as a probabilistic growth controlled by a tunable parameter have been proposed so far. A quite different approach based on the fully stochastic evolution of the fractal scale-free networks presented in this Letter counterpoises these former ideas. It is argued that the diffusive evolution of the network on the Cayley tree shapes its fractality, self-similarity and the branching number criticality without any control parameter. The last attribute of the scale-free network is an intrinsic property of the skeleton, a special type of spanning tree which determines its fractality.
[Modeling continuous scaling of NDVI based on fractal theory].
Luan, Hai-Jun; Tian, Qing-Jiu; Yu, Tao; Hu, Xin-Li; Huang, Yan; Du, Ling-Tong; Zhao, Li-Min; Wei, Xi; Han, Jie; Zhang, Zhou-Wei; Li, Shao-Peng
2013-07-01
Scale effect was one of the very important scientific problems of remote sensing. The scale effect of quantitative remote sensing can be used to study retrievals' relationship between different-resolution images, and its research became an effective way to confront the challenges, such as validation of quantitative remote sensing products et al. Traditional up-scaling methods cannot describe scale changing features of retrievals on entire series of scales; meanwhile, they are faced with serious parameters correction issues because of imaging parameters' variation of different sensors, such as geometrical correction, spectral correction, etc. Utilizing single sensor image, fractal methodology was utilized to solve these problems. Taking NDVI (computed by land surface radiance) as example and based on Enhanced Thematic Mapper Plus (ETM+) image, a scheme was proposed to model continuous scaling of retrievals. Then the experimental results indicated that: (a) For NDVI, scale effect existed, and it could be described by fractal model of continuous scaling; (2) The fractal method was suitable for validation of NDVI. All of these proved that fractal was an effective methodology of studying scaling of quantitative remote sensing.
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.......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....
Mouse Activity across Time Scales: Fractal Scenarios
Lima, G. Z. dos Santos; Lobão-Soares, B.; do Nascimento, G. C.; França, Arthur S. C.; Muratori, L.; Ribeiro, S.; Corso, G.
2014-01-01
In this work we devise a classification of mouse activity patterns based on accelerometer data using Detrended Fluctuation Analysis. We use two characteristic mouse behavioural states as benchmarks in this study: waking in free activity and slow-wave sleep (SWS). In both situations we find roughly the same pattern: for short time intervals we observe high correlation in activity - a typical 1/f complex pattern - while for large time intervals there is anti-correlation. High correlation of short intervals ( to : waking state and to : SWS) is related to highly coordinated muscle activity. In the waking state we associate high correlation both to muscle activity and to mouse stereotyped movements (grooming, waking, etc.). On the other side, the observed anti-correlation over large time scales ( to : waking state and to : SWS) during SWS appears related to a feedback autonomic response. The transition from correlated regime at short scales to an anti-correlated regime at large scales during SWS is given by the respiratory cycle interval, while during the waking state this transition occurs at the time scale corresponding to the duration of the stereotyped mouse movements. Furthermore, we find that the waking state is characterized by longer time scales than SWS and by a softer transition from correlation to anti-correlation. Moreover, this soft transition in the waking state encompass a behavioural time scale window that gives rise to a multifractal pattern. We believe that the observed multifractality in mouse activity is formed by the integration of several stereotyped movements each one with a characteristic time correlation. Finally, we compare scaling properties of body acceleration fluctuation time series during sleep and wake periods for healthy mice. Interestingly, differences between sleep and wake in the scaling exponents are comparable to previous works regarding human heartbeat. Complementarily, the nature of these sleep-wake dynamics could lead to a better
Some fractal properties of the percolating backbone in two dimensions
International Nuclear Information System (INIS)
Laidlaw, D.; MacKay, G.; Jan, N.
1987-01-01
A new algorithm is presented, based on elements of artificial intelligence theory, to determine the fractal properties of the backbone of the incipient infinite cluster. It is found that fractal dimensionality of the backbone is d/sub f//sup BB/ = 1.61 +/- 0.01, the chemical dimensionality is d/sub t/ = 1.40 +/- 0.01, and the fractal dimension of the minimum path d/sub min/ = 1.15 +/- 0.02 for the two-dimensional triangular lattice
Generating hierarchical scale free-graphs from fractals
Komjáthy, J.; Simon, K.
2011-01-01
Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabási, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal ¿. With rigorous mathematical results we verify that our model captures some of the most important features of
Fractals and the Large-Scale Structure in the Universe
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 4. Fractals and the Large-Scale Structure in the Universe - Is the Cosmological Principle Valid? A K Mittal T R Seshadri. General Article Volume 7 Issue 4 April 2002 pp 39-47 ...
Directory of Open Access Journals (Sweden)
Painter Page R
2005-08-01
Full Text Available Abstract Background A prominent theoretical explanation for 3/4-power allometric scaling of metabolism proposes that the nutrient exchange surface of capillaries has properties of a space-filling fractal. The theory assumes that nutrient exchange surface area has a fractal dimension equal to or greater than 2 and less than or equal to 3 and that the volume filled by the exchange surface area has a fractal dimension equal to or greater than 3 and less than or equal to 4. Results It is shown that contradicting predictions can be derived from the assumptions of the model. When errors in the model are corrected, it is shown to predict that metabolic rate is proportional to body mass (proportional scaling. Conclusion The presence of space-filling fractal nutrient exchange surfaces does not provide a satisfactory explanation for 3/4-power metabolic rate scaling.
A characteristic scale in radiation fields of fractal clouds
Energy Technology Data Exchange (ETDEWEB)
Wiscombe, W.; Cahalan, R.; Davis, A.; Marshak, A. [Goddard Space Flight Center, Greenbelt, MD (United States)
1996-04-01
The wavenumber spectrum of Landsat imagery for marine stratocumulus cloud shows a scale break when plotted on a double log plot. We offer an explanation of this scale break in terms of smoothing by horizontal radiative fluxes, which is parameterized and incorporated into an improved pixel approximation. We compute the radiation fields emerging from cloud models with horizontally variable optical depth fractal models. We use comparative spectral and multifractal analysis to qualify the validity of the independent pixel approximation at the largest scales and demonstrate it`s shortcomings on the smallest scales.
Space-coiling fractal metamaterial with multi-bandgaps on subwavelength scale
Man, Xianfeng; Liu, Tingting; Xia, Baizhan; Luo, Zhen; Xie, Longxiang; Liu, Jian
2018-06-01
Acoustic metamaterials are remarkably different from conventional materials, as they can flexibly manipulate and control the propagation of sound waves. Unlike the locally resonant metamaterials introduced in earlier studies, we designed an ultraslow artificial structure with a sound speed much lower than that in air. In this paper, the space-coiling approach is proposed for achieving artificial metamaterial for extremely low-frequency airborne sound. In addition, the self-similar fractal technique is utilized for designing space-coiling Mie-resonance-based metamaterials (MRMMs) to obtain a band-dispersive spectrum. The band structures of two-dimensional (2D) acoustic metamaterials with different fractal levels are illustrated using the finite element method. The low-frequency bandgap can easily be formed, and multi-bandgap properties are observed in high-level fractals. Furthermore, the designed MRMMs with higher order fractal space coiling shows a good robustness against irregular arrangement. Besides, the proposed artificial structure was found to modify and control the radiation field arbitrarily. Thus, this work provides useful guidelines for the design of acoustic filtering devices and acoustic wavefront shaping applications on the subwavelength scale.
Fractal Property in the Light Curve of BL Lac Object S5 0716+714
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... In this paper, we compile the historical R-band data of S5 0716+714 from literature and obtain its fractal dimension by using a fractal method and then simulate the data with the Weierstrass–Mandelbrot (W–M) function. It is considered that the light curve has a fractal property.
Thermal properties of bodies in fractal and cantorian physics
International Nuclear Information System (INIS)
Zmeskal, Oldrich; Buchnicek, Miroslav; Vala, Martin
2005-01-01
Fundamental laws describing the heat diffusion in fractal environment are discussed. It is shown that for the three-dimensional space the heat radiation process occur in structures with fractal dimension D element of heat conduction and convection have the upper hand (generally in the real gases). To describe the heat diffusion a new law has been formulated. Its validity is more general than the Plank's radiation law based on the quantum heat diffusion theory. The energy density w = f (K, D), where K is the fractal measure and D is the fractal dimension exhibit typical dependency peaking with agreement with Planck's radiation law and with the experimental data for the absolutely black body in the energy interval kT m m kT m ∼ 1.5275. The agreement of the fractal model with the experimental outcomes is documented for the spectral characteristics of the Sun. The properties of stellar objects (black holes, relict radiation, etc.) and the elementary particles fields and interactions between them (quarks, leptons, mesons, baryons, bosons and their coupling constants) will be discussed with the help of the described mathematic apparatus in our further contributions. The general gas law for real gases in its more applicable form than the widely used laws (e.g. van der Waals, Berthelot, Kammerlingh-Onnes) has been also formulated. The energy density, which is in this case represented by the gas pressure p = f (K, D), can gain generally complex value and represents the behaviour of real (cohesive) gas in interval D element of (1,3>. The gas behaves as the ideal one only for particular values of the fractal dimensions (the energy density is real-valued). Again, it is shown that above the critical temperature (kT > K h c) and for fractal dimension D m > 2.0269 the results are comparable to the kinetics theory of real (ideal) gas (van der Waals equation of state, compressibility factor, Boyle's temperature). For the critical temperature (K h c = kT r ) the compressibility
Temporal fractals in seabird foraging behaviour: diving through the scales of time
Macintosh, Andrew J. J.; Pelletier, Laure; Chiaradia, Andre; Kato, Akiko; Ropert-Coudert, Yan
2013-05-01
Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (Eudyptula minor) across full-day foraging trips (216 data points; 4 orders of temporal magnitude). Results from 4 fractal methods show that dive sequences are long-range dependent and persistent across ca. 2 orders of magnitude. This fractal structure correlated with trip length and time spent underwater, but individual traits had little effect. Fractal time is a fundamental characteristic of penguin foraging behaviour, and its investigation is thus a promising avenue for research on interactions between animals and their environments.
Fractal properties of percolation clusters in Euclidian neural networks
International Nuclear Information System (INIS)
Franovic, Igor; Miljkovic, Vladimir
2009-01-01
The process of spike packet propagation is observed in two-dimensional recurrent networks, consisting of locally coupled neuron pools. Local population dynamics is characterized by three key parameters - probability for pool connectedness, synaptic strength and neuron refractoriness. The formation of dynamic attractors in our model, synfire chains, exhibits critical behavior, corresponding to percolation phase transition, with probability for non-zero synaptic strength values representing the critical parameter. Applying the finite-size scaling method, we infer a family of critical lines for various synaptic strengths and refractoriness values, and determine the Hausdorff-Besicovitch fractal dimension of the percolation clusters.
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....
Geometrical study of astrocytomas through fractals and scaling analysis
International Nuclear Information System (INIS)
Torres H, F.; Baena N, R.; Vergara V, J.; Guerrero M, M.
2017-10-01
The tumor growth is a complex process characterized by the proliferation of uncontrollable cells which invade neighbor tissues. The understanding process of this type of phenomena is very relevant in order to establish diagnosis and proper therapy strategies and to start the valorization of its complexity with proper descriptors produced by the scaling analysis, which define the tumor growth geometry. In this work, obtained results through the scaling analysis for pilocytic astrocytomas, anaplastic and diffuse, are shown, which tumors of primary origin are. On them, it is calculated the fractal dimension and critic exponents of local roughness to characterize in vivo three-dimensional tumor growth. The acquisition of the images for this type of injuries was carried out according to the standard protocol used for brain radiotherapy and radiosurgery, i.e., axial, coronal and sagittal magnetic resonance T1 weighted images and comprising the brain volume for image registration. Image segmentation was performed by the application the K-means procedure upon contrasted images. The results show significant variations of the parameters depending on the tumor stage and its histological origin. (Author)
Czech Academy of Sciences Publication Activity Database
Krištoufek, Ladislav
2012-01-01
Roč. 15, č. 6 (2012), 1250065-1-1250065-13 ISSN 0219-5259 R&D Projects: GA ČR GA402/09/0965 Grant - others:GA UK(CZ) 118310; SVV(CZ) 265 504 Institutional support: RVO:67985556 Keywords : fractal markets hypothesis * scaling * fractality * investment horizons * efficient markets hypothesis Subject RIV: AH - Economics Impact factor: 0.647, year: 2012 http://library.utia.cas.cz/separaty/2012/E/kristoufek-fractal markets hypothesis and the global financial crisis scaling investment horizons and liquidity.pdf
Morphological Investigation and Fractal Properties of Realgar Nanoparticles
Directory of Open Access Journals (Sweden)
Amir Lashgari
2015-01-01
Full Text Available Some arsenic compounds can show extraordinary polymorphism. Realgar (As4S4 is among several minerals with various crystal forms and is one of the most important sources of arsenic for pharmaceutical use. Currently, realgar is used as an arsenic source in many industries, such as weaponry, publishing, textiles, cosmetics, and health products. In this paper, we used and reported new methods for the purification, nanonization, and structural morphological investigations of As4S4 by using planetary ball mills process for nanonization of the compound. The product was characterized using X-ray powder diffraction analysis, Fourier transform infrared spectrometry spectra, and field emission scanning electron microscope (FESEM imaging. We investigated the morphological properties of FESEM-imaged realgar nanoparticles by an image-processing technique that calculates fractal dimensions using values on a computer with MATLAB software. We applied the Statistical Package for the Social Sciences software for statistics data extracted from the FESEM image and obtained the statistics results of the fractal dimension and histogram plot for the FESEM image.
Fractals in several electrode materials
Energy Technology Data Exchange (ETDEWEB)
Zhang, Chunyong, E-mail: zhangchy@njau.edu.cn [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); Wu, Jingyu [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Fu, Degang [Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); State Key Laboratory of Bioelectronics, Southeast University, Nanjing 210096 (China)
2014-09-15
Highlights: • Fractal geometry was employed to characterize three important electrode materials. • The surfaces of all studied electrodes were proved to be very rough. • The fractal dimensions of BDD and ACF were scale dependent. • MMO film was more uniform than BDD and ACF in terms of fractal structures. - Abstract: In the present paper, the fractal properties of boron-doped diamond (BDD), mixed metal oxide (MMO) and activated carbon fiber (ACF) electrode have been studied by SEM imaging at different scales. Three materials are self-similar with mean fractal dimension in the range of 2.6–2.8, confirming that they all exhibit very rough surfaces. Specifically, it is found that MMO film is more uniform in terms of fractal structure than BDD and ACF. As a result, the intriguing characteristics make these electrodes as ideal candidates for high-performance decontamination processes.
Fractals and the Large-Scale Structure in the Universe
Indian Academy of Sciences (India)
of fractals. Measuring the Length of a Curve. Consider the problem of measuring the length of a ..... a two dimensional smooth surface embedded in 3 dimen- ... interesting measure of a I-dimensional object is its length and not the volume.
Evolution of atomic-scale surface structures during ion bombardment: A fractal simulation
International Nuclear Information System (INIS)
Shaheen, M.A.; Ruzic, D.N.
1993-01-01
Surfaces of interest in microelectronics have been shown to exhibit fractal topographies on the atomic scale. A model utilizing self-similar fractals to simulate surface roughness has been added to the ion bombardment code TRIM. The model has successfully predicted experimental sputtering yields of low energy (less then 1000 eV) Ar on Si and D on C using experimentally determined fractal dimensions. Under ion bombardment the fractal surface structures evolve as the atoms in the collision cascade are displaced or sputtered. These atoms have been tracked and the evolution of the surface in steps of one monolayer of flux has been determined. The Ar--Si system has been studied for incidence energies of 100 and 500 eV, and incidence angles of 0 degree, 30 degree, and 60 degree. As expected, normally incident ion bombardment tends to reduce the roughness of the surface, whereas large angle ion bombardment increases the degree of surface roughness. Of particular interest though, the surfaces are still locally self-similar fractals after ion bombardment and a steady state fractal dimension is reached, except at large angles of incidence
Fractal scaling behavior of heart rate variability in response to meditation techniques
International Nuclear Information System (INIS)
Alvarez-Ramirez, J.; Rodríguez, E.; Echeverría, J.C.
2017-01-01
Highlights: • The scaling properties of heart rate variability in premeditation and meditation states were studied. • Mindfulness meditation induces a decrement of the HRV long-range scaling correlations. • Mindfulness meditation can be regarded as a type of induced deep sleep-like dynamics. - Abstract: The rescaled range (R/S) analysis was used for analyzing the fractal scaling properties of heart rate variability (HRV) of subjects undergoing premeditation and meditation states. Eight novice subjects and four advanced practitioners were considered. The corresponding pre-meditation and meditation HRV data were obtained from the Physionet database. The results showed that mindfulness meditation induces a decrement of the HRV long-range scaling correlations as quantified with the time-variant Hurst exponent. The Hurst exponent for advanced meditation practitioners decreases up to values of 0.5, reflecting uncorrelated (e.g., white noise-like) HRV dynamics. Some parallelisms between mindfulness meditation and deep sleep (Stage 4) are discussed, suggesting that the former can be regarded as a type of induced deep sleep-like dynamics.
Saw, Vee-Liem; Chew, Lock Yue
2013-01-01
We formulate the helicaliser, which replaces a given smooth curve by another curve that winds around it. In our analysis, we relate this formulation to the geometrical properties of the self-similar circular fractal (the discrete version of the curved helical fractal). Iterative applications of the helicaliser to a given curve yields a set of helicalisations, with the infinitely helicalised object being a fractal. We derive the Hausdorff dimension for the infinitely helicalised straight line ...
Statistical properties and fractals of nucleotide clusters in DNA sequences
International Nuclear Information System (INIS)
Sun Tingting; Zhang Linxi; Chen Jin; Jiang Zhouting
2004-01-01
Statistical properties of nucleotide clusters in DNA sequences and their fractals are investigated in this paper. The average size of nucleotide clusters in non-coding sequence is larger than that in coding sequence. We investigate the cluster-size distribution P(S) for human chromosomes 21 and 22, and the results are different from previous works. The cluster-size distribution P(S 1 +S 2 ) with the total size of sequential Pu-cluster and Py-cluster S 1 +S 2 is studied. We observe that P(S 1 +S 2 ) follows an exponential decay both in coding and non-coding sequences. However, we get different results for human chromosomes 21 and 22. The probability distribution P(S 1 ,S 2 ) of nucleotide clusters with the size of sequential Pu-cluster and Py-cluster S 1 and S 2 respectively, is also examined. In the meantime, some of the linear correlations are obtained in the double logarithmic plots of the fluctuation F(l) versus nucleotide cluster distance l along the DNA chain. The power spectrums of nucleotide clusters are also discussed, and it is concluded that the curves are flat and hardly changed and the 1/3 frequency is neither observed in coding sequence nor in non-coding sequence. These investigations can provide some insights into the nucleotide clusters of DNA sequences
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.
Pandey, Apoorva; Chakrabarty, Rajan K.; Liu, Li; Mishchenko, Michael I.
2015-01-01
Soot aggregates (SAs)-fractal clusters of small, spherical carbonaceous monomers-modulate the incoming visible solar radiation and contribute significantly to climate forcing. Experimentalists and climate modelers typically assume a spherical morphology for SAs when computing their optical properties, causing significant errors. Here, we calculate the optical properties of freshly-generated (fractal dimension Df = 1.8) and aged (Df = 2.6) SAs at 550 nm wavelength using the numericallyexact superposition T-Matrix method. These properties were expressed as functions of equivalent aerosol diameters as measured by contemporary aerosol instruments. This work improves upon previous efforts wherein SA optical properties were computed as a function of monomer number, rendering them unusable in practical applications. Future research will address the sensitivity of variation in refractive index, fractal prefactor, and monomer overlap of SAs on the reported empirical relationships.
Fractal-Markovian scaling of turbulent bursting process in open channel flow
International Nuclear Information System (INIS)
Keshavarzi, Ali Reza; Ziaei, Ali Naghi; Homayoun, Emdad; Shirvani, Amin
2005-01-01
The turbulent coherent structure of flow in open channel is a chaotic and stochastic process in nature. The coherence structure of the flow or bursting process consists of a series of eddies with a variety of different length scales and it is very important for the entrainment of sediment particles from the bed. In this study, a fractal-Markovian process is applied to the measured turbulent data in open channel. The turbulent data was measured in an experimental flume using three-dimensional acoustic Doppler velocity meter (ADV). A fractal interpolation function (FIF) algorithm was used to simulate more than 500,000 time series data of measured instantaneous velocity fluctuations and Reynolds shear stress. The fractal interpolation functions (FIF) enables to simulate and construct time series of u', v', and u'v' for any particular movement and state in the Markov process. The fractal dimension of the bursting events is calculated for 16 particular movements with the transition probability of the events based on 1st order Markov process. It was found that the average fractal dimensions of the streamwise flow velocity (u') are; 1.73, 1.74, 1.71 and 1.74 with the transition probability of 60.82%, 63.77%, 59.23% and 62.09% for the 1-1, 2-2, 3-3 and 4-4 movements, respectively. It was also found that the fractal dimensions of Reynold stress u'v' for quadrants 1, 2, 3 and 4 are 1.623, 1.623, 1.625 and 1.618, respectively
Moscoso del Prado Martín, Fermín
2013-12-01
I introduce the Bayesian assessment of scaling (BAS), a simple but powerful Bayesian hypothesis contrast methodology that can be used to test hypotheses on the scaling regime exhibited by a sequence of behavioral data. Rather than comparing parametric models, as typically done in previous approaches, the BAS offers a direct, nonparametric way to test whether a time series exhibits fractal scaling. The BAS provides a simpler and faster test than do previous methods, and the code for making the required computations is provided. The method also enables testing of finely specified hypotheses on the scaling indices, something that was not possible with the previously available methods. I then present 4 simulation studies showing that the BAS methodology outperforms the other methods used in the psychological literature. I conclude with a discussion of methodological issues on fractal analyses in experimental psychology. PsycINFO Database Record (c) 2014 APA, all rights reserved.
On the Boundedness and Symmetry Properties of the Fractal Sets Generated from Alternated Complex Map
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Da Wang
2016-01-01
Full Text Available A complex map can give rise to two kinds of fractal sets: the Julia sets and the parameters sets (or the connectivity loci which represent different connectivity properties of the corresponding Julia sets. In the significative results of (Int. J. Bifurc. Chaos, 2009, 19:2123–2129 and (Nonlinear. Dyn. 2013, 73:1155–1163, the authors presented the two kinds of fractal sets of a class of alternated complex map and left some visually observations to be proved about the boundedness and symmetry properties of these fractal sets. In this paper, we improve the previous results by giving the strictly mathematical proofs of the two properties. Some simulations that verify the theoretical proofs are also included.
A Study on the Mechanical Properties of the Representative Volume Element in Fractal Porous Media
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Jianjun Liu
2017-01-01
Full Text Available Natural porous structure is extremely complex, and it is of great significance to study the macroscopic mechanical response of the representative volume element (RVE with the microstructure of porous media. The real porous media RVE is generated by an improved quartet structure generation set (QSGS, and the connectivity of the reconstructed porous media models is analyzed. The fractal dimension of the RVE is calculated by the box-counting method, which considers the different porosity, different fractal dimension, and different mechanical properties of the matrix. Thus, the stress-strain curves of the RVE in the elastoplastic stage under different conditions are obtained. The results show that when the matrix mechanics are consistent, the mechanical properties of the porous media RVE are negatively correlated with the porosity and fractal dimension; when the difference between the porosity and fractal dimension increases, the trend is more obvious. The mechanical properties of the RVE have a positive correlation with the modulus of elasticity of the matrix, though the correlation with Poisson’s ratio of the matrix is weak. The fractal dimension of complex porous media can better predict the RVE mechanical characteristics than the porosity.
International trade network: fractal properties and globalization puzzle.
Karpiarz, Mariusz; Fronczak, Piotr; Fronczak, Agata
2014-12-12
Globalization is one of the central concepts of our age. The common perception of the process is that, due to declining communication and transport costs, distance becomes less and less important. However, the distance coefficient in the gravity model of trade, which grows in time, indicates that the role of distance increases rather than decreases. This, in essence, captures the notion of the globalization puzzle. Here, we show that the fractality of the international trade system (ITS) provides a simple solution for the puzzle. We argue that the distance coefficient corresponds to the fractal dimension of ITS. We provide two independent methods, the box counting method and spatial choice model, which confirm this statement. Our results allow us to conclude that the previous approaches to solving the puzzle misinterpreted the meaning of the distance coefficient in the gravity model of trade.
Analyzing fractal property of species abundance distribution and diversity indexes.
Su, Qiang
2016-03-07
Community diversity is usually characterized by numerical indexes; however it indeed depends on the species abundance distribution (SAD). Diversity indexes and SAD are based on the same information but treating as separate themes. Ranking species abundance from largest to smallest, the decreasing pattern can give the information about the SAD. Frontier proposed such SAD might be a fractal structure, and first applied the Zipf-Mandelbrot model to the SAD study. However, this model fails to include the Zipf model, and also fails to ensure an integer rank. In this study, a fractal model of SAD was reconstructed, and tested with 104 community samples from 8 taxonomic groups. The results show that there was a good fit of the presented model. Fractal parameter (p) determines the SAD of a community. The ecological significance of p relates to the "dominance" of a community. The correlation between p and classical diversity indexes show that Shannon index decreases and Simpson index increases as p increases. The main purpose of this paper is not to compare with other SADs models; it simply provides a new interpretation of SAD model construction, and preliminarily integrates diversity indexes and SAD model into a broader perspective of community diversity. Copyright © 2015 Elsevier Ltd. All rights reserved.
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Yongqing Duan
2017-12-01
Full Text Available Stretchable nanogenerators that directly generate electricity are promising for a wide range of applications in wearable electronics. However, the stretchability of the devices has been a long-standing challenge. Here we present a newly-designed ultra-stretchable nanogenerator based on fractal-inspired piezoelectric nanofibers and liquid metal electrodes that can withstand strain as large as 200%. The large-scale fractal poly(vinylidene fluoride (PVDF micro/nanofibers are fabricated by combination of helix electrohydrodynamic printing (HE-Printing and buckling-driven self-assembly. HE-Printing exploits “whipping/buckling” instability of electrospinning to deposit serpentine fibers with diverse geometries in a programmable, accurately positioned, and individually-controlled manner. Self-organized buckling utilizes the driven force from the prestrained elastomer to assemble serpentine fibers into ultra-stretchable fractal inspired architecture. The nanogenerator with embedded fractal PVDF fibers and liquid-metal microelectrodes demonstrates high stretchability (>200% and electricity (currents >200 nA, it can harvest energy from all directions by arbitrary mechanical motion, and the rectified output has been applied to charge the commercial capacitor and drive LEDs, which enables wearable electronics applications in sensing and energy harvesting.
Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency
International Nuclear Information System (INIS)
Paradisi, Paolo; Allegrini, Paolo
2015-01-01
In many complex systems the non-linear cooperative dynamics determine the emergence of self-organized, metastable, structures that are associated with a birth–death process of cooperation. This is found to be described by a renewal point process, i.e., a sequence of crucial birth–death events corresponding to transitions among states that are faster than the typical long-life time of the metastable states. Metastable states are highly correlated, but the occurrence of crucial events is typically associated with a fast memory drop, which is the reason for the renewal condition. Consequently, these complex systems display a power-law decay and, thus, a long-range or scale-free behavior, in both time correlations and distribution of inter-event times, i.e., fractal intermittency. The emergence of fractal intermittency is then a signature of complexity. However, the scaling features of complex systems are, in general, affected by the presence of added white or short-term noise. This has been found also for fractal intermittency. In this work, after a brief review on metastability and noise in complex systems, we discuss the emerging paradigm of Temporal Complexity. Then, we propose a model of noisy fractal intermittency, where noise is interpreted as a renewal Poisson process with event rate r_p. We show that the presence of Poisson noise causes the emergence of a normal diffusion scaling in the long-time range of diffusion generated by a telegraph signal driven by noisy fractal intermittency. We analytically derive the scaling law of the long-time normal diffusivity coefficient. We find the surprising result that this long-time normal diffusivity depends not only on the Poisson event rate, but also on the parameters of the complex component of the signal: the power exponent μ of the inter-event time distribution, denoted as complexity index, and the time scale T needed to reach the asymptotic power-law behavior marking the emergence of complexity. In particular
Exploring the link between multiscale entropy and fractal scaling behavior in near-surface wind.
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Miguel Nogueira
Full Text Available The equivalency between the power law behavior of Multiscale Entropy (MSE and of power spectra opens a promising path for interpretation of complex time-series, which is explored here for the first time for atmospheric fields. Additionally, the present manuscript represents a new independent empirical validation of such relationship, the first one for the atmosphere. The MSE-fractal relationship is verified for synthetic fractal time-series covering the full range of exponents typically observed in the atmosphere. It is also verified for near-surface wind observations from anemometers and CFSR re-analysis product. The results show a ubiquitous β ≈ 5/3 behavior inside the inertial range. A scaling break emerges at scales around a few seconds, with a tendency towards 1/f noise. The presence, extension and fractal exponent of this intermediate range are dependent on the particular surface forcing and atmospheric conditions. MSE shows an identical picture which is consistent with the turbulent energy cascade model: viscous dissipation at the small-scale end of the inertial range works as an information sink, while at the larger (energy-containing scales the multiple forcings in the boundary layer act as widespread information sources. Another scaling transition occurs at scales around 1-10 days, with an abrupt flattening of the spectrum. MSE shows that this transition corresponds to a maximum of the new information introduced, occurring at the time-scales of the synoptic features that dominate weather patterns. At larger scales, a scaling regime with flatter slopes emerges extending to scales larger than 1 year. MSE analysis shows that the amount of new information created decreases with increasing scale in this low-frequency regime. Additionally, in this region the energy injection is concentrated in two large energy peaks: daily and yearly time-scales. The results demonstrate that the superposition of these periodic signals does not destroy the
Exploring the link between multiscale entropy and fractal scaling behavior in near-surface wind.
Nogueira, Miguel
2017-01-01
The equivalency between the power law behavior of Multiscale Entropy (MSE) and of power spectra opens a promising path for interpretation of complex time-series, which is explored here for the first time for atmospheric fields. Additionally, the present manuscript represents a new independent empirical validation of such relationship, the first one for the atmosphere. The MSE-fractal relationship is verified for synthetic fractal time-series covering the full range of exponents typically observed in the atmosphere. It is also verified for near-surface wind observations from anemometers and CFSR re-analysis product. The results show a ubiquitous β ≈ 5/3 behavior inside the inertial range. A scaling break emerges at scales around a few seconds, with a tendency towards 1/f noise. The presence, extension and fractal exponent of this intermediate range are dependent on the particular surface forcing and atmospheric conditions. MSE shows an identical picture which is consistent with the turbulent energy cascade model: viscous dissipation at the small-scale end of the inertial range works as an information sink, while at the larger (energy-containing) scales the multiple forcings in the boundary layer act as widespread information sources. Another scaling transition occurs at scales around 1-10 days, with an abrupt flattening of the spectrum. MSE shows that this transition corresponds to a maximum of the new information introduced, occurring at the time-scales of the synoptic features that dominate weather patterns. At larger scales, a scaling regime with flatter slopes emerges extending to scales larger than 1 year. MSE analysis shows that the amount of new information created decreases with increasing scale in this low-frequency regime. Additionally, in this region the energy injection is concentrated in two large energy peaks: daily and yearly time-scales. The results demonstrate that the superposition of these periodic signals does not destroy the underlying
The fourth dimension of life: fractal geometry and allometric scaling of organisms.
West, G B; Brown, J H; Enquist, B J
1999-06-04
Fractal-like networks effectively endow life with an additional fourth spatial dimension. This is the origin of quarter-power scaling that is so pervasive in biology. Organisms have evolved hierarchical branching networks that terminate in size-invariant units, such as capillaries, leaves, mitochondria, and oxidase molecules. Natural selection has tended to maximize both metabolic capacity, by maximizing the scaling of exchange surface areas, and internal efficiency, by minimizing the scaling of transport distances and times. These design principles are independent of detailed dynamics and explicit models and should apply to virtually all organisms.
Non-linear variability in geophysics scaling and fractals
Lovejoy, S
1991-01-01
consequences of broken symmetry -here parity-is studied. In this model, turbulence is dominated by a hierarchy of helical (corkscrew) structures. The authors stress the unique features of such pseudo-scalar cascades as well as the extreme nature of the resulting (intermittent) fluctuations. Intermittent turbulent cascades was also the theme of a paper by us in which we show that universality classes exist for continuous cascades (in which an infinite number of cascade steps occur over a finite range of scales). This result is the multiplicative analogue of the familiar central limit theorem for the addition of random variables. Finally, an interesting paper by Pasmanter investigates the scaling associated with anomolous diffusion in a chaotic tidal basin model involving a small number of degrees of freedom. Although the statistical literature is replete with techniques for dealing with those random processes characterized by both exponentially decaying (non-scaling) autocorrelations and exponentially decaying...
Energy Technology Data Exchange (ETDEWEB)
Souza, Jeferson de; Figueira, Isabela Francoso Rebutini; Santos, Thais Borba [Universidade Federal do Rio Grande do Norte (PPGG/DG/UFRN), Natal (Brazil). Dept. de Geologia. Programa de Pos-Graducao em Geologia; Rostirolla, Sidnei Pires [Universidade Federal do Rio Grande do Norte (DG/UFRN), Natal (Brazil). Dept. de Geologia; Pierin, Andre Ramiro; Spisila, Andre Luis [Universidade Federal do Rio Grande do Norte (DG/UFRN), Natal (Brazil). Dept. de Geologia. Programa de Iniciacao Cientifica
2008-03-15
The statistical and geometrical properties of fracture systems were obtained by analyzing remote sense images and outcrop data, in the Region of Guartela Canyon, in the central-eastern of Parana State. The probability distributions of fractures, with their parameters and attributes, were obtained through extensive statistical exploration of data. These parameters were used as input data for generating 3-D stochastic fractures models through the 'discrete fracture network - DFN' method. The modeling is performed by using the code FRED. To study the persistence of statistical parameters in multiple scales were used remote sensing images (SRTM, Landsat TM7 and aerial photos), covering a scale range from outcrops (few meters) to basin scales (hundreds of kilometers). The results indicated the presence of power-law (fractal) statistics for the spatial and size distributions. Fractals distributions were found for all sets studied, in some cases with different fractal exponents. The implications of fractal behavior for the generation of discrete fracture network, and consequently for the hydraulic properties, are briefly discussed. (author)
A study of radiative properties of fractal soot aggregates using the superposition T-matrix method
International Nuclear Information System (INIS)
Li Liu; Mishchenko, Michael I.; Patrick Arnott, W.
2008-01-01
We employ the numerically exact superposition T-matrix method to perform extensive computations of scattering and absorption properties of soot aggregates with varying state of compactness and size. The fractal dimension, D f , is used to quantify the geometrical mass dispersion of the clusters. The optical properties of soot aggregates for a given fractal dimension are complex functions of the refractive index of the material m, the number of monomers N S , and the monomer radius a. It is shown that for smaller values of a, the absorption cross section tends to be relatively constant when D f f >2. However, a systematic reduction in light absorption with D f is observed for clusters with sufficiently large N S , m, and a. The scattering cross section and single-scattering albedo increase monotonically as fractals evolve from chain-like to more densely packed morphologies, which is a strong manifestation of the increasing importance of scattering interaction among spherules. Overall, the results for soot fractals differ profoundly from those calculated for the respective volume-equivalent soot spheres as well as for the respective external mixtures of soot monomers under the assumption that there are no electromagnetic interactions between the monomers. The climate-research implications of our results are discussed
Directory of Open Access Journals (Sweden)
Lanfa Liu
2016-12-01
Full Text Available Visible and near-infrared diffuse reflectance spectroscopy has been demonstrated to be a fast and cheap tool for estimating a large number of chemical and physical soil properties, and effective features extracted from spectra are crucial to correlating with these properties. We adopt a novel methodology for feature extraction of soil spectroscopy based on fractal geometry. The spectrum can be divided into multiple segments with different step–window pairs. For each segmented spectral curve, the fractal dimension value was calculated using variation estimators with power indices 0.5, 1.0 and 2.0. Thus, the fractal feature can be generated by multiplying the fractal dimension value with spectral energy. To assess and compare the performance of new generated features, we took advantage of organic soil samples from the large-scale European Land Use/Land Cover Area Frame Survey (LUCAS. Gradient-boosting regression models built using XGBoost library with soil spectral library were developed to estimate N, pH and soil organic carbon (SOC contents. Features generated by a variogram estimator performed better than two other estimators and the principal component analysis (PCA. The estimation results for SOC were coefficient of determination (R2 = 0.85, root mean square error (RMSE = 56.7 g/kg, the ratio of percent deviation (RPD = 2.59; for pH: R2 = 0.82, RMSE = 0.49 g/kg, RPD = 2.31; and for N: R2 = 0.77, RMSE = 3.01 g/kg, RPD = 2.09. Even better results could be achieved when fractal features were combined with PCA components. Fractal features generated by the proposed method can improve estimation accuracies of soil properties and simultaneously maintain the original spectral curve shape.
Empirical analysis of scaling and fractal characteristics of outpatients
International Nuclear Information System (INIS)
Zhang, Li-Jiang; Liu, Zi-Xian; Guo, Jin-Li
2014-01-01
The paper uses power-law frequency distribution, power spectrum analysis, detrended fluctuation analysis, and surrogate data testing to evaluate outpatient registration data of two hospitals in China and to investigate the human dynamics of systems that use the “first come, first served” protocols. The research results reveal that outpatient behavior follow scaling laws. The results also suggest that the time series of inter-arrival time exhibit 1/f noise and have positive long-range correlation. Our research may contribute to operational optimization and resource allocation in hospital based on FCFS admission protocols.
Empirical analysis of scaling and fractal characteristics of outpatients
Energy Technology Data Exchange (ETDEWEB)
Zhang, Li-Jiang, E-mail: zljjiang@gmail.com [College of Management and Economics, Tianjin University, Tianjin 300072 (China); Management Institute, Xinxiang Medical University, Xinxiang 453003, Henan (China); Liu, Zi-Xian, E-mail: liuzixian@tju.edu.cn [College of Management and Economics, Tianjin University, Tianjin 300072 (China); Guo, Jin-Li, E-mail: phd5816@163.com [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China)
2014-01-31
The paper uses power-law frequency distribution, power spectrum analysis, detrended fluctuation analysis, and surrogate data testing to evaluate outpatient registration data of two hospitals in China and to investigate the human dynamics of systems that use the “first come, first served” protocols. The research results reveal that outpatient behavior follow scaling laws. The results also suggest that the time series of inter-arrival time exhibit 1/f noise and have positive long-range correlation. Our research may contribute to operational optimization and resource allocation in hospital based on FCFS admission protocols.
Energy Technology Data Exchange (ETDEWEB)
Ho, Clifford K. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Ortega, Jesus D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Christian, Joshua Mark [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Yellowhair, Julius E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Ray, Daniel A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Kelton, John W. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Peacock, Gregory [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Andraka, Charles E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Shinde, Subhash [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.
2016-09-01
Novel designs to increase light trapping and thermal efficiency of concentrating solar receivers at multiple length scales have been conceived, designed, and tested. The fractal-like geometries and features are introduced at both macro (meters) and meso (millimeters to centimeters) scales. Advantages include increased solar absorptance, reduced thermal emittance, and increased thermal efficiency. Radial and linear structures at the meso (tube shape and geometry) and macro (total receiver geometry and configuration) scales redirect reflected solar radiation toward the interior of the receiver for increased absorptance. Hotter regions within the interior of the receiver can reduce thermal emittance due to reduced local view factors to the environment, and higher concentration ratios can be employed with similar surface irradiances to reduce the effective optical aperture, footprint, and thermal losses. Coupled optical/fluid/thermal models have been developed to evaluate the performance of these designs relative to conventional designs. Modeling results showed that fractal-like structures and geometries can increase the effective solar absorptance by 5 – 20% and the thermal efficiency by several percentage points at both the meso and macro scales, depending on factors such as intrinsic absorptance. Meso-scale prototypes were fabricated using additive manufacturing techniques, and a macro-scale bladed receiver design was fabricated using Inconel 625 tubes. On-sun tests were performed using the solar furnace and solar tower at the National Solar Thermal Test facility. The test results demonstrated enhanced solar absorptance and thermal efficiency of the fractal-like designs.
Detecting abrupt dynamic change based on changes in the fractal properties of spatial images
Liu, Qunqun; He, Wenping; Gu, Bin; Jiang, Yundi
2017-10-01
Many abrupt climate change events often cannot be detected timely by conventional abrupt detection methods until a few years after these events have occurred. The reason for this lag in detection is that abundant and long-term observational data are required for accurate abrupt change detection by these methods, especially for the detection of a regime shift. So, these methods cannot help us understand and forecast the evolution of the climate system in a timely manner. Obviously, spatial images, generated by a coupled spatiotemporal dynamical model, contain more information about a dynamic system than a single time series, and we find that spatial images show the fractal properties. The fractal properties of spatial images can be quantitatively characterized by the Hurst exponent, which can be estimated by two-dimensional detrended fluctuation analysis (TD-DFA). Based on this, TD-DFA is used to detect an abrupt dynamic change of a coupled spatiotemporal model. The results show that the TD-DFA method can effectively detect abrupt parameter changes in the coupled model by monitoring the changing in the fractal properties of spatial images. The present method provides a new way for abrupt dynamic change detection, which can achieve timely and efficient abrupt change detection results.
Analyzing self-similar and fractal properties of the C. elegans neural network.
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Tyler M Reese
Full Text Available The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons. A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron "giant component" of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been "rewired" to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs.
Energy Technology Data Exchange (ETDEWEB)
Li Quanbao; Wang Jian; Jiao Zheng [Shanghai Applied Radiation Institute, Institute of Nanochemistry and Nanobiology, School of Environmental and Chemical Engineering, Shanghai University, Shanghai 200444 (China); Wu Minghong, E-mail: mhwu@staff.shu.edu.cn [Shanghai Applied Radiation Institute, Institute of Nanochemistry and Nanobiology, School of Environmental and Chemical Engineering, Shanghai University, Shanghai 200444 (China); Shek, Chan-Hung; Lawrence Wu, C.M.; Lai, Joseph K.L. [Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong (Hong Kong); Chen Zhiwen, E-mail: cnzwchen@yahoo.com.cn [Shanghai Applied Radiation Institute, Institute of Nanochemistry and Nanobiology, School of Environmental and Chemical Engineering, Shanghai University, Shanghai 200444 (China); Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong (Hong Kong)
2011-08-15
Highlights: > Ge fractal architectures were achieved by temperature-induced assembly. > The appearance of fractal architectures influences the thermoelectric power. > But it has little effect on the resistivity. > The values of the superlocalization exponent were within 1.22 {<=} {xi} {<=} 1.29. > It was higher than expected for two-dimension fractal system. - Abstract: Fractal architectures of semiconductor nanocrystals were successfully achieved by temperature-induced assembly of semiconductor nanocrystals in gold/germanium (Au/Ge) bilayer films. New assessment strategies of fractal architectures are of fundamental importance in the development of micro/nano-devices. Temperature-dependent properties including resistivity and thermoelectric power (TEP) of Au/Ge bilayer films with self-similar fractal patterns were investigated in detail. Experimental results indicated that the microstructure of Au film plays an important role in the characteristics of Au/Ge bilayer films after annealing and the crystallization processes of amorphous Ge accompany by fractal formation of Ge nanocrystals via temperature-induced assembly. The appearance of fractal architectures has significantly influence on the TEP but little effect on the resistivity of the annealed bilayer film. By analysis of the data, we found that the values of superlocalization exponent are within 1.22 {<=} {xi} {<=} 1.29, which are higher than expected for two-dimension fractal systems. The results provided possible evidence for the superlocalization on fractal architectures in Au/Ge bilayer films. The TEP measurements are considered a more effective method than the conductivity for investigating superlocalization in a percolating system.
Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue
Energy Technology Data Exchange (ETDEWEB)
Paggi, Marco [Politecnico di Torino, Department of Structural Engineering and Geotechnics, Corso Duca degli Abruzzi 24, 10129 Torino (Italy)], E-mail: marco.paggi@polito.it; Carpinteri, Alberto [Politecnico di Torino, Department of Structural Engineering and Geotechnics, Corso Duca degli Abruzzi 24, 10129 Torino (Italy)
2009-05-15
The enhanced ability to detect and measure very short cracks, along with a great interest in applying fracture mechanics formulae to smaller and smaller crack sizes, has pointed out the so-called anomalous behavior of short cracks with respect to their longer counterparts. The crack-size dependencies of both the fatigue threshold and the Paris' constant C are only two notable examples of these anomalous scaling laws. In this framework, a unified theoretical model seems to be missing and the behavior of short cracks can still be considered as an open problem. In this paper, we propose a critical reexamination of the fractal models for the analysis of crack-size effects in fatigue. The limitations of each model are put into evidence and removed. At the end, a new generalized theory based on fractal geometry is proposed, which permits to consistently interpret the short crack-related anomalous scaling laws within a unified theoretical formulation. Finally, this approach is herein used to interpret relevant experimental data related to the crack-size dependence of the fatigue threshold in metals.
Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue
International Nuclear Information System (INIS)
Paggi, Marco; Carpinteri, Alberto
2009-01-01
The enhanced ability to detect and measure very short cracks, along with a great interest in applying fracture mechanics formulae to smaller and smaller crack sizes, has pointed out the so-called anomalous behavior of short cracks with respect to their longer counterparts. The crack-size dependencies of both the fatigue threshold and the Paris' constant C are only two notable examples of these anomalous scaling laws. In this framework, a unified theoretical model seems to be missing and the behavior of short cracks can still be considered as an open problem. In this paper, we propose a critical reexamination of the fractal models for the analysis of crack-size effects in fatigue. The limitations of each model are put into evidence and removed. At the end, a new generalized theory based on fractal geometry is proposed, which permits to consistently interpret the short crack-related anomalous scaling laws within a unified theoretical formulation. Finally, this approach is herein used to interpret relevant experimental data related to the crack-size dependence of the fatigue threshold in metals.
Surface fractal dimensions and textural properties of mesoporous alkaline-earth hydroxyapatites
International Nuclear Information System (INIS)
Vilchis-Granados, J.; Granados-Correa, F.; Barrera-Díaz, C.E.
2013-01-01
This work examines the surface fractal dimensions (D f ) and textural properties of three different alkaline-earth hydroxyapatites. Calcium, strontium and barium hydroxyapatite compounds were successfully synthesized via chemical precipitation method and characterized using X-ray diffraction, scanning electron microscopy, energy dispersive X-ray spectrometry, Fourier transform infrared spectroscopy, and N 2 -physisorption measurements. Surface fractal dimensions were determined using single N 2 -adsorption/desorption isotherms method to quantify the irregular surface of as-prepared compounds. The obtained materials were also characterized through their surface hydroxyl group content, determined by the mass titration method. It was found that the D f values for the three materials covered the range of 0.77 ± 0.04–2.33 ± 0.11; these results indicated that the materials tend to have smooth surfaces, except the irregular surface of barium hydroxyapatite. Moreover, regarding the synthesized calcium hydroxyapatite exhibited better textural properties compared with the synthesized strontium and barium hydroxyapatites for adsorbent purposes. However, barium hydroxyapatite shows irregular surface, indicating a high population of active sites across the surface, in comparison with the others studied hydroxyapatites. Finally, the results showed a linear correlation between the surface hydroxyl group content at the external surface of materials and their surface fractal dimensions.
Scaling properties of Polish rain series
Licznar, P.
2009-04-01
Scaling properties as well as multifractal nature of precipitation time series have not been studied for local Polish conditions until recently due to lack of long series of high-resolution data. The first Polish study of precipitation time series scaling phenomena was made on the base of pluviograph data from the Wroclaw University of Environmental and Life Sciences meteorological station located at the south-western part of the country. The 38 annual rainfall records from years 1962-2004 were converted into digital format and transformed into a standard format of 5-minute time series. The scaling properties and multifractal character of this material were studied by means of several different techniques: power spectral density analysis, functional box-counting, probability distribution/multiple scaling and trace moment methods. The result proved the general scaling character of time series at the range of time scales ranging form 5 minutes up to at least 24 hours. At the same time some characteristic breaks at scaling behavior were recognized. It is believed that the breaks were artificial and arising from the pluviograph rain gauge measuring precision limitations. Especially strong limitations at the precision of low-intensity precipitations recording by pluviograph rain gauge were found to be the main reason for artificial break at energy spectra, as was reported by other authors before. The analysis of co-dimension and moments scaling functions showed the signs of the first-order multifractal phase transition. Such behavior is typical for dressed multifractal processes that are observed by spatial or temporal averaging on scales larger than the inner-scale of those processes. The fractal dimension of rainfall process support derived from codimension and moments scaling functions geometry analysis was found to be 0.45. The same fractal dimension estimated by means of the functional box-counting method was equal to 0.58. At the final part of the study
Impact of morphology on the radiative properties of fractal soot aggregates
International Nuclear Information System (INIS)
Doner, Nimeti; Liu, Fengshan
2017-01-01
The impact of morphology on the radiative properties of fractal soot aggregates was investigated using the discrete dipole approximation (DDA). The optical properties of four different types of aggregates of freshly emitted soot with a fractal dimension D f =1.65 and a fractal pre-factor k f =1.76 were calculated. The four types of aggregates investigated are formed by uniform primary particles in point-touch, by uniform but overlapping primary particles, by uniform but enlarged primary particles in point-touch, and formed by point-touch and polydisperse primary particles. The radiative properties of aggregates consisting of N=20, 56 and 103 primary particles were numerically evaluated for a given refractive index at 0.532 and 1.064 μm. The radiative properties of soot aggregates vary strongly with the volume equivalent radius a eff and wavelength. The accuracy of DDA was evaluated in the first and fourth cases against the generalized multi-sphere Mie (GMM) solution in terms of the vertical–vertical differential scattering cross section (C vv ). The model predicted the average relative deviations from the base case to be within 15–25% for C vv , depending on the number of particles for the aggregate. The scattering cross sections are only slightly affected by the overlapping but more significantly influenced by primary particle polydispersity. It was also found that the enlargement of primary particles by 20% has a strong effect on soot aggregate radiative properties. - Highlights: • The radiative properties of aggregates of N=20, 56 and 103 primary particles were investigated. • Four different cases, formed by point-touch, overlapping, aggregate expansion and polydispersion, were studied. • The effects of overlapping and aggregate expansion on morphology are found to be the same.
Time scale defined by the fractal structure of the price fluctuations in foreign exchange markets
Kumagai, Yoshiaki
2010-04-01
In this contribution, a new time scale named C-fluctuation time is defined by price fluctuations observed at a given resolution. The intraday fractal structures and the relations of the three time scales: real time (physical time), tick time and C-fluctuation time, in foreign exchange markets are analyzed. The data set used is trading prices of foreign exchange rates; US dollar (USD)/Japanese yen (JPY), USD/Euro (EUR), and EUR/JPY. The accuracy of the data is one minute and data within a minute are recorded in order of transaction. The series of instantaneous velocity of C-fluctuation time flowing are exponentially distributed for small C when they are measured by real time and for tiny C when they are measured by tick time. When the market is volatile, for larger C, the series of instantaneous velocity are exponentially distributed.
2-D Fractal Wire Antenna Design and Performance
Tebbens, S. F.; Barton, C. C.; Peterman, D. J.; Ewing, J. J.; Abbott, C. S.; Rizki, M. M.
2017-12-01
A 2-D fractal wire antenna uses a fractal (self-similar) pattern to increase its length by iteration and can receive or transmit electromagnetic radiation. 2-D fractals are shapes that, at their mathematical limit (of infinite iterations) have an infinite length. The fractal dimension describes the degree of space filling. A fundamental property of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that can be very compact, wideband and multiband. As the number of iterations increases, the antenna tends to have additional frequencies that minimize far field return loss. This differs from traditional antenna designs in that a single fractal antenna can operate well at multiple frequencies. We have created a MATLAB code to generate deterministic and stochastic modes of fractal wire antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, and number of iterations have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance.
Directory of Open Access Journals (Sweden)
Q. Zhang
2018-02-01
Full Text Available River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1 fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2 the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling – in the form of spectral slope (β or other equivalent scaling parameters (e.g., Hurst exponent – are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1 they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β = 0 to Brown noise (β = 2 and (2 their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb–Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among
Zhang, Qian; Harman, Ciaran J.; Kirchner, James W.
2018-02-01
River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling - in the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) - are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β = 0) to Brown noise (β = 2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb-Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among all methods for a wide range of
Feng, Guixiang; Ming, Dongping; Wang, Min; Yang, Jianyu
2017-06-01
Scale problems are a major source of concern in the field of remote sensing. Since the remote sensing is a complex technology system, there is a lack of enough cognition on the connotation of scale and scale effect in remote sensing. Thus, this paper first introduces the connotations of pixel-based scale and summarizes the general understanding of pixel-based scale effect. Pixel-based scale effect analysis is essentially important for choosing the appropriate remote sensing data and the proper processing parameters. Fractal dimension is a useful measurement to analysis pixel-based scale. However in traditional fractal dimension calculation, the impact of spatial resolution is not considered, which leads that the scale effect change with spatial resolution can't be clearly reflected. Therefore, this paper proposes to use spatial resolution as the modified scale parameter of two fractal methods to further analyze the pixel-based scale effect. To verify the results of two modified methods (MFBM (Modified Windowed Fractal Brownian Motion Based on the Surface Area) and MDBM (Modified Windowed Double Blanket Method)); the existing scale effect analysis method (information entropy method) is used to evaluate. And six sub-regions of building areas and farmland areas were cut out from QuickBird images to be used as the experimental data. The results of the experiment show that both the fractal dimension and information entropy present the same trend with the decrease of spatial resolution, and some inflection points appear at the same feature scales. Further analysis shows that these feature scales (corresponding to the inflection points) are related to the actual sizes of the geo-object, which results in fewer mixed pixels in the image, and these inflection points are significantly indicative of the observed features. Therefore, the experiment results indicate that the modified fractal methods are effective to reflect the pixel-based scale effect existing in remote sensing
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.
Effects of multiple scattering on radiative properties of soot fractal aggregates
International Nuclear Information System (INIS)
Yon, Jérôme; Liu, Fengshan; Bescond, Alexandre; Caumont-Prim, Chloé; Rozé, Claude; Ouf, François-Xavier; Coppalle, Alexis
2014-01-01
The in situ optical characterization of smokes composed of soot particles relies on light extinction, angular static light scattering (SLS), or laser induced incandescence (LII). These measurements are usually interpreted by using the Rayleigh–Debye–Gans theory for Fractal Aggregates (RDG-FA). RDG-FA is simple to use but it completely neglects the impact of multiple scattering (MS) within soot aggregates. In this paper, based on a scaling approach that takes into account MS effects, an extended form of the RDG-FA theory is proposed in order to take into account these effects. The parameters of this extended theory and their dependency on the number of primary sphere inside the aggregate (1 p <1006) and on the wavelength (266nm<λ<1064nm) are evaluated thanks to rigorous calculations based on discrete dipole approximation (DDA) and generalized multi-sphere Mie-solution (GMM) calculations. This study shows that size determination by SLS is not distorted by MS effect. On the contrary, it is shown that fractal dimension can be misinterpreted by light scattering experiments, especially at short wavelengths. MS effects should be taken into account for the interpretation of absorption measurements that are involved in LII or extinction measurements. -- Highlights: • We incorporate multiple scattering effects in a scaling approach for fractal aggregates. • A generalized structure factor is introduced for implementation in RDG-FA theory. • Forward scattering is affected by multiple scattering as well as power law regime. • Absorption cross sections are affected by multiple scattering. • Absorption cross sections are 11% higher than that for forward scattering
International Nuclear Information System (INIS)
Lebedev, D. V.; Filatov, M. V.; Kuklin, A. I.; Islamov, A. Kh.; Stellbrink, J.; Pantina, R. A.; Denisov, Yu. Yu.; Toperverg, B. P.; Isaev-Ivanov, V. V.
2008-01-01
The chromatin organization in chicken erythrocyte nuclei was studied by small-angle neutron scattering in the scattering-vector range from 1.5 x 10 -1 to 10 -4 A -1 with the use of the contrast-variation technique. This scattering-vector range corresponds to linear dimensions from 4 nm to 6 μm and covers the whole hierarchy of chromatin structures, from the nucleosomal structure to the entire nucleus. The results of the present study allowed the following conclusions to be drawn: (1) both the chromatin-protein structure and the structure of the nucleic acid component in chicken erythrocyte nuclei have mass-fractal properties, (2) the structure of the protein component of chromatin exhibits a fractal behavior on scales extending over two orders of magnitude, from the nucleosomal size to the size of an entire nucleus, and (3) the structure of the nucleic acid component of chromatin in chicken erythrocyte nuclei is likewise of a fractal nature and has two levels of organization or two phases with the crossover point at about 300-400 nm
Fractal assembly of micrometre-scale DNA origami arrays with arbitrary patterns
Tikhomirov, Grigory; Petersen, Philip; Qian, Lulu
2017-12-01
Self-assembled DNA nanostructures enable nanometre-precise patterning that can be used to create programmable molecular machines and arrays of functional materials. DNA origami is particularly versatile in this context because each DNA strand in the origami nanostructure occupies a unique position and can serve as a uniquely addressable pixel. However, the scale of such structures has been limited to about 0.05 square micrometres, hindering applications that demand a larger layout and integration with more conventional patterning methods. Hierarchical multistage assembly of simple sets of tiles can in principle overcome this limitation, but so far has not been sufficiently robust to enable successful implementation of larger structures using DNA origami tiles. Here we show that by using simple local assembly rules that are modified and applied recursively throughout a hierarchical, multistage assembly process, a small and constant set of unique DNA strands can be used to create DNA origami arrays of increasing size and with arbitrary patterns. We illustrate this method, which we term ‘fractal assembly’, by producing DNA origami arrays with sizes of up to 0.5 square micrometres and with up to 8,704 pixels, allowing us to render images such as the Mona Lisa and a rooster. We find that self-assembly of the tiles into arrays is unaffected by changes in surface patterns on the tiles, and that the yield of the fractal assembly process corresponds to about 0.95m - 1 for arrays containing m tiles. When used in conjunction with a software tool that we developed that converts an arbitrary pattern into DNA sequences and experimental protocols, our assembly method is readily accessible and will facilitate the construction of sophisticated materials and devices with sizes similar to that of a bacterium using DNA nanostructures.
Topology of the Italian airport network: A scale-free small-world network with a fractal structure?
International Nuclear Information System (INIS)
Guida, Michele; Maria, Funaro
2007-01-01
In this paper, for the first time we analyze the structure of the Italian Airport Network (IAN) looking at it as a mathematical graph and investigate its topological properties. We find that it has very remarkable features, being like a scale-free network, since both the degree and the 'betweenness centrality' distributions follow a typical power-law known in literature as a Double Pareto Law. From a careful analysis of the data, the Italian Airport Network turns out to have a self-similar structure. In short, it is characterized by a fractal nature, whose typical dimensions can be easily determined from the values of the power-law scaling exponents. Moreover, we show that, according to the period examined, these distributions exhibit a number of interesting features, such as the existence of some 'hubs', i.e. in the graph theory's jargon, nodes with a very large number of links, and others most probably associated with geographical constraints. Also, we find that the IAN can be classified as a small-world network because the average distance between reachable pairs of airports grows at most as the logarithm of the number of airports. The IAN does not show evidence of 'communities' and this result could be the underlying reason behind the smallness of the value of the clustering coefficient, which is related to the probability that two nearest neighbors of a randomly chosen airport are connected
a Fractal Network Model for Fractured Porous Media
Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung
2016-04-01
The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.
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)
Fractal correlation property of heart rate variability in chronic obstructive pulmonary disease
Directory of Open Access Journals (Sweden)
Tatiana D Carvalho
2011-01-01
/alpha-2 ratio.Conclusion: COPD subjects present reduced short-term fractal correlation properties of HRV, which indicates that this index can be used for risk stratification, assessment of systemic disease manifestations, and therapeutic procedures to monitor those patients.Keywords: pulmonary disease, chronic obstructive, heart rate, nervous system, cardiology
International Nuclear Information System (INIS)
Dickau, Jonathan J.
2009-01-01
The use of fractals and fractal-like forms to describe or model the universe has had a long and varied history, which begins long before the word fractal was actually coined. Since the introduction of mathematical rigor to the subject of fractals, by Mandelbrot and others, there have been numerous cosmological theories and analyses of astronomical observations which suggest that the universe exhibits fractality or is by nature fractal. In recent years, the term fractal cosmology has come into usage, as a description for those theories and methods of analysis whereby a fractal nature of the cosmos is shown.
Structural and fractal properties of particles emitted from spark ignition engines.
Chakrabarty, Rajan K; Moosmüller, Hans; Arnott, W Patrick; Garro, Mark A; Walker, John
2006-11-01
Size, morphology, and microstructure of particles emitted from one light-duty passenger vehicle (Buick Century; model year 1990; PM (particulate matter) mass emission rate 3.1 mg/km) and two light-duty trucks (Chevrolet C2; model year 1973; PM mass emission rate 282 mg/km, and Chevrolet El Camino; model year 1976; PM mass emission rate 31 mg/km), running California's unified driving cycles (UDC) on a chassis dynamometer, were studied using scanning electron microscopy (SEM). SEM images yielded particle properties including three-dimensional density fractal dimensions, monomer and agglomerate number size distributions, and three different shape descriptors, namely aspect ratio, root form factor, and roundness. The density fractal dimension of the particles was between 1.7 and 1.78, while the number size distribution of the particles placed the majority of the particles in the accumulation mode (0.1-0.3 microm). The shape descriptors were found to decrease with increasing particle size. Partial melting of particles, a rare and previously unreported phenomenon, was observed upon exposure of particles emitted during phase 2 of the UDC to the low accelerating voltage electron beam of the SEM. The rate of melting was quantified for individual particles, establishing a near linear relationship between the melting rate and the organic carbon 1 to elemental carbon ratio.
COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY
Energy Technology Data Exchange (ETDEWEB)
Deng, L. H.; Xiang, Y. Y.; Dun, G. T. [Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216 (China); Li, B., E-mail: wooden@escience.cn [Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, School of Space Science and Physics, Shandong University at Weihai, Weihai 264209 (China)
2016-01-15
The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaotic attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.
Distribution of petrophysical properties for sandy-clayey reservoirs by fractal interpolation
Directory of Open Access Journals (Sweden)
M. Lozada-Zumaeta
2012-04-01
Full Text Available The sandy-clayey hydrocarbon reservoirs of the Upper Paleocene and Lower Eocene located to the north of Veracruz State, Mexico, present highly complex geological and petrophysical characteristics. These reservoirs, which consist of sandstone and shale bodies within a depth interval ranging from 500 to 2000 m, were characterized statistically by means of fractal modeling and geostatistical tools. For 14 wells within an area of study of approximately 6 km^{2}, various geophysical well logs were initially edited and further analyzed to establish a correlation between logs and core data. The fractal modeling based on the R/S (rescaled range methodology and the interpolation method by successive random additions were used to generate pseudo-well logs between observed wells. The application of geostatistical tools, sequential Gaussian simulation and exponential model variograms contributed to estimate the spatial distribution of petrophysical properties such as effective porosity (PHIE, permeability (K and shale volume (VSH. From the analysis and correlation of the information generated in the present study, it can be said, from a general point of view, that the results not only are correlated with already reported information but also provide significant characterization elements that would be hardly obtained by means of conventional techniques.
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.
Directory of Open Access Journals (Sweden)
Shiquan Wan
2016-01-01
Full Text Available By using detrended fluctuation analysis (DFA, the present paper analyzed the nonlinearity and fractal properties of tree-ring records from two types of trees in northwestern China, and then we disclosed climate change characteristics during the past 500 years in this area. The results indicate that climate change in northwestern China displayed a long-range correlation (LRC, which can exist over time span of 100 years or longer. This conclusion provides a theoretical basis for long-term climate predictions. Combining the DFA results obtained from daily temperatures records at the Xi’an meteorological observation station, which is near the southern peak of the Huashan Mountains, self-similarities widely existed in climate change on monthly, seasonal, annual, and decadal timescales during the past 500 years in northwestern China, and this change was a typical nonlinear process.
Thermodynamics for Fractal Statistics
da Cruz, Wellington
1998-01-01
We consider for an anyon gas its termodynamics properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or Hausdorff dimension $h$. An exact equation of state is obtained in the high-temperature and low-temperature limits, for gases with a constant density of states.
Directory of Open Access Journals (Sweden)
Catherine K. Denny
2017-04-01
Full Text Available Spatial heterogeneity of vegetation is an important landscape characteristic, but is difficult to assess due to scale-dependence. Here we examine how spatial patterns in the forest canopy affect those of understory plants, using the shrub Canada buffaloberry (Shepherdia canadensis (L. Nutt. as a focal species. Evergreen and deciduous forest canopy and buffaloberry shrub presence were measured with line-intercept sampling along ten 2-km transects in the Rocky Mountain foothills of west-central Alberta, Canada. Relationships between overstory canopy and understory buffaloberry presence were assessed for scales ranging from 2 m to 502 m. Fractal dimensions of both canopy and buffaloberry were estimated and then related using box-counting methods to evaluate spatial heterogeneity based on patch distribution and abundance. Effects of canopy presence on buffaloberry were scale-dependent, with shrub presence negatively related to evergreen canopy cover and positively related to deciduous cover. The effect of evergreen canopy was significant at a local scale between 2 m and 42 m, while that of deciduous canopy was significant at a meso-scale between 150 m and 358 m. Fractal analysis indicated that buffaloberry heterogeneity positively scaled with evergreen canopy heterogeneity, but was unrelated to that of deciduous canopy. This study demonstrates that evergreen canopy cover is a determinant of buffaloberry heterogeneity, highlighting the importance of spatial scale and canopy composition in understanding canopy-understory relationships.
Fractal Analysis of Mobile Social Networks
International Nuclear Information System (INIS)
Zheng Wei; Pan Qian; Sun Chen; Deng Yu-Fan; Zhao Xiao-Kang; Kang Zhao
2016-01-01
Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mobile social networks (MSNs) are inadequately investigated. In this work, a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs. Using this method, we find that some MSNs are fractal at different time intervals. Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs. (paper)
McAteer, R. T. James
2015-08-01
My soul is spiraling in frozen fractals all around, And one thought crystallizes like an icy blast, I'm never going back, the past is in the past.Elsa, from Disney’s Frozen, characterizes two fundamental aspects of scale-free processes in Nature: fractals are everywhere in space; fractals can be used to probe changes in time. Self-Organized Criticality provides a powerful set of tools to study scale-free processes. It connects spatial fractals (more generically, multifractals) to temporal evolution. The drawback is that this usually results in scale-free, unit-less, indices, which can be difficult to connect to everyday physics. Here, I show a novel method that connects one of the most powerful SOC tools - the wavelet transform modulus maxima approach to calculating multifractality - to one of the most powerful equations in all of physics - Ampere’s law. In doing so I show how the multifractal spectra can be expressed in terms of current density, and how current density can then be used for the prediction of future energy release from such a system.Our physical understanding of the solar magnetic field structure, and hence our ability to predict solar activity, is limited by the type of data currently available. I show that the multifractal spectrum provides a powerful physical connection between the details of photospheric magnetic gradients of current data and the coronal magnetic structure. By decomposing Ampere’s law and comparing it to the wavelet transform modulus maximum method, I show how the scale-free Holder exponent provides a direct measure of current density across all relevant sizes. The prevalence of this current density across various scales is connected to its stability in time, and hence to the ability of the magnetic structure to store and then release energy. Hence (spatial) multifractals inform us of (future) solar activity.Finally I discuss how such an approach can be used in any study of scale-free processes, and highlight the necessary
Directory of Open Access Journals (Sweden)
Skatkov Leonid
2012-01-01
Full Text Available MDS capacitor (metal - dielectric - semiconductor is a structure in which metal plate is represented by compact bulk-porous pellets of niobium sintered powder, and semiconductor plate - by pyrolytic layer of MnO2. In the present paper we report the results of investigation of microporosity of sintered Nb and pyrolytic MnO2 and also the fractal properties of semiconductor layer.
Directory of Open Access Journals (Sweden)
Franz Konstantin Fuss
2013-01-01
Full Text Available Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal’s time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.
Fuss, Franz Konstantin
2013-01-01
Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.
Fractal properties of background noise and target signal enhancement using CSEM data
Benavides, Alfonso; Everett, Mark E.; Pierce, Carl; Nguyen, Cam
2003-09-01
Controlled-source electromagnetic (CSEM) spatial profiles and 2-D conductivity maps were obtained on the Brazos Valley, TX floodplain to study the fractal statistics of geological signals and effects of man-made conductive targets using Geonics EM34, EM31 and EM63. Using target-free areas, a consistent power-law power spectrum (|A(k)| ~ k ^-β) for the profiles was found with β values typical of fractional Brownian motion (fBm). This means that the spatial variation of conductivity does not correspond to Gaussian statistics, where there are spatial correlations at different scales. The presence of targets tends to flatten the power-law power spectrum (PS) at small wavenumbers. Detection and localization of targets can be achieved using short-time Fourier transform (STFT). The presence of targets is enhanced because the signal energy is spread to higher wavenumbers (small scale numbers) in the positions occupied by the targets. In the case of poor spatial sampling or small amount of data, the information available from the power spectrum is not enough to separate spatial correlations from target signatures. Advantages are gained by using the spatial correlations of the fBm in order to reject the background response, and to enhance the signals from highly conductive targets. This approach was tested for the EM31 using a pre-processing step that combines apparent conductivity readings from two perpendicular transmitter-receiver orientations at each station. The response obtained using time-domain CSEM is influence to a lesser degree by geological noise and the target response can be processed to recover target features. The homotopy method is proposed to solve the inverse problem using a set of possible target models and a dynamic library of responses used to optimize the starting model.
International Nuclear Information System (INIS)
Wang, Y.D.; Ren, Y.Q.; Hu, T.; Deng, B.; Xiao, T.Q.; Liu, K.Y.; Yang, Y.S.
2016-01-01
Three dimensional (3D) characterization of shales has recently attracted wide attentions in relation to the growing importance of shale oil and gas. Obtaining a complete 3D compositional distribution of shale has proven to be challenging due to its multi-scale characteristics. A combined multi-energy X-ray micro-CT technique and data-constrained modelling (DCM) approach has been used to quantitatively investigate the multi-scale mineral and porosity distributions of a heterogeneous shale from the Junger Basin, northwestern China by sub-sampling. The 3D sub-resolution structures of minerals and pores in the samples are quantitatively obtained as the partial volume fraction distributions, with colours representing compositions. The shale sub-samples from two areas have different physical structures for minerals and pores, with the dominant minerals being feldspar and dolomite, respectively. Significant heterogeneities have been observed in the analysis. The sub-voxel sized pores form large interconnected clusters with fractal structures. The fractal dimensions of the largest clusters for both sub-samples were quantitatively calculated and found to be 2.34 and 2.86, respectively. The results are relevant in quantitative modelling of gas transport in shale reservoirs
Scaling properties of paleomagnetic reversal sequence
Directory of Open Access Journals (Sweden)
S. S. Ivanov
1996-01-01
Full Text Available The history of reversals of main geomagnetic field during last 160 My is analyzed as a sequence of events, presented as a point set on the time axis. Different techniques were applied including the method of boxcounting, dispersion counter-scaling, multifractal analysis and examination of attractor behaviour in multidimensional phase space. The existence of a crossover point at time interval 0.5-1.0 My was clearly identified, dividing the whole time range into two subranges with different scaling properties. The long-term subrange is characterized by monofractal dimension 0.88 and by an attractor, whose correlation dimension converges to 1.0, that provides evidence of a deterministic dynamical system in this subrange, similar to most existing dynamo models. In the short-term subrange the fractal dimension estimated by different methods varies from 0.47 to 0.88 and the dimensionality of the attractor is obtained to be about 3.7. These results are discussed in terms of non-linear superposition of processes in the Earth's geospheres.
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.)
ABC of multi-fractal spacetimes and fractional sea turtles
International Nuclear Information System (INIS)
Calcagni, Gianluca
2016-01-01
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. (orig.)
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.
Aerodynamic properties of fractal grains: implications for the primordial solar nebula
International Nuclear Information System (INIS)
Meakin, P.; Donn, B.
1988-01-01
Under conditions in the primordial solar nebula and dense interstellar clouds, small grains have low relative velocities. This is the condition for efficient sticking and formation of fractal aggregates. A calculation of the ratio of cross section, sigma, to number of primary particles, N, for fractal clusters yielded 1n sigma/N = 0.2635 + 0.5189N sup (-0.1748). This ratio decreases slowly with N and approaches a constant for large N. Under the usual assumption of collisions producing spherical compact, uniform density aggregates, sigma/N varies as N sup -1/3 and decreases rapidly. Fractal grains are therefore much more closely coupled to the gas than are compact aggregates. This has a significant effect on the aerodynamic behavior of aggregates and consequently on their evolution and that of the nebula
Biometric feature extraction using local fractal auto-correlation
International Nuclear Information System (INIS)
Chen Xi; Zhang Jia-Shu
2014-01-01
Image texture feature extraction is a classical means for biometric recognition. To extract effective texture feature for matching, we utilize local fractal auto-correlation to construct an effective image texture descriptor. Three main steps are involved in the proposed scheme: (i) using two-dimensional Gabor filter to extract the texture features of biometric images; (ii) calculating the local fractal dimension of Gabor feature under different orientations and scales using fractal auto-correlation algorithm; and (iii) linking the local fractal dimension of Gabor feature under different orientations and scales into a big vector for matching. Experiments and analyses show our proposed scheme is an efficient biometric feature extraction approach. (condensed matter: structural, mechanical, and thermal properties)
On fractal properties of equipotentials over a real rough surface faced to plasma in fusion devices
International Nuclear Information System (INIS)
Budaev, V.P.; Yakovlev, M.
2008-01-01
We consider a sheath region bounded by a corrugated surface of material conductor and a flat boundary held to a constant voltage bias. The real profile of the film deposited from plasma on a limiter in a fusion device was used in numerical solving of the Poisson's equation to find a profile of electrostatic potential. The rough surface influences the equipotential lines over the surface. We characterized a shape of equipotential lines by a fractal dimension. The long-range correlation in the potential field is imposed by the non-trivial fractal structure of the surface. Dust particles bounced in such irregular potential field can accelerate due to the Fermi acceleration. (author)
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
Peleg, M
1993-01-01
Fractal geometry and related concepts have had only a very minor impact on food research. The very few reported food applications deal mainly with the characterization of the contours of agglomerated instant coffee particles, the surface morphology of treated starch particles, the microstructure of casein gels viewed as a product limited diffusion aggregation, and the jagged mechanical signatures of crunchy dry foods. Fractal geometry describes objects having morphological features that are scale invariant. A demonstration of the self-similarity of fractal objects can be found in the familiar morphology of cauliflower and broccoli, both foods. Processes regulated by nonlinear dynamics can exhibit a chaotic behavior that has fractal characteristics. Examples are mixing of viscous fluids, turbulence, crystallization, agglomeration, diffusion, and possibly food spoilage.
Fractal-based exponential distribution of urban density and self-affine fractal forms of cities
International Nuclear Information System (INIS)
Chen Yanguang; Feng Jian
2012-01-01
Highlights: ► The model of urban population density differs from the common exponential function. ► Fractal landscape influences the exponential distribution of urban density. ► The exponential distribution of urban population suggests a self-affine fractal. ► Urban space can be divided into three layers with scaling and non-scaling regions. ► The dimension of urban form with characteristic scale can be treated as 2. - Abstract: 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 verify the theoretical inference. Based on the empirical analysis, a three-ring model of cities is presented and a city is conceptually divided into three layers from core to periphery. The scaling region and non-scaling region appear alternately in the city. This model may be helpful for future urban studies and city planning.
A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions
Zborovský, I.
2018-04-01
Fractal self-similarity of hadron interactions demonstrated by the z-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable z is a function of the momentum fractions x1 and x2 of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions ya and yb of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the z-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.
Fractal Property in the Light Curve of BL Lac Object S5 0716+714 ...
Indian Academy of Sciences (India)
tal method and then simulate the data with the Weierstrass–Mandelbrot. (W–M) function. It is considered that the ... The infrared observation indicated that the interstellar clouds have a fractal structure with dimension ... The observational data of the R-band (top panel) and simulation data with W–M function (bottom panel).
Discrimination of Earthquakes and Explosions using Multi-fractal Singularity Spectrums Properties
Czech Academy of Sciences Publication Activity Database
Lyubushin, A. A.; Kaláb, Zdeněk; Lednická, Markéta; Haggag, H. M.
2013-01-01
Roč. 17, č. 3 (2013), s. 975-983 ISSN 1383-4649 Institutional support: RVO:68145535 Keywords : multi- fractal parameters * singularity spectrum * seismic event discrimination Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 1.386, year: 2013 http://link.springer.com/content/pdf/10.1007%2Fs10950-013-9366-3.pdf
International Nuclear Information System (INIS)
Jinsheng Wang; Rui Zuo; Yanguo Teng; Zongjian Sun; Qinhong Hu
2010-01-01
Because of the deposit and accumulation from the debris flow, the heterogeneous geological characteristics is obvious for a candidate very low level waste (VLLW) disposal site, with the grain size ranging from tens of microns to 75 cm. Therefore, it is challenging to directly measure the sorption capacity of the media and the distribution coefficient of some radionuclides, such as strontium. We have studies the correlation of the particle mass content with different grade size and the sorption capacity, which is important in the modeling of radionuclide migration in the heterogeneous disposal site. A total of three deep pits and five shallow trenches were excavated, and 21 solid samples were collected for laboratory experiments. The grade and percentage of the different-sized particles were obtained, and the fractal dimension (D) of the media was calculated from the results of sieved experiments. Steady state sorption time and sorption isotherm of strontium was determined in the heterogeneous media, and sorption and distribution of strontium in the heterogeneous media were evaluated by the relationship between the mass percentage and distribution coefficient (K d ) of the fine-particle media, which was comprised of selected particles with a diameter less than 1 mm, and the correlation on the K d and D was regressed fit. The results indicated that fractal dimension bounded from 2.39 to 2.62 in the media, and K d values of strontium ranged between 119 and 126 in the fine-particle media, and corresponding value was 11 and 43 in the original media. The correlation between K d and D was approximately linear. (author)
Fractal differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
like fractal subsets of the real line may be termed as fractal-time dynamical systems. Formulation ... involving scaling and memory effects. But most of ..... begin by recalling the definition of the Riemann integral in ordinary calculus [33]. Let g: [a ...
International Nuclear Information System (INIS)
Popescu, E.; Ardeleanu, L.; Bazacliu, O.; Popa, M.; Radulian, M.; Rizescu, M.
2002-01-01
now (first two stages) refer to the determination of the fractal properties of the time and space distributions for the Vrancea subcrustal earthquakes. The application of the variation coefficient method in time domain outlines the existence of different types of generation models in the two segments delimited on depth in the Vrancea subcrustal region: crack-like events (M D ≤ 3.6) which are more clustered in the upper segment of the subducted lithosphere; asperity-like events (M D > 3.6) which on the contrary are more clustered in the lower segment of the subducted lithosphere. Application of fractal statistics leads us to the following conclusions: Time fractal dimension, D t , of the Vrancea subcrustal earthquakes varies in a relative small interval, D t with in the range [0.81 - 0.92]; these values indicate a clustering tendency in all analyzed cases; Data set is well approximated by a fractal model for a time domain τ with in the range [2 to 2 7 days]; in the same time interval, deviations from the linearity are also noticed, indicating a superposition of the scale invariance behavior (fractal properties) with a Poisson distribution (random). As concerns the space clustering properties of the Vrancea subcrustal events, our purpose is to test the hypothesis of segmentation on depth of the subducted lithosphere. Our work emphasized consequently the existence of two maxima in the depth-earthquake distribution: a) 60 ≤ h ≤110 km; b)110 < h ≤ 220 km. The space clustering analysis showed also that: 1. In the case of the upper segment, the fractal dimension of the epicenter distribution decreases in time from 1.83 to 1.71; 2. In the case of the lower segment, the fractal dimension of the epicenter distribution has a tendency of increase in time from 1.65 to 1.91; 3. In the case of the whole subducted slab, there is a trend of increase in time from 1.65 to 1.91. In conclusion, the analysis of the clustering properties in time and space in the case of Vrancea
Fractal characterization of acupuncture-induced spike trains of rat WDR neurons
International Nuclear Information System (INIS)
Chen, Yingyuan; Guo, Yi; Wang, Jiang; Hong, Shouhai; Wei, Xile; Yu, Haitao; Deng, Bin
2015-01-01
Highlights: •Fractal analysis is a valuable tool for measuring MA-induced neural activities. •In course of the experiments, the spike trains display different fractal properties. •The fractal properties reflect the long-term modulation of MA on WDR neurons. •The results may explain the long-lasting effects induced by acupuncture. -- Abstract: The experimental and the clinical studies have showed manual acupuncture (MA) could evoke multiple responses in various neural regions. Characterising the neuronal activities in these regions may provide more deep insights into acupuncture mechanisms. This paper used fractal analysis to investigate MA-induced spike trains of Wide Dynamic Range (WDR) neurons in rat spinal dorsal horn, an important relay station and integral component in processing acupuncture information. Allan factor and Fano factor were utilized to test whether the spike trains were fractal, and Allan factor were used to evaluate the scaling exponents and Hurst exponents. It was found that these two fractal exponents before and during MA were different significantly. During MA, the scaling exponents of WDR neurons were regulated in a small range, indicating a special fractal pattern. The neuronal activities were long-range correlated over multiple time scales. The scaling exponents during and after MA were similar, suggesting that the long-range correlations not only displayed during MA, but also extended to after withdrawing the needle. Our results showed that fractal analysis is a useful tool for measuring acupuncture effects. MA could modulate neuronal activities of which the fractal properties change as time proceeding. This evolution of fractal dynamics in course of MA experiments may explain at the level of neuron why the effect of MA observed in experiment and in clinic are complex, time-evolutionary, long-range even lasting for some time after stimulation
Energy Technology Data Exchange (ETDEWEB)
Bramowicz, Miroslaw [University of Warmia and Mazury in Olsztyn, Faculty of Technical Sciences, Oczapowskiego 11, 10-719 Olsztyn (Poland); Braic, Laurentiu [National Institute for Optoelectronics, 409 Atomistilor, 077125, Magurele (Romania); Azem, Funda Ak [Dokuz Eylul University, Engineering Faculty, Metallurgical and Materials Engineering Department, Tinaztepe Campus, 35397, Izmir (Turkey); Kulesza, Slawomir [University of Warmia and Mazury in Olsztyn, Faculty of Mathematics and Computer Science, Sloneczna 54, 10-710 Olsztyn (Poland); Birlik, Isil [Dokuz Eylul University, Engineering Faculty, Metallurgical and Materials Engineering Department, Tinaztepe Campus, 35397, Izmir (Turkey); Vladescu, Alina, E-mail: alinava@inoe.ro [National Institute for Optoelectronics, 409 Atomistilor, 077125, Magurele (Romania)
2016-08-30
Highlights: • Hydroxyapatite were prepared at temperatures in the range from 400 to 800 °C. • The coatings prepared at 800 °C is closer to the stoichiometric hydroxyapatite. • Hardness and elastic modulus decreased with increasing deposition temperature. • The surface morphology strongly depends on the deposition temperature. • Mesokurtic height distribution pulled towards larger heights were formed at high temperature. - Abstract: This aim of this work is to establish a relationship between the surface morphology and mechanical properties of hydroxyapatite coatings prepared using RF magnetron sputtering at temperatures in the range from 400 to 800 °C. The topography of the samples was scanned using atomic force microscopy, and the obtained 3D maps were analyzed using fractal methods to derive the spatial characteristics of the surfaces. X-ray photoelectron spectroscopy revealed the strong influence of the deposition temperature on the Ca/P ratio in the growing films. The coatings deposited at 600–800 °C exhibited a Ca/P ratio between 1.63 and 1.69, close to the stoichiometric hydroxyapatite (Ca/P = 1.67), which is crucial for proper osseointegration. Fourier-transform infrared spectroscopy showed that the intensity of phosphate absorption bands increased with increasing substrate temperature. Each sample exhibited well defined and sharp hydroxyapatite band at 566 cm{sup −1}, although more pronounced for the coatings deposited above 500 °C. Both the hardness and elastic modulus of the coated samples decrease with increasing deposition temperature. The surface morphology strongly depends on the deposition temperature. The sample deposited at 400 °C exhibits circular cavities dug in an otherwise flat surface. At higher deposition temperatures, these cavities increase in size and start to overlap each other so that at 500 °C the surface is composed of closely packed peaks and ridges. At that point, the characteristics of the surface turns from the
International Nuclear Information System (INIS)
Bramowicz, Miroslaw; Braic, Laurentiu; Azem, Funda Ak; Kulesza, Slawomir; Birlik, Isil; Vladescu, Alina
2016-01-01
Highlights: • Hydroxyapatite were prepared at temperatures in the range from 400 to 800 °C. • The coatings prepared at 800 °C is closer to the stoichiometric hydroxyapatite. • Hardness and elastic modulus decreased with increasing deposition temperature. • The surface morphology strongly depends on the deposition temperature. • Mesokurtic height distribution pulled towards larger heights were formed at high temperature. - Abstract: This aim of this work is to establish a relationship between the surface morphology and mechanical properties of hydroxyapatite coatings prepared using RF magnetron sputtering at temperatures in the range from 400 to 800 °C. The topography of the samples was scanned using atomic force microscopy, and the obtained 3D maps were analyzed using fractal methods to derive the spatial characteristics of the surfaces. X-ray photoelectron spectroscopy revealed the strong influence of the deposition temperature on the Ca/P ratio in the growing films. The coatings deposited at 600–800 °C exhibited a Ca/P ratio between 1.63 and 1.69, close to the stoichiometric hydroxyapatite (Ca/P = 1.67), which is crucial for proper osseointegration. Fourier-transform infrared spectroscopy showed that the intensity of phosphate absorption bands increased with increasing substrate temperature. Each sample exhibited well defined and sharp hydroxyapatite band at 566 cm"−"1, although more pronounced for the coatings deposited above 500 °C. Both the hardness and elastic modulus of the coated samples decrease with increasing deposition temperature. The surface morphology strongly depends on the deposition temperature. The sample deposited at 400 °C exhibits circular cavities dug in an otherwise flat surface. At higher deposition temperatures, these cavities increase in size and start to overlap each other so that at 500 °C the surface is composed of closely packed peaks and ridges. At that point, the characteristics of the surface turns from the
Directory of Open Access Journals (Sweden)
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
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Adewale Amosu
2018-02-01
Full Text Available Reservoir modeling of carbonate rocks requires a proper understanding of the pore space distribution and its relationship to permeability. Using a pigeonhole fractal model we characterize the fractal geometry of moldic pore spaces and extract the fractal dimension. We apply the Kozeny-Carman equation and equations relating the tortuosity and the porosity to the fractal dimension to derive an empirical relationship between permeability and porosity.
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.)
Fractals and multifractals in physics
International Nuclear Information System (INIS)
Arcangelis, L. de.
1987-01-01
We present a general introduction to the world of fractals. The attention is mainly devoted to stress how fractals do indeed appear in the real world and to find quantitative methods for characterizing their properties. The idea of multifractality is also introduced and it is presented in more details within the framework of the percolation problem
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
Le Chatelier's principle in sensation and perception: fractal-like enfolding at different scales
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Ken Norwich
2010-06-01
Full Text Available Le Chatelier’s principle asserts that a disturbance, when applied to a resting system may drive the system away from its equilibrium state, but will invoke a countervailing influence that will counteract the effect of the disturbance. When applied to the field of sensation and perception, a generalized stimulus will displace the system from equilibrium, and a generalized adaptation process will serve as the countervailing influence tending to reduce the impact of the stimulus. The principle applies at all levels, from the behavioral to the neural, the larger enfolding the smaller in fractal-like form. Le Chatelier’s principle, so applied, leads to the unification of many concepts in sensory science. Ideas as diverse as sensory adaptation, reflex arcs, and simple deductive logic can be brought under the umbrella of a single orienting principle. Beyond unification, this principle allows us to approach many questions in pathophysiology from a different perspective. For example, we find new direction toward the reduction of phantom limb pain and possibly of vertigo.
Le Chatelier's Principle in Sensation and Perception: Fractal-Like Enfolding at Different Scales
Norwich, Kenneth H.
