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
Separation in Data Mining Based on Fractal Nature of Data
Czech Academy of Sciences Publication Activity Database
Jiřina, Marcel; Jiřina jr., M.
2013-01-01
Roč. 3, č. 1 (2013), s. 44-60 ISSN 2225-658X Institutional support: RVO:67985807 Keywords : nearest neighbor * fractal set * multifractal * IINC method * correlation dimension Subject RIV: JC - Computer Hardware ; Software http://sdiwc.net/digital-library/separation-in-data-mining-based-on-fractal-nature-of-data.html
A fractal-based image encryption system
Abd-El-Hafiz, S. K.
2014-12-01
This study introduces a novel image encryption system based on diffusion and confusion processes in which the image information is hidden inside the complex details of fractal images. A simplified encryption technique is, first, presented using a single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved through several parameters: feedback delay, multiplexing and independent horizontal or vertical shifts. The effect of each parameter is studied separately and, then, they are combined to illustrate their influence on the encryption quality. The encryption quality is evaluated using different analysis techniques such as correlation coefficients, differential attack measures, histogram distributions, key sensitivity analysis and the National Institute of Standards and Technology (NIST) statistical test suite. The obtained results show great potential compared to other techniques.
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 ...
Energy Technology Data Exchange (ETDEWEB)
Kearney, M; Kochergin, V; Hess, R; Foust, T; Herbst, R; Mann, N
2005-03-31
Large-scale displacement of petroleum will come from low-cost cellulosic feedstocks such as straw and corn stover crop residues. This project has taken a step toward making this projection a reality by reducing capital and energy costs, the two largest cost factors associated with converting cellulosic biomass to chemicals and fuels. The technology exists for using acid or enzyme hydrolysis processes to convert biomass feedstock (i.e., waste cellulose such as straw, corn stover, and wood) into their base monomeric sugar building blocks, which can, in turn, be processed into chemicals and fuels using a number of innovative fermentation technologies. However, while these processes are technically possible, practical and economic barriers make these processes only marginally feasible or not feasible at all. These barriers are due in part to the complexity and large fixed and recurring capital costs of unit operations including filtration, chromatographic separation, and ion exchange. This project was designed to help remove these barriers by developing and implementing new purification and separation technologies that will reduce the capital costs of the purification and chromatographic separation units by 50% to 70%. The technologies fundamental to these improvements are: (a) highly efficient clarification and purification systems that use screening and membrane filtration to eliminate suspended solids and colloidal material from feed streams and (b) fractal technology based chromatographic separation and ion exchange systems that can substitute for conventional systems but at much smaller size and cost. A non-hazardous ''raw sugar beet juice'' stream (75 to 100 gal/min) was used for prototype testing of these technologies. This raw beet juice stream from the Amalgamated Sugar LLC plant in Twin Falls, Idaho contained abrasive materials and membrane foulants. Its characteristics were representative of an industrial-scale heterogeneous plant extract
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.
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.
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.
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
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.
Lectures on fractal geometry and dynamical systems
Pesin, Yakov
2009-01-01
Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular "chaotic" motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory--Cantor sets, Hausdorff dimension, box dimension--using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples o...
Fractal Structure and Entropy Production within the Central Nervous System
Directory of Open Access Journals (Sweden)
Andrew J. E. Seely
2014-08-01
Full Text Available Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS. Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer’s and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.
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...
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 fractal analysis of the public transportation system of Paris
L Benguigui
1995-01-01
An analysis of the railway networks of the public transportation system of Paris, based on the notion of fractals, is presented. The two basic networks, (metropolitan and suburban) which have different functions, have also a different fractal dimension: 1.8 for the metropolitan network, and 1.5 for the suburban network. By means of computer simulation, it is concluded that the true dimension of the metro network is probably 2.0. A fractal model of the suburban network, with the same features ...
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.
Fractal reactor: An alternative nuclear fusion system based on nature's geometry
International Nuclear Information System (INIS)
Siler, T. L.
2007-01-01
The author presents his concept of the Fractal Reactor, which explores the possibility of building a plasma fusion power reactor based on the real geometry of nature [fractals], rather than the virtual geometry that Euclid postulated around 330 BC; nearly every architect of our plasma fusion devices has been influenced by his three-dimensional geometry. The idealized points, lines, planes, and spheres of this classical geometry continue to be used to represent the natural world and to describe the properties of all geometrical objects, even though they neither accurately nor fully convey nature's structures and processes. The Fractal Reactor concept contrasts the current containment mechanisms of both magnetic and inertial containment systems for confining and heating plasmas. All of these systems are based on Euclidean geometry and use geometrical designs that, ultimately, are inconsistent with the Non-Euclidean geometry and irregular, fractal forms of nature (3). The author explores his premise that a controlled, thermonuclear fusion energy system might be more effective if it more closely embodies the physics of a star
Hyper-Fractal Analysis: A visual tool for estimating the fractal dimension of 4D objects
Grossu, I. V.; Grossu, I.; Felea, D.; Besliu, C.; Jipa, Al.; Esanu, T.; Bordeianu, C. C.; Stan, E.
2013-04-01
This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03) Catalogue identifier: AEEG_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 745761 No. of bytes in distributed program, including test data, etc.: 12544491 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 100M Classification: 14 Catalogue identifier of previous version: AEEG_v2_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831-832 Does the new version supersede the previous version? Yes Nature of problem: Estimating the fractal dimension of 4D images. Solution method: Optimized implementation of the 4D box-counting algorithm. Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images. The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files. A new form was added for generating 2D, 3D, and 4D test data. The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1). The algorithm could be extended, with minimum effort, to
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.
Efficient RF energy harvesting by using a fractal structured rectenna system
Oh, Sechang; Ramasamy, Mouli; Varadan, Vijay K.
2014-04-01
A rectenna system delivers, collects, and converts RF energy into direct current to power the electronic devices or recharge batteries. It consists of an antenna for receiving RF power, an input filter for processing energy and impedance matching, a rectifier, an output filter, and a load resistor. However, the conventional rectenna systems have drawback in terms of power generation, as the single resonant frequency of an antenna can generate only low power compared to multiple resonant frequencies. A multi band rectenna system is an optimal solution to generate more power. This paper proposes the design of a novel rectenna system, which involves developing a multi band rectenna with a fractal structured antenna to facilitate an increase in energy harvesting from various sources like Wi-Fi, TV signals, mobile networks and other ambient sources, eliminating the limitation of a single band technique. The usage of fractal antennas effects certain prominent advantages in terms of size and multiple resonances. Even though, a fractal antenna incorporates multiple resonances, controlling the resonant frequencies is an important aspect to generate power from the various desired RF sources. Hence, this paper also describes the design parameters of the fractal antenna and the methods to control the multi band frequency.
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.
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.
Low-voltage puzzle-like fractal microelectromechanial system variable capacitor suppressing pull-in
Elshurafa, Amro M.
2012-10-01
This Letter introduces an electrostatically actuated fractal MEMS variable capacitor that, by utilising the substrate, extends the tuning range (TR) beyond the theoretical limit of 1.5 as dictated by the pull-in phenomenon. The backbone concept behind the fractal varactor is to create a suspended movable plate possessing a specific fractal geometry, and to simultaneously create a bottom fixed plate complementary in shape to the top plate. Thus, when the top plate is actuated, it moves towards the bottom plate and fills the void present within the bottom plate without touching it akin to how puzzle pieces are assembled. Further, a reasonable horizontal separation is maintained between both the plates to avoid shorting. The electrostatic forces come from the capacitance formed between the top plate and bottom plate, and from the capacitance formed between the top plate and the doped substrate. The variable capacitor was fabricated in the PolyMUMPS process and provided a TR of 4.1 at 6 V, and its resonant frequency was in excess of 40 GHz.
Low-voltage puzzle-like fractal microelectromechanial system variable capacitor suppressing pull-in
Elshurafa, Amro M.; Ho, P.H.; Ouda, Mahmoud H.; Radwan, Ahmed Gomaa; Salama, Khaled N.
2012-01-01
This Letter introduces an electrostatically actuated fractal MEMS variable capacitor that, by utilising the substrate, extends the tuning range (TR) beyond the theoretical limit of 1.5 as dictated by the pull-in phenomenon. The backbone concept behind the fractal varactor is to create a suspended movable plate possessing a specific fractal geometry, and to simultaneously create a bottom fixed plate complementary in shape to the top plate. Thus, when the top plate is actuated, it moves towards the bottom plate and fills the void present within the bottom plate without touching it akin to how puzzle pieces are assembled. Further, a reasonable horizontal separation is maintained between both the plates to avoid shorting. The electrostatic forces come from the capacitance formed between the top plate and bottom plate, and from the capacitance formed between the top plate and the doped substrate. The variable capacitor was fabricated in the PolyMUMPS process and provided a TR of 4.1 at 6 V, and its resonant frequency was in excess of 40 GHz.
Fractal systems of central places based on intermittency of space-filling
International Nuclear Information System (INIS)
Chen Yanguang
2011-01-01
Highlights: → The idea of intermittency is introduced into central place model. → The revised central place model suggests incomplete space filling. → New central place fractals are presented for urban analysis. → The average nearest distance is proposed to estimate the fractal dimension. → The concept of distance-based space is replaced by that of dimension-based space. - Abstract: The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies. However, the underlying rationale of central place fractals in the real world has not yet been revealed so far. This paper is devoted to illustrating the mechanisms by which the fractal patterns can be generated from central place systems. The structural dimension of the traditional central place models is d = 2 indicating no intermittency in the spatial distribution of human settlements. This dimension value is inconsistent with empirical observations. Substituting the complete space filling with the incomplete space filling, we can obtain central place models with fractional dimension D < d = 2 indicative of spatial intermittency. Thus the conventional central place models are converted into fractal central place models. If we further integrate the chance factors into the improved central place fractals, the theory will be able to explain the real patterns of urban places very well. As empirical analyses, the US cities and towns are employed to verify the fractal-based models of central places.
A penalty guided stochastic fractal search approach for system reliability optimization
International Nuclear Information System (INIS)
Mellal, Mohamed Arezki; Zio, Enrico
2016-01-01
Modern industry requires components and systems with high reliability levels. In this paper, we address the system reliability optimization problem. A penalty guided stochastic fractal search approach is developed for solving reliability allocation, redundancy allocation, and reliability–redundancy allocation problems. Numerical results of ten case studies are presented as benchmark problems for highlighting the superiority of the proposed approach compared to others from literature. - Highlights: • System reliability optimization is investigated. • A penalty guided stochastic fractal search approach is developed. • Results of ten case studies are compared with previously published methods. • Performance of the approach is demonstrated.
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.
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.
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 analysis for heat extraction in geothermal system
Directory of Open Access Journals (Sweden)
Shang Xiaoji
2017-01-01
Full Text Available Heat conduction and convection play a key role in geothermal development. These two processes are coupled and influenced by fluid seepage in hot porous rock. A number of integer dimension thermal fluid models have been proposed to describe this coupling mechanism. However, fluid flow, heat conduction and convection in porous rock are usually non-linear, tortuous and fractal, thus the integer dimension thermal fluid flow models can not well describe these phenomena. In this study, a fractal thermal fluid coupling model is proposed to describe the heat conduction and flow behaviors in fractal hot porous rock in terms of local fractional time and space derivatives. This coupling equation is analytically solved through the fractal travelling wave transformation method. Analytical solutions of Darcy’s velocity, fluid temperature with fractal time and space are obtained. The solutions show that the introduction of fractional parameters is essential to describe the mechanism of heat conduction and convection.
Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics.
Rhea, Christopher K; Kiefer, Adam W; D'Andrea, Susan E; Warren, William H; Aaron, Roy K
2014-08-01
Fractal patterns characterize healthy biological systems and are considered to reflect the ability of the system to adapt to varying environmental conditions. Previous research has shown that fractal patterns in gait are altered following natural aging or disease, and this has potential negative consequences for gait adaptability that can lead to increased risk of injury. However, the flexibility of a healthy neurological system to exhibit different fractal patterns in gait has yet to be explored, and this is a necessary step toward understanding human locomotor control. Fifteen participants walked for 15min on a treadmill, either in the absence of a visual stimulus or while they attempted to couple the timing of their gait with a visual metronome that exhibited a persistent fractal pattern (contained long-range correlations) or a random pattern (contained no long-range correlations). The stride-to-stride intervals of the participants were recorded via analog foot pressure switches and submitted to detrended fluctuation analysis (DFA) to determine if the fractal patterns during the visual metronome conditions differed from the baseline (no metronome) condition. DFA α in the baseline condition was 0.77±0.09. The fractal patterns in the stride-to-stride intervals were significantly altered when walking to the fractal metronome (DFA α=0.87±0.06) and to the random metronome (DFA α=0.61±0.10) (both p<.05 when compared to the baseline condition), indicating that a global change in gait dynamics was observed. A variety of strategies were identified at the local level with a cross-correlation analysis, indicating that local behavior did not account for the consistent global changes. Collectively, the results show that a gait dynamics can be shifted in a prescribed manner using a visual stimulus and the shift appears to be a global phenomenon. Copyright © 2014 Elsevier B.V. All rights reserved.
Development of Fractal Pattern Making Application using L-System for Enhanced Machine Controller
Directory of Open Access Journals (Sweden)
Gunawan Alexander A S
2014-03-01
Full Text Available One big issue facing the industry today is an automated machine lack of flexibility for customization because it is designed by the manufacturers based on certain standards. In this research, it is developed customized application software for CNC (Computer Numerically Controlled machines using open source platform. The application is enable us to create designs by means of fractal patterns using L-System, developed by turtle geometry interpretation and Python programming languages. The result of the application is the G-Code of fractal pattern formed by the method of L-System. In the experiment on the CNC machine, the G-Code of fractal pattern which involving the branching structure has been able to run well.
Fractal Communication System Using Digital Signal Processing Starter Kit (DSK TMS320c6713
Directory of Open Access Journals (Sweden)
Arsyad Ramadhan Darlis
2015-12-01
Full Text Available In 1992, Wornell and Oppenheim did research on a modulation which is formed by using wavelet theory. In some other studies, proved that this modulation can survive on a few channels and has reliability in some applications. Because of this modulation using the concept of fractal, then it is called as fractalmodulation. Fractal modulation is formed by inserting information signal into fractal signals that are selffractal similary. This modulation technique has the potential to replace the OFDM (Orthogonal Frequency Division Multiplexing, which is currently used on some of the latest telecommunication technologies. The purpose of this research is to implement the fractal communication system using Digital Signal Processing Starter Kit (DSK TMS320C6713 without using AWGN and Rayleigh channel in order to obtain the ideal performance of the system. From the simulation results using MATLAB7.4. it appears that this communication system has good performance on some channels than any other communication systems. While in terms of implementation by using (DSK via TMS320C6713 Code Composer Studio (CCS, it can be concluded that thefractal communication system has a better execution time on some tests.
Fractal Dimension of Particle Showers Measured in a Highly Granular Calorimeter
Ruan, Manqi; Bourdy, Vincent; Brients, Jean-Claude; Videau, Henri
2014-01-01
fractal dimension of showers measured in a high granularity calorimeter designed for a future lepton collider. The shower fractal dimension reveals detailed information of the spatial configuration of the shower. It is found to be characteristic of the type of interaction and highly sensitive to the nature of the incident particle. Using the shower fractal dimension, we demonstrate a particle identification algorithm that can efficiently separate electromagnetic showers, hadronic showers and non-showering tracks. We also find a logarithmic dependence of the shower fractal dimension on the particle energy.
Irreducible fractal structures for Moran's theorems
Energy Technology Data Exchange (ETDEWEB)
Fernandez-Martinez, M.; Sanchez-Granero, M.A.
2017-07-01
Along this talk, we shall deal with a classical problem in Fractal Geometry consisting of the calculation of the similarity dimension of self-similar sets. Clasically, the open set condition has been understood as the right separation condition for IFS-attractors since it becomes a sufficient (though not necessary) condition allowing to easily calculate their similarity dimensions. However, it depends on an external open set. Our contribution consists of a novel separation condition for self-similar sets we shall characterize in terms of the natural fractal structure which any IFS-attractor can be endowed with. We justify that such a separation condition is weaker than the strong open set condition and allows to prove some Moran's type theorems. (Author)
Electron spin-lattice relaxation in fractals
International Nuclear Information System (INIS)
Shrivastava, K.N.
1986-08-01
We have developed the theory of the spin-fracton interaction for paramagnetic ions in fractal structures. The interaction is exponentially damped by the self-similarity length of the fractal and by the range dimensionality d Φ . The relaxation time of the spin due to the absorption and emission of the fracton has been calculated for a general dimensionality called the Raman dimensionality d R , which for the fractons differs from the Hausdorff (fractal) dimensionality, D, as well as from the Euclidean dimensionality, d. The exponent of the energy level separation in the relaxation rate varies with d R d Φ /D. We have calculated the spin relaxation rate due to a new type of Raman process in which one fracton is absorbed to affect a spin transition from one electronic level to another and later another fracton is emitted along with a spin transition such that the difference in the energies of the two fractons is equal to the electronic energy level separation. The temperature and the dimensionality dependence of such a process has been found in several approximations. In one of the approximations where the van Vleck relaxation rate for a spin in a crystal is known to vary with temperature as T 9 , our calculated variation for fractals turns out to be T 6.6 , whereas the experimental value for Fe 3+ in frozen solutions of myoglobin azide is T 6.3 . Since we used d R =4/3 and the fracton range dimensionality d Φ =D/1.8, we expect to measure the dimensionalities of the problem by measuring the temperature dependence of the relaxation times. We have also calculated the shift of the paramagnetic resonance transition for a spin in a fractal for general dimensionalities. (author)
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.
Visual tool for estimating the fractal dimension of images
Grossu, I. V.; Besliu, C.; Rusu, M. V.; Jipa, Al.; Bordeianu, C. C.; Felea, D.
2009-10-01
This work presents a new Visual Basic 6.0 application for estimating the fractal dimension of images, based on an optimized version of the box-counting algorithm. Following the attempt to separate the real information from "noise", we considered also the family of all band-pass filters with the same band-width (specified as parameter). The fractal dimension can be thus represented as a function of the pixel color code. The program was used for the study of paintings cracks, as an additional tool which can help the critic to decide if an artistic work is original or not. Program summaryProgram title: Fractal Analysis v01 Catalogue identifier: AEEG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 29 690 No. of bytes in distributed program, including test data, etc.: 4 967 319 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 30M Classification: 14 Nature of problem: Estimating the fractal dimension of images. Solution method: Optimized implementation of the box-counting algorithm. Use of a band-pass filter for separating the real information from "noise". User friendly graphical interface. Restrictions: Although various file-types can be used, the application was mainly conceived for the 8-bit grayscale, windows bitmap file format. Running time: In a first approximation, the algorithm is linear.
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.
Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga
2016-04-01
for the reservoir' hydraulic units distribution in space and time, as well as for the corresponding well testing data. References: 1. Mandelbrot, B., 1995. Foreword to Fractals in Petroleum Geology and Earth Processes, Edited by: Christopher C. Barton and Paul R. La Pointe, Plenum Press, New York: vii-xii. 2. Jin-Zhou Zhao, Cui-Cui Sheng, Yong_Ming Li, and Shun-Chu Li, 2015. A Mathematical Model for the Analysis of the Pressure Transient Response of Fluid Flow in Fractal Reservoir. J. of Chemistry, ID 596597, 8p. 3. Siler, T. , 2007. Fractal Reactor. International Conference Series on Emerging Nuclear Energy Systems 4. Corbett, P. W. M., 2012. The Role of Geoengineering in field development. INTECH, Chapter 8: 181- 198. 5. Nelson, P.H. and J. Kibler, 2003. A Catalog of Porosity and Permeability from core plugs in siliciclastic rocks. U.S. Geological Survey. 6. Per Bak and Kan Chen, 1989. The Physics of Fractals. Physica D 38: 5-12.
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)
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
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)
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.
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.
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.
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.
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
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....
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.
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 Shapes Description with Parametric L-systems and Turtle Algebra
Ikbal Zammouri; Béchir Ayeb
2007-01-01
In this paper, we propose a new method to describe fractal shapes using parametric l-systems. First we introduce scaling factors in the production rules of the parametric l-systems grammars. Then we decorticate these grammars with scaling factors using turtle algebra to show the mathematical relation between l-systems and iterated function systems (IFS). We demonstrate that with specific values of the scaling factors, we find the exact relationship established by Prusinkiewicz and Hammel betw...
Delay Bound: Fractal Traffic Passes through Network Servers
Directory of Open Access Journals (Sweden)
Ming Li
2013-01-01
Full Text Available Delay analysis plays a role in real-time systems in computer communication networks. This paper gives our results in the aspect of delay analysis of fractal traffic passing through servers. There are three contributions presented in this paper. First, we will explain the reasons why conventional theory of queuing systems ceases in the general sense when arrival traffic is fractal. Then, we will propose a concise method of delay computation for hard real-time systems as shown in this paper. Finally, the delay computation of fractal traffic passing through severs is presented.
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
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.)
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.
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...
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 analysis of fractures and microstructures in rocks
International Nuclear Information System (INIS)
Merceron, T.; Nakashima, S.; Velde, B.; Badri, A.