2010-01-01
Le Chatelier's principle asserts that a disturbance, when applied to a resting system may drive the system away from its equilibrium state, but will invoke a countervailing influence that will counteract the effect of the disturbance. When applied to the field of sensation and perception, a generalized stimulus will displace the system from equilibrium, and a generalized adaptation process will serve as the countervailing influence tending to reduce the impact of the stimulus. The principle applies at all levels, from the behavioral to the neural, the larger enfolding the smaller in fractal-like form. Le Chatelier's principle, so applied, leads to the unification of many concepts in sensory science. Ideas as diverse as sensory adaptation, reflex arcs, and simple deductive logic can be brought under the umbrella of a single orienting principle. Beyond unification, this principle allows us to approach many questions in pathophysiology from a different perspective. For example, we find new direction toward the reduction of phantom-limb pain and possibly of vertigo. PMID:21423359
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.
Scaling properties of optical reflectance from quasi-periodic superlattices
International Nuclear Information System (INIS)
Wu Xiang; Yao Hesheng; Feng Weiguo
1991-08-01
The scaling properties of the optical reflectance from two types of quasi-periodic metal-insulator superlattices, one with the structure of Cantor bars and the other with the structure of Cantorian-Fibonaccian train, have been studied for the region of s-polarized soft x-rays and extreme ultraviolet. By using the hydrodynamic model of electron dynamics and transfer-matrix method, and be taking into account retardation effects, we have presented the formalism of the reflectivity for the superlattices. From our numerical results, we found that the reflection spectra of the quasi-superlattices have a rich structure of self-similarity. The interesting scaling indices, which are related to the fractal dimensions, of the spectra are also discussed for the two kinds of the quasi-superlattices. (author). 10 refs, 7 figs
The effect of ventricular assist devices on cerebral blood flow and blood pressure fractality
International Nuclear Information System (INIS)
Bellapart, Judith; Fraser, John F; Chan, Gregory S H; Tzeng, Yu-Chieh; Ainslie, Philip N; Dunster, Kimble R; Barnett, Adrian G; Boots, Rob
2011-01-01
Biological signals often exhibit self-similar or fractal scaling characteristics which may reflect intrinsic adaptability to their underlying physiological system. This study analysed fractal dynamics of cerebral blood flow in patients supported with ventricular assist devices (VAD) to ascertain if sustained modifications of blood pressure waveform affect cerebral blood flow fractality. Simultaneous recordings of arterial blood pressure and cerebral blood flow velocity using transcranial Doppler were obtained from five cardiogenic shock patients supported by VAD, five matched control patients and five healthy subjects. Computation of a fractal scaling exponent (α) at the low-frequency time scale by detrended fluctuation analysis showed that cerebral blood flow velocity exhibited 1/f fractal scaling in both patient groups (α = 0.95 ± 0.09 and 0.97 ± 0.12, respectively) as well as in the healthy subjects (α = 0.86 ± 0.07). In contrast, fluctuation in blood pressure was similar to non-fractal white noise in both patient groups (α = 0.53 ± 0.11 and 0.52 ± 0.09, respectively) but exhibited 1/f scaling in the healthy subjects (α = 0.87 ± 0.04, P < 0.05 compared with the patient groups). The preservation of fractality in cerebral blood flow of VAD patients suggests that normal cardiac pulsation and central perfusion pressure changes are not the integral sources of cerebral blood flow fractality and that intrinsic vascular properties such as cerebral autoregulation may be involved. However, there is a clear difference in the fractal scaling properties of arterial blood pressure between the cardiogenic shock patients and the healthy subjects
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
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.
International Nuclear Information System (INIS)
Li, W.; Bak, P.
1986-01-01
At a critical point the golden-mean Kolmogorov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is D = 0 and that the transition from the Kolmogorov-Arnol'd-Moser trajectory with dimension D = 1 to the cantorus is governed by an exponent ν = 0.98. . . and a universal scaling function. It is argued that the exponent is equal to that of the Lyapunov exponent
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Liliana Violeta Constantin
2012-01-01
Full Text Available Starting from the experimental data referring to the main parameters of the fracture surfaces of some 300-grade maraging steel reported by the classical work published in Nature 308, 721–722(1984, this work studied (a the multifractal scaling by the main parameters of the slit islands of fracture surfaces produced by a uniaxial tensile loading and (b the dependence of the impact energy to fracture and of the fractal dimensional increment on the temperature of the studied steels heat treatment, for the fracture surfaces produced by Charpy impact. The obtained results were analyzed, pointing out the spectral (size distribution of the found slit islands in the frame of some specific clusters (fractal components of the multifractal scaling of representative points of the logarithms of the slit islands areas and perimeters, respectively.
International Nuclear Information System (INIS)
Stemp, W James; Morozov, Mikhail; Key, Alastair J M
2015-01-01
Working load is one factor that affects wear on stone tools. Despite the recognition of the importance of the relationship between working load and the development of microwear on stone tools, there have been few attempts to quantify differences in wear due to changes in load. In a controlled experiment, we used 30 basalt flakes knapped from raw material collected in Olduvai Gorge, Tanzania, Africa, to cut oak branches for the same number of strokes. For each flake, a different loading level was applied starting at 150 g and increasing by increments of 150 g to a maximum load of 4.5 kg. A laser scanning confocal microscope was used to mathematically document the surface texture of the flakes. The worn surface data were compared using area-scale fractal complexity (Asfc), calculated from relative areas, to determine the degree to which variation in loading significantly affected the amount of wear on the flake surfaces. Our results indicate that working load does play a role in the development of lithic microwear on these flakes and that discrimination of two worn flake surfaces, using mean square ratios of Asfc, based on variable load is consistently possible with load differences between ∼100 g and 4.5 kg. However, discrimination of microwear on flake surfaces was not consistent for all load level differences and discrimination became less consistent when working load differences were below ∼100 g. (paper)
Fractals: Giant impurity nonlinearities in optics of fractal clusters
International Nuclear Information System (INIS)
Butenko, A.V.; Shalaev, V.M.; Stockman, M.I.
1988-01-01
A theory of nonlinear optical properties of fractals is developed. Giant enhancement of optical susceptibilities is predicted for impurities bound to a fractal. This enhancement occurs if the exciting radiation frequency lies within the absorption band of the fractal. The giant optical nonlinearities are due to existence of high local electric fields in the sites of impurity locations. Such fields are due to the inhomogeneously broadened character of a fractal spectrum, i.e. partial conservation of individuality of fractal-forming particles (monomers). The field enhancement is proportional to the Q-factor of the resonance of a monomer. The effects of coherent anti-Stokes Raman scattering (CARS) and phase conjugation (PC) of light waves are enhanced to a much greater degree than generation of higher harmonics. In a general case the susceptibility of a higher-order is enhanced in the maximum way if the process includes ''subtraction'' of photons (at least one of the strong field frequencies enters the susceptibility with the minus sign). Alternatively, enhancement for the highest-order harmonic generation (when all the photons are ''accumulated'') is minimal. The predicted phenomena bear information on spectral properties of both impurity molecules and a fractal. In particular, in the CARS spectra a narrow (with the natural width) resonant structure, which is proper to an isolated monomer of a fractal, is predicted to be observed. (orig.)
Randomness confidence bands of fractal scaling exponents for financial price returns
International Nuclear Information System (INIS)
Ibarra-Valdez, C.; Alvarez, J.; Alvarez-Ramirez, J.
2016-01-01
Highlights: • A robust test for randomness of price returns is proposed. • The DFA scaling exponent is contrasted against confidence bands for random sequences. • The size of the band depends of the sequence length. • Crude oil and USA stock markets have been rarely inefficient. - Abstract: The weak-form of the efficient market hypothesis (EMH) establishes that price returns behave as a pure random process and so their outcomes cannot be forecasted. The detrended fluctuation analysis (DFA) has been widely used to test the weak-form of the EMH by showing that time series of price returns are serially uncorrelated. In this case, the DFA scaling exponent exhibits deviations from the theoretical value of 0.5. This work considers the test of the EMH for DFA implementation on a sliding window, which is an approach that is intended to monitor the evolution of markets. Under these conditions, the scaling exponent exhibits important variations over the scrutinized period that can offer valuable insights in the behavior of the market provided the estimated scaling value is kept within strict statistical tests to verify the presence or not of serial correlations in the price returns. In this work, the statistical tests are based on comparing the estimated scaling exponent with the values obtained from pure Gaussian sequences with the length of the real time series. In this way, the presence of serial correlations can be guaranteed only in terms of the confidence bands of a pure Gaussian process. The crude oil (WTI) and the USA stock (DJIA) markets are used to illustrate the methodology.
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
Directory of Open Access Journals (Sweden)
Naside Ozer
2012-02-01
Full Text Available We analyzed statistical properties of earthquakes in western Anatolia as well as the North Anatolian Fault Zone (NAFZ in terms of spatio-temporal variations of fractal dimensions, p- and b-values. During statistically homogeneous periods characterized by closer fractal dimension values, we propose that occurrence of relatively larger shocks (M >= 5.0 is unlikely. Decreases in seismic activity in such intervals result in spatial b-value distributions that are primarily stable. Fractal dimensions decrease with time in proportion to increasing seismicity. Conversely, no spatiotemporal patterns were observed for p-value changes. In order to evaluate failure probabilities and simulate earthquake occurrence in the western NAFZ, we applied a modified version of the renormalization group method. Assuming an increase in small earthquakes is indicative of larger shocks, we apply the mentioned model to micro-seismic (M<= 3.0 activity, and test our results using San Andreas Fault Zone (SAFZ data. We propose that fractal dimension is a direct indicator of material heterogeneity and strength. Results from a model suggest simulated and observed earthquake occurrences are coherent, and may be used for seismic hazard estimation on creeping strike-slip fault zones.
Static friction between rigid fractal surfaces.
Alonso-Marroquin, Fernando; Huang, Pengyu; Hanaor, Dorian A H; Flores-Johnson, E A; Proust, Gwénaëlle; Gan, Yixiang; Shen, Luming
2015-09-01
Using spheropolygon-based simulations and contact slope analysis, we investigate the effects of surface topography and atomic scale friction on the macroscopically observed friction between rigid blocks with fractal surface structures. From our mathematical derivation, the angle of macroscopic friction is the result of the sum of the angle of atomic friction and the slope angle between the contact surfaces. The latter is obtained from the determination of all possible contact slopes between the two surface profiles through an alternative signature function. Our theory is validated through numerical simulations of spheropolygons with fractal Koch surfaces and is applied to the description of frictional properties of Weierstrass-Mandelbrot surfaces. The agreement between simulations and theory suggests that for interpreting macroscopic frictional behavior, the descriptors of surface morphology should be defined from the signature function rather than from the slopes of the contacting surfaces.
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.
a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution
Xia, Yuxuan; Cai, Jianchao; Wei, Wei; Hu, Xiangyun; Wang, Xin; Ge, Xinmin
Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.
Comparison of two fractal interpolation methods
Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo
2017-03-01
As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has
Fractal characterization of the compaction and sintering of ferrites
Glass, H.J.; With, de G.
2001-01-01
A novel parameter, the fractal exponent DE, is derived using the concept of fractal scaling. The fractal exponent DE relates the development of a feature within a material to the development of the size of the material. As an application, structural changes during the compaction and sintering of
Fractal vector optical fields.
Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2016-07-15
We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.
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.
International Nuclear Information System (INIS)
Jha, Shailendra K.; Kant, Rama
2010-01-01
We developed a mathematical model for the first order homogeneous catalytic chemical reaction coupled with an electron transfer (EC') on a rough working electrode. Results are obtained for the various roughness models of electrode corrugations, viz., (i) roughness as an exact periodic function, (ii) roughness as a random function with known statistical properties, and (iii) roughness as a random function with statistical self-affine fractality over a finite range of length scales. Method of Green's function is used in the formulation to obtain second-order perturbation (in roughness profile) expressions for the concentration, the local current density and the current transients. A general operator structure between these quantities and arbitrary roughness profile is emphasized. The statistically averaged (randomly rough) electrode response is obtained by an ensemble averaging over all possible surface configurations. An elegant mathematical formula between the average electrochemical current transient and surface structure factor or power-spectrum of roughness is obtained. This formula is used to obtain an explicit equation for the current on an approximately self-affine (or realistic) fractal electrode with a limited range of length scales of irregularities. This description of realistic fractal is obtained by cutoff power law power-spectrum of roughness. The realistic fractal power-spectrum consists of four physical characteristics, viz., the fractal dimension (D H ), lower (l) and upper (L) cutoff length scales of fractality and a proportionality factor (μ), which is related to the topothesy or strength of fractality. Numerical calculations are performed on final results to understand the effect of catalytic reaction and fractal morphological characteristics on potentiostatic current transients.
Scaling properties of foreign exchange volatility
Gençay, R.; Selçuk, F.; Whitcher, B.
2001-01-01
In this paper, we investigate the scaling properties of foreign exchange volatility. Our methodology is based on a wavelet multi-scaling approach which decomposes the variance of a time series and the covariance between two time series on a scale by scale basis through the application of a discrete
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
Energy Technology Data Exchange (ETDEWEB)
Davis, Ethan, E-mail: ethan.davis4@huskers.unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States); Liu, Ying; Jiang, Lijia; Lu, Yongfeng [Laser Assisted Nano Engineering Lab, Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, 209N Scott Engineering Center, Lincoln, NE 68588-0511 (United States); Ndao, Sidy, E-mail: sndao2@unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States)
2017-01-15
Highlights: • Hierarchically structured surfaces were fabricated on the micro/nano-scale. • These structures reduced the contact angle of the inherently hydrophilic material. • Similar surfaces have applications in two-phase heat transfer and microfluidics. - Abstract: This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
International Nuclear Information System (INIS)
Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy
2017-01-01
Highlights: • Hierarchically structured surfaces were fabricated on the micro/nano-scale. • These structures reduced the contact angle of the inherently hydrophilic material. • Similar surfaces have applications in two-phase heat transfer and microfluidics. - Abstract: This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
Applications of fractals in ecology.
Sugihara, G; M May, R
1990-03-01
Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems. Copyright © 1990. Published by Elsevier Ltd.
Taylor dispersion on a fractal
International Nuclear Information System (INIS)
Mazo, R.M.
1998-01-01
Taylor dispersion is the greatly enhanced diffusion in the direction of a fluid flow caused by ordinary diffusion in directions orthogonal to the flow. It is essential that the system be bounded in space in the directions orthogonal to the flow. We investigate the situation where the medium through which the flow occurs has fractal properties so that diffusion in the orthogonal directions is anomalous and non-Fickian. The effective diffusion in the flow direction remains normal; its width grows proportionally with the time. However, the proportionality constant depends on the fractal dimension of the medium as well as its walk dimension. (author)
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 ... Here a(t) is the cosmic scale factor and it measures the expansion of the Universe. ..... effectively appear as self-conserved dark energy, with a non-trivial ...
Two and Three-Phases Fractal Models Application in Soil Saturated Hydraulic Conductivity Estimation
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ELNAZ Rezaei abajelu
2017-03-01
Full Text Available Introduction: Soil Hydraulic conductivity is considered as one of the most important hydraulic properties in water and solutionmovement in porous media. In recent years, variousmodels as pedo-transfer functions, fractal models and scaling technique are used to estimate the soil saturated hydraulic conductivity (Ks. Fractal models with two subset of two (solid and pore and three phases (solid, pore and soil fractal (PSF are used to estimate the fractal dimension of soil particles. The PSF represents a generalization of the solid and pore mass fractal models. The PSF characterizes both the solid and pore phases of the porous material. It also exhibits self-similarity to some degree, in the sense that where local structure seems to be similar to the whole structure.PSF models can estimate interface fractal dimension using soil pore size distribution data (PSD and soil moisture retention curve (SWRC. The main objective of this study was to evaluate different fractal models to estimate the Ksparameter. Materials and Methods: The Schaapetal data was used in this study. The complex consists of sixty soil samples. Soil texture, soil bulk density, soil saturated hydraulic conductivity and soil particle size distribution curve were measured by hydrometer method, undistributed soil sample, constant head method and wet sieve method, respectively for all soil samples.Soil water retention curve were determined by using pressure plates apparatus.The Ks parameter could be estimated by Ralws model as a function of fractal dimension by seven fractal models. Fractal models included Fuentes at al. (1996, Hunt and Gee (2002, Bird et al. (2000, Huang and Zhang (2005, Tyler and Wheatcraft (1990, Kutlu et al. (2008, Sepaskhah and Tafteh (2013.Therefore The Ks parameter can be estimated as a function of the DS (fractal dimension by seven fractal models (Table 2.Sensitivity analysis of Rawls model was assessed by making changes±10%, ±20% and±30%(in input parameters
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.
Neutron scattering from fractals
DEFF Research Database (Denmark)
Kjems, Jørgen; Freltoft, T.; Richter, D.
1986-01-01
The scattering formalism for fractal structures is presented. Volume fractals are exemplified by silica particle clusters formed either from colloidal suspensions or by flame hydrolysis. The determination of the fractional dimensionality through scattering experiments is reviewed, and recent small...
Scale dependence of effective media properties
International Nuclear Information System (INIS)
Tidwell, V.C.; VonDoemming, J.D.; Martinez, K.
1992-01-01
For problems where media properties are measured at one scale and applied at another, scaling laws or models must be used in order to define effective properties at the scale of interest. The accuracy of such models will play a critical role in predicting flow and transport through the Yucca Mountain Test Site given the sensitivity of these calculations to the input property fields. Therefore, a research programhas been established to gain a fundamental understanding of how properties scale with the aim of developing and testing models that describe scaling behavior in a quantitative-manner. Scaling of constitutive rock properties is investigated through physical experimentation involving the collection of suites of gas permeability data measured over a range of discrete scales. Also, various physical characteristics of property heterogeneity and the means by which the heterogeneity is measured and described are systematically investigated to evaluate their influence on scaling behavior. This paper summarizes the approach that isbeing taken toward this goal and presents the results of a scoping study that was conducted to evaluate the feasibility of the proposed research
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.
2-D Fractal Carpet Antenna Design and Performance
Barton, C. C.; Tebbens, S. F.; Ewing, J. J.; Peterman, D. J.; Rizki, M. M.
2017-12-01
A 2-D fractal carpet antenna uses a fractal (self-similar) pattern to increase its perimeter by iteration and can receive or transmit electromagnetic radiation within its perimeter-bounded surface area. 2-D fractals are shapes that, at their mathematical limit (infinite iterations) have an infinite perimeter bounding a finite surface area. The fractal dimension describes the degree of space filling and lacunarity which quantifies the size and spatial distribution of open space bounded by a fractal shape. A key aspect of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that are very compact, wideband and multiband. As the number of iterations increases, the antenna operates at higher and higher frequencies. Manifestly different from traditional antenna designs, a fractal antenna can operate at multiple frequencies simultaneously. We have created a MATLAB code to generate deterministic and stochastic modes of Sierpinski carpet fractal antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, number of iterations, and lacunarities have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance
FRACTAL PROPERTY OF ADMINISTRATION
Zlatko Brnjas
2014-01-01
To understand the constant increase in administration, we need a new approach to the administration. For many years, the administration has intensified as a closed science, associated only with economics, law and political science. However, this approach did not bring anything good, because almost nothing in the administration has improved. Therefore, it is necessary to connect the administration with the natural sciences which give the best description of the world around us. Because of this...
FELICIA RAMONA BIRAU
2012-01-01
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...
Fractal description of fractures
International Nuclear Information System (INIS)
Lung, C.W.
1991-06-01
Recent studies on the fractal description of fractures are reviewed. Some problems on this subject are discussed. It seems hopeful to use the fractal dimension as a parameter for quantitative fractography and to apply fractal structures to the development of high toughness materials. (author). 28 refs, 7 figs
Elasticity of fractal materials using the continuum model with non-integer dimensional space
Tarasov, Vasily E.
2015-01-01
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.
Two-dimensional fractal geometry, critical phenomena and conformal invariance
International Nuclear Information System (INIS)
Duplantier, B.
1988-01-01
The universal properties of critical geometrical systems in two-dimensions (2D) like the O (n) and Potts models, are described in the framework of Coulomb gas methods and conformal invariance. The conformal spectrum of geometrical critical systems obtained is made of a discrete infinite series of scaling dimensions. Specific applications involve the fractal properties of self-avoiding walks, percolation clusters, and also some non trivial critical exponents or fractal dimensions associated with subsets of the planar Brownian motion. The statistical mechanics of the same critical models on a random 2D lattice (namely in presence of a critically-fluctuating metric, in the so-called 2D quantum gravity) is also addressed, and the above critical geometrical systems are shown to be exactly solvable in this case. The new ''gravitational'' conformal spectrum so derived is found to satisfy the recent Knizhnik, Polyakov and Zamolodchikov quadratic relation which links it to the standard conformal spectrum in the plane
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G C Young
Full Text Available We present a method to construct and analyse 3D models of underwater scenes using a single cost-effective camera on a standard laptop with (a free or low-cost software, (b no computer programming ability, and (c minimal man hours for both filming and analysis. This study focuses on four key structural complexity metrics: point-to-point distances, linear rugosity (R, fractal dimension (D, and vector dispersion (1/k. We present the first assessment of accuracy and precision of structure-from-motion (SfM 3D models from an uncalibrated GoPro™ camera at a small scale (4 m2 and show that they can provide meaningful, ecologically relevant results. Models had root mean square errors of 1.48 cm in X-Y and 1.35 in Z, and accuracies of 86.8% (R, 99.6% (D at scales 30-60 cm, 93.6% (D at scales 1-5 cm, and 86.9 (1/k. Values of R were compared to in-situ chain-and-tape measurements, while values of D and 1/k were compared with ground truths from 3D printed objects modelled underwater. All metrics varied less than 3% between independently rendered models. We thereby improve and rigorously validate a tool for ecologists to non-invasively quantify coral reef structural complexity with a variety of multi-scale metrics.
Fractal nature of hydrocarbon deposits. 2. Spatial distribution
International Nuclear Information System (INIS)
Barton, C.C.; Schutter, T.A; Herring, P.R.; Thomas, W.J.; Scholz, C.H.
1991-01-01
Hydrocarbons are unevenly distributed within reservoirs and are found in patches whose size distribution is a fractal over a wide range of scales. The spatial distribution of the patches is also fractal and this can be used to constrain the design of drilling strategies also defined by a fractal dimension. Fractal distributions are scale independent and are characterized by a power-law scaling exponent termed the fractal dimension. The authors have performed fractal analyses on the spatial distribution of producing and showing wells combined and of dry wells in 1,600-mi 2 portions of the Denver and Powder River basins that were nearly completely drilled on quarter-mile square-grid spacings. They have limited their analyses to wells drilled to single stratigraphic intervals so that the map pattern revealed by drilling is representative of the spatial patchiness of hydrocarbons at depth. The fractal dimensions for the spatial patchiness of hydrocarbons in the two basins are 1.5 and 1.4, respectively. The fractal dimension for the pattern of all wells drilled is 1.8 for both basins, which suggests a drilling strategy with a fractal dimension significantly higher than the dimensions 1.5 and 1.4 sufficient to efficiently and economically explore these reservoirs. In fact, the fractal analysis reveals that the drilling strategy used in these basins approaches a fractal dimension of 2.0, which is equivalent to random drilling with no geologic input. Knowledge of the fractal dimension of a reservoir prior to drilling would provide a basis for selecting and a criterion for halting a drilling strategy for exploration whose fractal dimension closely matches that of the spatial fractal dimension of the reservoir, such a strategy should prove more efficient and economical than current practice
Fractal dimension of turbulent black holes
Westernacher-Schneider, John Ryan
2017-11-01
We present measurements of the fractal dimension of a turbulent asymptotically anti-de Sitter black brane reconstructed from simulated boundary fluid data at the perfect fluid order using the fluid-gravity duality. We argue that the boundary fluid energy spectrum scaling as E (k )˜k-2 is a more natural setting for the fluid-gravity duality than the Kraichnan-Kolmogorov scaling of E (k )˜k-5 /3, but we obtain fractal dimensions D for spatial sections of the horizon H ∩Σ in both cases: D =2.584 (1 ) and D =2.645 (4 ), respectively. These results are consistent with the upper bound of D =3 , thereby resolving the tension with the recent claim in Adams et al. [Phys. Rev. Lett. 112, 151602 (2014), 10.1103/PhysRevLett.112.151602] that D =3 +1 /3 . We offer a critical examination of the calculation which led to their result, and show that their proposed definition of the fractal dimension performs poorly as a fractal dimension estimator on one-dimensional curves with known fractal dimension. Finally, we describe how to define and in principle calculate the fractal dimension of spatial sections of the horizon H ∩Σ in a covariant manner, and we speculate on assigning a "bootstrapped" value of fractal dimension to the entire horizon H when it is in a statistically quasisteady turbulent state.
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.
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 Structure and Entropy Production within the Central Nervous System
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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.
Classification of radar echoes using fractal geometry
International Nuclear Information System (INIS)
Azzaz, Nafissa; Haddad, Boualem
2017-01-01
Highlights: • Implementation of two concepts of fractal geometry to classify two types of meteorological radar echoes. • A new approach, called a multi-scale fractal dimension is used for classification between fixed echoes and rain echoes. • An Automatic identification system of meteorological radar echoes was proposed using fractal geometry. - Abstract: This paper deals with the discrimination between the precipitation echoes and the ground echoes in meteorological radar images using fractal geometry. This study aims to improve the measurement of precipitations by weather radars. For this, we considered three radar sites: Bordeaux (France), Dakar (Senegal) and Me lbourne (USA). We showed that the fractal dimension based on contourlet and the fractal lacunarity are pertinent to discriminate between ground and precipitation echoes. We also demonstrated that the ground echoes have a multifractal structure but the precipitations are more homogeneous than ground echoes whatever the prevailing climate. Thereby, we developed an automatic classification system of radar using a graphic interface. This interface, based on the fractal geometry makes possible the identification of radar echoes type in real time. This system can be inserted in weather radar for the improvement of precipitation estimations.
Heat kernels and zeta functions on fractals
International Nuclear Information System (INIS)
Dunne, Gerald V
2012-01-01
On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and quantum physics in systems having fractal properties. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (paper)
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.
Uritskaya, Olga Y.
2005-05-01
Results of fractal stability analysis of daily exchange rate fluctuations of more than 30 floating currencies for a 10-year period are presented. It is shown for the first time that small- and large-scale dynamical instabilities of national monetary systems correlate with deviations of the detrended fluctuation analysis (DFA) exponent from the value 1.5 predicted by the efficient market hypothesis. The observed dependence is used for classification of long-term stability of floating exchange rates as well as for revealing various forms of distortion of stable currency dynamics prior to large-scale crises. A normal range of DFA exponents consistent with crisis-free long-term exchange rate fluctuations is determined, and several typical scenarios of unstable currency dynamics with DFA exponents fluctuating beyond the normal range are identified. It is shown that monetary crashes are usually preceded by prolonged periods of abnormal (decreased or increased) DFA exponent, with the after-crash exponent tending to the value 1.5 indicating a more reliable exchange rate dynamics. Statistically significant regression relations (R=0.99, pcurrency crises and the degree of distortion of monofractal patterns of exchange rate dynamics are found. It is demonstrated that the parameters of these relations characterizing small- and large-scale crises are nearly equal, which implies a common instability mechanism underlying these events. The obtained dependences have been used as a basic ingredient of a forecasting technique which provided correct in-sample predictions of monetary crisis magnitude and duration over various time scales. The developed technique can be recommended for real-time monitoring of dynamical stability of floating exchange rate systems and creating advanced early-warning-system models for currency crisis prevention.
Scaling properties of localized quantum chaos
International Nuclear Information System (INIS)
Izrailev, F.M.
1991-01-01
Statistical properties of spectra and eigenfunctions are studied for the model of quantum chaos in the presence of dynamical localization. The main attention is paid to the scaling properties of localization length and level spacing distribution in the intermediate region between Poissonian and Wigner-Dyson statistics. It is shown that main features of such localized quantum chaos are well described by the introduced ensemble of band random matrices. 28 refs.; 7 figs
Fractal nature of humic materials
International Nuclear Information System (INIS)
Rice, J.A.
1992-01-01
Fractals are geometric representatives of strongly disordered systems whose structure is described by nonintegral dimensions. A fundamental tenet of fractal geometry is that disorder persists at any characterization scale-length used to describe the system. The nonintegral nature of these fractal dimensions is the result of the realization that a disordered system must possess more structural detail than an ordered system with classical dimensions of 1, 2, or 3 in order to accommodate this ''disorder within disorder.'' Thus from a fractal perspective, disorder is seen as an inherent characteristic of the system rather than as a perturbative phenomena forced upon it. Humic materials are organic substances that are formed by the profound alteration of organic matter in a natural environment. They can be operationally divided into 3 fractions; humic acid (soluble in base), fulvic acid (soluble in acid or base), and humin (insoluble in acid or base). Each of these fraction has been shown to be an extremely heterogeneous mixture. These mixtures have proven so intractable that they may represent the ultimate in molecular disorder. In fact, based on the characteristics that humic materials must possess in order to perform their functions in natural systems, it has been proposed that the fundamental chemical characteristic of a humic material is not a discrete chemical structure but a pronounced lack of order on a molecular level. If the fundamental chemical characteristic of a humic material is a strongly disordered nature, as has been proposed, then humic materials should be amenable to characterization by fractal geometry. The purpose of this paper is to test this hypothesis
Fractal analysis of agricultural nozzles spray
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Francisco Agüera
2012-02-01
Full Text Available Fractal scaling of the exponential type is used to establish the cumulative volume (V distribution applied through agricultural spray nozzles in size x droplets, smaller than the characteristic size X. From exponent d, we deduced the fractal dimension (Df which measures the degree of irregularity of the medium. This property is known as 'self-similarity'. Assuming that the droplet set from a spray nozzle is self-similar, the objectives of this study were to develop a methodology for calculating a Df factor associated with a given nozzle and to determine regression coefficients in order to predict droplet spectra factors from a nozzle, taking into account its own Df and pressure operating. Based on the iterated function system, we developed an algorithm to relate nozzle types to a particular value of Df. Four nozzles and five operating pressure droplet size characteristics were measured using a Phase Doppler Particle Analyser (PDPA. The data input consisted of droplet size spectra factors derived from these measurements. Estimated Df values showed dependence on nozzle type and independence of operating pressure. We developed an exponential model based on the Df to enable us to predict droplet size spectra factors. Significant coefficients of determination were found for the fitted model. This model could prove useful as a means of comparing the behavior of nozzles which only differ in not measurable geometric parameters and it can predict droplet spectra factors of a nozzle operating under different pressures from data measured only in extreme work pressures.
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
Fractal characterization of brain lesions in CT images
International Nuclear Information System (INIS)
Jauhari, Rajnish K.; Trivedi, Rashmi; Munshi, Prabhat; Sahni, Kamal
2005-01-01
Fractal Dimension (FD) is a parameter used widely for classification, analysis, and pattern recognition of images. In this work we explore the quantification of CT (computed tomography) lesions of the brain by using fractal theory. Five brain lesions, which are portions of CT images of diseased brains, are used for the study. These lesions exhibit self-similarity over a chosen range of scales, and are broadly characterized by their fractal dimensions
Hybrid 3D Fractal Coding with Neighbourhood Vector Quantisation
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Zhen Yao
2004-12-01
Full Text Available A hybrid 3D compression scheme which combines fractal coding with neighbourhood vector quantisation for video and volume data is reported. While fractal coding exploits the redundancy present in different scales, neighbourhood vector quantisation, as a generalisation of translational motion compensation, is a useful method for removing both intra- and inter-frame coherences. The hybrid coder outperforms most of the fractal coders published to date while the algorithm complexity is kept relatively low.
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J. Antonio Paramo
2015-01-01
Full Text Available Hydrozincite (Zn5(OH6(CO32 is, among others, a popular precursor used to synthesize nanoscale ZnO with complex morphologies. For many existing and potential applications utilizing nanostructures, performance is determined by the surface and subsurface properties. Current understanding of the relationship between the morphology and the defect properties of nanocrystalline ZnO and hydrozincite systems is still incomplete. Specifically, for the latter nanomaterial the structure-property correlations are largely unreported in the literature despite the extensive use of hydrozincite in the synthesis applications. In our work, we addressed this issue by studying precipitated nanostructures of Zn5(OH6(CO32 with varying quasi-fractal dimensionalities containing relatively small amounts of a ZnO phase. Crystal morphology of the samples was accurately controlled by the growth time. We observed a strong correlation between the morphology of the samples and their optoelectronic properties. Our results indicate that a substantial increase of the free surface in the nanocrystal samples generates higher relative concentration of defects, consistent with the model of defect-rich surface and subsurface layers.
Experimental study of circle grid fractal pattern on turbulent intensity in pipe flow
International Nuclear Information System (INIS)
Manshoor, B; Zaman, I; Othman, M F; Khalid, Amir
2013-01-01
Fractal turbulence is deemed much more efficient than grid turbulence in terms of a turbulence generation. In this paper, the hotwire experimental results for the circle grids fractal pattern as a turbulent generator will be presented. The self-similar edge characteristic of the circle grid fractal pattern is thought to play a vital role in the enhancement of turbulent intensity. Three different beta ratios of perforated plates based on circle grids fractal pattern were used in the experimental work and each paired with standard circle grids with similar porosity. The objectives were to study the fractal scaling influence on the flow and also to explore the potential of the circle grids fractal pattern in enhancing the turbulent intensity. The results provided an excellent insight of the fractal generated turbulence and the fractal flow physics. Across the circle grids fractal pattern, the pressure drop was lower but the turbulent intensity was higher than those across the paired standard circle grids
Fractal analytical approach of urban form based on spatial correlation function
International Nuclear Information System (INIS)
Chen, Yanguang
2013-01-01
Highlights: ► Many fractal parameter relations of cities can be derived by scaling analysis. ► The area-radius scaling of cities suggests a spatial correlation function. ► Spectral analysis can be used to estimate fractal dimension values of urban form. ► The valid range of fractal dimension of urban form comes between 1.5 and 2. ► The traditional scale concept will be replaced by scaling concept in geography. -- Abstract: Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities are not yet revealed in theory. By mathematical deduction and transform (e.g., Fourier transform), I find that scaling analysis, spectral analysis, and spatial correlation analysis are all associated with fractal concepts and can be integrated into a new approach to fractal analysis of cities. This method can be termed ‘3S analyses’ of urban form. Using the 3S analysis, I derived a set of fractal parameter equations, by which different fractal parameters of cities can be linked up with one another. Each fractal parameter has its own reasonable extent of values. According to the fractal parameter equations, the intersection of the rational ranges of different fractal parameters suggests the proper scale of the fractal dimension of urban patterns, which varies from 1.5 to 2. The fractal dimension equations based on the 3S analysis and the numerical relationships between different fractal parameters are useful for geographers to understand urban evolution and potentially helpful for future city planning
Categorization of fractal plants
International Nuclear Information System (INIS)
Chandra, Munesh; Rani, Mamta
2009-01-01
Fractals in nature are always a result of some growth process. The language of fractals which has been created specifically for the description of natural growth process is called L-systems. Recently, superior iterations (essentially, investigated by Mann [Mann WR. Mean value methods in iteration. Proc Am Math Soc 1953;4:506-10 [MR0054846 (14,988f)
Casati, Giulio; Maspero, Giulio; Shepelyansky, Dima L.
1997-01-01
We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on the classical fractal set.
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
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.
Fractal characteristic study of shearer cutter cutting resistance curves
Energy Technology Data Exchange (ETDEWEB)
Liu, C. [Heilongjiang Scientific and Technical Institute, Haerbin (China). Dept of Mechanical Engineering
2004-02-01
The cutting resistance curve is the most useful tool for reflecting the overall cutting performance of a cutting machine. The cutting resistance curve is influenced by many factors such as the pick structure and arrangement, the cutter operation parameters, coal quality and geologic conditions. This paper discusses the use of fractal geometry to study the properties of the cutting resistance curve, and the use of fractal dimensions to evaluate cutting performance. On the basis of fractal theory, the general form and calculation method of fractal characteristics are given. 4 refs., 3 figs., 1 tab.
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.
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.
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...
Echeverría, Juan C; Infante, Oscar; Pérez-Grovas, Héctor; González, Hortensia; José, Marco V; Lerma, Claudia
2017-11-01
The aim of this work was to evaluate the short-term fractal index (α 1 ) of heart rate variability (HRV) in chronic renal failure (CRF) patients by identifying the effects of orthostatism and hemodialysis (HD), and by evaluating the correlation between α 1 and the mean RR interval from sinus beats (meanNN). HRV time series were derived from ECG data of 19 CRF patients and 20 age-matched healthy subjects obtained at supine and orthostatic positions (lasting 5 min each). Data from CRF patients were collected before and after HD. α 1 was calculated from each time series and compared by analysis of variance. Pearson's correlations between meanNN and α 1 were calculated using the data from both positions by considering three groups: healthy subjects, CRF before HD and CRF after HD. At supine position, α 1 of CRF patients after HD (1.17 ± 0.30) was larger (P renal disease condition in itself. In conclusion, as in healthy subjects, α 1 of CRF patients correlates with meanNN after HD (indicating a more irregular-like HRV behavior at slower heart rates). This suggests that CRF patients with stable blood pressure preserve a regulatory adaptability despite a shifted setting point of the heart period (i.e., higher heart rate) in comparison with healthy subjects. © 2017 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.
Can The Pore Scale Geometry Explain Soil Sample Scale Hydrodynamic Properties?
Directory of Open Access Journals (Sweden)
Sarah Smet
2018-04-01
Full Text Available For decades, the development of new visualization techniques has brought incredible insights into our understanding of how soil structure affects soil function. X-ray microtomography is a technique often used by soil scientists but challenges remain with the implementation of the procedure, including how well the samples represent the uniqueness of the pore network and structure and the systemic compromise between sample size and resolution. We, therefore, chose to study soil samples from two perspectives: a macroscopic scale with hydrodynamic characterization and a microscopic scale with structural characterization through the use of X-ray microtomography (X-ray μCT at a voxel size of 21.53 μm3 (resampled at 433 μm3. The objective of this paper is to unravel the relationships between macroscopic soil properties and microscopic soil structure. The 24 samples came from an agricultural field (Cutanic Luvisol and the macroscopic hydrodynamic properties were determined using laboratory measurements of the saturated hydraulic conductivity (Ks, air permeability (ka, and retention curves (SWRC. The X-ray μCT images were segmented using a global method and multiple microscopic measurements were calculated. We used Bayesian statistics to report the credible correlation coefficients and linear regressions models between macro- and microscopic measurements. Due to the small voxel size, we observed unprecedented relationships, such as positive correlations between log(Ks and a μCT global connectivity indicator, the fractal dimension of the μCT images or the μCT degree of anisotropy. The air permeability measured at a water matric potential of −70 kPa was correlated to the average coordination number and the X-ray μCT porosity, but was best explained by the average pore volume of the smallest pores. Continuous SWRC were better predicted near saturation when the pore-size distributions calculated on the X-ray μCT images were used as model input. We
Low field scaling properties of high Tc superconductor glasses
Giovannella, C.; Fruchter, L.; Chappert, C.
We show that the zero field cooling (ZFC) M/H curves of both the YBaCuO and the LaSrCuO granular superconductor glasses (SuG) are subjected to scaling when plotted against the reduced variable t/H1/ψ . The breaking of the scaling for too weak or too strong magnetic fields is discussed and justified by the introduction of a phenomenological fractal picture, describing the behaviour of the disordered intergranular junction network. Nous montrons que les courbes M/H caractéristiques des verres de supraconducteurs granulaires sont sujettes à une loi d'échelle lorsqu'elles sont tracées en fonction de la variable réduite t/H1/ψ. La brisure de la loi d'échelle pour des champs trop forts ou trop faibles est justifiée par l'introduction d'un modèle phénoménologique fractal capable de décrire le comportement d'un réseau désordonné des jonctions.
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 ...
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.
Fractal analysis of rainfall occurrence observed in the synoptic ...
African Journals Online (AJOL)
Fractal analysis is important for characterizing and modeling rainfall's space-time variations in hydrology. The purpose of this study consists on determining, in a mono-fractal framework, the scale invariance of rainfall series in Benin synopticstations located in two main geographical area: Cotonou, Bohicon , Savè in a sub ...
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.
The fractal nature of vacuum arc cathode spots
International Nuclear Information System (INIS)
Anders, Andre
2005-01-01
Cathode spot phenomena show many features of fractals, for example self-similar patterns in the emitted light and arc erosion traces. Although there have been hints on the fractal nature of cathode spots in the literature, the fractal approach to spot interpretation is underutilized. In this work, a brief review of spot properties is given, touching the differences between spot type 1 (on cathodes surfaces with dielectric layers) and spot type 2 (on metallic, clean surfaces) as well as the known spot fragment or cell structure. The basic properties of self-similarity, power laws, random colored noise, and fractals are introduced. Several points of evidence for the fractal nature of spots are provided. Specifically power laws are identified as signature of fractal properties, such as spectral power of noisy arc parameters (ion current, arc voltage, etc) obtained by fast Fourier transform. It is shown that fractal properties can be observed down to the cutoff by measurement resolution or occurrence of elementary steps in physical processes. Random walk models of cathode spot motion are well established: they go asymptotically to Brownian motion for infinitesimal step width. The power spectrum of the arc voltage noise falls as 1/f 2 , where f is frequency, supporting a fractal spot model associated with Brownian motion
Biophysical Chemistry of Fractal Structures and Processes in Environmental Systems
Buffle, J.; Leeuwen, van H.P.
2008-01-01
This book aims to provide the scientific community with a novel and valuable approach based on fractal geometry concepts on the important properties and processes of diverse environmental systems. The interpretation of complex environmental systems using modern fractal approaches is compared and
A transfer matrix method for the analysis of fractal quantum potentials
International Nuclear Information System (INIS)
Monsoriu, Juan A; Villatoro, Francisco R; Marin, Maria J; UrchueguIa, Javier F; Cordoba, Pedro Fernandez de
2005-01-01
The scattering properties of quantum particles on a sequence of potentials converging towards a fractal one are obtained by means of the transfer matrix method. The reflection coefficients for both the fractal potential and finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal potential has a self-similar structure associated with the fractal distribution of the potential whose degree of self-similarity has been quantified by means of the correlation function
A transfer matrix method for the analysis of fractal quantum potentials
Energy Technology Data Exchange (ETDEWEB)
Monsoriu, Juan A [Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain); Villatoro, Francisco R [Departamento de Lenguajes y Ciencias de la Computacion, Universidad de Malaga, E-29071 Malaga (Spain); Marin, Maria J [Departamento de Termodinamica, Universitat de Valencia, E-46100 Burjassot (Spain); UrchueguIa, Javier F [Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain); Cordoba, Pedro Fernandez de [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain)
2005-07-01
The scattering properties of quantum particles on a sequence of potentials converging towards a fractal one are obtained by means of the transfer matrix method. The reflection coefficients for both the fractal potential and finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal potential has a self-similar structure associated with the fractal distribution of the potential whose degree of self-similarity has been quantified by means of the correlation function.
Pikkujamsa, S. M.; Makikallio, T. H.; Sourander, L. B.; Raiha, I. J.; Puukka, P.; Skytta, J.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.
1999-01-01
BACKGROUND: New methods of R-R interval variability based on fractal scaling and nonlinear dynamics ("chaos theory") may give new insights into heart rate dynamics. The aims of this study were to (1) systematically characterize and quantify the effects of aging from early childhood to advanced age on 24-hour heart rate dynamics in healthy subjects; (2) compare age-related changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling and complexity (chaos) theory; and (3) further test the hypothesis that there is loss of complexity and altered fractal scaling of heart rate dynamics with advanced age. METHODS AND RESULTS: The relationship between age and cardiac interbeat (R-R) interval dynamics from childhood to senescence was studied in 114 healthy subjects (age range, 1 to 82 years) by measurement of the slope, beta, of the power-law regression line (log power-log frequency) of R-R interval variability (10(-4) to 10(-2) Hz), approximate entropy (ApEn), short-term (alpha(1)) and intermediate-term (alpha(2)) fractal scaling exponents obtained by detrended fluctuation analysis, and traditional time- and frequency-domain measures from 24-hour ECG recordings. Compared with young adults (60 years, n=29). CONCLUSIONS: Cardiac interbeat interval dynamics change markedly from childhood to old age in healthy subjects. Children show complexity and fractal correlation properties of R-R interval time series comparable to those of young adults, despite lower overall heart rate variability. Healthy aging is associated with R-R interval dynamics showing higher regularity and altered fractal scaling consistent with a loss of complex variability.