1991-01-01
Fractal geometry was used to characterize the distribution of fracture fields in rocks, which represent main pathways for material migration such as groundwater flow. Fractal investigations of fracture distribution were performed on granite along Auriat and Shikoku boreholes. Fractal dimensions range between 0.3 and 0.5 according to the different sets of fracture planes selected for the analyses. Shear, tension and compressional modes exhibit different fractal values while the composite fracture patterns are also fractal but with a different, median, fractal value. These observations indicate that the fractal method can be used to distinguish fracture types of different origins in a complex system. Fractal results for Shikoku borehole also correlate with geophysical parameters recorded along, drill-holes such as resistivity and possibly permeability. These results represent the first steps of the fractal investigation along drill-holes. Future studies will be conducted to verify relationships between fractal dimensions and permeability by using available geophysical data. Microstructures and microcracks were analysed in the Inada granite. Microcrack patterns are fractal but fractal dimensions values vary according to both mineral type and orientations of measurement within the mineral. Microcracks in quartz are characterized by more irregular distribution (average D = 0.40) than those in feldspars (D = 0.50) suggesting a different mode of rupture. Highest values of D are reported along main cleavage planes for feldspars or C axis for quartz. Further fractal investigations of microstructure in granite will be used to characterize the potential pathways for fluid migration and diffusion in the rock matrix. (author)
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 ...
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.
Fractal dimension estimations of drainage network in the Carpathian-Pannonian system.
Dombradi, E.; Timar, G.; Bada, G.; Cloetingh, S.A.P.L.; Horvath, F.
2007-01-01
The development of drainage network in the intra-Carpathian realm is influenced by a complex Quaternary tectonic evolution manifested with differential vertical motions. The present-day configuration of the left-hand side tributary system of the Tisza river was studied by means of fractal analysis.
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
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
FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY
Directory of Open Access Journals (Sweden)
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.
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...).
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
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.
International Conference and Workshop on Fractals and Wavelets
Barnsley, Michael; Devaney, Robert; Falconer, Kenneth; Kannan, V; PB, Vinod
2014-01-01
Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.
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.
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
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.
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.
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...
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
Generating a fractal butterfly Floquet spectrum in a class of driven SU(2) systems
Wang, Jiao; Gong, Jiangbin
2010-02-01
A scheme for generating a fractal butterfly Floquet spectrum, first proposed by Wang and Gong [Phys. Rev. A 77, 031405(R) (2008)], is extended to driven SU(2) systems such as a driven two-mode Bose-Einstein condensate. A class of driven systems without a link with the Harper-model context is shown to have an intriguing butterfly Floquet spectrum. The found butterfly spectrum shows remarkable deviations from the known Hofstadter’s butterfly. In addition, the level crossings between Floquet states of the same parity and between Floquet states of different parities are studied and highlighted. The results are relevant to studies of fractal statistics, quantum chaos, and coherent destruction of tunneling, as well as the validity of mean-field descriptions of Bose-Einstein condensates.
Generating a fractal butterfly Floquet spectrum in a class of driven SU(2) systems
International Nuclear Information System (INIS)
Wang Jiao; Gong Jiangbin
2010-01-01
A scheme for generating a fractal butterfly Floquet spectrum, first proposed by Wang and Gong [Phys. Rev. A 77, 031405(R) (2008)], is extended to driven SU(2) systems such as a driven two-mode Bose-Einstein condensate. A class of driven systems without a link with the Harper-model context is shown to have an intriguing butterfly Floquet spectrum. The found butterfly spectrum shows remarkable deviations from the known Hofstadter's butterfly. In addition, the level crossings between Floquet states of the same parity and between Floquet states of different parities are studied and highlighted. The results are relevant to studies of fractal statistics, quantum chaos, and coherent destruction of tunneling, as well as the validity of mean-field descriptions of Bose-Einstein condensates.
Namazi, Hamidreza; Kulish, Vladimir V.; Akrami, Amin
2016-05-01
One of the major challenges in vision research is to analyze the effect of visual stimuli on human vision. However, no relationship has been yet discovered between the structure of the visual stimulus, and the structure of fixational eye movements. This study reveals the plasticity of human fixational eye movements in relation to the ‘complex’ visual stimulus. We demonstrated that the fractal temporal structure of visual dynamics shifts towards the fractal dynamics of the visual stimulus (image). The results showed that images with higher complexity (higher fractality) cause fixational eye movements with lower fractality. Considering the brain, as the main part of nervous system that is engaged in eye movements, we analyzed the governed Electroencephalogram (EEG) signal during fixation. We have found out that there is a coupling between fractality of image, EEG and fixational eye movements. The capability observed in this research can be further investigated and applied for treatment of different vision disorders.
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
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.
Toward a new “Fractals-General Science”
Directory of Open Access Journals (Sweden)
Hassen Taher Dorrah
2014-09-01
Full Text Available A recent study has shown that everywhere real systems follow common “fractals-general stacking behavior” during their change pathways (or evolutionary life cycles. This fact leads to the emergence of the new discipline “Fractals-General Science” as a mother-discipline (and acting as upper umbrella of existing natural and applied sciences to commonly handle their fractals-general change behavior. It is, therefore, the main targets of this short communication are to present the motives, objectives, relations with other existing sciences, and the development map of such new science. It is discussed that there are many foreseen illustrative applications in geology, archeology, astronomy, life sciences, ecology, environmental science, hydrology, agronomy, engineering, materials sciences, chemistry, nanotechnology, biology, medicine, psychiatry, sociology, humanities, education, and arts that could effectively lead the implementation and experimentation of such new science. It is highlighted that the new “Fractals-General Science” could provide through multi-stacking representations the necessary platforms for investigating interactions and mutual changes between real life systems belonging to several sciences and disciplines. Examples are handling problems of the processing of basic formation and changes of matter and substances, propagation of combined corrosion, creep, fatigue and sedimentation of engineering and industrial systems, and the progressing of humans’ evolutionary life cycles.
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)
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.
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.
International Conference on Advances of Fractals and Related Topics
Lau, Ka-Sing
2014-01-01
This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.
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
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...
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 ...
Design of silicon-based fractal antennas
Ghaffar, Farhan A.
2012-11-20
This article presents Sierpinski carpet fractal antennas implemented in conventional low resistivity (Ï =10 Ω cm) as well as high resistivity (Ï =1500 Ω cm) silicon mediums. The fractal antenna is 36% smaller as compared with a typical patch antenna at 24 GHz and provides 13% bandwidth on high resistivity silicon, suitable for high data rate applications. For the first time, an on-chip fractal antenna array is demonstrated in this work which provides double the gain of a single fractal element as well as enhanced bandwidth. A custom test fixture is utilized to measure the radiation pattern and gain of these probe-fed antennas. In addition to gain and impedance characterization, measurements have also been made to study intrachip communication through these antennas. The comparison between the low resistivity and high resistivity antennas indicate that the former is not a suitable medium for array implementation and is only suitable for short range communication whereas the latter is appropriate for short and medium range wireless communication. The design is well-suited for compact, high data rate System-on-Chip (SoC) applications as well as for intrachip communication such as wireless global clock distribution in synchronous systems. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:180-186, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27245 Copyright © 2012 Wiley Periodicals, Inc.
Design of silicon-based fractal antennas
Ghaffar, Farhan A.; Shamim, Atif
2012-01-01
This article presents Sierpinski carpet fractal antennas implemented in conventional low resistivity (Ï =10 Ω cm) as well as high resistivity (Ï =1500 Ω cm) silicon mediums. The fractal antenna is 36% smaller as compared with a typical patch antenna at 24 GHz and provides 13% bandwidth on high resistivity silicon, suitable for high data rate applications. For the first time, an on-chip fractal antenna array is demonstrated in this work which provides double the gain of a single fractal element as well as enhanced bandwidth. A custom test fixture is utilized to measure the radiation pattern and gain of these probe-fed antennas. In addition to gain and impedance characterization, measurements have also been made to study intrachip communication through these antennas. The comparison between the low resistivity and high resistivity antennas indicate that the former is not a suitable medium for array implementation and is only suitable for short range communication whereas the latter is appropriate for short and medium range wireless communication. The design is well-suited for compact, high data rate System-on-Chip (SoC) applications as well as for intrachip communication such as wireless global clock distribution in synchronous systems. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:180-186, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27245 Copyright © 2012 Wiley Periodicals, Inc.
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.
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)
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.
Fractal aspects and convergence of Newton`s method
Energy Technology Data Exchange (ETDEWEB)
Drexler, M. [Oxford Univ. Computing Lab. (United Kingdom)
1996-12-31
Newton`s Method is a widely established iterative algorithm for solving non-linear systems. Its appeal lies in its great simplicity, easy generalization to multiple dimensions and a quadratic local convergence rate. Despite these features, little is known about its global behavior. In this paper, we will explain a seemingly random global convergence pattern using fractal concepts and show that the behavior of the residual is entirely explicable. We will also establish quantitative results for the convergence rates. Knowing the mechanism of fractal generation, we present a stabilization to the orthodox Newton method that remedies the fractal behavior and improves convergence.
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 ...
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.
Fractal growth in impurity-controlled solidification in lipid monolayers
DEFF Research Database (Denmark)
Fogedby, Hans C.; Sørensen, Erik Schwartz; Mouritsen, Ole G.
1987-01-01
A simple two-dimensional microscopic model is proposed to describe solidifcation processes in systems with impurities which are miscible only in the fluid phase. Computer simulation of the model shows that the resulting solids are fractal over a wide range of impurity concentrations and impurity...... diffusional constants. A fractal-forming mechanism is suggested for impurity-controlled solidification which is consistent with recent experimental observations of fractal growth of solid phospholipid domains in monolayers. The Journal of Chemical Physics is copyrighted by The American Institute of Physics....
Fractal 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.
Directory of Open Access Journals (Sweden)
Giuseppe Vitiello
2014-05-01
Full Text Available In electrodynamics there is a mutual exchange of energy and momentum between the matter field and the electromagnetic field and the total energy and momentum are conserved. For a constant magnetic field and harmonic scalar potential, electrodynamics is shown to be isomorph to a system of damped/amplified harmonic oscillators. These can be described by squeezed coherent states which in turn are isomorph to self-similar fractal structures. Under the said conditions of constant magnetic field and harmonic scalar potential, electrodynamics is thus isomorph to fractal self-similar structures and squeezed coherent states. At a quantum level, dissipation induces noncommutative geometry with the squeezing parameter playing a relevant role. Ubiquity of fractals in Nature and relevance of coherent states and electromagnetic interaction point to a unified, integrated vision of Nature.
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
International Nuclear Information System (INIS)
Zivic, I.; Elezovic-Hadzic, S.; Milosevic, S.
2009-01-01
We study the polymer system consisting of two-polymer chains situated in a fractal container that belongs to the three-dimensional Sierpinski Gasket (3D SG) family of fractals. The two-polymer system is modeled by two interacting self-avoiding walks (SAW) immersed in a good solvent. To conceive the inter-chain interactions we apply the model of two crossing self-avoiding walks (CSAW) in which the chains can cross each other. By applying renormalization group (RG) method, we establish the relevant phase diagrams for b=2 and b=3 members of the 3D SG fractal family. Also, at the appropriate transition fixed points we calculate the contact critical exponents φ, associated with the number of contacts between monomers of different chains. For larger b(2≤b≤30) we apply Monte Carlo renormalization group (MCRG) method, and compare the obtained results for φ with phenomenological proposals for the contact critical exponent, as well as with results obtained for other similar models of two-polymer system.
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 and chaotic laws on seismic dissipated energy in an energy system of engineering structures
Cui, Yu-Hong; Nie, Yong-An; Yan, Zong-Da; Wu, Guo-You
1998-09-01
Fractal and chaotic laws of engineering structures are discussed in this paper, it means that the intrinsic essences and laws on dynamic systems which are made from seismic dissipated energy intensity E d and intensity of seismic dissipated energy moment I e are analyzed. Based on the intrinsic characters of chaotic and fractal dynamic system of E d and I e, three kinds of approximate dynamic models are rebuilt one by one: index autoregressive model, threshold autoregressive model and local-approximate autoregressive model. The innate laws, essences and systematic error of evolutional behavior I e are explained over all, the short-term behavior predictability and long-term behavior probability of which are analyzed in the end. That may be valuable for earthquake-resistant theory and analysis method in practical engineering structures.
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
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.
Fractal Metrology for biogeosystems analysis
Directory of Open Access Journals (Sweden)
V. Torres-Argüelles
2010-11-01
Full Text Available The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc. while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM. We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
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.
Vortex-ring-fractal Structure of Atom and Molecule
International Nuclear Information System (INIS)
Osmera, Pavel
2010-01-01
This chapter is an attempt to attain a new and profound model of the nature's structure using a vortex-ring-fractal theory (VRFT). Scientists have been trying to explain some phenomena in Nature that have not been explained so far. The aim of this paper is the vortex-ring-fractal modeling of elements in the Mendeleev's periodic table, which is not in contradiction to the known laws of nature. We would like to find some acceptable structure model of the hydrogen as a vortex-fractal-coil structure of the proton and a vortex-fractal-ring structure of the electron. It is known that planetary model of the hydrogen atom is not right, the classical quantum model is too abstract. Our imagination is that the hydrogen is a levitation system of the proton and the electron. Structures of helium, oxygen, and carbon atoms and a hydrogen molecule are presented too.
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
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.
Infrared Image Segmentation by Combining Fractal Geometry with Wavelet Transformation
Directory of Open Access Journals (Sweden)
Xionggang Tu
2014-11-01
Full Text Available An infrared image is decomposed into three levels by discrete stationary wavelet transform (DSWT. Noise is reduced by wiener filter in the high resolution levels in the DSWT domain. Nonlinear gray transformation operation is used to enhance details in the low resolution levels in the DSWT domain. Enhanced infrared image is obtained by inverse DSWT. The enhanced infrared image is divided into many small blocks. The fractal dimensions of all the blocks are computed. Region of interest (ROI is extracted by combining all the blocks, which have similar fractal dimensions. ROI is segmented by global threshold method. The man-made objects are efficiently separated from the infrared image by the proposed method.
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.
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....
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.
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)
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
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.
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.
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...
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.
Automatic generation of aesthetic patterns on fractal tilings by means of dynamical systems
International Nuclear Information System (INIS)
Chung, K.W.; Ma, H.M.
2005-01-01
A fractal tiling or f-tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. In this paper, we investigate the classification of fractal tilings with kite-shaped and dart-shaped prototiles from which three new f-tilings are found. Invariant mappings are constructed for the creation of aesthetic patterns on such tilings. A modified convergence time scheme is described, which reflects the rate of convergence of various orbits and at the same time, enhances the artistic appeal of a generated image. A scheme based on the frequency of visit at a pixel is used to generate chaotic attractors
Fractal-Based Image Analysis In Radiological Applications
Dellepiane, S.; Serpico, S. B.; Vernazza, G.; Viviani, R.
1987-10-01
We present some preliminary results of a study aimed to assess the actual effectiveness of fractal theory and to define its limitations in the area of medical image analysis for texture description, in particular, in radiological applications. A general analysis to select appropriate parameters (mask size, tolerance on fractal dimension estimation, etc.) has been performed on synthetically generated images of known fractal dimensions. Moreover, we analyzed some radiological images of human organs in which pathological areas can be observed. Input images were subdivided into blocks of 6x6 pixels; then, for each block, the fractal dimension was computed in order to create fractal images whose intensity was related to the D value, i.e., texture behaviour. Results revealed that the fractal images could point out the differences between normal and pathological tissues. By applying histogram-splitting segmentation to the fractal images, pathological areas were isolated. Two different techniques (i.e., the method developed by Pentland and the "blanket" method) were employed to obtain fractal dimension values, and the results were compared; in both cases, the appropriateness of the fractal description of the original images was verified.
Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.; de Melo, N.; Skea, J. E. F.
2012-09-01
, this version of the package only deals with systems of first-order differential equations. Unusual features This package provides user-friendly software tools for analyzing the character of a dynamical system, whether it displays chaotic behaviour, and so on. Options within the package allow the user to specify characteristics that separate the trajectories into families of curves. In conjunction with the facilities for altering the user's viewpoint, this provides a graphical interface for the speedy and easy identification of regions with interesting dynamics. An unusual characteristic of the package is its interface for performing the numerical integrations in C using a fifth-order Runge-Kutta method (default). This potentially improves the speed of the numerical integration by some orders of magnitude and, in cases where it is necessary to calculate thousands of graphs in regions of difficult integration, this feature is very desirable. Besides that tool, somewhat more experienced users can produce their own C integrator and, by using the commands available in the package, use it as the C integrator provided with the package as long as the new integrator manages the input and output in the same format as the default one does. Running time This depends strongly on the dynamical system. With an Intel® Core™ i3 CPU M330 @ 2.13 GHz, the integration of 50 graphs, for a system of two first-order equations, typically takes less than a second to run (with the C integration interface). Without the C interface, it takes a few seconds. In order to calculate the fractal dimension, where we typically use 10,000 points to integrate, using the C interface it takes from 20 to 30 s. Without the C interface, it becomes really impractical, taking, sometimes, for the same case, almost an hour. For some cases, it takes many hours.
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
Fractal character of structural control on uranium mineralization in south china
International Nuclear Information System (INIS)
Zhou Quanyu; Tan Kaixuan; Xie Yanshi
2009-01-01
South China is the most important uranium producer in the country. Most uranium ore deposits in south China are strictly controlled by NE-NNE trending regional fracture structure. Fractal analyses on spatial distribution of uranium ore deposits and regional fracture structure in south China have been done in this paper. It indicates that the spatial distribution of both uranium ore deposits and regional fracture structure in south China show fractal character. The fractal dimension D=1.414 2 for the spatial distribution of regional fracture structure in the whole area indicate a higher ripening degree in the fracture structure evolution and an advantages to fluid flow and uranium mineralization. The fractal dimension D=1.052 7 for the spatial distribution of uranium ore deposits in south China show a lower complexity than regional fracture structure. The fractal dimensions in three sub-areas in south China on spatial distribution of uranium ore deposits show a positive correlation to which of regional fracture structure. The fractal spatial distribution of uranium ore deposits in south China is the result of the evolution of the fractal fracture structure system. (authors)
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.
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
Launching the chaotic realm of iso-fractals: A short remark
Energy Technology Data Exchange (ETDEWEB)
O' Schmidt, Nathan [Department of Mathematics, Boise State University, 1910 University Drive, Boise, ID 83725 (United States); Katebi, Reza [Department of Physics, California State University in Fullerton, 800 North State College Boulevard, Fullerton, CA 92831 (United States); Corda, Christian [Institute for Theoretical Physics and Advanced Mathematics Einstein-Galilei (IFM), Via Santa Gonda 14, 59100 Prato (Italy)
2015-03-10
In this brief note, we introduce the new, emerging sub-discipline of iso-fractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, non-linear, and self-similar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the iso-fractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot iso-sets. Third, we present the cutting-edge notion of dynamic iso-spaces and explain how a mathematical space can be iso-topically lifted with iso-unit functions that (continuously or discretely) change; in the discrete case examples, we mention that iteratively generated sequences like Fibonacci’s numbers and (the complex moduli of) Mandelbrot’s numbers can supply a deterministic chain of iso-units to construct an ordered series of (magnified and/or de-magnified) iso-spaces that are locally iso-morphic. Fourth, we consider the initiation of iso-fractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D iso-spaces. In total, the reviewed iso-fractal results are a significant improvement over traditional fractals because the application of Santilli’s iso-mathematics arms us an extra degree of freedom for attacking problems in chaos. Finally, we conclude by proposing some questions and ideas for future research work.
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
Energy Technology Data Exchange (ETDEWEB)
Clausse, A; Delmastro, D F
1991-12-31
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). [Espanol] En este trabajo se presenta una descripcion de las lineas de investigacion que los autores estan llevando a cabo en teoria de caos y fractales orientadas al campo nuclear. Es de especial importancia las posibilidades que se abren en el area de la seguridad nuclear, en donde la informacion proveniente de las tecnicas de caos y fractales pueden ayudar al desarrollo de mejores criterios y disenos mas confiables. (Autor).
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.
An Allometric Algorithm for Fractal-Based Cobb-Douglas Function of Geographical Systems
Directory of Open Access Journals (Sweden)
Hongyu Luo
2014-01-01
Full Text Available The generalized Cobb-Douglas production function has been derived from a general input-output relation based on fractality assumptions. It was proved to be a useful self-affine model for geographical analysis. However, the ordinary least square calculation is always an ineffectual method for the Cobb-Douglas modeling because of the multicollinearity in the logarithmic linear regression. In this paper, a novel approach is proposed to build the geographical Cobb-Douglas models. Combining the concept of allometric scaling with the linear regression technique, we obtain a simple algorithm that can be employed to estimate the parameters of the Cobb-Douglas function. As a case, the algorithm and models are applied to the public transportation of China’s cities, and the results validate the allometric algorithm. A conclusion can be drawn that the allometric analysis is an effective way of modeling geographical systems with the general Cobb-Douglas function. This study is significant for integrating the notions of allometry, fractals, and scaling into a new framework to form a quantitative methodology of spatial analysis.