Children's separation anxiety scale (CSAS: psychometric properties.
Directory of Open Access Journals (Sweden)
Xavier Méndez
Full Text Available This study describes the psychometric properties of the Children's Separation Anxiety Scale (CSAS, which assesses separation anxiety symptoms in childhood. Participants in Study 1 were 1,908 schoolchildren aged between 8 and 11. Exploratory factor analysis identified four factors: worry about separation, distress from separation, opposition to separation, and calm at separation, which explained 46.91% of the variance. In Study 2, 6,016 children aged 8-11 participated. The factor model in Study 1 was validated by confirmatory factor analysis. The internal consistency (α = 0.82 and temporal stability (r = 0.83 of the instrument were good. The convergent and discriminant validity were evaluated by means of correlations with other measures of separation anxiety, childhood anxiety, depression and anger. Sensitivity of the scale was 85% and its specificity, 95%. The results support the reliability and validity of the CSAS.
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.
Willson, Stephen J.
1991-01-01
Described is a course designed to teach students about fractals using various teaching methods including the computer. Discussed are why the course drew students, prerequisites, clientele, textbook, grading, computer usage, and the syllabus. (KR)
Alberti, Tommaso; Lepreti, Fabio; Vecchio, Antonio; Carbone, Vincenzo
2017-04-01
The Earth's climate is an extremely unstable complex system consisting of nonlinear and still rather unknown interactions among atmosphere, land surface, ice and oceans. The system is mainly driven by solar irradiance, even if internal components as volcanic eruptions and human activities affect the atmospheric composition thus acting as a driver for climate changes. Since the extreme climate variability is the result of a set of phenomena operating from daily to multi-millennial timescales, with different correlation times, a study of the scaling properties of the system can evidence non-trivial persistent structures, internal or external physical processes. Recently, the scaling properties of the paleoclimate changes have been analyzed by distinguish between interglacial and glacial climates [Shao and Ditlevsen, 2016]. The results show that the last glacial record (20-120 kyr BP) presents some elements of multifractality, while the last interglacial period (0-10 kyr BP), say the Holocene period, seems to be characterized by a mono-fractal structure. This is associated to the absence of Dansgaard-Oeschger (DO) events in the interglacial climate that could be the cause for the absence of multifractality. This hypothesis is supported by the analysis of the period between 18 and 27 kyr BP, i.e. during the Last Glacial Period, in which a single DO event have been registred. Through the Empirical Mode Decomposition (EMD) we were able to detect a timescale separation within the Last Glacial Period (20-120 kyr BP) in two main components: a high-frequency component, related to the occurrence of DO events, and a low-frequency one, associated to the cooling/warming phase switch [Alberti et al., 2014]. Here, we investigate the scaling properties of the climate fluctuations within the Last Glacial Period, where abrupt climate changes, characterized by fast increase of temperature usually called Dansgaard-Oeschger (DO) events, have been particularly pronounced. By using the
Energy Technology Data Exchange (ETDEWEB)
Achik, I. [Laboratoire de Physique de la Matière Condensée, Université Hassan II-Mohammedia, Faculté des sciences Ben M' sik, Casablanca (Morocco); Boughaleb, Y., E-mail: yboughaleb@yahoo.fr [Laboratoire de Physique de la Matière Condensée, Université Hassan II-Mohammedia, Faculté des sciences Ben M' sik, Casablanca (Morocco); Université Chouaib Doukkali, Faculté des sciences, El Jadida (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Hader, A. [Laboratoire de Physique de la Matière Condensée, Université Hassan II-Mohammedia, Faculté des sciences Ben M' sik, Casablanca (Morocco); CRMEF Settat (Morocco); Sbiaai, K. [Université Chouaib Doukkali, Faculté des sciences, El Jadida (Morocco); Hajjaji, A. [Université Chouaib Doukkali, Ecole nationale des sciences appliquées, El Jadida (Morocco)
2013-10-31
The aim of the present work was to study numerically the scaling behavior and the morphological properties of the interfaces generated by the multilayer deposition process. We have noticed that, in the case where the ratio of the surface diffusion coefficient to the deposition rate reaches high values D/F > > 1, the interface consists of mound structures. By using the dynamic scaling, we have shown that the height–height correlation function scales with time t and length l as G(l,t) ∼ l{sup α}f(t/l{sup α/β}) with β = 0.25 ± 0.05 and α = 0.51 ± 0.02. These exponent values are equal to the ones predicted by the Edwards–Wilkinson approach. Besides, our results are in agreement with the growth system of Cu/Cu(100) at 300 K which has been characterized in more detail by a combined scanning tunneling microscopy and spot profile analysis — low energy electronic diffusion study. Moreover, by considering two different methods, we have examined the fractal aspect of the obtained interfaces. - Highlights: • The adlayer interfaces present mound morphologies. • The adlayer interfaces scale with the Family–Vicsek law. • The critical exponents (α, β) are in agreement with those of Edwards–Wilkinson approach.
International Nuclear Information System (INIS)
Achik, I.; Boughaleb, Y.; Hader, A.; Sbiaai, K.; Hajjaji, A.
2013-01-01
The aim of the present work was to study numerically the scaling behavior and the morphological properties of the interfaces generated by the multilayer deposition process. We have noticed that, in the case where the ratio of the surface diffusion coefficient to the deposition rate reaches high values D/F > > 1, the interface consists of mound structures. By using the dynamic scaling, we have shown that the height–height correlation function scales with time t and length l as G(l,t) ∼ l α f(t/l α/β ) with β = 0.25 ± 0.05 and α = 0.51 ± 0.02. These exponent values are equal to the ones predicted by the Edwards–Wilkinson approach. Besides, our results are in agreement with the growth system of Cu/Cu(100) at 300 K which has been characterized in more detail by a combined scanning tunneling microscopy and spot profile analysis — low energy electronic diffusion study. Moreover, by considering two different methods, we have examined the fractal aspect of the obtained interfaces. - Highlights: • The adlayer interfaces present mound morphologies. • The adlayer interfaces scale with the Family–Vicsek law. • The critical exponents (α, β) are in agreement with those of Edwards–Wilkinson approach
Incomplete information and fractal phase space
International Nuclear Information System (INIS)
Wang, Qiuping A.
2004-01-01
The incomplete statistics for complex systems is characterized by a so called incompleteness parameter ω which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the incompleteness of accessible information and of the physical signification of ω on the basis of fractal phase space. ω is shown to be proportional to the fractal dimension of the phase space and can be linked to the phase volume expansion and information growth during the scale refining process
Quantum waveguide theory of a fractal structure
International Nuclear Information System (INIS)
Lin Zhiping; Hou Zhilin; Liu Youyan
2007-01-01
The electronic transport properties of fractal quantum waveguide networks in the presence of a magnetic field are studied. A Generalized Eigen-function Method (GEM) is used to calculate the transmission and reflection coefficients of the studied systems unto the fourth generation Sierpinski fractal network with node number N=123. The relationship among the transmission coefficient T, magnetic flux Φ and wave vector k is investigated in detail. The numerical results are shown by the three-dimensional plots and contour maps. Some resonant-transmission features and the symmetry of the transmission coefficient T to flux Φ are observed and discussed, and compared with the results of the tight-binding model
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.
Fractal structures and intermittency in QCD
International Nuclear Information System (INIS)
Gustafson, Goesta.
1990-04-01
New results are presented for fractal structures and intermittency in QCD parton showers. A geometrical interpretation of the anomalous dimension in QCD is given. It is shown that model predications for factorial moments in the PEP-PETRA energy range are increased. if the properties of directly produced pions are more carefully taken into account
Fractal geometry of high temperature superconductors
International Nuclear Information System (INIS)
Mosolov, A.B.
1989-01-01
Microstructural geometry of superconducting structural composites of Ag-Yba 2 Cu 3 O x system with a volumetric shave of silver from 0 to 60% is investigated by light and electron microscopy methods. It is ascertained that the structure of cermets investigated is characterized by fractal geometry which is sufficient for describing the electrical and mechanical properties of these materials
A Tutorial Review on Fractal Spacetime and Fractional Calculus
He, Ji-Huan
2014-11-01
This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.
Seuront, Laurent
2015-08-01
Fractal analysis is increasingly used to describe, and provide further understanding to, zooplankton swimming behavior. This may be related to the fact that fractal analysis and the related fractal dimension D have the desirable properties to be independent of measurement scale and to be very sensitive to even subtle behavioral changes that may be undetectable to other behavioral variables. As early claimed by Coughlin et al. (1992), this creates "the need for fractal analysis" in behavioral studies, which has hence the potential to become a valuable tool in zooplankton behavioral ecology. However, this paper stresses that fractal analysis, as well as the more elaborated multifractal analysis, is also a risky business that may lead to irrelevant results, without paying extreme attention to a series of both conceptual and practical steps that are all likely to bias the results of any analysis. These biases are reviewed and exemplified on the basis of the published literature, and remedial procedures are provided not only for geometric and stochastic fractal analyses, but also for the more complicated multifractal analysis. The concept of multifractals is finally introduced as a direct, objective and quantitative tool to identify models of motion behavior, such as Brownian motion, fractional Brownian motion, ballistic motion, Lévy flight/walk and multifractal random walk. I finally briefly review the state of this emerging field in zooplankton behavioral research.
Variability of fractal dimension of solar radio flux
Bhatt, Hitaishi; Sharma, Som Kumar; Trivedi, Rupal; Vats, Hari Om
2018-04-01
In the present communication, the variation of the fractal dimension of solar radio flux is reported. Solar radio flux observations on a day to day basis at 410, 1415, 2695, 4995, and 8800 MHz are used in this study. The data were recorded at Learmonth Solar Observatory, Australia from 1988 to 2009 covering an epoch of two solar activity cycles (22 yr). The fractal dimension is calculated for the listed frequencies for this period. The fractal dimension, being a measure of randomness, represents variability of solar radio flux at shorter time-scales. The contour plot of fractal dimension on a grid of years versus radio frequency suggests high correlation with solar activity. Fractal dimension increases with increasing frequency suggests randomness increases towards the inner corona. This study also shows that the low frequency is more affected by solar activity (at low frequency fractal dimension difference between solar maximum and solar minimum is 0.42) whereas, the higher frequency is less affected by solar activity (here fractal dimension difference between solar maximum and solar minimum is 0.07). A good positive correlation is found between fractal dimension averaged over all frequencies and yearly averaged sunspot number (Pearson's coefficient is 0.87).
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 Electrochemical Microsupercapacitors
Hota, Mrinal Kanti; Jiang, Qiu; Mashraei, Yousof; Salama, Khaled N.; Alshareef, Husam N.
2017-01-01
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.
Random walk through fractal environments
Isliker, H.; Vlahos, L.
2002-01-01
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is ...
Fractality and the law of the wall
Xu, Haosen H. A.; Yang, X. I. A.
2018-05-01
Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the D =2.33 fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.
Positron annihilation near fractal surfaces
International Nuclear Information System (INIS)
Lung, C.W.; Deng, K.M.; Xiong, L.Y.
1991-07-01
A model for positron annihilation in the sub-surface region near a fractal surface is proposed. It is found that the power law relationship between the mean positron implantation depth and incident positron energy can be used to measure the fractal dimension of the fractal surface in materials. (author). 10 refs, 2 figs
DEFF Research Database (Denmark)
Malureanu, Radu; Jepsen, Peter Uhd; Xiao, S.
2010-01-01
applications. THz radiation can be employed for various purposes, among them the study of vibrations in biological molecules, motion of electrons in semiconductors and propagation of acoustic shock waves in crystals. We propose here a new THz fractal MTM design that shows very high transmission in the desired...... frequency range as well as a clear differentiation between one polarisation and another. Based on theoretical predictions we fabricated and measured a fractal based THz metamaterial that shows more than 60% field transmission at around 1THz for TE polarized light while the TM waves have almost 80% field...... transmission peak at 0.6THz. One of the main characteristics of this design is its tunability by design: by simply changing the length of the fractal elements one can choose the operating frequency window. The modelling, fabrication and characterisation results will be presented in this paper. Due to the long...
de Bartolo, S.; Fallico, C.; Straface, S.; Troisi, S.; Veltri, M.
2009-04-01
The complexity characterization of the porous media structure, in terms of the "pore" phase and the "solid" phase, can be carried out by means of the fractal geometry which is able to put in relationship the soil structural properties and the water content. It is particularly complicated to describe analytically the hydraulic conductivity for the irregularity of the porous media structure. However these can be described by many fractal models considering the soil structure as the distribution of particles dimensions, the distribution of the solid aggregates, the surface of the pore-solid interface and the fractal mass of the "pore" and "solid" phases. In this paper the fractal model of Yu and Cheng (2002) and Yu and Liu (2004), for a saturated bidispersed porous media, was considered. This model, using the Sierpinsky-type gasket scheme, doesn't contain empiric constants and furnishes a well accord with the experimental data. For this study an unconfined aquifer was reproduced by means of a tank with a volume of 10 Ã- 7 Ã- 3 m3, filled with a homogeneous sand (95% of SiO2), with a high percentage (86.4%) of grains between 0.063mm and 0.125mm and a medium-high permeability. From the hydraulic point of view, 17 boreholes, a pumping well and a drainage ring around its edge were placed. The permeability was measured utilizing three different methods, consisting respectively in pumping test, slug test and laboratory analysis of an undisturbed soil cores, each of that involving in the measurement a different support volume. The temporal series of the drawdown obtained by the pumping test were analyzed by the Neuman-type Curve method (1972), because the saturated part above the bottom of the facility represents an unconfined aquifer. The data analysis of the slug test were performed by the Bouwer & Rice (1976) method and the laboratory analysis were performed on undisturbed saturated soil samples utilizing a falling head permeameter. The obtained values either of the
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
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...... under surveillance. Based on fieldwork conducted in 2008 and 2011 in relation to my Master’s thesis and PhD respectively, I illustrate fractal concepts by describing the acts, actors and infrastructure that make up the ‘DNA surveillance’ conducted by the Danish police....
Våge, Selina; Thingstad, T. Frede
2015-01-01
Trophic interactions are highly complex and modern sequencing techniques reveal enormous biodiversity across multiple scales in marine microbial communities. Within the chemically and physically relatively homogeneous pelagic environment, this calls for an explanation beyond spatial and temporal heterogeneity. Based on observations of simple parasite-host and predator-prey interactions occurring at different trophic levels and levels of phylogenetic resolution, we present a theoretical perspective on this enormous biodiversity, discussing in particular self-similar aspects of pelagic microbial food web organization. Fractal methods have been used to describe a variety of natural phenomena, with studies of habitat structures being an application in ecology. In contrast to mathematical fractals where pattern generating rules are readily known, however, identifying mechanisms that lead to natural fractals is not straight-forward. Here we put forward the hypothesis that trophic interactions between pelagic microbes may be organized in a fractal-like manner, with the emergent network resembling the structure of the Sierpinski triangle. We discuss a mechanism that could be underlying the formation of repeated patterns at different trophic levels and discuss how this may help understand characteristic biomass size-spectra that hint at scale-invariant properties of the pelagic environment. If the idea of simple underlying principles leading to a fractal-like organization of the pelagic food web could be formalized, this would extend an ecologists mindset on how biological complexity could be accounted for. It may furthermore benefit ecosystem modeling by facilitating adequate model resolution across multiple scales. PMID:26648929
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.
Pepe, S.; Di Martino, G.; Iodice, A.; Manzo, M.; Pepe, A.; Riccio, D.; Ruello, G.; Sansosti, E.; Tizzani, P.; Zinno, I.
2012-04-01
In the last two decades several aspects relevant to volcanic activity have been analyzed in terms of fractal parameters that effectively describe natural objects geometry. More specifically, these researches have been aimed at the identification of (1) the power laws that governed the magma fragmentation processes, (2) the energy of explosive eruptions, and (3) the distribution of the associated earthquakes. In this paper, the study of volcano morphology via satellite images is dealt with; in particular, we use the complete forward model developed by some of the authors (Di Martino et al., 2012) that links the stochastic characterization of amplitude Synthetic Aperture Radar (SAR) images to the fractal dimension of the imaged surfaces, modelled via fractional Brownian motion (fBm) processes. Based on the inversion of such a model, a SAR image post-processing has been implemented (Di Martino et al., 2010), that allows retrieving the fractal dimension of the observed surfaces, dictating the distribution of the roughness over different spatial scales. The fractal dimension of volcanic structures has been related to the specific nature of materials and to the effects of active geodynamic processes. Hence, the possibility to estimate the fractal dimension from a single amplitude-only SAR image is of fundamental importance for the characterization of volcano structures and, moreover, can be very helpful for monitoring and crisis management activities in case of eruptions and other similar natural hazards. The implemented SAR image processing performs the extraction of the point-by-point fractal dimension of the scene observed by the sensor, providing - as an output product - the map of the fractal dimension of the area of interest. In this work, such an analysis is performed on Cosmo-SkyMed, ERS-1/2 and ENVISAT images relevant to active stratovolcanoes in different geodynamic contexts, such as Mt. Somma-Vesuvio, Mt. Etna, Vulcano and Stromboli in Southern Italy, Shinmoe
Passenger flow analysis of Beijing urban rail transit network using fractal approach
Li, Xiaohong; Chen, Peiwen; Chen, Feng; Wang, Zijia
2018-04-01
To quantify the spatiotemporal distribution of passenger flow and the characteristics of an urban rail transit network, we introduce four radius fractal dimensions and two branch fractal dimensions by combining a fractal approach with passenger flow assignment model. These fractal dimensions can numerically describe the complexity of passenger flow in the urban rail transit network and its change characteristics. Based on it, we establish a fractal quantification method to measure the fractal characteristics of passenger follow in the rail transit network. Finally, we validate the reasonability of our proposed method by using the actual data of Beijing subway network. It has been shown that our proposed method can effectively measure the scale-free range of the urban rail transit network, network development and the fractal characteristics of time-varying passenger flow, which further provides a reference for network planning and analysis of passenger flow.
DEFF Research Database (Denmark)
Sørensen, Erik Schwartz; Fogedby, Hans C.; Mouritsen, Ole G.
1989-01-01
temperature are studied as functions of temperature, time, and concentration. At zero temperature and high dilution, the growing solid is found to have a fractal morphology and the effective fractal exponent D varies with concentration and ratio of time scales of the two dynamical processes. The mechanism...... responsible for forming the fractal solid is shown to be a buildup of a locally high vacancy concentration in the active growth zone. The growth-probability measure of the fractals is analyzed in terms of multifractality by calculating the f(α) spectrum. It is shown that the basic ideas of relating...... probability measures of static fractal objects to the growth-probability distribution during formation of the fractal apply to the present model. The f(α) spectrum is found to be in the universality class of diffusion-limited aggregation. At finite temperatures, the fractal solid domains become metastable...
Shower fractal dimension analysis in a highly-granular calorimeter
Ruan, M
2014-01-01
We report on an investigation of the self-similar structure of particle showers recorded at a highly-granular calorimeter. On both simulated and experimental data, a strong correlation between the number of hits and the spatial scale of the readout channels is observed, from which we define the shower fractal dimension. The measured fractal dimension turns out to be strongly dependent on particle type, which enables new approaches for particle identification. A logarithmic dependence of the particle energy on the fractal dimension is also observed.
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 studies on the positron annihilation in metals
International Nuclear Information System (INIS)
Lung, C.W.
1994-06-01
Traditionally, the Euclidean lines, circles and spheres have served as the basis of the intuitive understanding of the geometry of nature. Recently, the concept of fractals has caught the imagination of scientists in many fields. This paper is to continue our previous work on position annihilation near fractal surfaces to demonstrate that the concept of fractals provides a powerful tool for understanding the structure and properties of defects and rough surfaces in relation to positron annihilation studies. Some problems on Berry geometrical phase have also been discussed. (author). 15 refs, fig., 1 tab
Short-term prediction method of wind speed series based on fractal interpolation
International Nuclear Information System (INIS)
Xiu, Chunbo; Wang, Tiantian; Tian, Meng; Li, Yanqing; Cheng, Yi
2014-01-01
Highlights: • An improved fractal interpolation prediction method is proposed. • The chaos optimization algorithm is used to obtain the iterated function system. • The fractal extrapolate interpolation prediction of wind speed series is performed. - Abstract: In order to improve the prediction performance of the wind speed series, the rescaled range analysis is used to analyze the fractal characteristics of the wind speed series. An improved fractal interpolation prediction method is proposed to predict the wind speed series whose Hurst exponents are close to 1. An optimization function which is composed of the interpolation error and the constraint items of the vertical scaling factors in the fractal interpolation iterated function system is designed. The chaos optimization algorithm is used to optimize the function to resolve the optimal vertical scaling factors. According to the self-similarity characteristic and the scale invariance, the fractal extrapolate interpolation prediction can be performed by extending the fractal characteristic from internal interval to external interval. Simulation results show that the fractal interpolation prediction method can get better prediction result than others for the wind speed series with the fractal characteristic, and the prediction performance of the proposed method can be improved further because the fractal characteristic of its iterated function system is similar to that of the predicted wind speed series
DEFF Research Database (Denmark)
Mäkikallio, T H; Høiber, S; Køber, L
1999-01-01
A number of new methods have been recently developed to quantify complex heart rate (HR) dynamics based on nonlinear and fractal analysis, but their value in risk stratification has not been evaluated. This study was designed to determine whether selected new dynamic analysis methods of HR...... variability predict mortality in patients with depressed left ventricular (LV) function after acute myocardial infarction (AMI). Traditional time- and frequency-domain HR variability indexes along with short-term fractal-like correlation properties of RR intervals (exponent alpha) and power-law scaling...
A TUTORIAL INTRODUCTION TO ADAPTIVE FRACTAL ANALYSIS
Directory of Open Access Journals (Sweden)
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.
Self-similarity and scaling theory of complex networks
Song, Chaoming
Scale-free networks have been studied extensively due to their relevance to many real systems as diverse as the World Wide Web (WWW), the Internet, biological and social networks. We present a novel approach to the analysis of scale-free networks, revealing that their structure is self-similar. This result is achieved by the application of a renormalization procedure which coarse-grains the system into boxes containing nodes within a given "size". Concurrently, we identify a power-law relation between the number of boxes needed to cover the network and the size of the box defining a self-similar exponent, which classifies fractal and non-fractal networks. By using the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks, we show that the key principle that gives rise to the fractal architecture of networks is a strong effective "repulsion" between the most connected nodes (hubs) on all length scales, rendering them very dispersed. We show that a robust network comprised of functional modules, such as a cellular network, necessitates a fractal topology, suggestive of a evolutionary drive for their existence. These fundamental properties help to understand the emergence of the scale-free property in complex networks.
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy
2017-01-01
This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
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...
Semiflexible crossing-avoiding trails on plane-filling fractals
International Nuclear Information System (INIS)
Živić, I.; Elezović-Hadžić, S.; Milošević, S.
2015-01-01
We have studied the statistics of semiflexible polymer chains modeled by crossing-avoiding trails (CAT) situated on the family of plane-filling (PF) fractals. The fractals are compact, that is, their fractal dimension d_f is equal to 2 for all members of the fractal family. By applying the exact and Monte Carlo real-space renormalization group method we have calculated the critical exponent ν, which governs the scaling behavior of the end-to-end distance of the polymer, as well as the entropic critical exponent γ, for a large set of fractals, and various values of polymer flexibility. Our results, obtained for CAT model on PF fractals, show that both critical exponents depend on the polymer flexibility, in such a way that less flexible polymer chains display enlarged values of ν, and diminished values of γ. We have compared the obtained results for CAT model with the known results for the self-avoiding walk and self-avoiding trail models and discussed the influence of excluded volume effect on the values of semiflexible polymer critical exponents, for a large set of studied compact fractals.
Random-fractal Ansatz for the configurations of two-dimensional critical systems.
Lee, Ching Hua; Ozaki, Dai; Matsueda, Hiroaki
2016-12-01
Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.
Single-Image Super-Resolution Based on Rational Fractal Interpolation.
Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming
2018-08-01
This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.
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)
Effect of noise on fractal structure
Energy Technology Data Exchange (ETDEWEB)
Serletis, Demitre [Division of Neurosurgery, Hospital for Sick Children, 1504-555 University Avenue, Toronto, Ont., M5G 1X8 (Canada)], E-mail: demitre.serletis@utoronto.ca
2008-11-15
In this paper, I investigate the effect of dynamical noise on the estimation of the Hurst exponent and the fractal dimension of time series. Recently, Serletis et al. [Serletis, Apostolos, Asghar Shahmoradi, Demitre Serletis. Effect of noise on estimation of Lyapunov exponents from a time series. Chaos, Solitons and Fractals, forthcoming] have shown that dynamical noise can make the detection of chaotic dynamics very difficult, and Serletis et al. [Serletis, Apostolos, Asghar Shahmoradi, Demitre Serletis. Effect of noise on the bifurcation behavior of dynamical systems. Chaos, Solitons and Fractals, forthcoming] have shown that dynamical noise can also shift bifurcation points and produce noise-induced transitions, making the determination of bifurcation boundaries difficult. Here I apply the detrending moving average (DMA) method, recently developed by Alessio et al. [Alessio E, Carbone A, Castelli G, Frappietro V. Second-order moving average and scaling of stochastic time series. The Eur Phys J B 2002;27:197-200] and Carbone et al. [Carbone A, Castelli G, Stanley HE. Time-dependent Hurst exponent in financial time series. Physica A 2004;344:267-71; Carbone A, Castelli G, Stanley HE. Analysis of clusters formed by the moving average of a long-range correlated time series. Phys Rev E 2004;69:026105], to estimate the Hurst exponent of a Brownian walk with a Hurst exponent of 0.5, coupled with low and high intensity noise, and show that dynamical noise has no effect on fractal structure.
Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals
Steinhurst, Benjamin; Teplyaev, Alexander
2012-01-01
We show that if a Barlow-Evans Markov process on a vermiculated space is symmetric, then one can study the spectral properties of the corresponding Laplacian using projective limits. For some examples, such as the Laakso spaces and a Spierpinski P\\^ate \\`a Choux, one can develop a complete spectral theory, including the eigenfunction expansions that are analogous to Fourier series. Also, one can construct connected fractal spaces isospectral to the fractal strings of Lapidus and van Frankenhu...
Nonlinear internal friction, chaos, fractal and musical instruments
International Nuclear Information System (INIS)
Sun, Z.Q.; Lung, C.W.
1995-08-01
Nonlinear and structure sensitive internal friction phenomena in materials are used for characterizing musical instruments. It may be one of the most important factors influencing timbre of instruments. As a nonlinear dissipated system, chaos and fractals are fundamental peculiarities of sound spectra. It is shown that the concept of multi range fractals can be used to decompose the frequency spectra of melody. New approaches are suggested to improve the fabrication, property characterization and physical understanding of instruments. (author). 18 refs, 4 figs
Shape characteristics of equilibrium and non-equilibrium fractal clusters.
Mansfield, Marc L; Douglas, Jack F
2013-07-28
It is often difficult in practice to discriminate between equilibrium and non-equilibrium nanoparticle or colloidal-particle clusters that form through aggregation in gas or solution phases. Scattering studies often permit the determination of an apparent fractal dimension, but both equilibrium and non-equilibrium clusters in three dimensions frequently have fractal dimensions near 2, so that it is often not possible to discriminate on the basis of this geometrical property. A survey of the anisotropy of a wide variety of polymeric structures (linear and ring random and self-avoiding random walks, percolation clusters, lattice animals, diffusion-limited aggregates, and Eden clusters) based on the principal components of both the radius of gyration and electric polarizability tensor indicates, perhaps counter-intuitively, that self-similar equilibrium clusters tend to be intrinsically anisotropic at all sizes, while non-equilibrium processes such as diffusion-limited aggregation or Eden growth tend to be isotropic in the large-mass limit, providing a potential means of discriminating these clusters experimentally if anisotropy could be determined along with the fractal dimension. Equilibrium polymer structures, such as flexible polymer chains, are normally self-similar due to the existence of only a single relevant length scale, and are thus anisotropic at all length scales, while non-equilibrium polymer structures that grow irreversibly in time eventually become isotropic if there is no difference in the average growth rates in different directions. There is apparently no proof of these general trends and little theoretical insight into what controls the universal anisotropy in equilibrium polymer structures of various kinds. This is an obvious topic of theoretical investigation, as well as a matter of practical interest. To address this general problem, we consider two experimentally accessible ratios, one between the hydrodynamic and gyration radii, the other
Development and Psychometric Properties of the Homophobic Bullying Scale
Prati, Gabriele
2012-01-01
The study aimed to develop the Homophobic Bullying Scale and to investigate its psychometric properties. The items of the Homophobic Bullying Scale were created to measure high school students' bullying behaviors motivated by homophobia, including verbal bullying, relational bullying, physical bullying, property bullying, sexual harassment, and…
International Nuclear Information System (INIS)
Huang, F.; Peng, R. D.; Liu, Y. H.; Chen, Z. Y.; Ye, M. F.; Wang, L.
2012-01-01
Fractal dust grains of different shapes are observed in a radially confined magnetized radio frequency plasma. The fractal dimensions of the dust structures in two-dimensional (2D) horizontal dust layers are calculated, and their evolution in the dust growth process is investigated. It is found that as the dust grains grow the fractal dimension of the dust structure decreases. In addition, the fractal dimension of the center region is larger than that of the entire region in the 2D dust layer. In the initial growth stage, the small dust particulates at a high number density in a 2D layer tend to fill space as a normal surface with fractal dimension D = 2. The mechanism of the formation of fractal dust grains is discussed.
Fractal statistics of brittle fragmentation
Directory of Open Access Journals (Sweden)
M. Davydova
2013-04-01
Full Text Available The study of fragmentation statistics of brittle materials that includes four types of experiments is presented. Data processing of the fragmentation of glass plates under quasi-static loading and the fragmentation of quartz cylindrical rods under dynamic loading shows that the size distribution of fragments (spatial quantity is fractal and can be described by a power law. The original experimental technique allows us to measure, apart from the spatial quantity, the temporal quantity - the size of time interval between the impulses of the light reflected from the newly created surfaces. The analysis of distributions of spatial (fragment size and temporal (time interval quantities provides evidence of obeying scaling laws, which suggests the possibility of self-organized criticality in fragmentation.
Scaling properties of the transverse mass spectra
International Nuclear Information System (INIS)
Schaffner-Bielich, J.
2002-01-01
Motivated from the formation of an initial state of gluon-saturated matter, we discuss scaling relations for the transverse mass spectra at BNL's relativistic heavy-ion collider (RHIC). We show on linear plots, that the transverse mass spectra for various hadrons can be described by an universal function in m t . The transverse mass spectra for different centralities can be rescaled into each other. Finally, we demonstrate that m t -scaling is also present in proton-antiproton collider data and compare it to m t -scaling at RHIC. (orig.)
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...
Categorization of new fractal carpets
International Nuclear Information System (INIS)
Rani, Mamta; Goel, Saurabh
2009-01-01
Sierpinski carpet is one of the very beautiful fractals from the historic gallery of classical fractals. Carpet designing is not only a fascinating activity in computer graphics, but it has real applications in carpet industry as well. One may find illusionary delighted carpets designed here, which are useful in real designing of carpets. In this paper, we attempt to systematize their generation and put them into categories. Each next category leads to a more generalized form of the fractal carpet.
Bilipschitz embedding of homogeneous fractals
Lü, Fan; Lou, Man-Li; Wen, Zhi-Ying; Xi, Li-Feng
2014-01-01
In this paper, we introduce a class of fractals named homogeneous sets based on some measure versions of homogeneity, uniform perfectness and doubling. This fractal class includes all Ahlfors-David regular sets, but most of them are irregular in the sense that they may have different Hausdorff dimensions and packing dimensions. Using Moran sets as main tool, we study the dimensions, bilipschitz embedding and quasi-Lipschitz equivalence of homogeneous fractals.
FONT DISCRIMINATIO USING FRACTAL DIMENSIONS
Directory of Open Access Journals (Sweden)
S. Mozaffari
2014-09-01
Full Text Available One of the related problems of OCR systems is discrimination of fonts in machine printed document images. This task improves performance of general OCR systems. Proposed methods in this paper are based on various fractal dimensions for font discrimination. First, some predefined fractal dimensions were combined with directional methods to enhance font differentiation. Then, a novel fractal dimension was introduced in this paper for the first time. Our feature extraction methods which consider font recognition as texture identification are independent of document content. Experimental results on different pages written by several font types show that fractal geometry can overcome the complexities of font recognition problem.
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.
Navigation performance in virtual environments varies with fractal dimension of landscape
Juliani, Arthur W.; Bies, Alexander J.; Boydston, Cooper R.; Taylor, Richard P.; Sereno, Margaret E.
2016-01-01
Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans’ ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D...
Aero-acoustic performance of Fractal Spoilers
Nedic, J.; Ganapathisubramani, B.; Vassilicos, C.; Boree, J.; Brizzi, L.; Spohn, A.
2010-11-01
One of the major environmental problems facing the aviation industry is that of aircraft noise. The work presented in this paper, done as part of the OPENAIR Project, looks at reducing spoiler noise through means of large-scale fractal porosity. It is hypothesised that the highly turbulent flow generated by these grids, which have multi-length-scales, would remove the re-circulation region and with it, the low frequency noise it generates. In its place, a higher frequency noise is introduced which is susceptible to atmospheric attenuation, and would be deemed less offensive to the human ear. A total of nine laboratory scaled spoilers were looked at, seven of which had a fractal design, one conventionally porous and one solid for reference. All of the spoilers were mounted on a flat plate and inclined at 30^o to the horizontal. Far-field, microphone array and PIV measurements were taken in an anechoic chamber to determine the acoustic performance and to study the flow coming through the spoilers. A significant reduction in sound pressure level is recorded and is found to be very sensitive to small changes in fractal grid parameters. Wake and drag force measurements indicated that the spoilers increase the drag whilst having minimal effect on the lift.
Long-range correlations and fractal dynamics in C. elegans: Changes with aging and stress
Alves, Luiz G. A.; Winter, Peter B.; Ferreira, Leonardo N.; Brielmann, Renée M.; Morimoto, Richard I.; Amaral, Luís A. N.
2017-08-01
Reduced motor control is one of the most frequent features associated with aging and disease. Nonlinear and fractal analyses have proved to be useful in investigating human physiological alterations with age and disease. Similar findings have not been established for any of the model organisms typically studied by biologists, though. If the physiology of a simpler model organism displays the same characteristics, this fact would open a new research window on the control mechanisms that organisms use to regulate physiological processes during aging and stress. Here, we use a recently introduced animal-tracking technology to simultaneously follow tens of Caenorhabdits elegans for several hours and use tools from fractal physiology to quantitatively evaluate the effects of aging and temperature stress on nematode motility. Similar to human physiological signals, scaling analysis reveals long-range correlations in numerous motility variables, fractal properties in behavioral shifts, and fluctuation dynamics over a wide range of timescales. These properties change as a result of a superposition of age and stress-related adaptive mechanisms that regulate motility.
Self-Similarity of Plasmon Edge Modes on Koch Fractal Antennas.
Bellido, Edson P; Bernasconi, Gabriel D; Rossouw, David; Butet, Jérémy; Martin, Olivier J F; Botton, Gianluigi A
2017-11-28
We investigate the plasmonic behavior of Koch snowflake fractal geometries and their possible application as broadband optical antennas. Lithographically defined planar silver Koch fractal antennas were fabricated and characterized with high spatial and spectral resolution using electron energy loss spectroscopy. The experimental data are supported by numerical calculations carried out with a surface integral equation method. Multiple surface plasmon edge modes supported by the fractal structures have been imaged and analyzed. Furthermore, by isolating and reproducing self-similar features in long silver strip antennas, the edge modes present in the Koch snowflake fractals are identified. We demonstrate that the fractal response can be obtained by the sum of basic self-similar segments called characteristic edge units. Interestingly, the plasmon edge modes follow a fractal-scaling rule that depends on these self-similar segments formed in the structure after a fractal iteration. As the size of a fractal structure is reduced, coupling of the modes in the characteristic edge units becomes relevant, and the symmetry of the fractal affects the formation of hybrid modes. This analysis can be utilized not only to understand the edge modes in other planar structures but also in the design and fabrication of fractal structures for nanophotonic applications.
Psychometric properties of Sternberg love scale | Askarpour ...
African Journals Online (AJOL)
Introduction: The aim of study was to evaluate the psychometric indices Sternberg love scale on married men and women in Iranian society. Methods: The study type is correlation (factor analysis). In this research factor analysis was used that is an exploratory and confirmatory technique to study the structure of a set of data, ...
Scaling properties of domain wall networks
International Nuclear Information System (INIS)
Leite, A. M. M.; Martins, C. J. A. P.
2011-01-01
We revisit the cosmological evolution of domain wall networks, taking advantage of recent improvements in computing power. We carry out high-resolution field theory simulations in two, three and four spatial dimensions to study the effects of dimensionality and damping on the evolution of the network. Our results are consistent with the expected scale-invariant evolution of the network, which suggests that previous hints of deviations from this behavior may have been due to the limited dynamical range of those simulations. We also use the results of very large (1024 3 ) simulations in three cosmological epochs to provide a calibration for the velocity-dependent one-scale model for domain walls: we numerically determine the two free model parameters to have the values c w =0.5±0.2 and k w =1.1±0.3.
The Brief Negative Symptom Scale: Psychometric Properties
Kirkpatrick, Brian; Strauss, Gregory P.; Nguyen, Linh; Fischer, Bernard A.; Daniel, David G.; Cienfuegos, Angel; Marder, Stephen R.
2010-01-01
The participants in the NIMH-MATRICS Consensus Development Conference on Negative Symptoms recommended that an instrument be developed that measured blunted affect, alogia, asociality, anhedonia, and avolition. The Brief Negative Symptom Scale (BNSS) is a 13-item instrument designed for clinical trials and other studies that measures these 5 domains. The interrater, test–retest, and internal consistency of the instrument were strong, with respective intraclass correlation coefficients of 0.93...
Electromagnetism on anisotropic fractal media
Ostoja-Starzewski, Martin
2013-04-01
Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.
Turbulent wakes of fractal objects
Staicu, A.D.; Mazzi, B.; Vassilicos, J.C.; Water, van de W.
2003-01-01
Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are
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.
Pulmonary vasculature in dogs assessed by three-dimensional fractal analysis and chemometrics
DEFF Research Database (Denmark)
Müller, Anna V; Marschner, Clara B; Kristensen, Annemarie T
2017-01-01
Fractal analysis of canine pulmonary vessels could allow quantification of their space-filling properties. Aims of this prospective, analytical, cross-sectional study were to describe methods for reconstructing three dimensional pulmonary arterial vascular trees from computed tomographic pulmonary...... angiogram, applying fractal analyses of these vascular trees in dogs with and without diseases that are known to predispose to thromboembolism, and testing the hypothesis that diseased dogs would have a different fractal dimension than healthy dogs. A total of 34 dogs were sampled. Based on computed...... for each dog using a semiautomated segmentation technique. Vascular three-dimensional reconstructions were then evaluated using fractal analysis. Fractal dimensions were analyzed, by group, using analysis of variance and principal component analysis. Fractal dimensions were significantly different among...
The brief negative symptom scale: psychometric properties.
Kirkpatrick, Brian; Strauss, Gregory P; Nguyen, Linh; Fischer, Bernard A; Daniel, David G; Cienfuegos, Angel; Marder, Stephen R
2011-03-01
The participants in the NIMH-MATRICS Consensus Development Conference on Negative Symptoms recommended that an instrument be developed that measured blunted affect, alogia, asociality, anhedonia, and avolition. The Brief Negative Symptom Scale (BNSS) is a 13-item instrument designed for clinical trials and other studies that measures these 5 domains. The interrater, test-retest, and internal consistency of the instrument were strong, with respective intraclass correlation coefficients of 0.93 for the BNSS total score and values of 0.89-0.95 for individual subscales. Comparisons with positive symptoms and other negative symptom instruments supported the discriminant and concurrent validity of the instrument.
A fractal model for heat transfer of nanofluids by convection in a pool
Energy Technology Data Exchange (ETDEWEB)
Xiao Boqi, E-mail: xiaoboqi2006@126.co [Department of Physics and Electromechanical Engineering, Sanming University, 25 Jingdong Road, Sanming 365004 (China); Yu Boming [School of Physics, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074 (China); Wang Zongchi; Chen Lingxia [Department of Physics and Electromechanical Engineering, Sanming University, 25 Jingdong Road, Sanming 365004 (China)
2009-11-02
Based on the fractal distribution of nanoparticles, a fractal model for heat transfer of nanofluids is presented in the Letter. Considering heat convection between nanoparticles and liquids due to the Brownian motion of nanoparticles in fluids, the formula of calculating heat flux of nanofluids by convection is given. The proposed model is expressed as a function of the average size of nanoparticle, concentration of nanoparticle, fractal dimension of nanoparticle, temperature and properties of fluids. It is shown that the fractal model is effectual according to a good agreement between the model predictions and experimental data.
A fractal model for heat transfer of nanofluids by convection in a pool
International Nuclear Information System (INIS)
Xiao Boqi; Yu Boming; Wang Zongchi; Chen Lingxia
2009-01-01
Based on the fractal distribution of nanoparticles, a fractal model for heat transfer of nanofluids is presented in the Letter. Considering heat convection between nanoparticles and liquids due to the Brownian motion of nanoparticles in fluids, the formula of calculating heat flux of nanofluids by convection is given. The proposed model is expressed as a function of the average size of nanoparticle, concentration of nanoparticle, fractal dimension of nanoparticle, temperature and properties of fluids. It is shown that the fractal model is effectual according to a good agreement between the model predictions and experimental data.
Generation of fractals from complex logistic map
Energy Technology Data Exchange (ETDEWEB)
Rani, Mamta [Galgotias College of Engg. and Technology, Greater Noida (India)], E-mail: mamtarsingh@rediffmail.com; Agarwal, Rashi [IEC College of Engg. and Tech., Greater Noida (India)], E-mail: agarwal_rashi@yahoo.com
2009-10-15
Remarkably benign looking logistic transformations x{sub n+1} = r x{sub n}(1 - x{sub n}) for choosing x{sub 0} between 0 and 1 and 0 < r {<=} 4 have found a celebrated place in chaos, fractals and discrete dynamics. The strong physical meaning of Mandelbrot and Julia sets is broadly accepted and nicely connected by Christian Beck [Beck C. Physical meaning for Mandelbrot and Julia sets. Physica D 1999;125(3-4):171-182. Zbl0988.37060] to the complex logistic maps, in the former case, and to the inverse complex logistic map, in the latter case. The purpose of this paper is to study the bounded behavior of the complex logistic map using superior iterates and generate fractals from the same. The analysis in this paper shows that many beautiful properties of the logistic map are extendable for a larger value of r.
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...
Generation of fractals from complex logistic map
International Nuclear Information System (INIS)
Rani, Mamta; Agarwal, Rashi
2009-01-01
Remarkably benign looking logistic transformations x n+1 = r x n (1 - x n ) for choosing x 0 between 0 and 1 and 0 < r ≤ 4 have found a celebrated place in chaos, fractals and discrete dynamics. The strong physical meaning of Mandelbrot and Julia sets is broadly accepted and nicely connected by Christian Beck [Beck C. Physical meaning for Mandelbrot and Julia sets. Physica D 1999;125(3-4):171-182. Zbl0988.37060] to the complex logistic maps, in the former case, and to the inverse complex logistic map, in the latter case. The purpose of this paper is to study the bounded behavior of the complex logistic map using superior iterates and generate fractals from the same. The analysis in this paper shows that many beautiful properties of the logistic map are extendable for a larger value of r.
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.
Psychometric properties of the Dissociative Experiences Scale.
Dubester, K A; Braun, B G
1995-04-01
The test-retest reliability of the Dissociative Experiences Scale (DES; Bernstein EM, Putnam FW [1986] Development, reliability, and validity of a dissociation scale. The Journal of Nervous and Mental Disease 174:727-735) in a clinical sample was found to be .93 for the total DES score and .95, .89, and .82 for the three subscale scores of amnesia, depersonalization-derealization, and absorption (dissociative identity disorder [DID], DSM-IV), respectively. Test-retest reliabilities within diagnostic groups of multiple personality disorder, dissociative disorder not otherwise specified, and a general other category of psychiatric diagnoses were obtained for total and subscale scores on the DES. These ranged from .78 to .96. Tests of mean scores across the two test sessions showed the total and subscale scores to be temporally stable. The DES was also found to be highly internally consistent: Cronbach's alphas of .96 and .97 were observed for the total DES scores taken at times 1 and 2, respectively. Construct validity of the DES was demonstrated by differentiation among the subscale scores in a repeated-measures analysis of variance (F[2,154] = 32.03, p < or = .001). Normality and general distribution issues were also addressed and provided a rationale for using the DES with parametric statistics. Reasons why the DES (as it was originally designed) is not appropriate as a dependent measure in outcome research are discussed, along with needed future research. Implications of the findings for the clinical usefulness of the DES as a diagnostic instrument are noted.