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.
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 analysis of bone architecture at distal radius
International Nuclear Information System (INIS)
Tomomitsu, Tatsushi; Mimura, Hiroaki; Murase, Kenya; Sone, Teruki; Fukunaga, Masao
2005-01-01
Bone strength depends on bone quality (architecture, turnover, damage accumulation, and mineralization) as well as bone mass. In this study, human bone architecture was analyzed using fractal image analysis, and the clinical relevance of this method was evaluated. The subjects were 12 healthy female controls and 16 female patients suspected of having osteoporosis (age range, 22-70 years; mean age, 49.1 years). High-resolution CT images of the distal radius were acquired and analyzed using a peripheral quantitative computed tomography (pQCT) system. On the same day, bone mineral densities of the lumbar spine (L-BMD), proximal femur (F-BMD), and distal radius (R-BMD) were measured by dual-energy X-ray absorptiometry (DXA). We examined the correlation between the fractal dimension and six bone mass indices. Subjects diagnosed with osteopenia or osteoporosis were divided into two groups (with and without vertebral fracture), and we compared measured values between these two groups. The fractal dimension correlated most closely with L-BMD (r=0.744). The coefficient of correlation between the fractal dimension and L-BMD was very similar to the coefficient of correlation between L-BMD and F-BMD (r=0.783) and the coefficient of correlation between L-BMD and R-BMD (r=0.742). The fractal dimension was the only measured value that differed significantly between both the osteopenic and the osteoporotic subjects with and without vertebral fracture. The present results suggest that the fractal dimension of the distal radius can be reliably used as a bone strength index that reflects bone architecture as well as bone mass. (author)
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
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
On Nonextensive Statistics, Chaos and Fractal Strings
Castro, C
2004-01-01
Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the Tsallis non-extensive statistics ( with a non-additive $ q$-entropy ) of an ensemble of fractal strings and branes of different dimensionalities. Non-equilibrium systems with complex dynamics in stationary states may exhibit large fluctuations of intensive quantities which are described in terms of generalized statistics. Tsallis statistics is a particular representative of such class. The non-extensive entropy and probability distribution of a canonical ensemble of fractal strings and branes is studied in terms of their dimensional spectrum which leads to a natural upper cutoff in energy and establishes a direct correlation among dimensions, energy and temperature. The absolute zero temperature ( Kelvin ) corresponds to zero dimensions (energy ) and an infinite temperature corresponds to infinite dimensions. In the concluding remarks some applications of fractal statistics, quasi-particles, knot theory, quantum...
Fractal electrodynamics via non-integer dimensional space approach
Tarasov, Vasily E.
2015-09-01
Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.
Two Dimensional Drug Diffusion Between Nanoparticles and Fractal Tumors
Samioti, S. E.; Karamanos, K.; Tsiantis, A.; Papathanasiou, A.; Sarris, I.
2017-11-01
Drug delivery methods based on nanoparticles are some of the most promising medical applications in nanotechnology to treat cancer. It is observed that drug released by nanoparticles to the cancer tumors may be driven by diffusion. A fractal tumor boundary of triangular Von Koch shape is considered here and the diffusion mechanism is studied for different drug concentrations and increased fractality. A high order Finite Elements method based on the Fenics library is incorporated in fine meshes to fully resolve these irregular boundaries. Drug concentration, its transfer rates and entropy production are calculated in an up to forth order fractal iteration boundaries. We observed that diffusion rate diminishes for successive prefractal generations. Also, the entropy production around the system changes greatly as the order of the fractal curve increases. Results indicate with precision where the active sites are, in which most of the diffusion takes place and thus drug arrives to the tumor.
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.)
24-GHz LTCC Fractal Antenna Array SoP With Integrated Fresnel Lens
Ghaffar, Farhan A.; Khalid, Muhammad Umair; Salama, Khaled N.; Shamim, Atif
2012-01-01
A novel 24-GHz mixed low-temperature co-fired ceramic (LTCC) tape based system-on-package (SoP) is presented, which incorporates a fractal antenna array with an integrated grooved Fresnel lens. The four-element fractal array employs a relatively low
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
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
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.
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.
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
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.
Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.
Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian
2018-01-22
We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.
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…
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.
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...
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.
Morphometric relations of fractal-skeletal based channel network model
Directory of Open Access Journals (Sweden)
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.
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.
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 in two-metal electrodeposition systems I: Pb and Zn
International Nuclear Information System (INIS)
Nakouzi, Elias; Sultan, Rabih
2011-01-01
Pattern formation in two-metal electrochemical deposition has been scarcely explored in the chemical literature. In this paper, we report new experiments on zinc-lead fractal co-deposition. Electrodeposits are grown in special cells at a fixed large value of the zinc ion concentration, while that of the lead ion is increased gradually. A very wide diversity of morphologies are obtained and classified. Most of the deposited domains are almost exclusively Pb or Zn. But certain regions originating at the base cathode, ranging from a short grass alley to dense, grown-up bushes or shrubs, manifest a combined Pb-Zn composition. Composition is determined using scanning electron microscopy/energy dispersive x ray measurements as well atomic absorption spectroscopy. Pb domains are characterized by shiny leaf-like and dense deposits as well as flowers with round, balloon-like corollas. The Zn zones display a greater variety of morphologies such as thick trunks and thin and fine branching, in addition to minute ''cigar flower'' structures. The various morphologies are analyzed and classified from the viewpoint of fractal nature, characterized by the box-count fractal dimension. Finally, macroscopic spatial alternation between two different characteristic morphologies is observed under certain conditions.
Password Authentication Based on Fractal Coding Scheme
Directory of Open Access Journals (Sweden)
Nadia M. G. Al-Saidi
2012-01-01
Full Text Available Password authentication is a mechanism used to authenticate user identity over insecure communication channel. In this paper, a new method to improve the security of password authentication is proposed. It is based on the compression capability of the fractal image coding to provide an authorized user a secure access to registration and login process. In the proposed scheme, a hashed password string is generated and encrypted to be captured together with the user identity using text to image mechanisms. The advantage of fractal image coding is to be used to securely send the compressed image data through a nonsecured communication channel to the server. The verification of client information with the database system is achieved in the server to authenticate the legal user. The encrypted hashed password in the decoded fractal image is recognized using optical character recognition. The authentication process is performed after a successful verification of the client identity by comparing the decrypted hashed password with those which was stored in the database system. The system is analyzed and discussed from the attacker’s viewpoint. A security comparison is performed to show that the proposed scheme provides an essential security requirement, while their efficiency makes it easier to be applied alone or in hybrid with other security methods. Computer simulation and statistical analysis are presented.
Closed contour fractal dimension estimation by the Fourier transform
International Nuclear Information System (INIS)
Florindo, J.B.; Bruno, O.M.
2011-01-01
Highlights: → A novel fractal dimension concept, based on Fourier spectrum, is proposed. → Computationally simple. Computational time smaller than conventional fractal methods. → Results are closer to Hausdorff-Besicovitch than conventional methods. → The method is more accurate and robustness to geometric operations and noise addition. - Abstract: This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand-Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.
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.
3D printing of wearable fractal-based sensor systems for neurocardiology and healthcare
Ramasamy, Mouli; Varadan, Vijay K.
2017-04-01
Neurocardiology is the pathophysiological interplay of nervous and cardiovascular systems. The communication between the heart and brain has revealed various methodologies in healthcare that could be investigated to study the heart-brain interactions and other cardiovascular and neurological diseases. A textile based wearable nanosensor system in the form of e-bra, e-shirt, e-headband, e-brief, underwear etc, was presented in this SPIE conferences earlier for noninvasive recording of EEG and EKG, and showing the correlation between the brain and heart signals. In this paper, the technology is expanded further using fractal based geometries using 3D printing system for low cost and flexible wearable sensor system for healthcare.
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.
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.
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
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.
Symmetric intersections of Rauzy fractals | Sellami | Quaestiones ...
African Journals Online (AJOL)
In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is re ection through the origin. Given an unimodular irreducible Pisot substitution, we consider the intersection of its Rauzy fractal with the Rauzy fractal of the reverse substitution. This set is ...
Fractal characteristic in the wearing of cutting tool
Mei, Anhua; Wang, Jinghui
1995-11-01
This paper studies the cutting tool wear with fractal geometry. The wearing image of the flank has been collected by machine vision which consists of CCD camera and personal computer. After being processed by means of preserving smoothing, binary making and edge extracting, the clear boundary enclosing the worn area has been obtained. The fractal dimension of the worn surface is calculated by the methods called `Slit Island' and `Profile'. The experiments and calciating give the conclusion that the worn surface is enclosed by a irregular boundary curve with some fractal dimension and characteristics of self-similarity. Furthermore, the relation between the cutting velocity and the fractal dimension of the worn region has been submitted. This paper presents a series of methods for processing and analyzing the fractal information in the blank wear, which can be applied to research the projective relation between the fractal structure and the wear state, and establish the fractal model of the cutting tool wear.
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
Directory of Open Access Journals (Sweden)
Sergey Haitun
2016-02-01
Full Text Available The article is devoted to the changes that have occurred over the last year in the author’s cos- mological picture of the world. As before, the author starts from the hypothesis of fractal Universe. From this follows that since the density of such a Universe is equal to zero, Universe, as a whole, can- not either expand or contract. In the previous works the author did not realize that in the framework of the accepted hypothesis (of the fractal Universe the processes of contraction of metagalaxies (and other cosmic macro-systems cannot prevail over the processes of their expansion and the other way around in. And therefore, the Universe, as a whole, cannot evolve. The evolution (in the “progres- sive” direction could occur only in metagalaxies taken separately on the stage of their expansion. At the stage of contraction, the results of local evolutions, including advanced forms of life, are always destroyed. As a consequence, any form of life arising in metagalaxies is unavoidably local, both — in time and space. Wherever any form of life has appeared, it is doomed to destruction in the process of contraction of metagalaxies. Locality of hotbeds of life in the fractal Universe is aggravated by impossibility for residents of different metagalaxies to contact, because the distances between them are much larger than the metagalaxy sizes (all fractals are arranged in such a way. So a signal propagates between nearest metagalaxies during the time that is much larger than the duration of their gravitational cycles of expansion and contraction.
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
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
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...
Fractal characteristics of an asphaltene deposited heterogeneous surface
International Nuclear Information System (INIS)
Amin, J. Sayyad; Ayatollahi, Sh.; Alamdari, A.
2009-01-01
Several methods have been employed in recent years to investigate homogeneous surface topography based on image analysis, such as AFM (atomic force microscopy) and SEM (scanning electron microscopy). Fractal analysis of the images provides fractal dimension of the surface which is used as one of the most common surface indices. Surface topography has generally been considered to be mono-fractal. On the other hand, precipitation of organic materials on a rough surface and its irregular growth result in morphology alteration and converts a homogeneous surface to a heterogeneous one. In this case a mono-fractal description of the surface does not completely describe the nature of the altered surface. This work aims to investigate the topography alteration of a glass surface as a result of asphaltene precipitation and its growth at various pressures using a bi-fractal approach. The experimental results of the deposited surfaces were clearly indicating two regions of micro- and macro-asperities namely, surface types I and II, respectively. The fractal plots were indicative of bi-fractal behavior and for each surface type one fractal dimension was calculated. The topography information of the surfaces was obtained by two image analyses, AFM and SEM imaging techniques. Results of the bi-fractal analysis demonstrated that topography alteration in surface type II (macro-asperities) is more evident than that in surface type I (micro-asperities). Compared to surface type II, a better correlation was observed between the fractal dimensions inferred from the AFM images (D A ) and those of the SEM images (D S ) in surface type I.
Poiseuille equation for steady flow of fractal fluid
Tarasov, Vasily E.
2016-07-01
Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.
Brief communication: age and fractal dimensions of human sagittal and coronal sutures
DEFF Research Database (Denmark)
Lynnerup, Niels; Jacobsen, Jens Christian Brings
2003-01-01
The fractal dimensions of human sagittal and coronal sutures were calculated on 31 complete skulls from the Terry Collection. The aim was to investigate whether the fractal dimension, relying on the whole sutural length, might yield a better description of age-related changes in sutural morphology......, as opposed to other methods of quantification, which generally rely on more arbitrary scoring systems. However, the fractal dimension did not yield better age correlations than other previously described methods. At best, the results reflected the general observation that young adults below age 40 years...
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volume 1 of Eric Hammel's Fractal Dimensions, Volume 2 is filled wit
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1, 2, and 3 of Eric Hammel's Fractal Dimensions, Volume 4 is
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1 and 2 of Eric Hammel's Fractal Dimensions, Volume 3 is fil
Fractal 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.
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.
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.
Feng, Yongjiu; Liu, Miaolong; Tong, Xiaohua
2007-06-01
An improved fractal measurement, the weighted radial dimension, is put forward for highway transportation networks distribution. The radial dimension (DL), originated from subway investigation in Stuttgart, is a fractal measurement for transportation systems under ideal assumption considering all the network lines to be homogeneous curves, ignoring the difference on spatial structure, quality and level, especially the highway networks. Considering these defects of radial dimension, an improved fractal measurement called weighted radial dimension (D WL) is introduced and the transportation system in Guangdong province is studied in detail using this novel method. Weighted radial dimensions are measured and calculated, and the spatial structure, intensity and connectivity of transportation networks are discussed in Guangdong province and the four sub-areas: the Pearl River Delta area, the East Costal area, the West Costal area and the Northern Guangdong area. In Guangdong province, the fractal spatial pattern characteristics of transportation system vary remarkably: it is the highest in the Pearl River Delta area, moderate in Costal area and lowest in the Northern Guangdong area. With the Pearl River Delta area as the centre, the weighted radial dimensions decrease with the distance increasing, while the decline level is smaller in the costal area and greater in the Northern Guangdong province. By analysis of the conic of highway density, it is recognized that the density decrease with the distance increasing from the calculation centre (Guangzhou), demonstrating the same trend as weighted radial dimensions shown. Evidently, the improved fractal measurement, weighted radial dimension, is an indictor describing the characteristics of highway transportation system more effectively and accurately.
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.
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.
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
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
Sharma, Vijay
2009-09-10
Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts.
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.
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
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).
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.
On the arithmetic of fractal dimension using hyperhelices
International Nuclear Information System (INIS)
Toledo-Suarez, Carlos D.
2009-01-01
A hyperhelix is a fractal curve generated by coiling a helix around a rect line, then another helix around the first one, a third around the second... an infinite number of times. A way to generate hyperhelices with any desired fractal dimension is presented, leading to the result that they have embedded an algebraic structure that allows making arithmetic with fractal dimensions and to the idea of an infinitesimal of fractal dimension
Coder and decoder of fractal signals of comb-type structure
Directory of Open Access Journals (Sweden)
Politanskyi R. L.
2014-08-01
Full Text Available The article presents a coder and decoder of fractal signals of comb-type structure (FSCS based on microcontrollers (MC. The coder and decoder consist of identical control modules, while their managed modules have different schematic constructions. The control module performs forming or recognition of signals, and also carries out the function of information exchange with a computer. The basic element of the control module is a PIC18F2550 microcontroller from MicroChip. The coder of the system forms fractal signals of a given order according to the information bits coming from the computer. Samples of the calculated values of the amplitudes of elementary rectangular pulses that constitute the structure of fractal pulses are stored in the memory of the microcontroller as a table. Minimum bit capacity of the DAC necessary for the generation of FSCS of fourth order is four bits. The operation algorithm, "wired" into the controller of the program, provides for encoding of the transmitted information by two-bit symbols. Recognition of the start of transmission of each byte in communication channel is performed by the transmission of the timing signal. In a decoder the microcontroller carries out reception and decoding of the received fractal signals which are then transmitted to the computer. The developed algorithm of the program for the microcontroller of the decoder is carried out by determination of order of fractal impulse after the value of sum of amplitudes of elementary impulses, constituents fractal signal. The programs for coder and decoder are written in "C". In the most critical places of the program influencing on the fast-acting of chart “assembler” insertions are done. The blocks of the coder and decoder were connected with a coaxial 10 meters long cable with an impendance of 75 Ohm. The signals generated by the developed coder of FSCS, were studied using a digital oscillograph. On the basis of the obtained spectrums, it is possible
Fractal characterization for noise signal validation in power reactors
International Nuclear Information System (INIS)
Aguilar Martinez, Omar
2003-01-01
Up to now, a great variety of methods is used for the dynamical characterization of different components of Nuclear Power Plants (NPPs). With this aim, time and spectral analysis are usually considered, and different tools of non-stationary and non-gaussian analysis are also presented. When applying non-lineal dynamics theory for noise signal validation purposes in power reactors, the extraction of fractal echoes plays a main role. Fractal characterization for noise signal validation purposes can be integrated to the task of processing and acquisition of time signals in noise (fluctuation parameters) analysis systems. The possibility of discrimination between deterministic chaotic signals and pure noise signals has been incorporated, as a complement; to noise signals analysis in normal and anomalous operational conditions in NPPs using a fractal approach. In this work the detailed analysis of a neutronic sensor response is considered and the fractal characterization of its dynamics state (i.e. sensor line) for noise signal classification, it is presented. The experiment from where the time series (signals) were obtained, was carried out at the Research Reactor of the Technical University of Budapest, Hungary, during a model experiment for ageing process study of in-core neutron detectors (author)
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 dynamics of heartbeat time series of young persons with metabolic syndrome
Muñoz-Diosdado, A.; Alonso-Martínez, A.; Ramírez-Hernández, L.; Martínez-Hernández, G.
2012-10-01
Many physiological systems have been in recent years quantitatively characterized using fractal analysis. We applied it to study heart variability of young subjects with metabolic syndrome (MS); we examined the RR time series (time between two R waves in ECG) with the detrended fluctuation analysis (DFA) method, the Higuchi's fractal dimension method and the multifractal analysis to detect the possible presence of heart problems. The results show that although the young persons have MS, the majority do not present alterations in the heart dynamics. However, there were cases where the fractal parameter values differed significantly from the healthy people values.
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.
Bony change of apical lesion healing process using fractal analysis
Energy Technology Data Exchange (ETDEWEB)
Lee, Ji Min; Park, Hyok; Jeong, Ho Gul; Kim, Kee Deog; Park, Chang Seo [Yonsei University College of Medicine, Seoul (Korea, Republic of)
2005-06-15
To investigate the change of bone healing process after endodontic treatment of the tooth with an apical lesion by fractal analysis. Radiographic images of 35 teeth from 33 patients taken on first diagnosis, 6 months, and 1 year after endodontic treatment were selected. Radiographic images were taken by JUPITER computerized Dental X-ray System. Fractal dimensions were calculated three times at each area by Scion Image PC program. Rectangular region of interest (30 x 30) were selected at apical lesion and normal apex of each image. The fractal dimension at apical lesion of first diagnosis (L{sub 0}) is 0.940 {+-} 0.361 and that of normal area (N{sub 0}) is 1.186 {+-} 0.727 (p<0.05). Fractal dimension at apical lesion of 6 months after endodontic treatment (L{sub 1}) is 1.076 {+-} 0.069 and that of normal area (N{sub 1}) is 1.192 {+-} 0.055 (p<0.05). Fractal dimension at apical lesion of 1 year after endodontic treatment (L{sub 2}) is 1.163 {+-} 0.074 and that of normal area (N{sub 2}) is 1.225 {+-} 0.079 (p<0.05). After endodontic treatment, the fractal dimensions at each apical lesions depending on time showed statistically significant difference. And there are statistically significant different between normal area and apical lesion on first diagnosis, 6 months after, 1 year after. But the differences were grow smaller as time flows. The evaluation of the prognosis after the endodontic treatment of the apical lesion was estimated by bone regeneration in apical region. Fractal analysis was attempted to overcome the limit of subjective reading, and as a result the change of the bone during the healing process was able to be detected objectively and quantitatively.
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.
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.
Generalized Warburg impedance on realistic self-affine fractals ...
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals.
Monitoring of dry sliding wear using fractal analysis
Zhang, Jindang; Regtien, Paulus P.L.; Korsten, Maarten J.
2005-01-01
Reliable online monitoring of wear remains a challenge to tribology research as well as to the industry. This paper presents a new method for monitoring of dry sliding wear using digital imaging and fractal analysis. Fractal values, namely fractal dimension and intercept, computed from the power
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
RF MEMS Fractal Capacitors With High Self-Resonant Frequencies
Elshurafa, Amro M.
2012-07-23
This letter demonstrates RF microelectromechanical systems (MEMS) fractal capacitors possessing the highest reported self-resonant frequencies (SRFs) in PolyMUMPS to date. Explicitly, measurement results show SRFs beyond 20 GHz. Furthermore, quality factors higher than 4 throughout a band of 1-15 GHz and reaching as high as 28 were achieved. Additional benefits that are readily attainable from implementing fractal capacitors in MEMS are discussed, including suppressing residual stress warping, eliminating the need for etching holes, and reducing parasitics. The latter benefits were acquired without any fabrication intervention. © 2011 IEEE.
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
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.
Generalized Warburg impedance on realistic self-affine fractals
Indian Academy of Sciences (India)
We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals. The information about the ...