Psychometric properties of Frustration Discomfort Scale in a Turkish sample.
Ozer, Bilge Uzun; Demir, Ayhan; Harrington, Neil
2012-08-01
The present study assessed the psychometric properties of the Frustration Discomfort Scale for Turkish college students. The Frustration Discomfort Scale (FDS), Procrastination Assessment Scale-Student, and Rosenberg Self-Esteem Scale were administered to a sample of 171 (98 women, 73 men) Turkish college students. The results of the confirmatory factor analysis yielded fit index values demonstrating viability of the four-dimensional solution as in the original. Findings also revealed that, as predicted, the Discomfort Intolerance subscale of Turkish FDS was most strongly correlated with procrastination. Overall results provided evidence for the factor validity and reliability of the Turkish version of the scale for use in a Turkish population.
Psychometric Properties of the Fatigue Severity Scale in Polio Survivors
Burger, Helena; Franchignoni, Franco; Puzic, Natasa; Giordano, Andrea
2010-01-01
The objective of this study was to evaluate by means of classical test theory and Rasch analysis the scaling characteristics and psychometric properties of the Fatigue Severity Scale (FSS) in polio survivors. A questionnaire, consisting of five general questions (sex, age, age at time of acute polio, sequelae of polio, and new symptoms), the FSS,…
Psychometric Properties of the Revised Teachers' Attitude toward Inclusion Scale
Monsen, Jeremy J.; Ewing, Donna L.; Boyle, James
2015-01-01
This paper presents the psychometric properties of a questionnaire measure that updates and extends Larrivee and Cook's (1979) Opinions Relative to Mainstreaming Scale in terms of structure, terminology, and language. The revised scale was tested using a sample of 106 teachers based in inclusive mainstream schools. Using Principal Component…
Scaling properties of ballistic nano-transistors
Directory of Open Access Journals (Sweden)
Wulf Ulrich
2011-01-01
Full Text Available Abstract Recently, we have suggested a scale-invariant model for a nano-transistor. In agreement with experiments a close-to-linear thresh-old trace was found in the calculated I D - V D-traces separating the regimes of classically allowed transport and tunneling transport. In this conference contribution, the relevant physical quantities in our model and its range of applicability are discussed in more detail. Extending the temperature range of our studies it is shown that a close-to-linear thresh-old trace results at room temperatures as well. In qualitative agreement with the experiments the I D - V G-traces for small drain voltages show thermally activated transport below the threshold gate voltage. In contrast, at large drain voltages the gate-voltage dependence is weaker. As can be expected in our relatively simple model, the theoretical drain current is larger than the experimental one by a little less than a decade.
Systematic analysis of scaling properties in deep inelastic scattering
International Nuclear Information System (INIS)
Beuf, Guillaume; Peschanski, Robi; Royon, Christophe; Salek, David
2008-01-01
Using the 'quality factor' method, we analyze the scaling properties of deep inelastic processes at the accelerator HERA and fixed target experiments for x≤10 -2 . We look for scaling formulas of the form σ γ * p (τ), where τ(L=logQ 2 ,Y) is a scaling variable suggested by the asymptotic properties of QCD evolution equations with rapidity Y. We consider four cases: 'fixed coupling', corresponding to the original geometric scaling proposal and motivated by the asymptotic properties of the Balitsky-Kovchegov equation with fixed QCD coupling constant; two versions, 'running coupling I, II,' of the scaling suggested by the Balitsky-Kovchegov equation with running coupling; and 'diffusive scaling' suggested by the QCD evolution equation with Pomeron loops. The quality factors, quantifying the phenomenological validity of the candidate scaling variables, are fitted on the total and deeply virtual Compton scattering cross-section data from HERA and predictions are made for the elastic vector meson and for the diffractive cross sections at fixed small x P or β. The first three scaling formulas have comparably good quality factors while the fourth one is disfavored. Adjusting initial conditions gives a significant improvement of the running coupling II scaling.
The fractal nature materials microstructure influence on electrochemical energy sources
Directory of Open Access Journals (Sweden)
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
Fractals and the birth of Gothic: reflections on the biologic basis of creativity.
Goldberger, A L
1996-05-01
The birth of Gothic, one of the great triumphs of human spiritual and artistic expression, would appear to be a topic remote from the enterprise of contemporary neurobiology. The intent of this brief essay is to explore the possibility that this singular architectural movement may have important implications for understanding the nonlinear dynamics of the brain. We explore the hypothesis that the Gothic cathedral, with its porous, scale-free structures, may represent an externalization of the fractal properties of our physiology in general, and of our neural architectures and neuro-dynamics, in particular.
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.
Fractal theory of radon emanation from solids
International Nuclear Information System (INIS)
Semkow, T.M.
1991-01-01
The author developed a fractal theory of Rn emanation from solids, based on α recoil from the α decay of Ra. Range straggling of the recoiling Rn atoms in the solid state is included and the fractal geometry is used to describe the roughness of the emanating surface. A fractal dimension D of the surface and the median projected range become important parameters in calculating the radon emanating power E R from solids. A relation between E R and the specific surface area measured by the gas adsorption is derived for the first time, assuming a uniform distribution of the precursor Ra throughout the samples. It is suggested that the E R measurements can be used to determine D of the surfaces on the scale from tens to hundreds of nm. One obtains, for instance, D = 2.17 ± 0.06 for Lipari volcanic glass and D = 2.83 ± 0.03 for pitchblende. In addition, the author suggests a new process of penetrating recoil and modify the role of indirect recoil. The penetrating recoil may be important for rough surfaces, in which case Rn loses its kinetic energy by penetrating a large number of small surface irregularities. The indirect recoil may be important at the very last stage of energy-loss process, for kinetic energies below ∼ 5 keV
Fractal analysis of sulphidic mineral
Directory of Open Access Journals (Sweden)
Miklúová Viera
2002-03-01
Full Text Available In this paper, the application of fractal theory in the characterization of fragmented surfaces, as well as the mass-size distributions are discussed. The investigated mineral-chalcopyrite of Slovak provenience is characterised after particle size reduction processes-crushing and grinding. The problem how the different size reduction methods influence the surface irregularities of obtained particles is solved. Mandelbrot (1983, introducing the fractal geometry, offered a new way of characterization of surface irregularities by the fractal dimension. The determination of the surface fractal dimension DS consists in measuring the specific surface by the BET method in several fractions into which the comminuted chalcopyrite is sieved. This investigation shows that the specific surface of individual fractions were higher for the crushed sample than for the short-term (3 min ground sample. The surface fractal dimension can give an information about the adsorption sites accessible to molecules of nitrogen and according to this, the value of the fractal dimension is higher for crushed sample.The effect of comminution processes on the mass distribution of particles crushed and ground in air as well as in polar liquids is also discussed. The estimation of fractal dimensions of particles mass distribution is done on the assumption that the particle size distribution is described by the power-law (1. The value of fractal dimension for the mass distribution in the crushed sample is lower than in the sample ground in air, because it is influenced by the energy required for comminution.The sample of chalcopyrite was ground (10min in ethanol and i-butanol [which according to Ikazaki (1991] are characterized by the parameter µ /V, where µ is its dipole moment and V is the molecular volume. The values of µ /V for the used polar liquids are of the same order. That is why the expressive differences in particle size distributions as well as in the values of
Scaling laws and properties of compositional data
Buccianti, Antonella; Albanese, Stefano; Lima, AnnaMaria; Minolfi, Giulia; De Vivo, Benedetto
2016-04-01
Many random processes occur in geochemistry. Accurate predictions of the manner in which elements or chemical species interact each other are needed to construct models able to treat presence of random components. Geochemical variables actually observed are the consequence of several events, some of which may be poorly defined or imperfectly understood. Variables tend to change with time/space but, despite their complexity, may share specific common traits and it is possible to model them stochastically. Description of the frequency distribution of the geochemical abundances has been an important target of research, attracting attention for at least 100 years, starting with CLARKE (1889) and continued by GOLDSCHMIDT (1933) and WEDEPOHL (1955). However, it was AHRENS (1954a,b) who focussed on the effect of skewness distributions, for example the log-normal distribution, regarded by him as a fundamental law of geochemistry. Although modeling of frequency distributions with some probabilistic models (for example Gaussian, log-normal, Pareto) has been well discussed in several fields of application, little attention has been devoted to the features of compositional data. When compositional nature of data is taken into account, the most typical distribution models for compositions are the Dirichlet and the additive logistic normal (or normal on the simplex) (AITCHISON et al. 2003; MATEU-FIGUERAS et al. 2005; MATEU-FIGUERAS and PAWLOWSKY-GLAHN 2008; MATEU-FIGUERAS et al. 2013). As an alternative, because compositional data have to be transformed from simplex space to real space, coordinates obtained by the ilr transformation or by application of the concept of balance can be analyzed by classical methods (EGOZCUE et al. 2003). In this contribution an approach coherent with the properties of compositional information is proposed and used to investigate the shape of the frequency distribution of compositional data. The purpose is to understand data-generation processes
Moghilevsky, Débora Estela
2011-01-01
A lo largo de los últimos años del siglo veinte se ha desarrollado la teoría de la complejidad. Este modelo relaciona las ciencias duras tales como la matemática, la teoría del caos, la física cuántica y la geometría fractal con las llamadas seudo ciencias. Dentro de este contexto podemos definir la Psicología Fractal como la ciencia que estudia los aspectos psíquicos como dinámicamente fractales.
Fractal analysis as a potential tool for surface morphology of thin films
Soumya, S.; Swapna, M. S.; Raj, Vimal; Mahadevan Pillai, V. P.; Sankararaman, S.
2017-12-01
Fractal geometry developed by Mandelbrot has emerged as a potential tool for analyzing complex systems in the diversified fields of science, social science, and technology. Self-similar objects having the same details in different scales are referred to as fractals and are analyzed using the mathematics of non-Euclidean geometry. The present work is an attempt to correlate fractal dimension for surface characterization by Atomic Force Microscopy (AFM). Taking the AFM images of zinc sulphide (ZnS) thin films prepared by pulsed laser deposition (PLD) technique, under different annealing temperatures, the effect of annealing temperature and surface roughness on fractal dimension is studied. The annealing temperature and surface roughness show a strong correlation with fractal dimension. From the regression equation set, the surface roughness at a given annealing temperature can be calculated from the fractal dimension. The AFM images are processed using Photoshop and fractal dimension is calculated by box-counting method. The fractal dimension decreases from 1.986 to 1.633 while the surface roughness increases from 1.110 to 3.427, for a change of annealing temperature 30 ° C to 600 ° C. The images are also analyzed by power spectrum method to find the fractal dimension. The study reveals that the box-counting method gives better results compared to the power spectrum method.
Fractal Characteristics Analysis of Blackouts in Interconnected Power Grid
DEFF Research Database (Denmark)
Wang, Feng; Li, Lijuan; Li, Canbing
2018-01-01
The power failure models are a key to understand the mechanism of large scale blackouts. In this letter, the similarity of blackouts in interconnected power grids (IPGs) and their sub-grids is discovered by the fractal characteristics analysis to simplify the failure models of the IPG. The distri......The power failure models are a key to understand the mechanism of large scale blackouts. In this letter, the similarity of blackouts in interconnected power grids (IPGs) and their sub-grids is discovered by the fractal characteristics analysis to simplify the failure models of the IPG....... The distribution characteristics of blackouts in various sub-grids are demonstrated based on the Kolmogorov-Smirnov (KS) test. The fractal dimensions (FDs) of the IPG and its sub-grids are then obtained by using the KS test and the maximum likelihood estimation (MLE). The blackouts data in China were used...
Fractal spectra in generalized Fibonacci one-dimensional magnonic quasicrystals
Energy Technology Data Exchange (ETDEWEB)
Costa, C.H.O. [Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio grande do Norte, 59072-970 Natal-RN (Brazil); Vasconcelos, M.S., E-mail: manoelvasconcelos@yahoo.com.br [Escola de Ciencias e Tecnologia, Universidade Federal do Rio grande do Norte, 59072-970 Natal-RN (Brazil); Barbosa, P.H.R.; Barbosa Filho, F.F. [Departamento de Fisica, Universidade Federal do Piaui, 64049-550 Teresina-Pi (Brazil)
2012-07-15
In this work we carry out a theoretical analysis of the spectra of magnons in quasiperiodic magnonic crystals arranged in accordance with generalized Fibonacci sequences in the exchange regime, by using a model based on a transfer-matrix method together random-phase approximation (RPA). The generalized Fibonacci sequences are characterized by an irrational parameter {sigma}(p,q), which rules the physical properties of the system. We discussed the magnonic fractal spectra for first three generalizations, i.e., silver, bronze and nickel mean. By varying the generation number, we have found that the fragmentation process of allowed bands makes possible the emergence of new allowed magnonic bulk bands in spectra regions that were magnonic band gaps before, such as which occurs in doped semiconductor devices. This interesting property arises in one-dimensional magnonic quasicrystals fabricated in accordance to quasiperiodic sequences, without the need to introduce some deferent atomic layer or defect in the system. We also make a qualitative and quantitative investigations on these magnonic spectra by analyzing the distribution and magnitude of allowed bulk bands in function of the generalized Fibonacci number F{sub n} and as well as how they scale as a function of the number of generations of the sequences, respectively. - Highlights: Black-Right-Pointing-Pointer Quasiperiodic magnonic crystals are arranged in accordance with the generalized Fibonacci sequence. Black-Right-Pointing-Pointer Heisenberg model in exchange regime is applied. Black-Right-Pointing-Pointer We use a theoretical model based on a transfer-matrix method together random-phase approximation. Black-Right-Pointing-Pointer Fractal spectra are characterized. Black-Right-Pointing-Pointer We analyze the distribution of allowed bulk bands in function of the generalized Fibonacci number.
Fractal Globule as a model of DNA folding in eukaryotes
Imakaev, Maksim; Mirny, Leonid
2012-02-01
A recent study (Lieberman-Aiden et al., Science, 2009) observed that the structure of the genome, on the scale of a few megabases, is consistent with a fractal globule. The fractal globule is a quasi-equilibrium state of a polymer after a rapid collapse. First proposed theoretically in 1988, this structure had never been simulated. Fractal globule was seen as a state, in which each subchain is compact, and doesn't mix with other subchains due to their mutual unentanglement (topological constraints). We use GPU-assisted dynamics to create fractal globules of different sizes and observe their dynamics. Our simulations confirm that a polymer after rapid collapse has compact subchains. We measure the scaling of looping probability of a subchain with it's length, and observe the remarkably robust inverse proportionality. Dynamic simulation of the equilibration of this state show that it exhibits Rose type subdiffusion. Due to diffusion, fractal globule quickly degrades to a quasi-equilibrium state, in which subchains of a polymer are mixed, but topologically unentangled. We propose that separation of spatial and topological equilibration of a polymer chain might have implications in different fields of physics.
A fractal derivative constitutive model for three stages in granite creep
Directory of Open Access Journals (Sweden)
R. Wang
Full Text Available In this paper, by replacing the Newtonian dashpot with the fractal dashpot and considering damage effect, a new constitutive model is proposed in terms of time fractal derivative to describe the full creep regions of granite. The analytic solutions of the fractal derivative creep constitutive equation are derived via scaling transform. The conventional triaxial compression creep tests are performed on MTS 815 rock mechanics test system to verify the efficiency of the new model. The granite specimen is taken from Beishan site, the most potential area for the China’s high-level radioactive waste repository. It is shown that the proposed fractal model can characterize the creep behavior of granite especially in accelerating stage which the classical models cannot predict. The parametric sensitivity analysis is also conducted to investigate the effects of model parameters on the creep strain of granite. Keywords: Beishan granite, Fractal derivative, Damage evolution, Scaling transformation
Electrical conductivity modeling in fractal non-saturated porous media
Wei, W.; Cai, J.; Hu, X.; Han, Q.
2016-12-01
The variety of electrical conductivity in non-saturated conditions is important to study electric conduction in natural sedimentary rocks. The electrical conductivity in completely saturated porous media is a porosity-function representing the complex connected behavior of single conducting phases (pore fluid). For partially saturated conditions, the electrical conductivity becomes even more complicated since the connectedness of pore. Archie's second law is an empirical electrical conductivity-porosity and -saturation model that has been used to predict the formation factor of non-saturated porous rock. However, the physical interpretation of its parameters, e.g., the cementation exponent m and the saturation exponent n, remains questionable. On basis of our previous work, we combine the pore-solid fractal (PSF) model to build an electrical conductivity model in non-saturated porous media. Our theoretical porosity- and saturation-dependent models contain endmember properties, such as fluid electrical conductivities, pore fractal dimension and tortuosity fractal dimension (representing the complex degree of electrical flowing path). We find the presented model with non-saturation-dependent electrical conductivity datasets indicate excellent match between theory and experiments. This means the value of pore fractal dimension and tortuosity fractal dimension change from medium to medium and depends not only on geometrical properties of pore structure but also characteristics of electrical current flowing in the non-saturated porous media.
Map of fluid flow in fractal porous medium into fractal continuum flow.
Balankin, Alexander S; Elizarraraz, Benjamin Espinoza
2012-05-01
This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.
Fractals as macroscopic manifestation of squeezed coherent states and brain dynamics
International Nuclear Information System (INIS)
Vitiello, Giuseppe
2012-01-01
Recent results on the relation between self-similarity and squeezed coherent states are presented. I consider fractals which are generated iteratively according to a prescribed recipe, the so-called deterministic fractals. Fractal properties are incorporated in the framework of the theory of the entire analytical functions and deformed coherent states. Conversely, fractal properties of squeezed coherent states are recognized. This sheds some light on the understanding of the dynamical origin of fractals and their global nature emerging from local deformation processes. The self-similarity in brain background activity suggested by laboratory observations of power-law distributions of power spectral densities of electrocorticograms is also discussed and accounted in the frame of the dissipative many-body model of brain.
Ulam method and fractal Weyl law for Perron-Frobenius operators
Ermann, L.; Shepelyansky, D. L.
2010-06-01
We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we numerically find the Weyl exponent ν = d/2 where d is the fractal dimension of strange attractor. The Weyl exponent can be also expressed via the relation ν = d0/2 where d0 is the fractal dimension of the invariant sets. We also discuss the properties of eigenvalues and eigenvectors of such operators characterized by the fractal Weyl law.
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...
Fractal analysis in oral leukoplakia
Directory of Open Access Journals (Sweden)
Prashant Bhai Pandey
2015-01-01
Full Text Available Introduction: Fractal analysis (FA quantifies complex geometric structures by generating a fractal dimension (FD, which can measure the complexity of mucosa. FA is a quantitative tool used to measure the complexity of self-similar or semi-self-similar structures. Aim and Objective: The study was done to perform the FA of oral mucosa with keratotic changes, as it is also made up of self-similar tissues, and thus, its FD can be calculated. Results: In oral leukoplakia, keratinization increases the complexity of mucosa, which denotes fractal geometry. We evaluated and compared pretreated and post-treated oral leukoplakia in 50 patients with clinically proven oral leukoplakia and analyzed the normal oral mucosa and lesional or keratinized mucosa in oral leukoplakia patients through FA using box counting method. Conclusion: FA using the fractal geometry is an efficient, noninvasive prediction tool for early detection of oral leukoplakia and other premalignant conditions in patients.
Beyond Fractals and 1/f Noise: Multifractal Analysis of Complex Physiological Time Series
Ivanov, Plamen Ch.; Amaral, Luis A. N.; Ashkenazy, Yosef; Stanley, H. Eugene; Goldberger, Ary L.; Hausdorff, Jeffrey M.; Yoneyama, Mitsuru; Arai, Kuniharu
2001-03-01
We investigate time series with 1/f-like spectra generated by two physiologic control systems --- the human heartbeat and human gait. We show that physiological fluctuations exhibit unexpected ``hidden'' structures often described by scaling laws. In particular, our studies indicate that when analyzed on different time scales the heartbeat fluctuations exhibit cascades of branching patterns with self-similar (fractal) properties, characterized by long-range power-law anticorrelations. We find that these scaling features change during sleep and wake phases, and with pathological perturbations. Further, by means of a new wavelet-based technique, we find evidence of multifractality in the healthy human heartbeat even under resting conditions, and show that the multifractal character and nonlinear properties of the healthy heart are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure. In contrast to the heartbeat, we find that the interstride interval time series of healthy human gait, a voluntary process under neural regulation, is described by a single fractal dimension (such as classical 1/f noise) indicating monofractal behavior. Thus our approach can help distinguish physiological and physical signals with comparable frequency spectra and two-point correlations, and guide modeling of their control mechanisms.
Fractals in Power Reactor Noise
International Nuclear Information System (INIS)
Aguilar Martinez, O.
1994-01-01
In this work the non- lineal dynamic problem of power reactor is analyzed using classic concepts of fractal analysis as: attractors, Hausdorff-Besikovics dimension, phase space, etc. A new non-linear problem is also analyzed: the discrimination of chaotic signals from random neutron noise signals and processing for diagnosis purposes. The advantages of a fractal analysis approach in the power reactor noise are commented in details
Persistent fluctuations in stride intervals under fractal auditory stimulation.
Directory of Open Access Journals (Sweden)
Vivien Marmelat
Full Text Available 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.
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.
Random walk through fractal environments
International Nuclear Information System (INIS)
Isliker, H.; Vlahos, L.
2003-01-01
We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D F of the fractal is less than 2, there is though, always a finite rate of unaffected escape. Random walks through fractal sets with D F ≤2 can thus be considered as defective Levy walks. The distribution of jump increments for D F >2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk increments. It is shown that the particles undergo anomalous, enhanced diffusion for D F F >2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality models give rise to enhanced diffusion. The analytical results are illustrated by Monte Carlo simulations
Psychometric properties of Conversion Disorder Scale- Revised (CDS) for children.
Ijaz, Tazvin; Nasir, Attikah; Sarfraz, Naema; Ijaz, Shirmeen
2017-05-01
To revise conversion disorder scale and to establish the psychometric properties of the revised scale. This case-control study was conducted from February to June, 2014, at the Government College University, Lahore, Pakistan, and comprised schoolchildren and children with conversion disorder. In order to generate items for revised version of conversion disorder scale, seven practising mental health professionals were consulted. A list of 42 items was finalised for expert ratings. After empirical validation, a scale of 40 items was administered on the participants and factor analysis was conducted. Of the240 participants, 120(50%) were schoolchildren (controls group) and 120(50%)were children with conversion disorder (clinical group).The results of factor analysis revealed five factors (swallowing and speech symptoms, motor symptoms, sensory symptoms, weakness and fatigue, and mixed symptoms) and retention of all 40 items of revised version of conversion disorder scale. Concurrent validity of the revised scale was found to be 0.81 which was significantly high. Similarly, discriminant validity of the scale was also high as both clinical and control groups had significant difference (pconversion disorder scale was 76% sensitive to predicting conversion disorder while specificity showed that the scale was 73% accurate in specifying participants of the control group. The revised version of conversion disorder scale was a reliable and valid tool to be used for screening of children with conversion disorder.
Analysis of the Psychometric Properties of a Parental Alienation Scale
Directory of Open Access Journals (Sweden)
Paula Inez Cunha Gomide
Full Text Available Abstract The development of forensic evaluation scales is fundamental. This study's purpose was to explore the psychometric properties of a parental alienation scale. Forensic technicians completed 193 scales concerning parents involved in a lawsuit: 48 families with at least one parent indicated as the alienator (group A and 48 families with no parental alienation claim (group B. The scale consisted of five categories and 69 items: denying access to the child; derogatory comparisons; emotional manipulation; behavior of parent and child during assessment. The results show Cronbach's alpha = .965 and split-half = .745; KMO = .884 and Bartlett's sphericity test ( p < .001. Concurrent criterion validity applied to data showed that the scale is able to distinguish between the alienator and target parent. The results showed significant and consistent standards in the instrument's psychometric characteristics.
Towards Video Quality Metrics Based on Colour Fractal Geometry
Directory of Open Access Journals (Sweden)
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.
Fractal markets: Liquidity and investors on different time horizons
Li, Da-Ye; Nishimura, Yusaku; Men, Ming
2014-08-01
In this paper, we propose a new agent-based model to study the source of liquidity and the “emergent” phenomenon in financial market with fractal structure. The model rests on fractal market hypothesis and agents with different time horizons of investments. What is interesting is that though the agent-based model reveals that the interaction between these heterogeneous agents affects the stability and liquidity of the financial market the real world market lacks detailed data to bring it to light since it is difficult to identify and distinguish the investors with different time horizons in the empirical approach. results show that in a relatively short period of time fractal market provides liquidity from investors with different horizons and the market gains stability when the market structure changes from uniformity to diversification. In the real world the fractal structure with the finite of horizons can only stabilize the market within limits. With the finite maximum horizons, the greater diversity of the investors and the fractal structure will not necessarily bring more stability to the market which might come with greater fluctuation in large time scale.
Global scaling properties of the spectrum for the Fibonacci chains
Zheng, W. M.
1987-02-01
By means of the approximate renormalization approach of Niu and Nori [Phys. Rev. Lett. 57, 2057 (1986)] the widths of subband segments in the spectrum and the occupation probabilities on subbands are obtained to the lowest order for the two-value Fibonacci chains. The global scaling properties of the spectrum are then analytically calculated.
Psychometric properties of the Multidimensional Anxiety Scale for ...
African Journals Online (AJOL)
Aim: To determine the psychometric properties of the Multidimensional Anxiety Scale for Children (MASC) in Nairobi public secondary school children, Kenya. Method: Concurrent self-administration of the MASC and Children's Depression Inventory (CDI) to students in Nairobi public secondary schools. Results: The MASC ...
Investigating the Scaling Properties of Extreme Rainfall Depth ...
African Journals Online (AJOL)
Investigating the Scaling Properties of Extreme Rainfall Depth Series in Oromia Regional State, Ethiopia. ... Science, Technology and Arts Research Journal ... for storm duration ranging from 0.5 to 24 hr observed at network of rain gauges sited in Oromia regional state were analyzed using an approach based on moments.
A Esmailpour; N Mostoufi; R Zarghami
2016-01-01
A study has been conducted to determine the effects of operating conditions such as vibration frequency, vibration amplitude on the fractal structure of silica (SiO2) nanoparticle agglomerate in a vibro-fluidized bed. An improved model was proposed by assimilation of fractal theory, Richardson-Zaki equation and mass balance. This model has been developed to predict the properties of nanoparticle agglomerate, such as fractal dimension and its size. It has been found out the vibration intensity...
Optimized Ultrawideband and Uniplanar Minkowski Fractal Branch Line Coupler
Directory of Open Access Journals (Sweden)
Mohammad Jahanbakht
2012-01-01
Full Text Available The non-Euclidean Minkowski fractal geometry is used in design, optimization, and fabrication of an ultrawideband (UWB branch line coupler. Self-similarities of the fractal geometries make them act like an infinite length in a finite area. This property creates a smaller design with broader bandwidth. The designed 3 dB microstrip coupler has a single layer and uniplanar platform with quite easy fabrication process. This optimized 180° coupler also shows a perfect isolation and insertion loss over the UWB frequency range of 3.1–10.6 GHz.
A fractal model for intergranular fractures in nanocrystals
International Nuclear Information System (INIS)
Lung, C.W.; Xiong, L.Y.; Zhou, X.Z.
1993-09-01
A fractal model for intergranular fractures in nanocrystals is proposed to explain the dependence of fracture toughness with grain size in this range of scale. Based on positron annihilation and internal friction experimental results, we point out that the assumption of a constant grain boundary thickness in previous models is too simplified to be true. (author). 7 refs, 6 figs
Fractal analysis of electrolytically-deposited palladium hydride dendrites
International Nuclear Information System (INIS)
Bursill, L.A.; Julin, Peng; Xudong, Fan.
1990-01-01
The fractal scaling characteristics of the surface profile of electrolytically-deposited palladium hydride dendritic structures have been obtained using conventional and high resolution transmission electron microscopy. The results are in remarkable agreement with the modified diffusion-limited aggregation model. 19 refs., 3 tabs., 13 figs
A new modified fast fractal image compression algorithm
DEFF Research Database (Denmark)
Salarian, Mehdi; Nadernejad, Ehsan; MiarNaimi, Hossein
2013-01-01
In this paper, a new fractal image compression algorithm is proposed, in which the time of the encoding process is considerably reduced. The algorithm exploits a domain pool reduction approach, along with the use of innovative predefined values for contrast scaling factor, S, instead of searching...
arXiv Generalized Fragmentation Functions for Fractal Jet Observables
Elder, Benjamin T.; Thaler, Jesse; Waalewijn, Wouter J.; Zhou, Kevin
2017-06-15
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 cross sections involving identified final-state hadrons. Fragmentation functions are fundamentally nonperturbative, but have a calculable renormalization group evolution. Unlike ordinary fragmentation functions, generalized fragmentation functions exhibit nonlinear evolution, since fractal observables involve correlated subsets of hadrons within a jet. Some special cases of generalized fragmentation functions are reviewed, including jet charge and track functions. We then consider fractal jet observables that are based on hierarchical clustering trees, where the nonlinear evolution equations also exhibit tree-like structure at leading order. We develop a numeric code for performing this evolution and study its phen...
Cathodic Arcs From Fractal Spots to Energetic Condensation
Anders, Andre
2009-01-01
Emphasizes the fractal character of cathode spots, and describes strongly fluctuating plasma properties such as the presence of multiply charged ions that move with supersonic velocity. This book also deals with issues, such as arc source construction, and macroparticle removal. It is intended for scientists, practitioners, and students alike
Estimation of soil water retention curve using fractal dimension ...
African Journals Online (AJOL)
The soil water retention curve (SWRC) is a fundamental hydraulic property majorly used to study flow transport in soils and calculate plant-available water. Since, direct measurement of SWRC is time-consuming and expensive, different models have been developed to estimate SWRC. In this study, a fractal-based model ...
From quantum fields to fractal structures: intermittency in particle physics
International Nuclear Information System (INIS)
Peschanski, R.
1991-01-01
Some features and theoretical interpretations of the intermittency phenomenon observed in high-energy multi-particle production are recalled. One develops on the various connections found with fractal structuration of fluctuations in turbulence, spin-glass physics and aggregation phenomena described by the non-linear Smoluchowski equation. This may lead to a new approach to quantum field properties
Psychometric properties of the Thai Spiritual Well-Being Scale.
Chaiviboontham, Suchira; Phinitkhajorndech, Noppawan; Hanucharurnkul, Somchit; Noipiang, Thaniya
2016-04-01
The purpose of this study was to investigate the psychometric properties of the modified Thai Spiritual Well-Being Scale in patients with advanced cancer. This cross-sectional study was employed to investigate psychometric properties. Some 196 participants from three tertiary hospitals in Bangkok and suburban Thailand were asked to complete a Personal Information Questionnaire (PIQ), The Memorial Symptom Assessment Scale (MSAS), and the Spiritual Well-Being Scale (SWBS). Validity was determined by known-group, concurrent, and constructs validity. Reliability was estimated using internal consistency by Cronbach's α coefficients. Three factors were extracted: so-called existential well-being, religious well-being, and peacefulness accounted for 71.44% of total variance. The Cronbach's α coefficients for total SWB, EWB, RWB, and peacefulness were 0.96, 0.94, and 0.93, respectively. These findings indicate that the Thai SWBS is a valid and reliable instrument, and it presented one more factor than the original version.
Navigation performance in virtual environments varies with fractal dimension of landscape.
Juliani, Arthur W; Bies, Alexander J; Boydston, Cooper R; Taylor, Richard P; Sereno, Margaret E
2016-09-01
Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans' ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D. In Experiment 2, participants completed a map-reading and location-judgment task in separate sets of fractal landscapes. In both experiments, task performance was highest at the low-to-mid range of D, which was previously reported as most preferred and discriminable in studies of fractal aesthetics and discrimination, respectively, supporting a theory of visual fluency. The applicability of these findings to architecture, urban planning, and the general design of constructed spaces is discussed.
An Examination of Psychometric Properties of Positive Functional Attitudes Scale
Directory of Open Access Journals (Sweden)
Saide Umut ZEYBEK
2017-08-01
Full Text Available The aim of this study is to investigate the applicability of Coping Attitudes Scale: Measure of Positive Attitudes in Depression (CAS among Turkish young adult community sample and determine the psychometric properties (validity and reliability of this scale. This study was conducted with 419 students attending different departments in Mugla Sitki Kocman University, Faculty of Education in the spring semester of academic year of 2015-2016. Positive Functional Attitudes Scale, Beck Depression Scale, Beck Hopelessness Scale, Automatic Thoughts Scale, Positivity Scale and Developed Automatic Thoughts Scale.were used as data collection tools. Confirmatory factor analysis (CFA were used for investigation of the psychometric properties of the PFAS. Also, criterion-related validity, test-retest validity, and internal consistency were used calculated. The CFA results showed that standardized item estimates of the CAS ranged between 0.45 and 0.47. Also the CFA results showed that the original factor structure of the PFAS confirmed on the Turkish sample. internal consistency was calculated using the total community samples PFAS score. Cronbachs alpha coefficient ort he total scale (.93 was high. Test-retest results of the subscales were 0.76. The findings showed that factor structures of the PFAS life perspective, personal accomplishment, positive future, self-worth, coping with problems had psychometric quality in Turkish version. As a result of the study, the Turkish version of PFAS has good validity and reliability for young adult community sample. [JCBPR 2017; 6(2.000: 59-66
Asymmetric multi-fractality in the U.S. stock indices using index-based model of A-MFDFA
International Nuclear Information System (INIS)
Lee, Minhyuk; Song, Jae Wook; Park, Ji Hwan; Chang, Woojin
2017-01-01
Highlights: • ‘Index-based A-MFDFA’ model is proposed to assess the asymmetric multi-fractality. • The asymmetric multi-fractality in the U.S. stock indices are investigated using ‘Index-based’ and ‘Return-based’ A-MFDFA. • The asymmetric feature is more significantly identified by ‘Index-based’ model than ‘return-based’ model. • Source of multi-fractality and time-varying features are analyzed. - Abstract: We detect the asymmetric multi-fractality in the U.S. stock indices based on the asymmetric multi-fractal detrended fluctuation analysis (A-MFDFA). Instead using the conventional return-based approach, we propose the index-based model of A-MFDFA where the trend based on the evolution of stock index rather than stock price return plays a role for evaluating the asymmetric scaling behaviors. The results show that the multi-fractal behaviors of the U.S. stock indices are asymmetric and the index-based model detects the asymmetric multi-fractality better than return-based model. We also discuss the source of multi-fractality and its asymmetry and observe that the multi-fractal asymmetry in the U.S. stock indices has a time-varying feature where the degree of multi-fractality and asymmetry increase during the financial crisis.
Arctic sea ice melt pond fractal dimension - explained
Popovic, Predrag
As Arctic sea ice starts to melt in the summer, pools of melt water quickly form on its surface, significantly changing its albedo, and impacting its subsequent evolution. These melt ponds often form complex geometric shapes. One characteristic of their shape, the fractal dimension of the pond boundaries, D, when plotted as a function of pond size, has been shown to transition between the two fundamental limits of D = 1 and D = 2 at some critical pond size. Here, we provide an explanation for this behavior. First, using aerial photographs, we show how this fractal transition curve changes with time, and show that there is a qualitative difference in the pond shape as ice transitions from impermeable to permeable. Namely, while ice is impermeable, maximum fractal dimension is less than 2, whereas after it becomes permeable, maximum fractal dimension becomes very close to 2. We then show how the fractal dimension of a collection of overlapping circles placed randomly on a plane also transitions from D = 1 to D = 2 at a size equal to the average size of a single circle. We, therefore, conclude that this transition is a simple geometric consequence of regular shapes connecting. The one physical parameter that can be extracted from the fractal transition curve is the length scale at which transition occurs. We provide a possible explanation for this length scale by noting that the flexural wavelength of the ice poses a fundamental limit on the size of melt ponds on permeable ice. If this is true, melt ponds could be used as a proxy for ice thickness.
Design of LTCC Based Fractal Antenna
AdbulGhaffar, Farhan
2010-01-01
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
Fractal Structures For Mems Variable Capacitors
Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.
2014-01-01
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
A fractal-based image encryption system
Abd-El-Hafiz, S. K.; Radwan, Ahmed Gomaa; Abdel Haleem, Sherif H.; Barakat, Mohamed L.
2014-01-01
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
Research on the fractal structure in the Chinese stock market
Zhuang, Xin-tian; Huang, Xiao-yuan; Sha, Yan-li
2004-02-01
Applying fractal theory, this paper probes and discusses self-similarity and scale invariance of the Chinese stock market. It analyses three kinds of scale indexes, i.e., autocorrelation index, Hurst index and the scale index on the basis of detrended fluctuation analysis (DFA) algorithm and promotes DFA into a recursive algorithm. Using the three kinds of scale indexes, we conduct empirical research on the Chinese Shanghai and Shenzhen stock markets. The results indicate that the rate of returns of the two stock markets does not obey the normal distribution. A correlation exists between the stock price indexes over time scales. The stock price indexes exhibit fractal time series. It indicates that the policy guide hidden at the back influences the characteristic of the Chinese stock market.
Effects of fractal pore on coal devolatilization
Energy Technology Data Exchange (ETDEWEB)
Chen, Yongli; He, Rong [Tsinghua Univ., Beijing (China). Dept. of Thermal Engineering; Wang, Xiaoliang; Cao, Liyong [Dongfang Electric Corporation, Chengdu (China). Centre New Energy Inst.
2013-07-01
Coal devolatilization is numerically investigated by drop tube furnace and a coal pyrolysis model (Fragmentation and Diffusion Model). The fractal characteristics of coal and char pores are investigated. Gas diffusion and secondary reactions in fractal pores are considered in the numerical simulations of coal devolatilization, and the results show that the fractal dimension is increased firstly and then decreased later with increased coal conversions during devolatilization. The mechanisms of effects of fractal pores on coal devolatilization are analyzed.
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....
Fractal Structures For Fixed Mems Capacitors
Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.
2014-01-01
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.
The number of elementary particles in a fractal M-theory of 11.2360667977 dimensions
International Nuclear Information System (INIS)
He, J.-H.
2007-01-01
It is generally accepted that there are 60 experimentally found particles. The standard model strongly predicts two more hypothetical particles, the Higgs and the graviton. This paper reveals other possible scenario for predicting 69 particles at different energy scales in 11+φ 3 fractal dimensions of a fractal M theory, where φ=(5-1)/2. A modified Newton's law is suggested to experimentally verify our predictions at extremely small quantum scales. The modified Newton's law is in harmony with Heisenberg's uncertainty principle
Song, Fei; Zhang, Li-Ming; Shi, Jun-Feng; Li, Nan-Nan
2010-12-01
The supramolecular hydrogels derived from low-molecular-mass gelators represent a unique class of soft matters and have important potential applications in biomedical fields, separation technology and cosmetic science. However, they suffer usually from weak mechanical and viscoelastic properties. In this work, we carry out the in situ hybridization of clay nanoparticles (Laponite RD) into the supramolecular hydrogel formed from a low-molecular-mass hydrogelator, 2,6-di[N-(carboxyethyl carbonyl)amino]pyridine (DAP), and investigate the viscoelastic and structural characteristics of resultant hybrid hydrogel. It was found that a small concentration of Laponite RD could lead to a significant increase in the storage modulus, loss modulus or complex viscosity. Compared with neat DAP hydrogel, the hybrid hydrogel has a greater hydrogel strength and a lower relaxation exponent. In particular, the enhancement of the clay nanoparticles to the viscoelastic properties of the DAP hydrogel is more effective in the case of higher DAP concentration. By relating its macroscopic elastic properties to a scaling fractal model, such a hybrid hydrogel was confirmed to be in the strong-link regime and to have a more complex network structure with a higher fractal dimension when compared with neat DAP hydrogel. Copyright © 2010 Elsevier B.V. All rights reserved.
Properties Important To Mixing For WTP Large Scale Integrated Testing
International Nuclear Information System (INIS)
Koopman, D.; Martino, C.; Poirier, M.
2012-01-01
Large Scale Integrated Testing (LSIT) is being planned by Bechtel National, Inc. to address uncertainties in the full scale mixing performance of the Hanford Waste Treatment and Immobilization Plant (WTP). Testing will use simulated waste rather than actual Hanford waste. Therefore, the use of suitable simulants is critical to achieving the goals of the test program. External review boards have raised questions regarding the overall representativeness of simulants used in previous mixing tests. Accordingly, WTP requested the Savannah River National Laboratory (SRNL) to assist with development of simulants for use in LSIT. Among the first tasks assigned to SRNL was to develop a list of waste properties that matter to pulse-jet mixer (PJM) mixing of WTP tanks. This report satisfies Commitment 5.2.3.1 of the Department of Energy Implementation Plan for Defense Nuclear Facilities Safety Board Recommendation 2010-2: physical properties important to mixing and scaling. In support of waste simulant development, the following two objectives are the focus of this report: (1) Assess physical and chemical properties important to the testing and development of mixing scaling relationships; (2) Identify the governing properties and associated ranges for LSIT to achieve the Newtonian and non-Newtonian test objectives. This includes the properties to support testing of sampling and heel management systems. The test objectives for LSIT relate to transfer and pump out of solid particles, prototypic integrated operations, sparger operation, PJM controllability, vessel level/density measurement accuracy, sampling, heel management, PJM restart, design and safety margin, Computational Fluid Dynamics (CFD) Verification and Validation (V and V) and comparison, performance testing and scaling, and high temperature operation. The slurry properties that are most important to Performance Testing and Scaling depend on the test objective and rheological classification of the slurry (i
PROPERTIES IMPORTANT TO MIXING FOR WTP LARGE SCALE INTEGRATED TESTING
Energy Technology Data Exchange (ETDEWEB)
Koopman, D.; Martino, C.; Poirier, M.
2012-04-26
Large Scale Integrated Testing (LSIT) is being planned by Bechtel National, Inc. to address uncertainties in the full scale mixing performance of the Hanford Waste Treatment and Immobilization Plant (WTP). Testing will use simulated waste rather than actual Hanford waste. Therefore, the use of suitable simulants is critical to achieving the goals of the test program. External review boards have raised questions regarding the overall representativeness of simulants used in previous mixing tests. Accordingly, WTP requested the Savannah River National Laboratory (SRNL) to assist with development of simulants for use in LSIT. Among the first tasks assigned to SRNL was to develop a list of waste properties that matter to pulse-jet mixer (PJM) mixing of WTP tanks. This report satisfies Commitment 5.2.3.1 of the Department of Energy Implementation Plan for Defense Nuclear Facilities Safety Board Recommendation 2010-2: physical properties important to mixing and scaling. In support of waste simulant development, the following two objectives are the focus of this report: (1) Assess physical and chemical properties important to the testing and development of mixing scaling relationships; (2) Identify the governing properties and associated ranges for LSIT to achieve the Newtonian and non-Newtonian test objectives. This includes the properties to support testing of sampling and heel management systems. The test objectives for LSIT relate to transfer and pump out of solid particles, prototypic integrated operations, sparger operation, PJM controllability, vessel level/density measurement accuracy, sampling, heel management, PJM restart, design and safety margin, Computational Fluid Dynamics (CFD) Verification and Validation (V and V) and comparison, performance testing and scaling, and high temperature operation. The slurry properties that are most important to Performance Testing and Scaling depend on the test objective and rheological classification of the slurry (i
Breakdown coefficients and scaling properties of rain fields
Directory of Open Access Journals (Sweden)
D. Harris
1998-01-01
Full Text Available The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width, σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.
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.
An enhanced fractal image denoising algorithm
International Nuclear Information System (INIS)
Lu Jian; Ye Zhongxing; Zou Yuru; Ye Ruisong
2008-01-01
In recent years, there has been a significant development in image denoising using fractal-based method. This paper presents an enhanced fractal predictive denoising algorithm for denoising the images corrupted by an additive white Gaussian noise (AWGN) by using quadratic gray-level function. Meanwhile, a quantization method for the fractal gray-level coefficients of the quadratic function is proposed to strictly guarantee the contractivity requirement of the enhanced fractal coding, and in terms of the quality of the fractal representation measured by PSNR, the enhanced fractal image coding using quadratic gray-level function generally performs better than the standard fractal coding using linear gray-level function. Based on this enhanced fractal coding, the enhanced fractal image denoising is implemented by estimating the fractal gray-level coefficients of the quadratic function of the noiseless image from its noisy observation. Experimental results show that, compared with other standard fractal-based image denoising schemes using linear gray-level function, the enhanced fractal denoising algorithm can improve the quality of the restored image efficiently
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.
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 ...
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...... 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 for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0.......0002) in monozygotic twins than in dizygotic twins (0.108, P = 0.46), corresponding to a heritability h2 for the fractal dimension of 0.79. In quantitative genetic models, dominant genetic effects explained 54% of the variation and 46% was individually environmentally determined. Conclusions: In young adult twins...
Towards thermomechanics of fractal media
Ostoja-Starzewski, Martin
2007-11-01
Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.
A fractal nature for polymerized laminin.
Directory of Open Access Journals (Sweden)
Camila Hochman-Mendez
Full Text Available Polylaminin (polyLM is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM, scanning electron microscopy (SEM and atomic force microscopy (AFM to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.
A fractal nature for polymerized laminin.
Hochman-Mendez, Camila; Cantini, Marco; Moratal, David; Salmeron-Sanchez, Manuel; Coelho-Sampaio, Tatiana
2014-01-01
Polylaminin (polyLM) is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM), scanning electron microscopy (SEM) and atomic force microscopy (AFM) to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM) was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.
Fractal universe and quantum gravity.
Calcagni, Gianluca
2010-06-25
We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.
Fractals control in particle's velocity
International Nuclear Information System (INIS)
Zhang Yongping; Liu Shutang; Shen Shulan
2009-01-01
Julia set, a fractal set of the literature of nonlinear physics, has significance for the engineering applications. For example, the fractal structure characteristics of the generalized M-J set could visually reflect the change rule of particle's velocity. According to the real world requirement, the system need show various particle's velocity in some cases. Thus, the control of the nonlinear behavior, i.e., Julia set, has attracted broad attention. In this work, an auxiliary feedback control is introduced to effectively control the Julia set that visually reflects the change rule of particle's velocity. It satisfies the performance requirement of the real world problems.
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
, 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...... 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 for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0...
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.
Psychometric properties of a scale to measure alexithymia.
Blanchard, E B; Arena, J G; Pallmeyer, T P
1981-01-01
Four studies were conducted on a sample of 230 undergraduates to determine the psychometric properties of a measure of alexithymia, the Schalling-Sifneos Scale. In the first study it was found that scores on the scale are approximately normally distributed for each sex with 8.2% of males and 1.8% of females in the alexithymia range. In the second study a factor analysis of the scale revealed three distinct factors: (1) 'difficulty in expression of feelings'; (2) 'the importance of feelings especially about people'; (3) 'day-dreaming or introspection'. In the second factor analytic study, scores from several standard psychological tests on the same subjects were introduced with the scale items. Two factors in this analysis were comprised almost entirely of the other test scores: a 'general psychological distress factor' and a 'concerns about physical symptoms factor'. The other two factors were similar to factors 1 and 2 above in terms of items. The Rathus Assertiveness Scale loaded positively on the equivalent of factor 1. In the lst study, it was shown that Schalling-Sifneos Scale score is relatively orthogonal to other psychological tests with the exception of a Psychosomatic Symptom Checklist and thus is measuring something other than depression, anxiety, etc.
Development and application of 3-D fractal reservoir model based on collage theorem
Energy Technology Data Exchange (ETDEWEB)
Kim, I.K.; Kim, K.S.; Sung, W.M. [Hanyang Univ., Seoul (Korea, Republic of)
1995-04-30
Reservoir characterization is the essential process to accurately evaluate the reservoir and has been conducted by geostatistical method, SRA algorithm, and etc. The characterized distribution of heterogeneous property by these methods shows randomly distributed phenomena, and does not present anomalous shape of property variation at discontinued space as compared with the observed shape in nature. This study proposed a new algorithm of fractal concept based on collage theorem, which can virtually present not only geometric shape of irregular and anomalous pore structures or coastlines, but also property variation for discontinuously observed data. With a basis of fractal concept, three dimensional fractal reservoir model was developed to more accurately characterize the heterogeneous reservoir. We performed analysis of pre-predictable hypothetically observed permeability data by using the fractal reservoir model. From the results, we can recognize that permeability distributions in the areal view or the cross-sectional view were consistent with the observed data. (author). 8 refs., 1 tab., 6 figs.
Properties of Brownian Image Models in Scale-Space
DEFF Research Database (Denmark)
Pedersen, Kim Steenstrup
2003-01-01
Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empirically that the second order statistics of natural images mapped into jet space may, within some scale interval, be modeled by the Brownian image model. This is consistent with the 1/f 2 power spectrum...... law that apparently governs natural images. Furthermore, the distribution of Brownian images mapped into jet space is Gaussian and an analytical expression can be derived for the covariance matrix of Brownian images in jet space. This matrix is also a good approximation of the covariance matrix......In this paper it is argued that the Brownian image model is the least committed, scale invariant, statistical image model which describes the second order statistics of natural images. Various properties of three different types of Gaussian image models (white noise, Brownian and fractional...
Scaling properties in time-varying networks with memory
Kim, Hyewon; Ha, Meesoon; Jeong, Hawoong
2015-12-01
The formation of network structure is mainly influenced by an individual node's activity and its memory, where activity can usually be interpreted as the individual inherent property and memory can be represented by the interaction strength between nodes. In our study, we define the activity through the appearance pattern in the time-aggregated network representation, and quantify the memory through the contact pattern of empirical temporal networks. To address the role of activity and memory in epidemics on time-varying networks, we propose temporal-pattern coarsening of activity-driven growing networks with memory. In particular, we focus on the relation between time-scale coarsening and spreading dynamics in the context of dynamic scaling and finite-size scaling. Finally, we discuss the universality issue of spreading dynamics on time-varying networks for various memory-causality tests.
[Psychometric properties of the Activities Daily Life Scale (ADL)].
Boyer, L; Murcia, A; Belzeaux, R; Loundou, A; Azorin, J-M; Chabannes, J-M; Dassa, D; Naudin, J; Samuelian, J-C; Lancon, C
2010-10-01
Deficits in social functioning are an important core feature of mental health. Recently in France, the Activities Daily Life (ADL) scale has been proposed by the French authorities to assess social functioning for all hospitalized patients in a psychiatric ward. The perspective is to use this scale in the financing and organization of mental health services in France. The ADL scale is a 6-item (dressing/undressing, walking/mobility, eating/drinking, using toilets, behaviour, relationships/communication) heteroquestionnaire completed by a health care professional at the beginning of each hospitalization, assessing functioning of patients suffering from mental health diseases. However, limited consensus exists on this scale. The psychometric properties of the ADL scale have not been assessed. There is a pressing need for detailed examination of its performance. The aim of this study was to explore ADL psychometric properties in a sample of hospitalized patients in a psychiatric ward. We retrospectively analyzed data for all episodes of care delivered to hospitalized patients in a psychiatric ward in our French Public Hospital from January 1, 2008 to June 30, 2008. The study involved retrospective review of administrative and medical databases. The following data were collected: age, gender, diagnoses based on the International Classification of Diseases - 10th version, ADL scale and Assessment of Social Self-Sufficiency scale (ASSS). The psychometric properties were examined using construct validity, reliability, external validity, reproducibility and sensitivity to change. Data analysis was performed using SPSS 15.0 and WINSTEP software. A total of 1066 patients completed the ADL scale. Among them, 49.7% were male, mean age was 36.5 ± 10.8, and 83.5% were single. Schizophrenia, schizotypal and delusional disorders (40.0%), mood disorders (27.9%) and mental and behavioural disorders due to psychoactive substance use (12%) were the most common diagnoses. Factor
Development and psychometric properties of the Inner Strength Scale.
Lundman, Berit; Viglund, Kerstin; Aléx, Lena; Jonsén, Elisabeth; Norberg, Astrid; Fischer, Regina Santamäki; Strandberg, Gunilla; Nygren, Björn
2011-10-01
Four dimensions of inner strength were previously identified in a meta-theoretical analysis: firmness, creativity, connectedness, and flexibility. The aim of this study was to develop an Inner Strength Scale (ISS) based on those four dimensions and to evaluate its psychometric properties. An initial version of ISS was distributed for validation purpose with the Rosenberg Self-Esteem Scale, the resilience scale, and the sense of Coherence Scale. A convenience sample of 391 adults, aged 19-90 years participated. Principal component analysis (PCA) and confirmatory factor analysis (CFA) were used in the process of exploring, evaluating, and reducing the 63-item ISS to the 20-item ISS. Cronbach's alpha and test-retest were used to measure reliability. CFA showed satisfactory goodness-of-fit for the 20-item ISS. The analysis supported a fourfactor solution explaining 51% of the variance. Cronbach's alpha on the 20-item ISS was 0.86, and the test-retest showed stability over time (r=0.79). The ISS was found to be a valid and reliable instrument for capturing a multifaceted understanding of inner strength. Further tests of psychometric properties of the ISS will be performed in forthcoming studies. Copyright © 2011 Elsevier Ltd. All rights reserved.
Disruptive behavior scale for adolescents (DISBA): development and psychometric properties.
Karimy, Mahmood; Fakhri, Ahmad; Vali, Esmaeel; Vali, Farzaneh; Veiga, Feliciano H; Stein, L A R; Araban, Marzieh
2018-01-01
Growing evidence indicates that if disruptive behavior is left unidentified and untreated, a significant proportion of these problems will persist and may develop into problems linked with delinquency, substance abuse, and violence. Research is needed to develop valid and reliable measures of disruptive behavior to assist recognition and impact of treatments on disruptive behavior. The aim of this study was to develop and evaluate the psychometric properties of a scale for disruptive behavior in adolescents. Six hundred high school students (50% girls), ages ranged 15-18 years old, selected through multi stage random sampling. Psychometrics of the disruptive behavior scale for adolescents (DISBA) (Persian version) was assessed through content validity, explanatory factor analysis (EFA) using Varimax rotation and confirmatory factor analysis (CFA). The reliability of this scale was assessed via internal consistency and test-retest reliability. EFA revealed four factors accounting for 59% of observed variance. The final 29-item scale contained four factors: (1) aggressive school behavior, (2) classroom defiant behavior, (3) unimportance of school, and (4) defiance to school authorities. Furthermore, CFA produced a sufficient Goodness of Fit Index > 0.90. Test-retest and internal consistency reliabilities were acceptable at 0.85 and 0.89, respectively. The findings from this study suggest that the Iranian version of DISBA questionnaire has content validity. Further studies are needed to evaluate stronger psychometric properties for DISBA.
The Metacognitions about Online Gaming Scale: Development and psychometric properties.
Spada, Marcantonio M; Caselli, Gabriele
2017-01-01
Recent research has suggested that metacognitions may play a role across the spectrum of addictive behaviours. The goal of our studies was to develop the first self-report scale of metacognitions about online gaming. We conducted two studies with samples of online gamers (n=225, n=348) to test the structure and psychometric properties of the Metacognitions about Online Gaming Scale and examined its capacity to predict weekly online gaming hours and Internet addiction. Exploratory and confirmatory factor analyses supported a three-factor solution: positive metacognitions about online gaming, negative metacognitions about the uncontrollability of online gaming, and negative metacognitions about the dangers of online gaming. Internal consistency, predictive and divergent validity were acceptable. All the factors of the Metacognitions about Online Gaming Scale correlated positively with weekly online gaming hours and Internet addiction. Regression analyses showed that negative metacognitions about the uncontrollability of online gaming and levels of Internet addiction were the only significant predictors of weekly online gaming hours, and that positive metacognitions about online gaming and negative metacognitions about the uncontrollability of online gaming were the only significant predictors of Internet addiction. The Metacognitions about Online Gaming Scale was shown to possess good psychometric properties, as well as predictive and divergent validity within the populations that were tested. Copyright © 2015 Elsevier Ltd. All rights reserved.
Assessing organizational climate: psychometric properties of the CLIOR Scale.
Peña-Suárez, Elsa; Muñiz, José; Campillo-Álvarez, Angela; Fonseca-Pedrero, Eduardo; García-Cueto, Eduardo
2013-02-01
Organizational climate is the set of perceptions shared by workers who occupy the same workplace. The main goal of this study is to develop a new organizational climate scale and to determine its psychometric properties. The sample consisted of 3,163 Health Service workers. A total of 88.7% of participants worked in hospitals, and 11.3% in primary care; 80% were women and 20% men, with a mean age of 51.9 years (SD= 6.28). The proposed scale consists of 50 Likert-type items, with an alpha coefficient of 0.97, and an essentially one-dimensional structure. The discrimination indexes of the items are greater than 0.40, and the items show no differential item functioning in relation to participants' sex. A short version of the scale was developed, made up of 15 items, with discrimination indexes higher than 0.40, an alpha coefficient of 0.94, and its structure was clearly one-dimensional. These results indicate that the new scale has adequate psychometric properties, allowing a reliable and valid assessment of organizational climate.
Properties of the Magnitude Terms of Orthogonal Scaling Functions.
Tay, Peter C; Havlicek, Joseph P; Acton, Scott T; Hossack, John A
2010-09-01
The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processing, the spectrum of the contiuous Fourier transform and the discrete time Fourier transform are approximately determined by numerical integration or by densely taking the discrete Fourier transform. It has been shown that all three transforms share many analogous properties. In this paper we will show another useful property of determining the spectrum terms of the convolution of two finite length sequences by determining the discrete Fourier transform of the modified cross-correlation function. In addition, two properties of the magnitude terms of orthogonal wavelet scaling functions are developed. These properties are used as constraints for an exhaustive search to determine an robust lower bound on conjoint localization of orthogonal scaling functions.
Theoretical concepts of fractal geometry semkow by radon emanation in solids
International Nuclear Information System (INIS)
Cruz G, H.
1996-01-01
The objective of this work is to introduce the fractal geometry concept to the study of gaseous emanations in solids, specially with reference to radon emission in mineral grains. The basic elements of fractals theory are developed. A fractal is defined as an auto similar subassembly, which fractal dimension is greater than the topological dimension. Starting from this, and making a brief description of the physicals basis of radon emission in solids, a model between emanation power (E R ) and the ratio s/v (surface to volume), is founded. A Gaussian model is assumed for extent of recoil from alpha decay of Ra-226. Using the results of Pfeifer it is obtained that distribution of pore size is scaled like Br -D-1 , where D: fractal[dimension, B: constant and r: pore radius. After an adequate mathematics expansion, it is found that the expression for emanation power is scaled like r 0 D-3 (r 0 grain radius). We may concluded that if we have a logarithmic graph of E R vs size of grain we can deduce the fractal dimension of the emanation surface. The experimental data of different materials provides an interval into fractal dimension D , between 2.1 to 2.86. (author). 5 refs., 1 tab
Improved visibility graph fractality with application for the diagnosis of Autism Spectrum Disorder
Ahmadlou, Mehran; Adeli, Hojjat; Adeli, Amir
2012-10-01
Recently, the visibility graph (VG) algorithm was proposed for mapping a time series to a graph to study complexity and fractality of the time series through investigation of the complexity of its graph. The visibility graph algorithm converts a fractal time series to a scale-free graph. VG has been used for the investigation of fractality in the dynamic behavior of both artificial and natural complex systems. However, robustness and performance of the power of scale-freeness of VG (PSVG) as an effective method for measuring fractality has not been investigated. Since noise is unavoidable in real life time series, the robustness of a fractality measure is of paramount importance. To improve the accuracy and robustness of PSVG to noise for measurement of fractality of time series in biological time-series, an improved PSVG is presented in this paper. The proposed method is evaluated using two examples: a synthetic benchmark time series and a complicated real life Electroencephalograms (EEG)-based diagnostic problem, that is distinguishing autistic children from non-autistic children. It is shown that the proposed improved PSVG is less sensitive to noise and therefore more robust compared with PSVG. Further, it is shown that using improved PSVG in the wavelet-chaos neural network model of Adeli and c-workers in place of the Katz fractality dimension results in a more accurate diagnosis of autism, a complicated neurological and psychiatric disorder.
Molecularly-Limited Fractal Surface Area of Mineral Powders
Directory of Open Access Journals (Sweden)
Petr Jandacka
2016-05-01
Full Text Available The topic of the specific surface area (SSA of powders is not sufficiently described in the literature in spite of its nontrivial contribution to adsorption and dissolution processes. Fractal geometry provides a way to determine this parameter via relation SSA ~ x(D − 3s(2 − D, where x (m is the particle size and s (m is a scale. Such a relation respects nano-, micro-, or macro-topography on the surface. Within this theory, the fractal dimension 2 ≤ D < 3 and scale parameter s plays a significant role. The parameter D may be determined from BET or dissolution measurements on several samples, changing the powder particle sizes or sizes of adsorbate molecules. If the fractality of the surface is high, the SSA does not depend on the particle size distribution and vice versa. In this paper, the SSA parameter is analyzed from the point of view of adsorption and dissolution processes. In the case of adsorption, a new equation for the SSA, depending on the term (2 − D∙(s2 − sBET/sBET, is derived, where sBET and s2 are effective cross-sectional diameters for BET and new adsorbates. Determination of the SSA for the dissolution process appears to be very complicated, since the fractality of the surface may change in the process. Nevertheless, the presented equations have good application potential.
Invited Article: Plasmonic growth of patterned metamaterials with fractal geometry
Directory of Open Access Journals (Sweden)
Nobuyuki Takeyasu
2016-08-01
Full Text Available Large-scale metallic three-dimensional (3D structures composed of sub-wavelength fine details, called metamaterials, have attracted optical scientists and materials scientists because of their unconventional and extraordinary optical properties that are not seen in nature. However, existing nano-fabrication technologies including two-photon fabrication, e-beam, focused ion-beam, and probe microscopy are not necessarily suitable for fabricating such large-scale 3D metallic nanostructures. In this article, we propose a different method of fabricating metamaterials, which is based on a bottom-up approach. We mimicked the generation of wood forest under the sunlight and rain in nature. In our method, a silver nano-forest is grown from the silver seeds (nanoparticles placed on the glass substrate in silver-ion solution. The metallic nano-forest is formed only in the area where ultraviolet light is illuminated. The local temperature increases at nano-seeds and tips of nano-trees and their branches due to the plasmonic heating as a result of UV light excitation of localized mode of surface plasmon polaritons. We have made experiments of growth of metallic nano-forest patterned by the light distribution. The experimental results show a beautiful nano-forest made of silver with self-similarity. Fractal dimension and spectral response of the grown structure are discussed. The structures exhibit a broad spectral response from ultraviolet to infrared, which was used for surface-enhanced Raman detection of molecules.
On fractal space-time and fractional calculus
Directory of Open Access Journals (Sweden)
Hu Yue
2016-01-01
Full Text Available This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.
Theoretical aspects of the Semkow fractal model in the radon emanation in solids
International Nuclear Information System (INIS)
Cruz G, H.S.
1997-01-01
The basic elements of the Fractals theory are developed. The physical basis of radon emission in solids are described briefly. It is obtained that the emanation power E R of mineral grains is scaled as r 0 D-3 (r 0 : grain radius). From a logarithmic graph E R versus grain size is deduced the fractal dimension of the emanation surface. The experimental data of different materials give an interval in the fractal dimension D between 2.1 and 2.8 (Author)
Determination of effective thermal conductivity for polyurethane foam by use of fractal method
Institute of Scientific and Technical Information of China (English)
SHI Mingheng; LI Xiaochuan; CHEN Yongping
2006-01-01
The microstructure of polyurethane foam is disordered, which influences the foam heat conduction process significantly. In this paper foam structure is described by using the local area fractal dimension in a certain small range of length scales. An equivalent element cell is constructed based on the local fractal dimensions along the directions parallel and transverse to the heat flux. By use of fractal void fraction a simplified heat conduction model is proposed to calculate the effective thermal conductivity of polyurethane foam. The predicted effective thermal conductivity agrees well with the experimental data.
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...
Micro-Scale Properties of Different Bora Types
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Vinko Šoljan
2018-03-01
Full Text Available In this paper we use 20 Hz wind measurements on three levels (2, 5, and 10 m to investigate the differences in micro-scale properties of different bora types, i.e., deep and shallow bora with further subdivision to cyclonic and anticyclonic bora cases. Using Fourier spectral analysis, we investigate a suitable turbulence averaging scale and bora gust pulsations. The obtained data set is further used to test the Monin–Obukhov similarity theory, the surface layer stratification, the behavior of the terms in the prognostic turbulence kinetic energy equation, and the wind profiles. One of our main goals is to identify possible micro-scale differences between shallow and deep bora types because of the possible different mountain wave dynamics in those flows. We found that a turbulence averaging scale of 30 min is suitable for this location and is in agreement with previous bora studies. The wind speed power spectral densities of all selected bora episodes showed pulsations with periods of 2–8 min. This suggests that mountain wave breaking was present in all cases, regardless of flow depth and synoptic type. The stability parameter analysis confirmed the near-neutral thermal stratification of bora; a consequence of intensive mechanical mixing. No significant differences related to bora type were observed in other micro-scale parameters.
Psychometric properties of the positivity scale - Brazilian version
Directory of Open Access Journals (Sweden)
Juliane Callegaro Borsa
2015-03-01
Full Text Available This study presents the psychometric properties of the Brazilian version of the Positivity Scale (P-Scale. Participants were 730 subjects (65% women, aged from 17 to 70 years old (M = 31.0 years; SD = 11.43, from 21 Brazilian states. The sample was randomly split in two halves to cross-validate the results. With the first half of the sample (n1 = 365, an exploratory factor analysis (EFA was conducted. With the second half of the sample (n2 = 365, a confirmatory factor analysis (CFA assessed the fit of the exploratory model. Convergent validity and group differences were also evaluated. The EFA and CFA presented a one-dimensional structure for the P-Scale. Moderate correlations were found between the P-Scale and mental-health, subjective happiness and life-satisfaction. The levels of positivity presented a low positive correlation with age, educational level and financial income. Slightly significant effects were found for occupational status and marital status. Positivity appears to be more closely related to personal dispositions than to sociodemographic aspects. Our results suggest that the P-Scale is a reliable measure with which to evaluate the levels of positivity in Brazil.
Fractals in DNA sequence analysis
Institute of Scientific and Technical Information of China (English)
Yu Zu-Guo(喻祖国); Vo Anh; Gong Zhi-Min(龚志民); Long Shun-Chao(龙顺潮)
2002-01-01
Fractal methods have been successfully used to study many problems in physics, mathematics, engineering, finance,and even in biology. There has been an increasing interest in unravelling the mysteries of DNA; for example, how can we distinguish coding and noncoding sequences, and the problems of classification and evolution relationship of organisms are key problems in bioinformatics. Although much research has been carried out by taking into consideration the long-range correlations in DNA sequences, and the global fractal dimension has been used in these works by other people, the models and methods are somewhat rough and the results are not satisfactory. In recent years, our group has introduced a time series model (statistical point of view) and a visual representation (geometrical point of view)to DNA sequence analysis. We have also used fractal dimension, correlation dimension, the Hurst exponent and the dimension spectrum (multifractal analysis) to discuss problems in this field. In this paper, we introduce these fractal models and methods and the results of DNA sequence analysis.
The distribution function of a probability measure on a space with a fractal structure
Energy Technology Data Exchange (ETDEWEB)
Sanchez-Granero, M.A.; Galvez-Rodriguez, J.F.
2017-07-01
In this work we show how to define a probability measure with the help of a fractal structure. One of the keys of this approach is to use the completion of the fractal structure. Then we use the theory of a cumulative distribution function on a Polish ultrametric space and describe it in this context. Finally, with the help of fractal structures, we prove that a function satisfying the properties of a cumulative distribution function on a Polish ultrametric space is a cumulative distribution function with respect to some probability measure on the space. (Author)
Fractal analysis of urban environment: land use and sewer system
Gires, A.; Ochoa Rodriguez, S.; Van Assel, J.; Bruni, G.; Murla Tulys, D.; Wang, L.; Pina, R.; Richard, J.; Ichiba, A.; Willems, P.; Tchiguirinskaia, I.; ten Veldhuis, M. C.; Schertzer, D. J. M.
2014-12-01
Land use distribution are usually obtained by automatic processing of satellite and airborne pictures. The complexity of the obtained patterns which are furthermore scale dependent is enhanced in urban environment. This scale dependency is even more visible in a rasterized representation where only a unique class is affected to each pixel. A parameter commonly analysed in urban hydrology is the coefficient of imperviousness, which reflects the proportion of rainfall that will be immediately active in the catchment response. This coefficient is strongly scale dependent with a rasterized representation. This complex behaviour is well grasped with the help of the scale invariant notion of fractal dimension which enables to quantify the space occupied by a geometrical set (here the impervious areas) not only at a single scale but across all scales. This fractal dimension is also compared to the ones computed on the representation of the catchments with the help of operational semi-distributed models. Fractal dimensions of the corresponding sewer systems are also computed and compared with values found in the literature for natural river networks. This methodology is tested on 7 pilot sites of the European NWE Interreg IV RainGain project located in France, Belgium, Netherlands, United-Kingdom and Portugal. Results are compared between all the case study which exhibit different physical features (slope, level of urbanisation, population density...).
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.
Mechanical Properties and Acoustic Emission Properties of Rocks with Different Transverse Scales
Directory of Open Access Journals (Sweden)
Xi Yan
2017-01-01
Full Text Available Since the stability of engineering rock masses has important practical significance to projects like mining, tunneling, and petroleum engineering, it is necessary to study mechanical properties and stability prediction methods for rocks, cementing materials that are composed of minerals in all shapes and sizes. Rocks will generate acoustic emission during damage failure processes, which is deemed as an effective means of monitoring the stability of coal rocks. In the meantime, actual mining and roadway surrounding rocks tend to have transverse effects; namely, the transverse scale is larger than the length scale. Therefore, it is important to explore mechanical properties and acoustic emission properties of rocks under transverse size effects. Considering the transverse scale effects of rocks, this paper employs the microparticle flow software PFC2D to explore the influence of different aspect ratios on damage mechanics and acoustic emission properties of rocks. The results show that (1 the transverse scale affects uniaxial compression strength of rocks. As the aspect ratio increases, uniaxial compression strength of rocks decreases initially and later increases, showing a V-shape structure and (2 although it affects the maximum hit rate and the strain range of acoustic emission, it has little influence on the period of occurrence. As the transverse scale increases, both damage degree and damage rate of rocks decrease initially and later increase.
Shirazinodeh, Alireza; Noubari, Hossein Ahmadi; Rabbani, Hossein; Dehnavi, Alireza Mehri
2015-01-01
Recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. It is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. In this paper, for fractal modeling, the original image is first segmented into appropriate fractal boxes followed by identifying the fractal dimension of each windowed section using a computationally efficient two-dimensional box-counting algorithm. Furthermore, using appropriate wavelet sub-bands and image Reconstruction based on modified wavelet coefficients, it is shown that it is possible to arrive at enhanced features for detection of cancerous zones. In this paper, we have attempted to benefit from the advantages of both fractals and wavelets by introducing a new algorithm. By using a new algorithm named F1W2, the original image is first segmented into appropriate fractal boxes, and the fractal dimension of each windowed section is extracted. Following from that, by applying a maximum level threshold on fractal dimensions matrix, the best-segmented boxes are selected. In the next step, the segmented Cancerous zones which are candidates are then decomposed by utilizing standard orthogonal wavelet transform and db2 wavelet in three different resolution levels, and after nullifying wavelet coefficients of the image at the first scale and low frequency band of the third scale, the modified reconstructed image is successfully utilized for detection of breast cancer regions by applying an appropriate threshold. For detection of cancerous zones, our simulations indicate the accuracy of 90.9% for masses and 88.99% for microcalcifications detection results using the F1W2 method. For classification of detected mictocalcification into benign and malignant cases, eight features are identified and
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)
Fractal based modelling and analysis of electromyography (EMG) to identify subtle actions.
Arjunan, Sridhar P; Kumar, Dinesh K
2007-01-01
The paper reports the use of fractal theory and fractal dimension to study the non-linear properties of surface electromyogram (sEMG) and to use these properties to classify subtle hand actions. The paper reports identifying a new feature of the fractal dimension, the bias that has been found to be useful in modelling the muscle activity and of sEMG. Experimental results demonstrate that the feature set consisting of bias values and fractal dimension of the recordings is suitable for classification of sEMG against the different hand gestures. The scatter plots demonstrate the presence of simple relationships of these features against the four hand gestures. The results indicate that there is small inter-experimental variation but large inter-subject variation. This may be due to differences in the size and shape of muscles for different subjects. The possible applications of this research include use in developing prosthetic hands, controlling machines and computers.
Dynamics and Scaling Properties of Fractures in clay-like Materials
Energy Technology Data Exchange (ETDEWEB)
Walmann, Thomas
1998-12-31
Computer models that can help oil companies predict realistic and physically correct fracture patterns are important. To verify such a model, experiments described in this thesis were undertaken, using wet clay and powder. The main focus was on extensional fractures, but other types of fractures were also studied. High resolution digital images of the fracture patterns were recorded and analyzed using statistical physics and fractal geometry. The characteristic shapes and size distributions of individual fractures and the overall fracture patterns obtained from laboratory model studies were compared to results from aerial photographs of a fracture pattern in a collapsed glacier that had undergone a similar deformation. A new scaling relation (a power-law) between the length of a fracture and the projected area is derived for fractures formed during clay model experiments. This scaling relation is found also in a field study of a fracture pattern in a glacier. The forms of the different distributions that characterizes fractures in clay experiments are discussed. Several characteristic lengths are associated with the laboratory experiments. They are related to the sample size and shape, the model material and the nature of the imposed deformation. The roughness of the fracture traces obtained from powder experiments was found to have a self-affine form. The roughness, or Hurst exponent, was found to have the value 0.73, plus or minus 0.09. A large number of interacting fractures were formed in the systems studied, and under such conditions the fluctuations about the direction perpendicular to the principle strain direction are influenced by neighbouring fractures. As expected, an upper cutoff for the scaling range was observed. But the length at which the crossover from a self-affine shape to a flat shape took place did not depend systematically on any of the experimental parameters or characteristic length scales. The total fracture trace patterns could not be
Polarization properties of linearly polarized parabolic scaling Bessel beams
Energy Technology Data Exchange (ETDEWEB)
Guo, Mengwen; Zhao, Daomu, E-mail: zhaodaomu@yahoo.com
2016-10-07
The intensity profiles for the dominant polarization, cross polarization, and longitudinal components of modified parabolic scaling Bessel beams with linear polarization are investigated theoretically. The transverse intensity distributions of the three electric components are intimately connected to the topological charge. In particular, the intensity patterns of the cross polarization and longitudinal components near the apodization plane reflect the sign of the topological charge. - Highlights: • We investigated the polarization properties of modified parabolic scaling Bessel beams with linear polarization. • We studied the evolution of transverse intensity profiles for the three components of these beams. • The intensity patterns of the cross polarization and longitudinal components can reflect the sign of the topological charge.
ECG scaling properties of cardiac arrhythmias using detrended fluctuation analysis
International Nuclear Information System (INIS)
Rodriguez, E; Echeverria, J C; Alvarez-Ramirez, J; Lerma, C
2008-01-01
We applied detrended fluctuation analysis to characterize at very short time scales during episodes of cardiac arrhythmias the raw electrocardiogram (ECG) waveform, aiming to get a global insight into its dynamical behaviour in patients who experienced sudden death. We found that in 15 recordings involving different types of arrhythmias (taken from PhysioNet's Sudden Cardiac Death Holter Database), the ECG waveform, besides showing a less-random dynamics, becomes more regular during bigeminy, ventricular tachycardia or even atrial fibrillation and ventricular fibrillation. The ECG waveform scaling properties thus suggest that reduced complexity dominates the underlying mechanisms of arrhythmias. Among other explanations, this may result from shorted or restricted (i.e. less diverse) pathways of conduction of the electrical activity within ventricles
The new Intragroup Conflict Scale: testing and psychometric properties.
Cox, Kathleen B
2014-01-01
The importance of healthy work environments has received attention. Health care organizations are plagued with conflict which is detrimental to work environments. Thus, conflict must be studied. The purpose of this article is to describe the testing of a measure of conflict. A survey was used to evaluate the psychometric properties. The sample consisted of 430 nurses at an academic medical center. Using principal component analysis (PCA) with varimax rotation, a six-factor solution (30 items) that explained 74.3% of variance emerged. Coefficient alpha ranged from .95 to .81. Correlations with existing scales supported construct validity (r = -.32(-)-.58). The results are encouraging. Use of the scale may provide insight into the impact of conflict on patient, staff, and organizational outcomes.
Psychometric properties of a pictorial scale measuring correct condom use.
Li, Qing; Li, Xiaoming; Stanton, Bonita; Wang, Bo
2011-02-01
This study was designed to assess the psychometric properties of a pictorial scale of correct condom use (PSCCU) using data from female sex workers (FSWs) in China. The psychometric properties assessed in this study include construct validity by correlations and known-group validation. The study sample included 396 FSWs in Guangxi, China. The results demonstrate adequate validity of the PSCCU among the study population. FSWs with a higher level of education scored significantly higher on the PSCCU than those with a lower level of education. FSWs who self-reported appropriate condom use with stable partners scored significantly higher on PSCCU than their counterparts. The PSCCU should provide HIV/STI prevention researchers and practitioners with a valid alternative assessment tool among high-risk populations, especially in resource-limited settings.
Zipf’s law, 1/f noise, and fractal hierarchy
International Nuclear Information System (INIS)
Chen Yanguang
2012-01-01
Highlights: ► I developed a general scaling method based on hierarchies of cites. ► Hierarchy is classified into three types based on monofractal and multifractals. ► Zipf’s law can be used to estimate the capacity dimension of a multifractal set. ► I derive the self-similar hierarchy from the rank-size distribution. ► The hierarchical scaling method can be applied to the 1/f spectra. - Abstract: Fractals, 1/f noise, and Zipf’s laws are frequently observed within the natural living world as well as in social institutions, representing three signatures of complex systems. All these observations are associated with scaling laws and therefore have created much research interest in many diverse scientific circles. However, the inherent relationships between these scaling phenomena are not yet clear. In this paper, theoretical demonstration and mathematical experiments based on urban studies are employed to reveal the analogy between fractal patterns, 1/f spectra, and the Zipf distribution. First, the multifractal process empirically suggests the Zipf distribution. Second, a 1/f spectrum is mathematically identical to Zipf’s law. Third, both 1/f spectra and Zipf’s law can be converted into a self-similar hierarchy. Fourth, fractals, 1/f spectra, Zipf’s law can be rescaled with similar exponential laws and power laws. The self-similar hierarchy is a more general scaling method which can be used to unify different scaling phenomena and rules in both physical and social systems such as cities, rivers, earthquakes, fractals, 1/f noise, and rank-size distributions. The mathematical laws of this hierarchical structure can provide us with a holistic perspective of looking at complexity and complex systems.
Psychometric Properties of the Dutch Rosenberg Self-Esteem Scale
Erik Franck; Rudi De Raedt; Catherine Barbez; Yves Rosseel
2008-01-01
Interest in self-esteem has been fuelled by the suggestion that level of self-esteem is associated with psychological well-being. In the present study, we translated the Rosenberg Self-Esteem Scale (RSES) into the Dutch language and evaluated its psychometric properties in a sample of 442 adults. The results of both exploratory and confirmatory factor analyses confirmed that a single-factor solution provides the best fit. In addition, the Dutch RSES showed high internal consistency as well as...
Psychometric Properties of the Dutch Rosenberg Self-Esteem Scale
Directory of Open Access Journals (Sweden)
Erik Franck
2008-01-01
Full Text Available Interest in self-esteem has been fuelled by the suggestion that level of self-esteem is associated with psychological well-being. In the present study, we translated the Rosenberg Self-Esteem Scale (RSES into the Dutch language and evaluated its psychometric properties in a sample of 442 adults. The results of both exploratory and confirmatory factor analyses confirmed that a single-factor solution provides the best fit. In addition, the Dutch RSES showed high internal consistency as well as high congruent validity. Overall, these findings support the usefulness of the Dutch RSES as a measure for global self-esteem.
Multi-fractal measures of city-size distributions based on the three-parameter Zipf model
International Nuclear Information System (INIS)
Chen Yanguang; Zhou Yixing
2004-01-01
A multi-fractal framework of urban hierarchies is presented to address the rank-size distribution of cities. The three-parameter Zipf model based on a pair of exponential-type scaling laws is generalized to multi-scale fractal measures. Then according to the equivalent relationship between Zipf's law and Pareto distribution, a set of multi-fractal equations are derived using dual conversion and the Legendre transform. The US city population data coming from the 2000 census are employed to verify the multi-fractal models and the results are satisfying. The multi-fractal measures reveal some strange symmetry regularity of urban systems. While explaining partially the remains of the hierarchical step-like frequency distribution of city sizes suggested by central place theory, the mathematical framework can be interpreted with the entropy-maximizing principle and some related ideas from self-organization
Terahertz response of fractal meta-atoms based on concentric rectangular square resonators
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Song, Zhiqiang; Zhao, Zhenyu, E-mail: zyzhao@shnu.edu.cn; Shi, Wangzhou [Department of Physics, Shanghai Normal University, Shanghai 200234 (China); Peng, Wei [State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050 (China)
2015-11-21
We investigate the terahertz electromagnetic responses of fractal meta-atoms (MAs) induced by different mode coupling mechanisms. Two types of MAs based on concentric rectangular square (CRS) resonators are presented: independent CRS (I-CRS) and junctional-CRS (J-CRS). In I-CRS, each resonator works as an independent dipole so as to result in the multiple resonance modes when the fractal level is above 1. In J-CRS, however, the generated layer is rotated by π/2 radius to the adjacent CRS in one MA. The multiple resonance modes are coupled into a single mode resonance. The fractal level increasing induces resonance modes redshift in I-CRS while blueshift in J-CRS. When the fractal level is below 4, the mode Q factor of J-CRS is in between the two modes of I-CRS; when the fractal level is 4 or above, the mode Q factor of J-CRS exceeds the two modes of I-CRS. Furthermore, the modulation depth (MD) decreases in I-CRS while it increases in J-CRS with the increase in fractal levels. The surface currents analysis reveals that the capacitive coupling of modes in I-CRS results in the modes redshift, while the conductive coupling of modes in J-CRS induces the mode blueshift. A high Q mode with large MD can be achieved via conductive coupling between the resonators of different scales in a fractal MA.
Energy Technology Data Exchange (ETDEWEB)
Chamousis, RL; Chang, LL; Watterson, WJ; Montgomery, RD; Taylor, RP; Moule, AJ; Shaheen, SE; Ilan, B; van de Lagemaat, J; Osterloh, FE
2014-08-21
Living organisms use fractal structures to optimize material and energy transport across regions of differing size scales. Here we test the effect of fractal silver electrodes on light distribution and charge collection in organic semiconducting polymer films made of P3HT and PCBM. The semiconducting polymers were deposited onto electrochemically grown fractal silver structures (5000 nm x 500 nm; fractal dimension of 1.71) with PEDOT:PSS as hole-selective interlayer. The fractal silver electrodes appear black due to increased horizontal light scattering, which is shown to improve light absorption in the polymer. According to surface photovoltage spectroscopy, fractal silver electrodes outperform the flat electrodes when the BHJ film thickness is large (>400 nm, 0.4 V photovoltage). Photocurrents of up to 200 microamperes cm(-2) are generated from the bulk heterojunction (BHJ) photoelectrodes under 435 nm LED (10-20 mW cm(-2)) illumination in acetonitrile solution containing 0.005 M ferrocenium hexafluorophosphate as the electron acceptor. The low IPCE values (0.3-0.7%) are due to slow electron transfer to ferrocenium ion and due to shunting along the large metal-polymer interface. Overall, this work provides an initial assessment of the potential of fractal electrodes for organic photovoltaic cells.
Atypical extended electronic states in an infinite Vicsek fractal: An exact result
International Nuclear Information System (INIS)
Chakrabarti, A.; Bhattacharyya, B.
1996-01-01
We present a class of extended electronic wave functions on a Vicsek fractal. The transmittivity of arbitrarily large fractal lattices corresponding to these particular extended-state eigenvalues exhibits a power-law decay with increasing system size. The eigenvalues corresponding to the above extended states as well as the scaling law for the transmittivity have been exactly calculated using a real-space renormalization-group method. copyright 1996 The American Physical Society
Fractal based observables to probe jet substructure of quarks and gluons
Davighi, Joe; Harris, Philip
2018-04-01
New jet observables are defined which characterize both fractal and scale-dependent contributions to the distribution of hadrons in a jet. These infrared safe observables, named Extended Fractal Observables (EFOs), have been applied to quark-gluon discrimination to demonstrate their potential utility. The EFOs are found to be individually discriminating and only weakly correlated to variables used in existing discriminators. Consequently, their inclusion improves discriminator performance, as here demonstrated with particle level simulation from the parton shower.
Directory of Open Access Journals (Sweden)
Vesa J Kiviniemi
2009-07-01
Full Text Available Temporal blood oxygen level dependent (BOLD contrast signals in functional MRI during rest may be characterized by power spectral distribution (PSD trends of the form 1/f α. Trends with 1/f characteristics comprise fractal properties with repeating oscillation patterns in multiple time scales. Estimates of the fractal properties enable the quantification of phenomena that may otherwise be difficult to measure, such as transient, non-linear changes. In this study it was hypothesized that the fractal metrics of 1/f BOLD signal trends can map changes related to dynamic, multi-scale alterations in cerebral blood flow (CBF after a transient hyperventilation challenge. Twenty-three normal adults were imaged in a resting-state before and after hyperventilation. Different variables (1/f trend constant α, fractal dimension Df, and, Hurst exponent H characterizing the trends were measured from BOLD signals. The results show that fractal metrics of the BOLD signal follow the fractional Gaussian noise model, even during the dynamic CBF change that follows hyperventilation. The most dominant effect on the fractal metrics was detected in grey matter, in line with previous hyperventilation vaso-reactivity studies. The α was able to differentiate also blood vessels from grey matter changes. Df was most sensitive to grey matter. H correlated with default mode network areas before hyperventilation but this pattern vanished after hyperventilation due to a global increase in H. In the future, resting-state fMRI combined with fractal metrics of the BOLD signal may be used for analyzing multi-scale alterations of cerebral blood flow.
Kiviniemi, Vesa; Remes, Jukka; Starck, Tuomo; Nikkinen, Juha; Haapea, Marianne; Silven, Olli; Tervonen, Osmo
2009-01-01
Temporal blood oxygen level dependent (BOLD) contrast signals in functional MRI during rest may be characterized by power spectral distribution (PSD) trends of the form 1/f(alpha). Trends with 1/f characteristics comprise fractal properties with repeating oscillation patterns in multiple time scales. Estimates of the fractal properties enable the quantification of phenomena that may otherwise be difficult to measure, such as transient, non-linear changes. In this study it was hypothesized that the fractal metrics of 1/f BOLD signal trends can map changes related to dynamic, multi-scale alterations in cerebral blood flow (CBF) after a transient hyperventilation challenge. Twenty-three normal adults were imaged in a resting-state before and after hyperventilation. Different variables (1/f trend constant alpha, fractal dimension D(f), and, Hurst exponent H) characterizing the trends were measured from BOLD signals. The results show that fractal metrics of the BOLD signal follow the fractional Gaussian noise model, even during the dynamic CBF change that follows hyperventilation. The most dominant effect on the fractal metrics was detected in grey matter, in line with previous hyperventilation vaso-reactivity studies. The alpha was able to differentiate also blood vessels from grey matter changes. D(f) was most sensitive to grey matter. H correlated with default mode network areas before hyperventilation but this pattern vanished after hyperventilation due to a global increase in H. In the future, resting-state fMRI combined with fractal metrics of the BOLD signal may be used for analyzing multi-scale alterations of cerebral blood flow.
Fractal structures and fractal functions as disease indicators
Escos, J.M; Alados, C.L.; Emlen, J.M.