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
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
Convergence of trajectories in fractal interpolation of stochastic processes
International Nuclear Information System (INIS)
MaIysz, Robert
2006-01-01
The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, MaIysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873-88.], [MaIysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415-28.], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171-8.]. We prove that trajectories of fractal interpolation stochastic processes converge to the trajectory of the original process. We also show that convergence of the trajectories in fractal interpolation of stochastic processes is equivalent to the convergence of trajectories in linear interpolation
Fractal Dimension Of CT Images Of Normal Parotid Glands
International Nuclear Information System (INIS)
Lee, Sang Jin; Heo, Min Suk; You, Dong Soo
1999-01-01
This study was to investigate the age and sex differences of the fractal dimension of the normal parotid glands in the digitized CT images. The six groups, which were composed of 42 men and women from 20's, 40's and 60's and over were picked. Each group contained seven people of the same sex. The normal parotid CT images were digitized, and their fractal dimensions were calculated using Scion Image PC program. The mean of fractal dimensions in males was 1.7292 (+/-0.0588) and 1.6329 (+/-0.0425) in females. The mean of fractal dimensions in young males was 1.7617, 1.7328 in middle males, and 1.6933 in old males. The mean of fractal dimensions in young females was 1.6318, 1.6365 in middle females, and 1.6303 in old females. There was no statistical difference in fractal dimension between left and right parotid gland of the same subject (p>0.05). Fractal dimensions in male were decreased in older group (p 0.05). The fractal dimension of parotid glands in the digitized CT images will be useful to evaluate the age and sex differences.
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.
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
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)
Electro-chemical manifestation of nanoplasmonics in fractal media
Baskin, Emmanuel; Iomin, Alexander
2013-06-01
Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.
FAST TRACK COMMUNICATION: Weyl law for fat fractals
Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos
2010-10-01
It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.
Paper-based inkjet-printed ultra-wideband fractal antennas
Maza, Armando Rodriguez
2012-01-01
For the first time, paper-based inkjet-printed ultra-wideband (UWB) fractal antennas are presented. Two new designs, a miniaturised UWB monopole, which utilises a fractal matching network and is the smallest reported inkjet-printed UWB printed antenna to date, and a fourth-order Koch Snowflake monopole, which utilises a Sierpinski gasket fractal for ink reduction, are demonstrated. It is shown that fractals prove to be a successful method of reducing fabrication costs in inkjet-printed antennas, while retaining or enhancing printed antenna performance. © 2012 The Institution of Engineering and Technology.
Effective degrees of freedom of a random walk on a fractal
Balankin, Alexander S.
2015-12-01
We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.
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.
Facile fabrication of superhydrophobic films with fractal structures using epoxy resin microspheres
Energy Technology Data Exchange (ETDEWEB)
Quan, Yun-Yun; Zhang, Li-Zhi, E-mail: lzzhang@scut.edu.cn
2014-02-15
A simple method has been developed to fabricate superhydrophobic surfaces with fractal structures with epoxy resin microspheres (ERMs). The ERMs is produced by phase separation in an epoxy-amine curing system with a silica sol (SS) dispersant. The transparent epoxy solution becomes cloudy and turns into epoxy suspension (ES) in this process. The fractal structure (two tier structure) generated by synthetic epoxy resin microspheres (ERMs) and deposited nanoincrutations on the surfaces of these ERMs, which have been observed by scanning electron microscope (SEM). The curing time of ES is an important condition to obtain films with good comprehensive performances. Superhydrophobic films can be prepared by adding extra SS into ES with a curing time longer than 5 h. The optimal curing time is 10 h to fabricate a film with good mechanical stability and high superhydrophobicity. In addition, a surface with anti-wetting property of impacting microdroplets can be fabricated by prolonging the curing time of ES to 24 h. The gradually decreased hydrophilic groups resulted from a longer curing time enable the surface to have smaller surface adhesions to water droplets, which is the main reason to keep its superhydrophobicity under impacting conditions. The coated surface is highly hydrophobic and the impacting water droplets are bounced off from the surface.
Facile fabrication of superhydrophobic films with fractal structures using epoxy resin microspheres
Quan, Yun-Yun; Zhang, Li-Zhi
2014-02-01
A simple method has been developed to fabricate superhydrophobic surfaces with fractal structures with epoxy resin microspheres (ERMs). The ERMs is produced by phase separation in an epoxy-amine curing system with a silica sol (SS) dispersant. The transparent epoxy solution becomes cloudy and turns into epoxy suspension (ES) in this process. The fractal structure (two tier structure) generated by synthetic epoxy resin microspheres (ERMs) and deposited nanoincrutations on the surfaces of these ERMs, which have been observed by scanning electron microscope (SEM). The curing time of ES is an important condition to obtain films with good comprehensive performances. Superhydrophobic films can be prepared by adding extra SS into ES with a curing time longer than 5 h. The optimal curing time is 10 h to fabricate a film with good mechanical stability and high superhydrophobicity. In addition, a surface with anti-wetting property of impacting microdroplets can be fabricated by prolonging the curing time of ES to 24 h. The gradually decreased hydrophilic groups resulted from a longer curing time enable the surface to have smaller surface adhesions to water droplets, which is the main reason to keep its superhydrophobicity under impacting conditions. The coated surface is highly hydrophobic and the impacting water droplets are bounced off from the surface.
Naturaleza fractal en redes de cristales de grasas
Directory of Open Access Journals (Sweden)
Gómez Herrera, C.
2004-06-01
Full Text Available The determination of the mechanical and rheological characterisÂtics of several plastic fats requires a detailed understanding of the microstructure of the fat crystal network aggregates. The (or A fractal approach is useful for the characterization of this microsÂtructure. This review begins with information on fractality and statistical self-similar structure. Estimations for fractal dimension by means of equations relating the volume fraction of solid fat to shear elastic modulus G' in linear region are described. The influence of interesterification on fractal dimension decrease (from 2, 46 to 2 ,15 for butterfat-canola oil blends is notable . This influence is not significant for fat blends without butterfat. The need for an increase in research concerning the relationship between fractality and rheology in plastic fats is emphasized.La determinación de las características mecánicas y reológicas de ciertas grasas plásticas requiere conocimientos detallados sobre las microestructuras de los agregados que forman la red de cristales grasos. El estudio de la naturaleza fractal de estas microestructuras resulta útil para su caracÂterización. Este artículo de información se inicia con descripciones de la dimensión fractal y de la "autosimilitud estadística". A continuación se describe el cálculo de la dimensión fractal mediante ecuaciones que relacionan la fracción en volumen de grasa sólida con el módulo de recuperación (G' dentro de un comportamiento viscoelástico lineal. Se destaca la influencia que la interesterificación ejerce sobre la dimensión fractal de una mezcla de grasa láctea y aceite de canola (que pasa de 2,64 a 2,15. Esta influencia no se presenta en mezclas sin grasa láctea. Se insiste sobre la necesidad de incrementar las investiÂgaciones sobre la relación entre reología y estructura fractal en grasas plásticas.
Naik, Ganesh R; Kumar, Dinesh K; Arjunan, Sridhar
2009-01-01
This paper has experimentally verified and compared features of sEMG (Surface Electromyogram) such as ICA (Independent Component Analysis) and Fractal Dimension (FD) for identification of low level forearm muscle activities. The fractal dimension was used as a feature as reported in the literature. The normalized feature values were used as training and testing vectors for an Artificial neural network (ANN), in order to reduce inter-experimental variations. The identification accuracy using FD of four channels sEMG was 58%, and increased to 96% when the signals are separated to their independent components using ICA.
Fractal analysis of cervical intraepithelial neoplasia.
Directory of Open Access Journals (Sweden)
Markus Fabrizii
Full Text Available INTRODUCTION: Cervical intraepithelial neoplasias (CIN represent precursor lesions of cervical cancer. These neoplastic lesions are traditionally subdivided into three categories CIN 1, CIN 2, and CIN 3, using microscopical criteria. The relation between grades of cervical intraepithelial neoplasia (CIN and its fractal dimension was investigated to establish a basis for an objective diagnosis using the method proposed. METHODS: Classical evaluation of the tissue samples was performed by an experienced gynecologic pathologist. Tissue samples were scanned and saved as digital images using Aperio scanner and software. After image segmentation the box counting method as well as multifractal methods were applied to determine the relation between fractal dimension and grades of CIN. A total of 46 images were used to compare the pathologist's neoplasia grades with the predicted groups obtained by fractal methods. RESULTS: Significant or highly significant differences between all grades of CIN could be found. The confusion matrix, comparing between pathologist's grading and predicted group by fractal methods showed a match of 87.1%. Multifractal spectra were able to differentiate between normal epithelium and low grade as well as high grade neoplasia. CONCLUSION: Fractal dimension can be considered to be an objective parameter to grade cervical intraepithelial neoplasia.
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
Nontrivial paths and periodic orbits of the T-fractal billiard table
Lapidus, Michel L.; Miller, Robyn L.; Niemeyer, Robert G.
2016-07-01
We introduce and prove numerous new results about the orbits of the T-fractal billiard. Specifically, in section 3, we give a variety of sufficient conditions for the existence of a sequence of compatible periodic orbits. In section 4, we examine the limiting behavior of particular sequences of compatible periodic orbits. Additionally, sufficient conditions for the existence of particular nontrivial paths are given in section 4. The proofs of two results of Lapidus and Niemeyer (2013 The current state of fractal billiards Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics (Contemporary Mathematics vol 601) ed D Carfi et al (Providence, RI: American Mathematical Society) pp 251-88 (e-print: arXiv:math.DS.1210.0282v2, 2013) appear here for the first time, as well. In section 5, an orbit with an irrational initial direction reaches an elusive point in a way that yields a nontrivial path of finite length, yet, by our convention, constitutes a singular orbit of the fractal billiard table. The existence of such an orbit seems to indicate that the classification of orbits may not be so straightforward. A discussion of our results and directions for future research is then given in section 6.
Near-Field Optical Microscopy of Fractal Structures
DEFF Research Database (Denmark)
Coello, Victor; Bozhevolnyi, Sergey I.
1999-01-01
Using a photon scanning tunnelling microscope combined with a shear-force feedback system, we image both topographical and near-field optical images (at the wavelengths of 633 and 594 nm) of silver colloid fractals. Near-field optical imaging is calibrated with a standing evanescent wave pattern...