1995-01-01
Developmental instability is an early indicator of stress, and has been used to monitor the impacts of human disturbance on natural ecosystems. Here we investigate the use of different measures of developmental instability on two species, green peppers (Capsicum annuum), a plant, and Spanish ibex (Capra pyrenaica), an animal. For green peppers we compared the variance in allometric relationship between control plants, and a treatment group infected with the tomato spotted wilt virus. The results show that infected plants have a greater variance about the allometric regression line than the control plants. We also observed a reduction in complexity of branch structure in green pepper with a viral infection. Box-counting fractal dimension of branch architecture declined under stress infection. We also tested the reduction in complexity of behavioral patterns under stress situations in Spanish ibex (Capra pyrenaica). Fractal dimension of head-lift frequency distribution measures predator detection efficiency. This dimension decreased under stressful conditions, such as advanced pregnancy and parasitic infection. Feeding distribution activities reflect food searching efficiency. Power spectral analysis proves to be the most powerful tool for character- izing fractal behavior, revealing a reduction in complexity of time distribution activity under parasitic infection.
Large Scale Emerging Properties from Non Hamiltonian Complex Systems
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Marco Bianucci
2017-06-01
Full Text Available The concept of “large scale” depends obviously on the phenomenon we are interested in. For example, in the field of foundation of Thermodynamics from microscopic dynamics, the spatial and time large scales are order of fraction of millimetres and microseconds, respectively, or lesser, and are defined in relation to the spatial and time scales of the microscopic systems. In large scale oceanography or global climate dynamics problems the time scales of interest are order of thousands of kilometres, for space, and many years for time, and are compared to the local and daily/monthly times scales of atmosphere and ocean dynamics. In all the cases a Zwanzig projection approach is, at least in principle, an effective tool to obtain class of universal smooth “large scale” dynamics for few degrees of freedom of interest, starting from the complex dynamics of the whole (usually many degrees of freedom system. The projection approach leads to a very complex calculus with differential operators, that is drastically simplified when the basic dynamics of the system of interest is Hamiltonian, as it happens in Foundation of Thermodynamics problems. However, in geophysical Fluid Dynamics, Biology, and in most of the physical problems the building block fundamental equations of motions have a non Hamiltonian structure. Thus, to continue to apply the useful projection approach also in these cases, we exploit the generalization of the Hamiltonian formalism given by the Lie algebra of dissipative differential operators. In this way, we are able to analytically deal with the series of the differential operators stemming from the projection approach applied to these general cases. Then we shall apply this formalism to obtain some relevant results concerning the statistical properties of the El Niño Southern Oscillation (ENSO.
International Nuclear Information System (INIS)
Chen Yanguang; Lin Jingyi
2009-01-01
This paper demonstrates self-affine fractal structure of city systems by means of theoretical and empirical analyses. A Cobb-Douglas-type function (C-D function) of city systems is derived from a general urban response equation, and the partial scaling exponent of the C-D function proved to be the fractal dimension reflecting the self-affine features of city systems. As a case, the self-affine fractal model is applied to the city of Zhengzhou, China, and the result is satisfying. A fractal parameter equation indicative of structural optimization conditions is then obtained from the C-D function. The equation suggests that priority should be given to the development of the urban element with a lower fractal dimension, or a higher partial scaling exponent, for utility maximization. Moreover, the fractal dimensions of different urban elements tend to become equivalent to each other in the long term. Accordingly, it is self-similar fractals rather than self-affine fractals that represent the optimal structure of city systems under ideal conditions.
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.
Stochastic and fractal analysis of fracture trajectories
Bessendorf, Michael H.
1987-01-01
Analyses of fracture trajectories are used to investigate structures that fall between 'micro' and 'macro' scales. It was shown that fracture trajectories belong to the class of nonstationary processes. It was also found that correlation distance, which may be related to a characteristic size of a fracture process, increases with crack length. An assemblage of crack trajectory processes may be considered as a diffusive process. Chudnovsky (1981-1985) introduced a 'crack diffusion coefficient' d which reflects the ability of the material to deviate the crack trajectory from the most energetically efficient path and thus links the material toughness to its structure. For the set of fracture trajectories in AISI 304 steel, d was found to be equal to 1.04 microns. The fractal dimension D for the same set of trajectories was found to be 1.133.
Fuzzy fractals, chaos, and noise
Energy Technology Data Exchange (ETDEWEB)
Zardecki, A.
1997-05-01
To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the concept of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.
Fractal like charge transport in polyaniline nanostructures
International Nuclear Information System (INIS)
Nath, Chandrani; Kumar, A.
2013-01-01
The structural and electrical properties of camphorsulfonic acid (CSA) doped nanotubes, and hydrochloric acid (HCl) doped nanofibers and nanoparticles of polyaniline have been studied as a function of doping level. The crystallinity increases with doping for all the nanostructures. Electrical transport measurements in the temperature range of 5–300 K show an increase in conductivity with doping for the nanostructures. All the nanostructures exhibit metal to insulator (MIT) transition below 40 K. The metallic behavior is ascribed to the electron–electron interaction effects. In the insulating regime of the nanotubes conduction follows the Mott quasi-1D variable range hopping model, whereas the conduction in the nanofibers and nanoparticles occur by variable range hopping of charge carriers among superlocalized states without and with Coulomb interaction, respectively. The smaller dopant size in case of HCl makes the polymer fractal resulting in superlocalization of electronic wave-functions. The confined morphology of the nanoparticles results in effective Coulomb interaction dominating the intersite hopping
International Nuclear Information System (INIS)
Chełminiak, Przemysław
2012-01-01
A new approach to the assemblage of complex networks displaying the scale-free architecture is proposed. While the growth and the preferential attachment of incoming nodes assure an emergence of such networks according to the Barabási–Albert model, it is argued here that the preferential linking condition needs not to be a principal rule. To assert this statement a simple computer model based on random walks on fractal lattices is introduced. It is shown that the model successfully reproduces the degree distributions, the ultra-small-worldness and the high clustering arising from the topology of scale-free networks. -- Highlights: ► A new mechanism of evolution for scale-free complex networks is proposed. ► The preferential attachment rule is not necessary to construct such networks. ► It is shown that they reveal some basic properties of classical scale-free nets.
Inkjet-Printed Ultra Wide Band Fractal Antennas
Maza, Armando Rodriguez
2012-01-01
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
Porosity-dependent fractal nature of the porous silicon surface
Energy Technology Data Exchange (ETDEWEB)
Rahmani, N.; Dariani, R. S., E-mail: dariani@alzahra.ac.ir [Department of Physics, Alzahra University, Tehran, 1993893973 (Iran, Islamic Republic of)
2015-07-15
Porous silicon films with porosity ranging from 42% to 77% were fabricated by electrochemical anodization under different current density. We used atomic force microscopy and dynamic scaling theory for deriving the surface roughness profile and processing the topography of the porous silicon layers, respectively. We first compared the topography of bare silicon surface with porous silicon and then studied the effect of the porosity of porous silicon films on their scaling behavior by using their self-affinity nature. Our work demonstrated that silicon compared to the porous silicon films has the highest Hurst parameter, indicating that the formation of porous layer due to the anodization etching of silicon surface leads to an increase of its roughness. Fractal analysis revealed that the evolution of the nanocrystallites’ fractal dimension along with porosity. Also, we found that both interface width and Hurst parameter are affected by the increase of porosity.
On the fractal characterization of Paretian Poisson processes
Eliazar, Iddo I.; Sokolov, Igor M.
2012-06-01
Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto's law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of 'fractal processes' exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes-with respect to physical randomness-based measures of statistical heterogeneity-is characterized by exponential Poissonian intensities.
Fractals via iterated functions and multifunctions
International Nuclear Information System (INIS)
Singh, S.L.; Prasad, Bhagwati; Kumar, Ashish
2009-01-01
Fractals have wide applications in biology, computer graphics, quantum physics and several other areas of applied sciences (see, for instance [Daya Sagar BS, Rangarajan Govindan, Veneziano Daniele. Preface - fractals in geophysics. Chaos, Solitons and Fractals 2004;19:237-39; El Naschie MS. Young double-split experiment Heisenberg uncertainty principles and cantorian space-time. Chaos, Solitons and Fractals 1994;4(3):403-09; El Naschie MS. Quantum measurement, information, diffusion and cantorian geodesics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 191-205; El Naschie MS. Iterated function systems, information and the two-slit experiment of quantum mechanics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 185-9; El Naschie MS, Rossler OE, Prigogine I. Forward. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995; El Naschie MS. A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons and Fractals 2004;19:209-36; El Naschie MS. Fractal black holes and information. Chaos, Solitons and Fractals 2006;29:23-35; El Naschie MS. Superstring theory: what it cannot do but E-infinity could. Chaos, Solitons and Fractals 2006;29:65-8). Especially, the study of iterated functions has been found very useful in the theory of black holes, two-slit experiment in quantum mechanics (cf. El Naschie, as mentioned above). The intent of this paper is to give a brief account of recent developments of fractals arising from IFS. We also discuss iterated multifunctions.
Node insertion in Coalescence Fractal Interpolation Function
International Nuclear Information System (INIS)
Prasad, Srijanani Anurag
2013-01-01
The Iterated Function System (IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) depends on the interpolation data. The insertion of a new point in a given set of interpolation data is called the problem of node insertion. In this paper, the effect of insertion of new point on the related IFS and the Coalescence Fractal Interpolation Function is studied. Smoothness and Fractal Dimension of a CHFIF obtained with a node are also discussed
Fractional hydrodynamic equations for fractal media
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2005-01-01
We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered
Power Load Prediction Based on Fractal Theory
Jian-Kai, Liang; Cattani, Carlo; Wan-Qing, Song
2015-01-01
The basic theories of load forecasting on the power system are summarized. Fractal theory, which is a new algorithm applied to load forecasting, is introduced. Based on the fractal dimension and fractal interpolation function theories, the correlation algorithms are applied to the model of short-term load forecasting. According to the process of load forecasting, the steps of every process are designed, including load data preprocessing, similar day selecting, short-term load forecasting, and...
Fractal Metrology for biogeosystems analysis
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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...
Space-Filling Supercapacitor Carpets: Highly scalable fractal architecture for energy storage
Tiliakos, Athanasios; Trefilov, Alexandra M. I.; Tanasǎ, Eugenia; Balan, Adriana; Stamatin, Ioan
2018-04-01
Revamping ground-breaking ideas from fractal geometry, we propose an alternative micro-supercapacitor configuration realized by laser-induced graphene (LIG) foams produced via laser pyrolysis of inexpensive commercial polymers. The Space-Filling Supercapacitor Carpet (SFSC) architecture introduces the concept of nested electrodes based on the pre-fractal Peano space-filling curve, arranged in a symmetrical equilateral setup that incorporates multiple parallel capacitor cells sharing common electrodes for maximum efficiency and optimal length-to-area distribution. We elucidate on the theoretical foundations of the SFSC architecture, and we introduce innovations (high-resolution vector-mode printing) in the LIG method that allow for the realization of flexible and scalable devices based on low iterations of the Peano algorithm. SFSCs exhibit distributed capacitance properties, leading to capacitance, energy, and power ratings proportional to the number of nested electrodes (up to 4.3 mF, 0.4 μWh, and 0.2 mW for the largest tested model of low iteration using aqueous electrolytes), with competitively high energy and power densities. This can pave the road for full scalability in energy storage, reaching beyond the scale of micro-supercapacitors for incorporating into larger and more demanding applications.
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
Properties and effects of remaining carbon from waste plastics gasifying on iron scale reduction.
Zhang, Chongmin; Chen, Shuwen; Miao, Xincheng; Yuan, Hao
2011-06-01
The carbonous activities of three kinds of carbon-bearing materials gasified from plastics were tested with coal coke as reference. The results showed that the carbonous activities of these remaining carbon-bearing materials were higher than that of coal-coke. Besides, the fractal analyses showed that the porosities of remaining carbon-bearing materials were higher than that of coal-coke. It revealed that these kinds of remaining carbon-bearing materials are conducive to improve the kinetics conditions of gas-solid phase reaction in iron scale reduction. Copyright © 2011 The Research Centre for Eco-Environmental Sciences, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Chia-Hung Lin
2010-01-01
Full Text Available This paper proposes combining the biometric fractal pattern and particle swarm optimization (PSO-based classifier for fingerprint recognition. Fingerprints have arch, loop, whorl, and accidental morphologies, and embed singular points, resulting in the establishment of fingerprint individuality. An automatic fingerprint identification system consists of two stages: digital image processing (DIP and pattern recognition. DIP is used to convert to binary images, refine out noise, and locate the reference point. For binary images, Katz's algorithm is employed to estimate the fractal dimension (FD from a two-dimensional (2D image. Biometric features are extracted as fractal patterns using different FDs. Probabilistic neural network (PNN as a classifier performs to compare the fractal patterns among the small-scale database. A PSO algorithm is used to tune the optimal parameters and heighten the accuracy. For 30 subjects in the laboratory, the proposed classifier demonstrates greater efficiency and higher accuracy in fingerprint recognition.
Directory of Open Access Journals (Sweden)
M.H. Giménez
2011-06-01
Full Text Available This work presents a new virtual laboratory, Difract, developed with Easy Java Simulations, for using in Optics courses as a computer tool for the mathematical modelling of the diffraction properties of 1D and 2D fractal gratings. This virtual laboratory enables students to quickly and easily analyze the influence on the Fraunhofer diffraction pattern of the different construction parameters of the fractal grating. As an application example, the Cantor fractal set has been considered.
A simple method for estimating the size of nuclei on fractal surfaces
Zeng, Qiang
2017-10-01
Determining the size of nuclei on complex surfaces remains a big challenge in aspects of biological, material and chemical engineering. Here the author reported a simple method to estimate the size of the nuclei in contact with complex (fractal) surfaces. The established approach was based on the assumptions of contact area proportionality for determining nucleation density and the scaling congruence between nuclei and surfaces for identifying contact regimes. It showed three different regimes governing the equations for estimating the nucleation site density. Nuclei in the size large enough could eliminate the effect of fractal structure. Nuclei in the size small enough could lead to the independence of nucleation site density on fractal parameters. Only when nuclei match the fractal scales, the nucleation site density is associated with the fractal parameters and the size of the nuclei in a coupling pattern. The method was validated by the experimental data reported in the literature. The method may provide an effective way to estimate the size of nuclei on fractal surfaces, through which a number of promising applications in relative fields can be envisioned.
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)...
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.
Scaling properties of cosmic (super)string networks
International Nuclear Information System (INIS)
Martins, C J A P
2014-01-01
I use a combination of state-of-the-art numerical simulations and analytic modelling to discuss the scaling properties of cosmic defect networks, including superstrings. Particular attention is given to the role of extra degrees of freedom in the evolution of these networks. Compared to the 'plain vanilla' case of Goto-Nambu strings, three such extensions play important but distinct roles in the network dynamics: the presence of charges/currents on the string worldsheet, the existence of junctions, and the possibility of a hierarchy of string tensions. I also comment on insights gained from studying simpler defect networks, including Goto-Nambu strings themselves, domain walls and semilocal strings
Magnetic Properties of Large-Scale Nanostructured Graphene Systems
DEFF Research Database (Denmark)
Gregersen, Søren Schou
The on-going progress in two-dimensional (2D) materials and nanostructure fabrication motivates the study of altered and combined materials. Graphene—the most studied material of the 2D family—displays unique electronic and spintronic properties. Exceptionally high electron mobilities, that surpass...... those in conventional materials such as silicon, make graphene a very interesting material for high-speed electronics. Simultaneously, long spin-diffusion lengths and spin-life times makes graphene an eligible spin-transport channel. In this thesis, we explore fundamental features of nanostructured...... graphene systems using large-scale modeling techniques. Graphene perforations, or antidots, have received substantial interest in the prospect of opening large band gaps in the otherwise gapless graphene. Motivated by recent improvements of fabrication processes, such as forming graphene antidots and layer...
Scaling properties of rainfall records in some Mexican zones
Angulo-Fernández, Fercia; Reyes-Ramírez, Israel; Flores-Márquez, Elsa Leticia
2018-04-01
Since the 1990 decade, it has been suggested that atmospheric processes associated with rainfall could be a self-organized critical (SOC) phenomenon similar, for example, to seismicity. In this sense, the rain events taken as the output of the complex atmospheric system (sun's radiation, water evaporation, clouds, etc.) are analogous to earthquakes, as the output of a relaxation process of the earth crust. A clue on this possible SOC behavior of rain phenomenon has been the ubiquitous presence of power laws in rain statistics. In the present article, we report the scaling properties of rain precipitation data taken from meteorological stations located at six zones of Mexico. Our results are consistent with those that assert that rainfall is a SOC phenomenon. We also analyze the Hurst exponent, which is appropriate to measure long-term memory of time series.
Psychometric properties of the Adolescent Sleep Hygiene Scale.
Storfer-Isser, Amy; Lebourgeois, Monique K; Harsh, John; Tompsett, Carolyn J; Redline, Susan
2013-12-01
This study evaluated the psychometric properties of the Adolescent Sleep Hygiene Scale (ASHS), a self-report measure assessing sleep practices theoretically important for optimal sleep. Data were collected on a community sample of 514 adolescents (16-19; 17.7 ± 0.4 years; 50% female) participating in the late adolescent examination of a longitudinal study on sleep and health. Sleep hygiene and daytime sleepiness were obtained from adolescent reports, behavior from caretaker reports, and sleep-wake estimation on weekdays from wrist actigraphy. Confirmatory factor analysis indicated the empirical and conceptually based factor structure were similar for six of the eight proposed sleep hygiene domains. Internal consistency of the revised scale (ASHSr) was α = 0.84; subscale alphas were: physiological: α = 0.60; behavioural arousal: α = 0.62; cognitive/emotional: α = 0.81; sleep environment: α = 0.61; sleep stability: α = 0.68; daytime sleep: α = 0.78. Sleep hygiene scores were associated positively with sleep duration (r = 0.16) and sleep efficiency (r = 0.12) and negatively with daytime sleepiness (r = -0.26). Results of extreme-groups analyses comparing ASHSr scores in the lowest and highest quintile provided further evidence for concurrent validity. Correlations between sleep hygiene scores and caretaker reports of school competence, internalizing and externalizing behaviours provided support for convergent validity. These findings indicate that the ASHSr has satisfactory psychometric properties for a research instrument and is a useful research tool for assessing sleep hygiene in adolescents. © 2013 European Sleep Research Society.
Ducharme, Scott W; Liddy, Joshua J; Haddad, Jeffrey M; Busa, Michael A; Claxton, Laura J; van Emmerik, Richard E A
2018-04-01
Human locomotion is an inherently complex activity that requires the coordination and control of neurophysiological and biomechanical degrees of freedom across various spatiotemporal scales. Locomotor patterns must constantly be altered in the face of changing environmental or task demands, such as heterogeneous terrains or obstacles. Variability in stride times occurring at short time scales (e.g., 5-10 strides) is statistically correlated to larger fluctuations occurring over longer time scales (e.g., 50-100 strides). This relationship, known as fractal dynamics, is thought to represent the adaptive capacity of the locomotor system. However, this has not been tested empirically. Thus, the purpose of this study was to determine if stride time fractality during steady state walking associated with the ability of individuals to adapt their gait patterns when locomotor speed and symmetry are altered. Fifteen healthy adults walked on a split-belt treadmill at preferred speed, half of preferred speed, and with one leg at preferred speed and the other at half speed (2:1 ratio asymmetric walking). The asymmetric belt speed condition induced gait asymmetries that required adaptation of locomotor patterns. The slow speed manipulation was chosen in order to determine the impact of gait speed on stride time fractal dynamics. Detrended fluctuation analysis was used to quantify the correlation structure, i.e., fractality, of stride times. Cross-correlation analysis was used to measure the deviation from intended anti-phasing between legs as a measure of gait adaptation. Results revealed no association between unperturbed walking fractal dynamics and gait adaptability performance. However, there was a quadratic relationship between perturbed, asymmetric walking fractal dynamics and adaptive performance during split-belt walking, whereby individuals who exhibited fractal scaling exponents that deviated from 1/f performed the poorest. Compared to steady state preferred walking
Fractal fluctuations in spatiotemporal variables when walking on a self-paced treadmill.
Choi, Jin-Seung; Kang, Dong-Won; Seo, Jeong-Woo; Tack, Gye-Rae
2017-12-08
This study investigated the fractal dynamic properties of stride time (ST), stride length (SL) and stride speed (SS) during walking on a self-paced treadmill (STM) in which the belt speed is automatically controlled by the walking speed. Twelve healthy young subjects participated in the study. The subjects walked at their preferred walking speed under four conditions: STM, STM with a metronome (STM+met), fixed-speed (conventional) treadmill (FTM), and FTM with a metronome (FTM+met). To compare the fractal dynamics between conditions, the mean, variability, and fractal dynamics of ST, SL, and SS were compared. Moreover, the relationship among the variables was examined under each walking condition using three types of surrogates. The mean values of all variables did not differ between the two treadmills, and the variability of all variables was generally larger for STM than for FTM. The use of a metronome resulted in a decrease in variability in ST and SS for all conditions. The fractal dynamic characteristics of SS were maintained with STM, in contrast to FTM, and only the fractal dynamic characteristics of ST disappeared when using a metronome. In addition, the fractal dynamic patterns of the cross-correlated surrogate results were identical to those of all variables for the two treadmills. In terms of the fractal dynamic properties, STM walking was generally closer to overground walking than FTM walking. Although further research is needed, the present results will be useful in research on gait fractal dynamics and rehabilitation. Copyright © 2017 Elsevier Ltd. All rights reserved.
The magnetic properties of mill scale-derived permanent magnet
International Nuclear Information System (INIS)
Woon, H.S.; Hashim, M.M.; Yahya, N.; Zakaria, A.; Lim, K.P.
2005-01-01
In the permanent magnet SrO-FeO-Fe 2 O 3 system, there exist several magnetically ordered compounds with a stable phase at room temperature. The most important are the M(SrFe 12 O 19 ), X(SrFe 15 O 23 ) and W(SrFe 18 O 27 ) phases with hexagonal close packed structure. In this project, M(SrFe 12 O 19 ) was prepared using mill scale, a steel-maker byproduct, as raw material. The Malaysia steel industry generates approximately 30,000 metric tons of waste products such as mill scale every year. Transportation and disposal of the byproducts are costly and the environmental regulations are becoming stricter. Hence, local steel mills are to find new ways to recycle the waste as a feedstock for the steel-making process or as a saleable product. The M(SrFe 12 O 19 ) was synthesized using the conventional ceramic process. The formation of the SrFe 12 O 19 was confirmed by X-ray diffraction. The magnetic properties such as the energy product (BH)max, coercive force (iHc) and remanence (Br) were also reported in this paper. (Author)
Scaling properties of planetary calderas and terrestrial volcanic eruptions
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L. Sanchez
2012-11-01
Full Text Available Volcanism plays an important role in transporting internal heat of planetary bodies to their surface. Therefore, volcanoes are a manifestation of the planet's past and present internal dynamics. Volcanic eruptions as well as caldera forming processes are the direct manifestation of complex interactions between the rising magma and the surrounding host rock in the crust of terrestrial planetary bodies. Attempts have been made to compare volcanic landforms throughout the solar system. Different stochastic models have been proposed to describe the temporal sequences of eruptions on individual or groups of volcanoes. However, comprehensive understanding of the physical mechanisms responsible for volcano formation and eruption and more specifically caldera formation remains elusive. In this work, we propose a scaling law to quantify the distribution of caldera sizes on Earth, Mars, Venus, and Io, as well as the distribution of calderas on Earth depending on their surrounding crustal properties. We also apply the same scaling analysis to the distribution of interevent times between eruptions for volcanoes that have the largest eruptive history as well as groups of volcanoes on Earth. We find that when rescaled with their respective sample averages, the distributions considered show a similar functional form. This result implies that similar processes are responsible for caldera formation throughout the solar system and for different crustal settings on Earth. This result emphasizes the importance of comparative planetology to understand planetary volcanism. Similarly, the processes responsible for volcanic eruptions are independent of the type of volcanism or geographical location.
Svartdal, Frode
2017-01-01
Procrastination has been defined in different ways. Two instruments--the Irrational Procrastination Scale (IPS) and the Pure Procrastination Scale (PPS)--focus on a core problem in procrastination--the irrational delay of intended behavior. The present paper examined the psychometric properties of the Norwegian translations of these scales. In…
Psychometric properties of the Chinese Internet Gaming Disorder Scale.
Sigerson, Leif; Li, Angel Y-L; Cheung, Mike W-L; Luk, Jeremy W; Cheng, Cecilia
2017-11-01
To develop a consensus on the definition and measurement of Internet gaming disorder (IGD), several recent studies have used the DSM-5's proposed criteria for IGD as the basis in scale construction. This study contributes to this emerging consensus by developing and validating a new Chinese Internet Gaming Disorder Scale (C-IGDS) based on the DSM-5 criteria. A representative sample of Hong Kong community adults (n=502, 50% men, mean age=37.1, age range=18-60) was recruited for a telephone survey with random digit dialing. Various statistical techniques were used to assess the psychometric properties of the C-IGDS. The C-IGDS had good reliability (Cronbach's α=0.91) and structural validity (CFA model fit: RMSEA=0.027, CFI=0.991, TLI=0.988) in our sample. Moderate to moderately strong correlations with depressive symptoms (r=0.617, pgaming hours (r=0.412, p<0.001) supported the criterion validity of the C-IGDS. In addition, the C-IGDS exhibited strict measurement invariance for sex and at least strong measurement invariance for age. In addition to providing the first Chinese scale for measuring IGD based on the DSM-5's proposed criteria, this study provides empirical support for the validity of these diagnostic criteria as the basis for a universal measure of IGD. Most important, this study is the first to reveal the criteria's measurement invariance, thereby indicating their suitability for use with diverse demographic groups. Copyright © 2017 Elsevier Ltd. All rights reserved.
Fractal Dimension Analysis of Subcortical Gray Matter Structures in Schizophrenia.
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Guihu Zhao
Full Text Available A failure of adaptive inference-misinterpreting available sensory information for appropriate perception and action-is at the heart of clinical manifestations of schizophrenia, implicating key subcortical structures in the brain including the hippocampus. We used high-resolution, three-dimensional (3D fractal geometry analysis to study subtle and potentially biologically relevant structural alterations (in the geometry of protrusions, gyri and indentations, sulci in subcortical gray matter (GM in patients with schizophrenia relative to healthy individuals. In particular, we focus on utilizing Fractal Dimension (FD, a compact shape descriptor that can be computed using inputs with irregular (i.e., not necessarily smooth surfaces in order to quantify complexity (of geometrical properties and configurations of structures across spatial scales of subcortical GM in this disorder. Probabilistic (entropy-based information FD was computed based on the box-counting approach for each of the seven subcortical structures, bilaterally, as well as the brainstem from high-resolution magnetic resonance (MR images in chronic patients with schizophrenia (n = 19 and age-matched healthy controls (n = 19 (age ranges: patients, 22.7-54.3 and healthy controls, 24.9-51.6 years old. We found a significant reduction of FD in the left hippocampus (median: 2.1460, range: 2.07-2.18 vs. median: 2.1730, range: 2.15-2.23, p<0.001; Cohen's effect size, U3 = 0.8158 (95% Confidence Intervals, CIs: 0.6316, 1.0, the right hippocampus (median: 2.1430, range: 2.05-2.19 vs. median: 2.1760, range: 2.12-2.21, p = 0.004; U3 = 0.8421 (CIs: 0.5263, 1, as well as left thalamus (median: 2.4230, range: 2.40-2.44, p = 0.005; U3 = 0.7895 (CIs: 0.5789, 0.9473 in schizophrenia patients, relative to healthy individuals. Our findings provide in-vivo quantitative evidence for reduced surface complexity of hippocampus, with reduced FD indicating a less complex, less regular GM surface detected in
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)
Iterons, fractals and computations of automata
Siwak, Paweł
1999-03-01
Processing of strings by some automata, when viewed on space-time (ST) diagrams, reveals characteristic soliton-like coherent periodic objects. They are inherently associated with iterations of automata mappings thus we call them the iterons. In the paper we present two classes of one-dimensional iterons: particles and filtrons. The particles are typical for parallel (cellular) processing, while filtrons, introduced in (32) are specific for serial processing of strings. In general, the images of iterated automata mappings exhibit not only coherent entities but also the fractals, and quasi-periodic and chaotic dynamics. We show typical images of such computations: fractals, multiplication by a number, and addition of binary numbers defined by a Turing machine. Then, the particles are presented as iterons generated by cellular automata in three computations: B/U code conversion (13, 29), majority classification (9), and in discrete version of the FPU (Fermi-Pasta-Ulam) dynamics (7, 23). We disclose particles by a technique of combinational recoding of ST diagrams (as opposed to sequential recoding). Subsequently, we recall the recursive filters based on FCA (filter cellular automata) window operators, and considered by Park (26), Ablowitz (1), Fokas (11), Fuchssteiner (12), Bruschi (5) and Jiang (20). We present the automata equivalents to these filters (33). Some of them belong to the class of filter automata introduced in (30). We also define and illustrate some properties of filtrons. Contrary to particles, the filtrons interact nonlocally in the sense that distant symbols may influence one another. Thus their interactions are very unusual. Some examples have been given in (32). Here we show new examples of filtron phenomena: multifiltron solitonic collisions, attracting and repelling filtrons, trapped bouncing filtrons (which behave like a resonance cavity) and quasi filtrons.
Dendritic design as an archetype for growth patterns in Nature: fractal and constructal views
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Antonio F. Miguel
2014-02-01
Full Text Available The occurrence of configuration (design, shape, structure, rhythm is a universal phenomenon that occurs in every flow system. Dendritic configuration (or tree-shaped configurations is ubiquitous in nature and likely to arise in both animate and inanimate flow systems. Why is it so important? Is there a principle from which this configuration can be deduced? In this review paper we show that these systems own two of the most important properties of fractals that are self-similarity and scaling. Their configuration do not develop by chance. It´s occurrence is a universal phenomenon of physics covered by a principle. Here we also show that the emergence of dendritic configuration in flow systems constitutes a basic supportive flow path along which order need to persist is propagated.
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP
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
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
Fractal Image Coding with Digital Watermarks
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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.
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.
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
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…
Chaos and fractals. Applications to nuclear engineering
International Nuclear Information System (INIS)
Clausse, A.; Delmastro, D.F.
1990-01-01
This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author) [es
Fractal behaviour of the seismicity in the Southern Iberian Peninsula
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X. Lana
2005-01-01
Full Text Available The fractal behaviour of the seismicity in the Southern Iberian Peninsula is analysed by considering two different series of data: the distance and the elapsed time between consecutive seismic events recorded by the seismic network of the Andalusian Institute of Geophysics (AIG. The fractal analyses have been repeated by considering four threshold magnitudes of 2.5, 3.0, 3.5 and 4.0. The re-scaled analysis lets to determine if the seismicity shows strong randomness or if it is characterised by time-persistence and the cluster dimension indicates the degree of time and spatial clustering of the seismicity. Another analysis, based on the reconstruction theorem, permits to evaluate the minimum number of nonlinear equations describing the dynamical mechanism of the seismicity, its 'loss of memory', its chaotic character and the instability of a possible predicting algorithm. The results obtained depict some differences depending on distances or elapsed times and the different threshold levels of magnitude also lead to slightly different results. Additionally, only a part of the fractal tools, the re-scaled analysis, have been applied to five seismic crises in the same area.
The Impact of The Fractal Paradigm on Geography
De Cola, L.
2001-12-01
Being itself somewhat fractal, Benoit Mandelbrot's magnum opus THE FRACTAL GEOMETRY OF NATURE may be deconstructed in many ways, including geometrically, systematically, and epistemologically. Viewed as a work of geography it may be used to organize the major topics of interest to scientists preoccupied with the understanding of real-world space in astronomy, geology, meteorology, hydrology, and biology. We shall use it to highlight such recent geographic accomplishments as automated feature detection, understanding urban growth, and modeling the spread of disease in space and time. However, several key challenges remain unsolved, among them: 1. It is still not possible to move continuously from one map scale to another so that objects change their dimension smoothly. I.e. as a viewer zooms in on a map the zero-dimensional location of a city should gradually become a 2-dimensional polygon, then a network of 1-dimensional streets, then 3-dimensional buildings, etc. 2. Spatial autocorrelation continues to be regarded more as an econometric challenge than as a problem of scaling. Similarities of values among closely-spaced observation is not so much a problem to be overcome as a source of information about spatial structure. 3. Although the fractal paradigm is a powerful model for data analysis, its ideas and techniques need to be brought to bear on the problems of understanding such hierarchies as ecosystems (the flow networks of energy and matter), taxonomies (biological classification), and knowledge (hierarchies of bureaucratic information, networks of linked data, etc).
Dielectric dispersion of porous media as a fractal phenomenon
Thevanayagam, S.
1997-09-01
It is postulated that porous media is made up of fractal solid skeleton structure and fractal pore surface. The model thus developed satisfies measured anomalous dielectric behavior of three distinctly different porous media: kaolin, montmorillonite, and shaly sand rock. It is shown that the underlying mechanism behind dielectric dispersion in the kHz range to high MHz range is indeed Maxwell-Wagner mechanism but modified to take into account the multiphase nature of the porous media as opposed to the traditional two-phase Maxwell-Wagner charge accumulation effect. The conductivity of the surface water associated with the solid surface and charge accumulation across the surface irregularities, asperity, and bridging between particles at the micro-scale-level pores are shown to contribute to this modified Maxwell-Wagner mechanism. The latter is dominant at low frequencies. The surface water thickness is calculated to be about 2-6 nm for a variety of porous media.
Characteristics of Pore Structure and Fractal Dimension of Isometamorphic Anthracite
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Di Gao
2017-11-01
Full Text Available The geologic conditions of No. 3 coal seams are similar to Sihe and Zhaozhuang Collieries, however, the gas production is significantly different. To better understand the effect of pores, by means of experimental measurements and quantitative analysis, the pore properties of high-rank isometamorphic anthracite were thoroughly studied. Our study showed that the pore structures were predominantly adsorptive, accounting for more than 88% of the specific surface area. The coal pores showed typical three-stage fractal characteristics at boundary points of 1 nm and 9 nm (7 nm of coal samples from Zhaozhuang Colliery, and the fractal dimension with 1–9 nm (or 1–7 nm, as being significantly larger than those measured outside the given ranges. Pores in samples from Sihe Colliery were mainly open spherical or ellipsoidal pores in shape; conversely, those from Zhaozhuang Colliery were mainly Y-shaped, V-shaped, or ‘ink-bottle’ type.
Fractal approach to computer-analytical modelling of tree crown
International Nuclear Information System (INIS)
Berezovskaya, F.S.; Karev, G.P.; Kisliuk, O.F.; Khlebopros, R.G.; Tcelniker, Yu.L.
1993-09-01
In this paper we discuss three approaches to the modeling of a tree crown development. These approaches are experimental (i.e. regressive), theoretical (i.e. analytical) and simulation (i.e. computer) modeling. The common assumption of these is that a tree can be regarded as one of the fractal objects which is the collection of semi-similar objects and combines the properties of two- and three-dimensional bodies. We show that a fractal measure of crown can be used as the link between the mathematical models of crown growth and light propagation through canopy. The computer approach gives the possibility to visualize a crown development and to calibrate the model on experimental data. In the paper different stages of the above-mentioned approaches are described. The experimental data for spruce, the description of computer system for modeling and the variant of computer model are presented. (author). 9 refs, 4 figs
Surface structures of equilibrium restricted curvature model on two fractal substrates
International Nuclear Information System (INIS)
Song Li-Jian; Tang Gang; Zhang Yong-Wei; Han Kui; Xun Zhi-Peng; Xia Hui; Hao Da-Peng; Li Yan
2014-01-01
With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature (ERC) model on Sierpinski arrowhead and crab substrates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension d f , but possess different dynamic exponents of random walk z rw . The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension d f , but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk z rw . The ERC model growing on the two substrates follows the well-known Family—Vicsek scaling law and satisfies the scaling relations 2α + d f ≍ z ≍ 2z rw . In addition, the values of the scaling exponents are in good agreement with the analytical prediction of the fractional Mullins—Herring equation. (general)
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
Stochastic self-similar and fractal universe
International Nuclear Information System (INIS)
Iovane, G.; Laserra, E.; Tortoriello, F.S.
2004-01-01
The structures formation of the Universe appears as if it were a classically self-similar random process at all astrophysical scales. An agreement is demonstrated for the present hypotheses of segregation with a size of astrophysical structures by using a comparison between quantum quantities and astrophysical ones. We present the observed segregated Universe as the result of a fundamental self-similar law, which generalizes the Compton wavelength relation. It appears that the Universe has a memory of its quantum origin as suggested by R. Penrose with respect to quasi-crystal. A more accurate analysis shows that the present theory can be extended from the astrophysical to the nuclear scale by using generalized (stochastically) self-similar random process. This transition is connected to the relevant presence of the electromagnetic and nuclear interactions inside the matter. In this sense, the presented rule is correct from a subatomic scale to an astrophysical one. We discuss the near full agreement at organic cell scale and human scale too. Consequently the Universe, with its structures at all scales (atomic nucleus, organic cell, human, planet, solar system, galaxy, clusters of galaxy, super clusters of galaxy), could have a fundamental quantum reason. In conclusion, we analyze the spatial dimensions of the objects in the Universe as well as space-time dimensions. The result is that it seems we live in an El Naschie's E-infinity Cantorian space-time; so we must seriously start considering fractal geometry as the geometry of nature, a type of arena where the laws of physics appear at each scale in a self-similar way as advocated long ago by the Swedish school of astrophysics
KILOPARSEC-SCALE PROPERTIES OF EMISSION-LINE GALAXIES
Energy Technology Data Exchange (ETDEWEB)
Hemmati, Shoubaneh; Miller, Sarah H.; Mobasher, Bahram; Nayyeri, Hooshang [University of California, Riverside, CA 92512 (United States); Ferguson, Henry C.; Koekemoer, Anton M. [Space Telescope Science Institute, Baltimore, MD 21218 (United States); Guo, Yicheng; Koo, David C. [UCO/Lick Observatory and Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064 (United States); Papovich, Casey, E-mail: shoubaneh.hemmati@ucr.edu [Texas A and M University, College Station, TX 77843 (United States)
2014-12-20
We perform a detailed study of the resolved properties of emission-line galaxies at kiloparsec scales to investigate how small-scale and global properties of galaxies are related. We use a sample of 119 galaxies in the GOODS fields. The galaxies are selected to cover a wide range in morphologies over the redshift range 0.2 < z < 1.3. High resolution spectroscopic data from Keck/DEIMOS observations are used to fix the redshift of all the galaxies in our sample. Using the HST/ACS and HST/WFC3 imaging data taken as a part of the CANDELS project, for each galaxy, we perform spectral energy distribution fitting per resolution element, producing resolved rest-frame U – V color, stellar mass, star formation rate (SFR), age, and extinction maps. We develop a technique to identify ''regions'' of statistical significance within individual galaxies, using their rest-frame color maps to select red and blue regions, a broader definition for what are called ''clumps'' in other works. As expected, for any given galaxy, the red regions are found to have higher stellar mass surface densities and older ages compared to the blue regions. Furthermore, we quantify the spatial distribution of red and blue regions with respect to both redshift and stellar mass, finding that the stronger concentration of red regions toward the centers of galaxies is not a significant function of either redshift or stellar mass. We find that the ''main sequence'' of star-forming galaxies exists among both red and blue regions inside galaxies, with the median of blue regions forming a tighter relation with a slope of 1.1 ± 0.1 and a scatter of ∼0.2 dex compared to red regions with a slope of 1.3 ± 0.1 and a scatter of ∼0.6 dex. The blue regions show higher specific SFRs (sSFRs) than their red counterparts with the sSFR decreasing since z ∼ 1, driven primarily by the stellar mass surface densities rather than the SFRs at a given
Small scale variability of snow properties on Antarctic sea ice
Wever, Nander; Leonard, Katherine; Paul, Stephan; Jacobi, Hans-Werner; Proksch, Martin; Lehning, Michael
2016-04-01
Snow on sea ice plays an important role in air-ice-sea interactions, as snow accumulation may for example increase the albedo. Snow is also able to smooth the ice surface, thereby reducing the surface roughness, while at the same time it may generate new roughness elements by interactions with the wind. Snow density is a key property in many processes, for example by influencing the thermal conductivity of the snow layer, radiative transfer inside the snow as well as the effects of aerodynamic forcing on the snowpack. By comparing snow density and grain size from snow pits and snow micro penetrometer (SMP) measurements, highly resolved density and grain size profiles were acquired during two subsequent cruises of the RV Polarstern in the Weddell Sea, Antarctica, between June and October 2013. During the first cruise, SMP measurements were done along two approximately 40 m transects with a horizontal resolution of approximately 30 cm. During the second cruise, one transect was made with approximately 7.5 m resolution over a distance of 500 m. Average snow densities are about 300 kg/m3, but the analysis also reveals a high spatial variability in snow density on sea ice in both horizontal and vertical direction, ranging from roughly 180 to 360 kg/m3. This variability is expressed by coherent snow structures over several meters. On the first cruise, the measurements were accompanied by terrestrial laser scanning (TLS) on an area of 50x50 m2. The comparison with the TLS data indicates that the spatial variability is exhibiting similar spatial patterns as deviations in surface topology. This suggests a strong influence from surface processes, for example wind, on the temporal development of density or grain size profiles. The fundamental relationship between variations in snow properties, surface roughness and changes therein as investigated in this study is interpreted with respect to large-scale ice movement and the mass balance.
Iron phosphate glasses: Bulk properties and atomic scale structure
Energy Technology Data Exchange (ETDEWEB)
Joseph, Kitheri; Stennett, Martin C.; Hyatt, Neil C.; Asuvathraman, R.; Dube, Charu L.; Gandy, Amy S.; Govindan Kutty, K. V.; Jolley, Kenny; Vasudeva Rao, P. R.; Smith, Roger
2017-10-01
Bulk properties such as glass transition temperature, density and thermal expansion of iron phosphate glass compositions, with replacement of Cs by Ba, are investigated as a surrogate for the transmutation of 137Cs to 137Ba, relevant to the immobilisation of Cs in glass. These studies are required to establish the appropriate incorporation rate of 137Cs in iron phosphate glass. Density and glass transition temperature increases with the addition of BaO indicating the shrinkage and reticulation of the iron phosphate glass network. The average thermal expansion coefficient reduces from 19.8 × 10-6 K-1 to 13.4 × 10-6 K-1, when 25 wt. % of Cs2O was replaced by 25 wt. % of BaO in caesium loaded iron phosphate glass. In addition to the above bulk properties, the role of Ba as a network modifier in the structure of iron phosphate glass is examined using various spectroscopic techniques. The FeII content and average coordination number of iron in the glass network was estimated using Mössbauer spectroscopy. The FeII content in the un-doped iron phosphate glass and barium doped iron phosphate glasses was 20, 21 and 22 ± 1% respectively and the average Fe coordination varied from 5.3 ± 0.2 to 5.7 ± 0.2 with increasing Ba content. The atomic scale structure was further probed by Fe K-edge X-ray absorption spectroscopy. The average coordination number provided by extended X-ray absorption fine structure spectroscopy and X-ray absorption near edge structure was in good agreement with that given by the Mössbauer data.
The Role of Resolution in the Estimation of Fractal Dimension Maps From SAR Data
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Gerardo Di Martino
2017-12-01
Full Text Available This work is aimed at investigating the role of resolution in fractal dimension map estimation, analyzing the role of the different surface spatial scales involved in the considered estimation process. The study is performed using a data set of actual Cosmo/SkyMed Synthetic Aperture Radar (SAR images relevant to two different areas, the region of Bidi in Burkina Faso and the city of Naples in Italy, acquired in stripmap and enhanced spotlight modes. The behavior of fractal dimension maps in the presence of areas with distinctive characteristics from the viewpoint of land-cover and surface features is discussed. Significant differences among the estimated maps are obtained in the presence of fine textural details, which significantly affect the fractal dimension estimation for the higher resolution spotlight images. The obtained results show that if we are interested in obtaining a reliable estimate of the fractal dimension of the observed natural scene, stripmap images should be chosen in view of both economic and computational considerations. In turn, the combination of fractal dimension maps obtained from stripmap and spotlight images can be used to identify areas on the scene presenting non-fractal behavior (e.g., urban areas. Along this guideline, a simple example of stripmap-spotlight data fusion is also presented.
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Alireza Keshavarzi
2017-07-01
Full Text Available In this study, the fractal dimensions of velocity fluctuations and the Reynolds shear stresses propagation for flow around a circular bridge pier are presented. In the study reported herein, the fractal dimension of velocity fluctuations (u′, v′, w′ and the Reynolds shear stresses (u′v′ and u′w′ of flow around a bridge pier were computed using a Fractal Interpolation Function (FIF algorithm. The velocity fluctuations of flow along a horizontal plane above the bed were measured using Acoustic Doppler Velocity meter (ADV and Particle Image Velocimetry (PIV. The PIV is a powerful technique which enables us to attain high resolution spatial and temporal information of turbulent flow using instantaneous time snapshots. In this study, PIV was used for detection of high resolution fractal scaling around a bridge pier. The results showed that the fractal dimension of flow fluctuated significantly in the longitudinal and transverse directions in the vicinity of the pier. It was also found that the fractal dimension of velocity fluctuations and shear stresses increased rapidly at vicinity of pier at downstream whereas it remained approximately unchanged far downstream of the pier. The higher value of fractal dimension was found at a distance equal to one times of the pier diameter in the back of the pier. Furthermore, the average fractal dimension for the streamwise and transverse velocity fluctuations decreased from the centreline to the side wall of the flume. Finally, the results from ADV measurement were consistent with the result from PIV, therefore, the ADV enables to detect turbulent characteristics of flow around a circular bridge pier.
FRACTAL ANALYSIS OF PHYSICAL ADSORPTION ON SURFACES OF ACID ACTIVATED BENTONITES FROM SERBIA
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Ljiljana Rožić
2008-11-01
Full Text Available Solid surfaces are neither ideally regular, that is, morphological and energeticcally homogeneous, nor are they fully irregular or fractal. Instead, real solid surfaces exhibit a limited degree of organization quantified by the fractal dimension, D. Fractal analysis was applied to investigate the effect of concentrations of HCl solutions on the structural and textural properties of chemically activated bentonite from southern Serbia. Acid treatment of bentonites is applied in order to remove impurities and various exchangeable cations from bentonite clay. Important physical changes in acid-activated smectite are the increase of the specific surface area and of the average pore volume, depending on acid strength, time and temperature of a treatment. On the basis of the sorption-structure analysis, the fractal dimension of the bentonite surfaces was determined by Mahnke and Mögel method. The fractal dimension evaluated by this method was 2.11 for the AB3 and 1.94 for the AB4.5 sample. The estimation of the values of the fractal dimension of activated bentonites was performed in the region of small pores, 0.5 nm < rp < 2 nm.
Ga-doped ZnO thin film surface characterization by wavelet and fractal analysis
Energy Technology Data Exchange (ETDEWEB)
Jing, Chenlei; Tang, Wu, E-mail: tang@uestc.edu.cn
2016-02-28
Graphical abstract: - Highlights: • Multi-resolution signal decomposition of wavelet transform is applied to Ga-doped ZnO thin films with various thicknesses. • Fractal properties of GZO thin films are investigated by box counting method. • Fractal dimension is not in conformity with original RMS roughness. • Fractal dimension mainly depends on the underside diameter (grain size) and distance between adjacent grains. - Abstract: The change in roughness of various thicknesses Ga-doped ZnO (GZO) thin films deposited by magnetron reactive sputtering on glass substrates at room temperature was measured by atomic force microscopy (AFM). Multi-resolution signal decomposition based on wavelet transform and fractal geometry was applied to process surface profiles, to evaluate the roughness trend of relevant frequency resolution. The results give a six-level decomposition and the results change with deposited time and surface morphology. Also, it is found that fractal dimension is closely connected to the underside diameter (grain size) and the distance between adjacent grains that affect the change rate of surface and the increase of the defects such as abrupt changes lead to a larger value of fractal dimension.
Fractal corrections of BaTiO3-ceramic sintering parameters
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Mitić V.V.
2014-01-01
Full Text Available Morphology of ceramics grains and pores as well as Brownian character of particle dynamics inside ceramics specimen contributes to better understanding of the sintering process. BaTiO3-ceramics, studied in this paper, has light fractal form and it is emanated in three aspects. First, the surface of grains, even in starting green body as well as distribution of grains shows fractal behavior. Second, existence of pores and their distribution follow the rules of fractal geometry. Third, movement of particles inside viscous flow underlies the rule of Brownian motion, which is essentially a fractal category. These three elements, each in its domain influence sintering dynamics, and can be described by dimensionless quantitative factors, αs αp and αm, being normalized to the interval [0,1]. Following sintering process, the associate formulae of Frenkel, Scherer and Mackenzie-Shuttleworth are shown from the angle of view of ceramics fractal dimension changing that approaches to 3. Also, it is shown that the energy balance is not violated after applying fractal correction to quasi equilibrium of the energy emanating from surface area reduction ES and energy adopted by viscous flow Ef .[Projekat Ministarstva nauke Republike Srbije, br. 172057: Directed synthesis, structure and properties of multifunctional materials
Time Series Analysis OF SAR Image Fractal Maps: The Somma-Vesuvio Volcanic Complex Case Study
Pepe, Antonio; De Luca, Claudio; Di Martino, Gerardo; Iodice, Antonio; Manzo, Mariarosaria; Pepe, Susi; Riccio, Daniele; Ruello, Giuseppe; Sansosti, Eugenio; Zinno, Ivana
2016-04-01
The fractal dimension is a significant geophysical parameter describing natural surfaces representing the distribution of the roughness over different spatial scale; in case of volcanic structures, it has been related to the specific nature of materials and to the effects of active geodynamic processes. In this work, we present the analysis of the temporal behavior of the fractal dimension estimates generated from multi-pass SAR images relevant to the Somma-Vesuvio volcanic complex (South Italy). To this aim, we consider a Cosmo-SkyMed data-set of 42 stripmap images acquired from ascending orbits between October 2009 and December 2012. Starting from these images, we generate a three-dimensional stack composed by the corresponding fractal maps (ordered according to the acquisition dates), after a proper co-registration. The time-series of the pixel-by-pixel estimated fractal dimension values show that, over invariant natural areas, the fractal dimension values do not reveal significant changes; on the contrary, over urban areas, it correctly assumes values outside the natural surfaces fractality range and show strong fluctuations. As a final result of our analysis, we generate a fractal map that includes only the areas where the fractal dimension is considered reliable and stable (i.e., whose standard deviation computed over the time series is reasonably small). The so-obtained fractal dimension map is then used to identify areas that are homogeneous from a fractal viewpoint. Indeed, the analysis of this map reveals the presence of two distinctive landscape units corresponding to the Mt. Vesuvio and Gran Cono. The comparison with the (simplified) geological map clearly shows the presence in these two areas of volcanic products of different age. The presented fractal dimension map analysis demonstrates the ability to get a figure about the evolution degree of the monitored volcanic edifice and can be profitably extended in the future to other volcanic systems with
International Nuclear Information System (INIS)
Guo Jing; Posnansky, Oleg; Hirsch, Sebastian; Scheel, Michael; Taupitz, Matthias; Sack, Ingolf; Braun, Juergen
2012-01-01
The dynamics of the complex shear modulus, G*, of soft biological tissue is governed by the rigidity and topology of multiscale mechanical networks. Multifrequency elastography can measure the frequency dependence of G* in soft biological tissue, providing information about the structure of tissue networks at multiple scales. In this study, the viscoelastic properties of structure-mimicking phantoms containing tangled paper stripes embedded in agarose gel are investigated by multifrequency magnetic resonance elastography within the dynamic range of 40–120 Hz. The effective media viscoelastic properties are analyzed in terms of the storage modulus (the real part of G*), the loss modulus (the imaginary part of G*) and the viscoelastic powerlaw given by the two-parameter springpot model. Furthermore, diffusion tensor imaging is used for investigating the effect of network structures on water mobility. The following observations were made: the random paper networks with fractal dimensions between 2.481 and 2.755 had no or minor effects on the storage modulus, whereas the loss modulus was significantly increased about 2.2 kPa per fractal dimension unit (R = 0.962, P < 0.01). This structural sensitivity of the loss modulus was significantly correlated with the springpot powerlaw exponent (0.965, P < 0.01), while for the springpot elasticity modulus, a trend was discernable (0.895, P < 0.05). No effect of the paper network on water diffusion was observed. The gel phantoms with embedded paper stripes presented here are a feasible way for experimentally studying the effect of network topology on soft-tissue viscoelastic parameters. In the dynamic range of in vivo elastography, the fractal network dimension primarily correlates to the loss behavior of soft tissue as can be seen from the loss modulus or the powerlaw exponent of the springpot model. These findings represent the experimental underpinning of structure-sensitive elastography for an improved characterization of
Psychometric Properties of the Parent-Infant Caregiving Touch Scale
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Artemis eKoukounari
2015-12-01
Full Text Available Recent work in animals suggests that the extent of early tactile stimulation by parents of offspring is an important element in early caregiving. We evaluate the psychometric properties of a new parent-report measure designed to assess frequency of tactile stimulation across multiple caregiving domains in infancy. We describe the full item set of the Parent-Infant Caregiving Touch Scale (PICTS and, using data from a UK longitudinal Child Health and Development Study, the response frequencies and factor structure and whether it was invariant over two time points in early development (5 and 9 weeks. When their infant was 9 weeks old, 838 mothers responded on the PICTS while a stratified subsample of 268 mothers completed PICTS at an earlier 5 week old assessment (229 responded on both occasions. Three PICTS factors were identified reflecting stroking, holding and affective communication. These were moderately to strongly correlated at each of the two time points of interest and were unrelated to, and therefore distinct from, a traditional measure of maternal sensitivity at 7-months. A wholly stable psychometry over 5 and 9-week assessments was not identified which suggests that behavior profiles differ slightly for younger and older infants. Tests of measurement invariance demonstrated that all three factors are characterized by full configural and metric invariance, as well as a moderate degree of evidence of scalar invariance for the stroking factor. We propose the PICTS as a valuable new measure of important aspects of caregiving in infancy.
Weighted Scale-Free Network Properties of Ecological Network
International Nuclear Information System (INIS)
Lee, Jae Woo; Maeng, Seong Eun
2013-01-01
We investigate the scale-free network properties of the bipartite ecological network, in particular, the plant-pollinator network. In plant-pollinator network, the pollinators visit the plant to get the nectars. In contrast to the other complex network, the plant-pollinator network has not only the trophic relationships among the interacting partners but also the complexities of the coevolutionary effects. The interactions between the plant and pollinators are beneficial relations. The plant-pollinator network is a bipartite and weighted network. The networks have two types of the nodes: plant and pollinator. We consider the visiting frequency of a pollinator to a plant as the weighting value of the link. We defined the strength of a node as the sum of the weighting value of the links. We reported the cumulative distribution function (CDF) of the degree and the strength of the plant-pollinator network. The CDF of the plants followed stretched exponential functions for both degree and strength, but the CDF of the pollinators showed the power law for both degree and strength. The average strength of the links showed the nonlinear dependence on the degree of the networks.
Fractales y series de datos geofísicos
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Montes Vides Luis Alfredo
1993-10-01
Full Text Available
There is a new Geometry which provides a potentially tool for the characterization of geophysical data: The Fractal Geometry. Generally, Geophysical data consist of records in time or data series, for example yearly records of temperature, and they show a random behavior or variation on both a short and a long-term time scale. The trace of a record is a curve with a fractal dimension D, and it is characterized by an exponent H. In this paper, the Hurt's rescaled range analysis method is used to determine the fractal dimension of a geophysical data serie D and H, his self-affinity measure.
La geometría de fractales ha surgido como una herramienta potencialmente útil para la caracterización de datos en Geofísica. Comúnmente, los datos geofísicos conforman series de tiempo, que exhiben un comportamiento aleatorio o variación a corto y a largo plazo. Un ejemplo típico son los registros anuales de temperatura. La traza de un registro es una curva con una dimensión fractal D, caracterizada por un exponente H.
En el presente trabajo se utiliza el método de análisis de rango en cambios de escala, creado por H. E. Hurst, para determinar la dimensión fractal de una serie de datos geofísicos, y su medida de auto-afinidad.
Phase space properties of local observables and structure of scaling limits
International Nuclear Information System (INIS)
Buchholz, D.
1995-05-01
For any given algebra of local observables in relativistic quantum field theory there exists an associated scaling algebra which permits one to introduce renormalization group transformations and to construct the scaling (short distance) limit of the theory. On the basis of this result it is discussed how the phase space properties of a theory determine the structure of its scaling limit. Bounds on the number of local degrees of freedom appearing in the scaling limit are given which allow one to distinguish between theories with classical and quantum scaling limits. The results can also be used to establish physically significant algebraic properties of the scaling limit theories, such as the split property. (orig.)
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…
Morphometric relations of fractal-skeletal based channel network model
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B. S. Daya Sagar
1998-01-01
Full Text Available A fractal-skeletal based channel network (F-SCN model is proposed. Four regular sided initiator-basins are transformed as second order fractal basins by following a specific generating mechanism with non-random rule. The morphological skeletons, hereafter referred to as channel networks, are extracted from these fractal basins. The morphometric and fractal relationships of these F-SCNs are shown. The fractal dimensions of these fractal basins, channel networks, and main channel lengths (computed through box counting method are compared with those of estimated length–area measures. Certain morphometric order ratios to show fractal relations are also highlighted.
International Nuclear Information System (INIS)
Jung, Kyu-Nam; Pyun, Su-Il
2006-01-01
The effect of pore structure on anomalous behaviour of the lithium intercalation into porous V 2 O 5 film electrode has been investigated in terms of fractal geometry by employing ac-impedance spectroscopy combined with N 2 gas adsorption method and atomic force microscopy (AFM). For this purpose, porous V 2 O 5 film electrodes with different pore structures were prepared by the polymer surfactant templating method. From the analysis of N 2 gas adsorption isotherms and the triangulation analysis of AFM images, it was found that porous V 2 O 5 surfaces exhibited self-similar scaling properties with different fractal dimensions depending upon amount of the polymer surfactant in solution and the spatial cut-off ranges. All the ac-impedance spectra measured on porous V 2 O 5 film electrodes showed the non-ideal behaviour of the charge-transfer reaction and the diffusion reaction, which resulted from the interfacial capacitance dispersion and the frequency dispersion of the diffusion impedance, respectively. From the comparison between the surface fractal dimensions by using N 2 gas adsorption method and AFM, and the analysis of ac-impedance spectra by employing a constant phase element (CPE), it is experimentally confirmed that the lithium intercalation into porous V 2 O 5 film electrode is crucially influenced by the pore surface irregularity and the film surface irregularity
Parsec-Scale Properties of Gamma-Ray Bright Blazars
Linford, Justin Dee
The parsec-scale radio properties of blazars detected by the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope have been investigated using observations with the Very Long Baseline Array (VLBA). Comparisons between LAT and non-LAT detected samples were made using both archival and contemporaneous data. In total, 244 sources were used in the LAT-detected sample. This very large, radio flux-limited sample of active galactic nuclei (AGN) provides insights into the mechanism that produces strong gamma-ray emission. It has been found that LAT-detected BL Lac objects are very similar to the non-LAT BL Lac objects in most properties, although LAT BL Lac objects may have longer jets. The LAT flat spectrum radio quasars (FSRQs) are significantly different from non-LAT FSRQs and are likely extreme members of the FSRQ population. Archival radio data indicated that there was no significant correlation between radio flux density and gamma-ray flux, especially at lower flux levels. However, contemporaneous observations showed a strong correlation. Most of the differences between the LAT and non-LAT populations are related to the cores of the sources, indicating that the gamma-ray emission may originate near the base of the jets (i.e., within a few pc of the central engine). There is some indication that LAT-detected sources may have larger jet opening angles than the non-LAT sources. Strong core polarization is significantly more common among the LAT sources, suggesting that gamma-ray emission is related to strong, uniform magnetic fields at the base of the jets of the blazars. Observations of sources in two epochs indicate that core fractional polarization was higher when the objects were detected by the LAT. The low-synchrotron peaked (LSP) BL Lac object sample shows indications of contamination by FSRQs which happen to have undetectable emission lines. There is evidence that the LSP BL Lac objects are more strongly beamed than the rest of the BL Lac
International Nuclear Information System (INIS)
Ul'yanov, A S; Lyapina, A M; Ulianova, O V; Fedorova, V A; Uianov, S S
2011-01-01
Specific statistical characteristics of biospeckles, emerging under the diffraction of coherent beams on the bacterial colonies, are studied. The dependence of the fractal dimensions of biospeckles on the conditions of both illumination and growth of the colonies is studied theoretically and experimentally. Particular attention is paid to the fractal properties of biospeckles, emerging under the scattering of light by the colonies of the vaccinal strain of the plague microbe. The possibility in principle to classify the colonies of Yersinia pestis EV NIIEG using the fractal dimension analysis is demonstrated. (optical technologies in biophysics and medicine)
Bisht, Konark; Klumpp, Stefan; Banerjee, Varsha; Marathe, Rahul
2017-11-01
A human pathogen, Neisseria gonorrhoeae (NG), moves on surfaces by attaching and retracting polymeric structures called Type IV pili. The tug-of-war between the pili results in a two-dimensional stochastic motion called twitching motility. In this paper, with the help of real-time NG trajectories, we develop coarse-grained models for their description. The fractal properties of these trajectories are determined and their influence on first passage time and formation of bacterial microcolonies is studied. Our main observations are as follows: (i) NG performs a fast ballistic walk on small time scales and a slow diffusive walk over long time scales with a long crossover region; (ii) there exists a characteristic persistent length lp*, which yields the fastest growth of bacterial aggregates or biofilms. Our simulations reveal that lp*˜L0.6 , where L ×L is the surface on which the bacteria move; (iii) the morphologies have distinct fractal characteristics as a consequence of the ballistic and diffusive motion of the constituting bacteria.
Fractal properties of critical invariant curves
International Nuclear Information System (INIS)
Hunt, B.R.; Yorke, J.A.; Khanin, K.M.; Sinai, Y.G.
1996-01-01
We examine the dimension of the invariant measure for some singular circle homeomorphisms for a variety of rotation numbers, through both the thermodynamic formalism and numerical computation. The maps we consider include those induced by the action of the standard map on an invariant curve at the critical parameter value beyond which the curve is destroyed. Our results indicate that the dimension is universal for a given type of singularity and rotation number, and that among all rotation numbers, the golden mean produces the largest dimension
Fractal Properties of the Financial Market
Czech Academy of Sciences Publication Activity Database
Vácha, Lukáš
4 15, č. 4 (2007), s. 49-55 ISSN 0572-3043 R&D Projects: GA ČR GD402/03/H057; GA ČR(CZ) GA402/06/1417 Institutional research plan: CEZ:AV0Z10750506 Keywords : Agents’ trading strategies * Heterogeneous agents model with stochastic memory * worst out algorithm * Mood change Subject RIV: BD - Theory of Information
Bifurcation and Fractal of the Coupled Logistic Map
Wang, Xingyuan; Luo, Chao
The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot-Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.
Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems
Agarwal, S.; Wettlaufer, J. S.
2014-12-01
We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.
Fractal dimensions from a 3-dimensional intermittency analysis in e+e- annihilation
International Nuclear Information System (INIS)
Behrend, H.J.; Criegee, L.; Field, J.H.; Franke, G.; Jung, H.; Meyer, J.; Podobrin, O.; Schroeder, V.; Winter, G.G.; Bussey, P.J.; Campbell, A.J.; Hendry, D.; Lumsdon, S.J.; Skillicorn, I.O.; Ahme, J.; Blobel, V.; Feindt, M.; Fenner, H.; Harjes, J.; Koehne, J.H.; Peters, J.H.; Spitzer, H.; Weihrich, T.; Boer, W. de; Buschhorn, G.; Grindhammer, G.; Gunderson, B.; Kiesling, C.; Kotthaus, R.; Kroha, H.; Lueers, D.; Oberlack, H.; Schacht, P.; Scholz, S.; Wiedenmann, W.; Davier, M.; Grivaz, J.F.; Haissinski, J.; Journe, V.; Le Diberder, F.; Veillet, J.J.; Cozzika, G.; Ducros, Y.; Alexander, G.; Beck, A.; Bella, G.; Grunhaus, J.; Klatchko, A.; Levy, A.; Milstene, C.
1990-10-01
The intermittency structure of multihadronic e + e - annihilation is analyzed by evaluating the factorial moments F 2 -F 5 in 3-dimensional Lorentz invariant phase space as a function of the resolution scale. We interpret our data in the language of fractal objects. It turns out that the fractal dimension depends on the resolution scale in a way that can be attributed to geometrical resolution effects and dynamical effects, such as the π 0 Dalitz decay. The LUND 7.2 hadronization model provides an excellent description of the data. There is no indication of unexplained multiplicity fluctuations in small phase space regions. (orig.)
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.
Lévy processes on a generalized fractal comb
Sandev, Trifce; Iomin, Alexander; Méndez, Vicenç
2016-09-01
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two-dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of the structure can destroy this Markovian transport. These effects can be described by the memory and spatial kernels. In particular, the fractal structure of the fingers, which is controlled by the spatial kernel in both the real and the Fourier spaces, leads to the Lévy processes (Lévy flights) and superdiffusion. This generalization of the fractional diffusion is described by the Riesz space fractional derivative. In the framework of this generalized fractal comb model, Lévy processes are considered, and exact solutions for the probability distribution functions are obtained in terms of the Fox H-function for a variety of the memory kernels, and the rate of the superdiffusive spreading is studied by calculating the fractional moments. For a special form of the memory kernels, we also observed a competition between long rests and long jumps. Finally, we considered the fractal structure of the fingers controlled by a Weierstrass function, which leads to the power-law kernel in the Fourier space. This is a special case, when the second moment exists for superdiffusion in this competition between long rests and long jumps.
Diagnosis of Lung Cancer by Fractal Analysis of Damaged DNA
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Hamidreza Namazi
2015-01-01
Full Text Available Cancer starts when cells in a part of the body start to grow out of control. In fact cells become cancer cells because of DNA damage. A DNA walk of a genome represents how the frequency of each nucleotide of a pairing nucleotide couple changes locally. In this research in order to study the cancer genes, DNA walk plots of genomes of patients with lung cancer were generated using a program written in MATLAB language. The data so obtained was checked for fractal property by computing the fractal dimension using a program written in MATLAB. Also, the correlation of damaged DNA was studied using the Hurst exponent measure. We have found that the damaged DNA sequences are exhibiting higher degree of fractality and less correlation compared with normal DNA sequences. So we confirmed this method can be used for early detection of lung cancer. The method introduced in this research not only is useful for diagnosis of lung cancer but also can be applied for detection and growth analysis of different types of cancers.
Lévy processes on a generalized fractal comb
International Nuclear Information System (INIS)
Sandev, Trifce; Iomin, Alexander; Méndez, Vicenç
2016-01-01
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two-dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of the structure can destroy this Markovian transport. These effects can be described by the memory and spatial kernels. In particular, the fractal structure of the fingers, which is controlled by the spatial kernel in both the real and the Fourier spaces, leads to the Lévy processes (Lévy flights) and superdiffusion. This generalization of the fractional diffusion is described by the Riesz space fractional derivative. In the framework of this generalized fractal comb model, Lévy processes are considered, and exact solutions for the probability distribution functions are obtained in terms of the Fox H -function for a variety of the memory kernels, and the rate of the superdiffusive spreading is studied by calculating the fractional moments. For a special form of the memory kernels, we also observed a competition between long rests and long jumps. Finally, we considered the fractal structure of the fingers controlled by a Weierstrass function, which leads to the power-law kernel in the Fourier space. This is a special case, when the second moment exists for superdiffusion in this competition between long rests and long jumps. (paper)
Chlordecone retention in the fractal structure of volcanic clay
International Nuclear Information System (INIS)
Woignier, Thierry; Clostre, Florence; Macarie, Hervé; Jannoyer, Magalie
2012-01-01
Highlights: ► Allophanic soils are highly polluted but less contaminant for cultivated vegetables. ► SAXS and TEM show the fractal structure of allophane aggregates at the nanoscale. ► Allophane aggregates play the role of a labyrinth which fixes and traps chlordecone. ► Allophane physical properties contribute to chlordecone retention in andosols. - Abstract: Chlordecone (CHLD), a soil and foodstuff pollutant, as well as an environmentally persistent organochlorine insecticide, was used intensively in banana fields. The chlordecone uptake of three crops was measured for two types of polluted soils: allophanic and non-allophanic. The uptake is lower for allophanic soils even if their chlordecone content is higher than with non-allophanic soils. The fractal structure of the allophane aggregates was characterized at the nanoscale by small angle X-rays scattering, pore size distribution and transmission electron microscopy. We showed that clay microstructures should be an important physico-chemical factor governing the fate of chlordecone in the environment. Allophanic clays result in two counterintuitive findings: higher contaminant trappings yet lower contaminant availability. We propose that this specific, tortuous structure, along with its associated low accessibility, partly explains the low availability of chlordecone confined in allophanic soils. Capsule The fractal and tortuous microstructure of allophane clay favours the chlordecone retention in soils and disfavours the crop uptake.
Energy Technology Data Exchange (ETDEWEB)
Lenormand, R.; Thiele, M.R. [Institut Francais du Petrole, Rueil Malmaison (France)
1997-08-01
The paper describes the method and presents preliminary results for the calculation of homogenized relative permeabilities
Seepage Characteristics Study on Power-Law Fluid in Fractal Porous Media
Directory of Open Access Journals (Sweden)
Meijuan Yun
2014-01-01
Full Text Available We present fractal models for the flow rate, velocity, effective viscosity, apparent viscosity, and effective permeability for power-law fluid based on the fractal properties of porous media. The proposed expressions realize the quantitative description to the relation between the properties of the power-law fluid and the parameters of the microstructure of the porous media. The model predictions are compared with related data and good agreement between them is found. The analytical expressions will contribute to the revealing of physical principles for the power-law fluid flow in porous media.
Singularity spectra of fractional Brownian motions as a multi-fractal
International Nuclear Information System (INIS)
Kim, T.S.; Kim, S.
2004-01-01
Fractional Brownian motion acts as a random process with statistical self-similarity in time and self-affinity in shape. From these properties, the complicated patterns can be suitably represented by it with a minimal parameter and less memory. By considering its statistical property through the power spectrum density we can see that this process is not stationary, even though its differential motion is stationary. So in this paper, by taking the wavelet transform instead of Fourier transformation we investigate its multi-fractal spectrum as a multi-fractal model
Undergraduate experiment with fractal diffraction gratings
International Nuclear Information System (INIS)
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 laboratories and compared with those obtained with conventional periodic gratings. It is shown that fractal gratings produce self-similar diffraction patterns which can be evaluated analytically. Good agreement is obtained between experimental and numerical results.
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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.
International Nuclear Information System (INIS)
Tokarev, M.V.; Aparin, A.A.; Zborovsky, I.
2014-01-01
The concept of z-scaling previously developed for analysis of inclusive reactions in proton-proton collisions is applied for description of processes with polarized protons at the planned Spin Physics Detector NICA in Dubna. A hypothesis of self-similarity and fractality of the proton spin structure is discussed. The possibilities to extract information on spin-dependent fractal dimensions of hadrons and fragmentation process from asymmetries and coefficients of polarization transfer are justified. The double longitudinal spin asymmetry A LL of π 0 -meson production and the coefficient of the polarization transfer D LL of Λ hyperon production in proton-proton collisions measured at RHIC are analyzed in the framework of z-scaling. The spin-dependent fractal dimensions of proton and fragmentation process with polarized Λ hyperon are estimated. A study of the spin-dependent constituent energy loss as a function of transverse momentum of the inclusive hadron and collision energy is suggested.
Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications
Directory of Open Access Journals (Sweden)
Alexandru Grigorovici
2017-03-01
Full Text Available In classical concepts, theoretical models are built assuming that the dynamics of the complex system’s stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more complicated. These difficulties can be overcome in a complementary approach, using the fractal concept and the corresponding non-differentiable theoretical model, such as the scale relativity theory or the extended scale relativity theory. Thus, using the last theory, fractal entropy through non-differentiable Lie groups was established and, moreover, the pairs generating mechanisms through fractal entanglement states were explained. Our model has implications in the dynamics of biological structures, in the form of the “chameleon-like” behavior of cholesterol.
International Nuclear Information System (INIS)
Barton, C.C.; Larsen, E.
1985-01-01
Fracture traces exposed on three 214- to 260-m 2 pavements in the same Miocene ash-flow tuff at Yucca Mountain, southwestern Nevada, have been mapped at a scale of 1:50. The maps are two-dimensional sections through the three-dimensional network of strata-bound fractures. All fractures with trace lengths greater than 0.20 m were mapped. The distribution of fracture-trace lengths is log-normal. The fractures do not exhibit well-defined sets based on orientation. Since fractal characterization of such complex fracture-trace networks may prove useful for modeling fracture flow and mechanical responses of fractured rock, an analysis of each of the three maps was done to test whether such networks are fractal. These networks proved to be fractal and the fractal dimensions (D) are tightly clustered (1.12, 1.14, 1.16) for three laterally separated pavements, even though visually the fracture networks appear quite different. The fractal analysis also indicates that the network patterns are scale independent over two orders of magnitude for trace lengths ranging from 0.20 to 25 m. 7 refs., 7 figs
Assessing the Psychometric Properties of Two Food Addiction Scales
Lemeshow, Adina; Gearhardt, Ashley; Genkinger, Jeanine; Corbin, William R.
2016-01-01
Background While food addiction is well accepted in popular culture and mainstream media, its scientific validity as an addictive behavior is still under investigation. This study evaluated the reliability and validity of the Yale Food Addiction Scale and Modified Yale Food Addiction Scale using data from two community-based convenience samples. Methods We assessed the internal and test-retest reliability of the Yale Food Addiction Scale and Modified Yale Food Addiction Scale, and estimated the sensitivity and negative predictive value of the Modified Yale Food Addiction Scale using the Yale Food Addiction Scale as the benchmark. We calculated Cronbach’s alphas and 95% confidence intervals (CIs) for internal reliability and Cohen’s Kappa coefficients and 95% CIs for test-retest reliability. Results Internal consistency (n=232) was marginal to good, ranging from α=0.63 to 0.84. The test-retest reliability (n=45) for food addiction diagnosis was substantial, with Kappa=0.73 (95% CI, 0.48–0.88) (Yale Food Addiction Scale) and 0.79 (95% CI, 0.66–1.00) (Modified Yale Food Addiction Scale). Sensitivity and negative predictive value for classifying food addiction status were excellent: compared to the Yale Food Addiction Scale, the Modified Yale Food Addiction Scale’s sensitivity was 92.3% (95% CI, 64%–99.8%), and the negative predictive value was 99.5% (95% CI, 97.5%–100%). Conclusions Our analyses suggest that the Modified Yale Food Addiction Scale may be an appropriate substitute for the Yale Food Addiction Scale when a brief measure is needed, and support the continued use of both scales to investigate food addiction. PMID:27623221
Directory of Open Access Journals (Sweden)
Xiang Niu
2015-12-01
Full Text Available Based on fractal theory, the fractal characteristics of soil particle size distribution (PSD and soil water retention curve (WRC under the five vegetation types were studied in the mountainous land of Northern China. Results showed that: (1 the fractal parameters of soil PSD and soil WRC varied greatly under each different vegetation type, with Quercus acutissima Carr. and Robina pseudoacacia Linn. mixed plantation (QRM > Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation (PPM > Pinus thunbergii Parl. (PTP > Juglans rigia Linn. (JRL > abandoned grassland (ABG; (2 the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL were significantly higher than that in ABG, and mixed forests (QRM and PPM were higher than that in pure forests (PTP and JRL; (3 the fractal dimension of soil was positively correlated with the silt and clay content but negatively correlated with the sand content; and (4 the fractal dimension of soil PSD was positively correlated with the soil WRC. These indicated that the fractal parameters of soil PSD and soil WRC could act as quantitative indices to reflect the physical properties of the soil, and could be used to describe the influences of the Return Farmland to Forests Projects on soil structure.
Niu, Xiang; Gao, Peng; Wang, Bing; Liu, Yu
2015-01-01
Based on fractal theory, the fractal characteristics of soil particle size distribution (PSD) and soil water retention curve (WRC) under the five vegetation types were studied in the mountainous land of Northern China. Results showed that: (1) the fractal parameters of soil PSD and soil WRC varied greatly under each different vegetation type, with Quercus acutissima Carr. and Robina pseudoacacia Linn. mixed plantation (QRM) > Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation (PPM) > Pinus thunbergii Parl. (PTP) > Juglans rigia Linn. (JRL) > abandoned grassland (ABG); (2) the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL) were significantly higher than that in ABG, and mixed forests (QRM and PPM) were higher than that in pure forests (PTP and JRL); (3) the fractal dimension of soil was positively correlated with the silt and clay content but negatively correlated with the sand content; and (4) the fractal dimension of soil PSD was positively correlated with the soil WRC. These indicated that the fractal parameters of soil PSD and soil WRC could act as quantitative indices to reflect the physical properties of the soil, and could be used to describe the influences of the Return Farmland to Forests Projects on soil structure. PMID:26633458
Model of fractal aggregates induced by shear
Directory of Open Access Journals (Sweden)
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.
A Parallel Approach to Fractal Image Compression
Lubomir Dedera
2004-01-01
The paper deals with a parallel approach to coding and decoding algorithms in fractal image compressionand presents experimental results comparing sequential and parallel algorithms from the point of view of achieved bothcoding and decoding time and effectiveness of parallelization.
Random walks of oriented particles on fractals
International Nuclear Information System (INIS)
Haber, René; Prehl, Janett; Hoffmann, Karl Heinz; Herrmann, Heiko
2014-01-01
Random walks of point particles on fractals exhibit subdiffusive behavior, where the anomalous diffusion exponent is smaller than one, and the corresponding random walk dimension is larger than two. This is due to the limited space available in fractal structures. Here, we endow the particles with an orientation and analyze their dynamics on fractal structures. In particular, we focus on the dynamical consequences of the interactions between the local surrounding fractal structure and the particle orientation, which are modeled using an appropriate move class. These interactions can lead to particles becoming temporarily or permanently stuck in parts of the structure. A surprising finding is that the random walk dimension is not affected by the orientation while the diffusion constant shows a variety of interesting and surprising features. (paper)
Multiscale properties of DNA primary structure: cross-scale correlations
International Nuclear Information System (INIS)
Altajskij, M.V.; Ivanov, V.V.; Polozov, R.V.
2000-01-01
Cross-scale correlations of wavelet coefficients of the DNA coding sequences are calculated and compared to that of the generated random sequence of the same length. The coding sequences are shown to have strong correlation between large and small scale structures, while random sequences have not
Small scale plasticity and compressive properties of composites
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
in the commercial finite element code Abaqus [3]. In addition, in a supplementary study, taken into account the length scale effect of the yielding behavior using a strain gradient dependent plasticity law [4] implemented as a user element [5], it is possible investigating the scale effect on the yielding behavior...
The Alzheimer's Disease Knowledge Scale: Development and Psychometric Properties
Carpenter, Brian D.; Balsis, Steve; Otilingam, Poorni G.; Hanson, Priya K.; Gatz, Margaret
2009-01-01
Purpose: This study provides preliminary evidence for the acceptability, reliability, and validity of the new Alzheimer's Disease Knowledge Scale (ADKS), a content and psychometric update to the Alzheimer's Disease Knowledge Test. Design and Methods: Traditional scale development methods were used to generate items and evaluate their psychometric…
Designing a fractal antenna of 2400 MHz
International Nuclear Information System (INIS)
Miranda Hamburger, Fabio
2012-01-01
The design of a fractal antenna with 2400 MHz of frequency has been studied. The fractal used is described by Waclaw Spierpi.ski. The initial figure, also known as seed, is divided using equilateral triangles with the aim of obtaining a perimeter similar to a meaningful portion of wave length. The use of λ to establish an ideal perimeter has reduced the radiation resistance. The adequate number of iterations needed to design the antenna is calculated based on λ. (author) [es
Fractal effects on excitations in diluted ferromagnets
International Nuclear Information System (INIS)
Kumar, D.
1981-08-01
The low energy spin-wave like excitations in diluted ferromagnets near percolation threshold are studied. For this purpose an explicit use of the fractal model for the backbone of the infinite percolating cluster due to Kirkpatrick is made. Three physical effects are identified, which cause the softening of spin-waves as the percolation point is approached. The importance of fractal effects in the calculation of density of states and the low temperature thermodynamics is pointed out. (author)
A fractal-like resistive network
International Nuclear Information System (INIS)
Saggese, A; De Luca, R
2014-01-01
The equivalent resistance of a fractal-like network is calculated by means of approaches similar to those employed in defining the equivalent resistance of an infinite ladder. Starting from an elementary triangular circuit, a fractal-like network, named after Saggese, is developed. The equivalent resistance of finite approximations of this network is measured, and the didactical implications of the model are highlighted. (paper)
International Nuclear Information System (INIS)
Lim, Sin Liang; Koo, Voon Chet; Daya Sagar, B.S.
2009-01-01
Multiscale convexity analysis of certain fractal binary objects-like 8-segment Koch quadric, Koch triadic, and random Koch quadric and triadic islands-is performed via (i) morphologic openings with respect to recursively changing the size of a template, and (ii) construction of convex hulls through half-plane closings. Based on scale vs convexity measure relationship, transition levels between the morphologic regimes are determined as crossover scales. These crossover scales are taken as the basis to segment binary fractal objects into various morphologically prominent zones. Each segmented zone is characterized through normalized morphologic complexity measures. Despite the fact that there is no notably significant relationship between the zone-wise complexity measures and fractal dimensions computed by conventional box counting method, fractal objects-whether they are generated deterministically or by introducing randomness-possess morphologically significant sub-zones with varied degrees of spatial complexities. Classification of realistic fractal sets and/or fields according to sub-zones possessing varied degrees of spatial complexities provides insight to explore links with the physical processes involved in the formation of fractal-like phenomena.
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.
Directory of Open Access Journals (Sweden)
Trajanović Nikola N.
2013-01-01
Full Text Available Introduction. Since inception of the alexithymia construct in 1970’s, there has been a continuous effort to improve both its theoretical postulates and the clinical utility through development, standardization and validation of assessment scales. Objective. The aim of this study was to validate the Serbian translation of the 20-item Toronto Alexithymia Scale (TAS-20 and to propose a new method of translation of scales with a property of temporal stability. Methods. The scale was expertly translated by bilingual medical professionals and a linguist, and given to a sample of bilingual participants from the general population who completed both the English and the Serbian version of the scale one week apart. Results. The findings showed that the Serbian version of the TAS-20 had a good internal consistency reliability regarding total scale (α=0.86, and acceptable reliability of the three factors (α=0.71-0.79. Conclusion. The analysis confirmed the validity and consistency of the Serbian translation of the scale, with observed weakness of the factorial structure consistent with studies in other languages. The results also showed that the method of utilizing a self-control bilingual subject is a useful alternative to the back-translation method, particularly in cases of linguistically and structurally sensitive scales, or in cases where a larger sample is not available. This method, dubbed as ‘forth-translation’, could be used to translate psychometric scales measuring properties which have temporal stability over the period of at least several weeks.
Laboratory investigation of constitutive property up-scaling in volcanic tuffs
International Nuclear Information System (INIS)
Tidwell, V.C.
1996-08-01
One of the critical issues facing the Yucca Mountain site characterization and performance assessment programs is the manner in which property up-scaling is addressed. Property up-scaling becomes an issue whenever heterogeneous media properties are measured at one scale but applied at another. A research program has been established to challenge current understanding of property up-scaling with the aim of developing and testing improved models that describe up-scaling behavior in a quantitative manner. Up-scaling of constitutive rock properties is investigated through physical experimentation involving the collection of suites of gas-permeability data measured over a range of discrete scales. To date, up-scaling studies have been performed on a series of tuff and sandstone (used as experimental controls) blocks. Samples include a welded, anisotropic tuff (Tiva Canyon Member of the Paintbrush Tuff, upper cliff microstratigraphic unit), and a moderately welded tuff (Tiva Canyon Member of the Paintbrush Tuff, Caprock microstratigraphic unit). A massive fluvial sandstone (Berea Sandstone) was also investigated as a means of evaluating the experimental program and to provide a point of comparison for the tuff data. Because unsaturated flow is of prime interest to the Yucca Mountain Program, scoping studies aimed at investigating the up-scaling of hydraulic properties under various saturated conditions were performed to compliment these studies of intrinsic permeability. These studies focused on matrix sorptivity, a constitutive property quantifying the capillarity of a porous medium. 113 refs
Psychometric properties of the Positive Mental Health Scale (PMH-scale)
Lukat, J.; Margraf, J.; Lutz, R.; Veld, W.M. van der; Becker, E.S.
2016-01-01
Background: In recent years, it has been increasingly recognized that the absence of mental disorder is not the same as the presence of positive mental health (PMH). With the PMH-scale we propose a short, unidimensional scale for the assessment of positive mental health. The scale consists of 9
Decoding the Margins: What Can the Fractal Geometry of Basaltic Flow Margins Tell Us?
Schaefer, E. I.; Hamilton, C.; Neish, C.; Beard, S. P.; Bramson, A. M.; Sori, M.; Rader, E. L.
2016-12-01
Studying lava flows on other planetary bodies is essential to characterizing eruption styles and constraining the bodies' thermal evolution. Although planetary basaltic flows are common, many key features are not resolvable in orbital imagery. We are thus developing a technique to characterize basaltic flow type, sub-meter roughness, and sediment mantling from these data. We will present the results from upcoming fieldwork at Craters of the Moon National Monument and Preserve with FINESSE (August) and at Hawai'i Volcanoes National Park (September). We build on earlier work that showed that basaltic flow margins are approximately fractal [Bruno et al., 1992; Gaonac'h et al., 1992] and that their fractal dimensions (D) have distinct `a`ā and pāhoehoe ranges under simple conditions [Bruno et al., 1994]. Using a differential GPS rover, we have recently shown that the margin of Iceland's 2014 Holuhraun flow exhibits near-perfect (R2=0.9998) fractality for ≥24 km across dm to km scales [Schaefer et al., 2016]. This finding suggests that a fractal-based technique has significant potential to characterize flows at sub-resolution scales. We are simultaneously seeking to understand how margin fractality can be modified. A preliminary result for an `a'ā flow in Hawaii's Ka'ū Desert suggests that although aeolian mantling obscures the original flow margin, the apparent margin (i.e., sediment-lava interface) remains fractal [Schaefer et al., 2015]. Further, the apparent margin's D is likely significantly modified from that of the original margin. Other factors that we are exploring include erosion, transitional flow types, and topographic confinement. We will also rigorously test the intriguing possibility that margin D correlates with the sub-meter Hurst exponent H of the flow surface, a common metric of roughness scaling [e.g., Shepard et al., 2001]. This hypothesis is based on geometric arguments [Turcotte, 1997] and is qualitatively consistent with all results so far.
Spatiotemporal property and predictability of large-scale human mobility
Zhang, Hai-Tao; Zhu, Tao; Fu, Dongfei; Xu, Bowen; Han, Xiao-Pu; Chen, Duxin
2018-04-01
Spatiotemporal characteristics of human mobility emerging from complexity on individual scale have been extensively studied due to the application potential on human behavior prediction and recommendation, and control of epidemic spreading. We collect and investigate a comprehensive data set of human activities on large geographical scales, including both websites browse and mobile towers visit. Numerical results show that the degree of activity decays as a power law, indicating that human behaviors are reminiscent of scale-free random walks known as Lévy flight. More significantly, this study suggests that human activities on large geographical scales have specific non-Markovian characteristics, such as a two-segment power-law distribution of dwelling time and a high possibility for prediction. Furthermore, a scale-free featured mobility model with two essential ingredients, i.e., preferential return and exploration, and a Gaussian distribution assumption on the exploration tendency parameter is proposed, which outperforms existing human mobility models under scenarios of large geographical scales.
On the Lipschitz condition in the fractal calculus
International Nuclear Information System (INIS)
Golmankhaneh, Alireza K.; Tunc, Cemil
2017-01-01
In this paper, the existence and uniqueness theorems are proved for the linear and non-linear fractal differential equations. The fractal Lipschitz condition is given on the F"α-calculus which applies for the non-differentiable function in the sense of the standard calculus. More, the metric spaces associated with fractal sets and about functions with fractal supports are defined to build fractal Cauchy sequence. Furthermore, Picard iterative process in the F"α-calculus which have important role in the numerical and approximate solution of fractal differential equations is explored. We clarify the results using the illustrative examples.
Band structures in fractal grading porous phononic crystals
Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin
2018-05-01
In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.
Fractal geometry and number theory complex dimensions of fractal strings and zeros of zeta functions
Lapidus, Michael L
1999-01-01
A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which ...