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
International Nuclear Information System (INIS)
Ancillao, Andrea; Galli, Manuela; Rigoldi, Chiara; Albertini, Giorgio
2014-01-01
Fractal dimension was demonstrated to be able to characterize the complexity of biological signals. The EMG time series are well known to have a complex behavior and some other studies already tried to characterize these signals by their fractal dimension. This paper is aimed at studying the correlation between the fractal dimension of surface EMG signal recorded over Rectus Femoris muscles during a vertical jump and the height reached in that jump. Healthy subjects performed vertical jumps at different heights. Surface EMG from Rectus Femoris was recorded and the height of each jump was measured by an optoelectronic motion capture system. Fractal dimension of sEMG was computed and the correlation between fractal dimension and eight of the jump was studied. Linear regression analysis showed a very high correlation coefficient between the fractal dimension and the height of the jump for all the subjects. The results of this study show that the fractal dimension is able to characterize the EMG signal and it can be related to the performance of the jump. Fractal dimension is therefore an useful tool for EMG interpretation
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.
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.
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
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…
Pore Structure and Fractal Characteristics of Niutitang Shale from China
Directory of Open Access Journals (Sweden)
Zhaodong Xi
2018-04-01
Full Text Available A suite of shale samples from the Lower Cambrian Niutitang Formation in northwestern Hunan Province, China, were investigated to better understand the pore structure and fractal characteristics of marine shale. Organic geochemistry, mineralogy by X-ray diffraction, porosity, permeability, mercury intrusion and nitrogen adsorption and methane adsorption experiments were conducted for each sample. Fractal dimension D was obtained from the nitrogen adsorption data using the fractal Frenkel-Halsey-Hill (FHH model. The relationships between total organic carbon (TOC content, mineral compositions, pore structure parameters and fractal dimension are discussed, along with the contributions of fractal dimension to shale gas reservoir evaluation. Analysis of the results showed that Niutitang shale samples featured high TOC content (2.51% on average, high thermal maturity (3.0% on average, low permeability and complex pore structures, which are highly fractal. TOC content and mineral compositions are two major factors affecting pore structure but they have different impacts on the fractal dimension. Shale samples with higher TOC content had a larger specific surface area (SSA, pore volume (PV and fractal dimension, which enhanced the heterogeneity of the pore structure. Quartz content had a relatively weak influence on shale pore structure, whereas SSA, PV and fractal dimension decreased with increasing clay mineral content. Shale with a higher clay content weakened pore structure heterogeneity. The permeability and Langmuir volume of methane adsorption were affected by fractal dimension. Shale samples with higher fractal dimension had higher adsorption capacity but lower permeability, which is favorable for shale gas adsorption but adverse to shale gas seepage and diffusion.
Energy Technology Data Exchange (ETDEWEB)
Das, Bipul; Bag, Swarup; Pal, Sukhomay [Indian Institute of Technology Guwahati, Assam (India)
2017-05-15
Providing solutions towards the improvisation of welding technologies is the recent trend in the Friction stir welding (FSW) process. We present a monitoring approach for ultimate tensile strength of the friction stir welded joints based on information extracted from process signals through implementing fractal theory. Higuchi and Katz algorithms were executed on current and tool rotational speed signals acquired during friction stir welding to estimate fractal dimensions. Estimated fractal dimensions when correlated with the ultimate tensile strength of the joints deliver an increasing trend with the increase in joint strength. It is observed that dynamicity of the system strengthens the weld joint, i.e., the greater the fractal dimension, the better will be the quality of the weld. Characterization of signals by fractal theory indicates that the single-valued indicator can be an alternative for effective monitoring of the friction stir welding process.
International Nuclear Information System (INIS)
Das, Bipul; Bag, Swarup; Pal, Sukhomay
2017-01-01
Providing solutions towards the improvisation of welding technologies is the recent trend in the Friction stir welding (FSW) process. We present a monitoring approach for ultimate tensile strength of the friction stir welded joints based on information extracted from process signals through implementing fractal theory. Higuchi and Katz algorithms were executed on current and tool rotational speed signals acquired during friction stir welding to estimate fractal dimensions. Estimated fractal dimensions when correlated with the ultimate tensile strength of the joints deliver an increasing trend with the increase in joint strength. It is observed that dynamicity of the system strengthens the weld joint, i.e., the greater the fractal dimension, the better will be the quality of the weld. Characterization of signals by fractal theory indicates that the single-valued indicator can be an alternative for effective monitoring of the friction stir welding process.
Higgs field and cosmological parameters in the fractal quantum system
Directory of Open Access Journals (Sweden)
Abramov Valeriy
2017-01-01
Full Text Available For the fractal model of the Universe the relations of cosmological parameters and the Higgs field are established. Estimates of the critical density, the expansion and speed-up parameters of the Universe (the Hubble constant and the cosmological redshift; temperature and anisotropy of the cosmic microwave background radiation were performed.
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....
RF MEMS Fractal Capacitors With High Self-Resonant Frequencies
Elshurafa, Amro M.; Emira, Ahmed; Radwan, Ahmed Gomaa; Salama, Khaled N.
2012-01-01
This letter demonstrates RF microelectromechanical systems (MEMS) fractal capacitors possessing the highest reported self-resonant frequencies (SRFs) in PolyMUMPS to date. Explicitly, measurement results show SRFs beyond 20 GHz. Furthermore, quality
Fractal dimension analysis of complexity in Ligeti piano pieces
Bader, Rolf
2005-04-01
Fractal correlation dimensional analysis has been performed with whole solo piano pieces by Gyrgy Ligeti at every 50ms interval of the pieces. The resulting curves of development of complexity represented by the fractal dimension showed up a very reasonable correlation with the perceptional density of events during these pieces. The seventh piece of Ligeti's ``Musica ricercata'' was used as a test case. Here, each new part of the piece was followed by an increase of the fractal dimension because of the increase of information at the part changes. The second piece ``Galamb borong,'' number seven of the piano Etudes was used, because Ligeti wrote these Etudes after studying fractal geometry. Although the piece is not fractal in the strict mathematical sense, the overall structure of the psychoacoustic event-density as well as the detailed event development is represented by the fractal dimension plot.
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)
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.
Quantitative assessment of early diabetic retinopathy using fractal analysis.
Cheung, Ning; Donaghue, Kim C; Liew, Gerald; Rogers, Sophie L; Wang, Jie Jin; Lim, Shueh-Wen; Jenkins, Alicia J; Hsu, Wynne; Li Lee, Mong; Wong, Tien Y
2009-01-01
Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes. We conducted a cross-sectional study of 729 patients with type 1 diabetes (aged 12-20 years) who had seven-field stereoscopic retinal photographs taken of both eyes. From these photographs, retinopathy was graded according to the modified Airlie House classification, and fractal dimension was quantified using a computer-based program following a standardized protocol. In this study, 137 patients (18.8%) had diabetic retinopathy signs; of these, 105 had mild retinopathy. Median (interquartile range) retinal fractal dimension was 1.46214 (1.45023-1.47217). After adjustment for age, sex, diabetes duration, A1C, blood pressure, and total cholesterol, increasing retinal vascular fractal dimension was significantly associated with increasing odds of retinopathy (odds ratio 3.92 [95% CI 2.02-7.61] for fourth versus first quartile of fractal dimension). In multivariate analysis, each 0.01 increase in retinal vascular fractal dimension was associated with a nearly 40% increased odds of retinopathy (1.37 [1.21-1.56]). This association remained after additional adjustment for retinal vascular caliber. Greater retinal fractal dimension, representing increased geometric complexity of the retinal vasculature, is independently associated with early diabetic retinopathy signs in type 1 diabetes. Fractal analysis of fundus photographs may allow quantitative measurement of early diabetic microvascular damage.
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 (…) ...
Usefulness of fractal analysis for the diagnosis of periodontitis
Energy Technology Data Exchange (ETDEWEB)
Cha, Sang Yun; Han, Won Jeong; Kim, Eun Kyung [Dankook Univ. School of Dentistry, Seoul (Korea, Republic of)
2001-03-15
To evaluate the usefulness of fractal analysis for diagnosis of periodontitis. Each 30 cases of periapical films of male mandibular molar were selected in normal group and patient group which had complete furcation involvement. They were digitized at 300 dpi, 256 gray levels and saved with gif format. Rectangular ROIs (10 X 20 pixel) were selected at furcation, interdental crest, and interdental middle 1/3 area. Fractal dimensions were calculated three times at each area by mass radius method and were determined using a mean of three measurements. We computed fractal dimensions at furcation and interdental crest area of normal group with those of patient group. And then we compared ratio of fractal dimensions at furcation area, interdental crest area to interdental middle 1/3 area. Fractal dimension at interdental crest area of normal group was 1.979{+-}0.018 (p<0.05). The radio of fractal dimension at furcation area to interdental middle 1/3 of normal group was 1.006{+-}0.018 and that of patient group 0.9940.018 (p<0.05). The radio of fractal dimension at interdental crest and furcation area to interdental middle 1/3 area showed a statistically significant difference between normal and patient group. In conclusion, it is thought that fractal analysis might be useful for the diagnosis of periodontitis.
Heterogeneity of cerebral blood flow: a fractal approach
International Nuclear Information System (INIS)
Kuikka, J.T.; Hartikainen, P.
2000-01-01
Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and single-photon emission computed tomography (SPECT). Method: Tc-99m-labelled ethylcysteine dimer was injected intravenously in 10 healthy controls and in 10 patients with dementia of frontal lobe type. The head was imaged with a gamma camera and transaxial, sagittal and coronal slices were reconstructed. Two hundred fifty-six symmetrical regions of interest (ROIs) were drawn onto each hemisphere of functioning brain matter. Fractal analysis was used to examine the spatial heterogeneity of blood flow as a function of the number of ROIs. Results: Relative dispersion (=coefficient of variation of the regional flows) was fractal-like in healthy subjects and could be characterized by a fractal dimension of 1.17±0.05 (mean±SD) for the left hemisphere and 1.15±0.04 for the right hemisphere, respectively. The fractal dimension of 1.0 reflects completely homogeneous blood flow and 1.5 indicates a random blood flow distribution. Patients with dementia of frontal lobe type had a significantly lower fractal dimension of 1.04±0.03 than in healthy controls. (orig.) [de
Using Peano Curves to Construct Laplacians on Fractals
Molitor, Denali; Ott, Nadia; Strichartz, Robert
2015-12-01
We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.
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
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.
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...
Selvam, A. M.
2017-01-01
Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and, therefore, the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts the following. (1) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being the integrated mean of enclosed smaller-scale fluctuations. (2) The probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the universal Boltzmann inverse power law expressed as a function of the golden mean. (3) Fractal fluctuations are signatures of quantum-like chaos since the additive amplitudes of eddies when squared represent probability densities analogous to the sub-atomic dynamics of quantum systems such as the photon or electron. (4) The model predicted distribution is very close to statistical normal distribution for moderate events within two standard deviations from the mean but exhibits a fat long tail that are associated with hazardous extreme events. Continuous periodogram power spectral analyses of available GHCN annual total rainfall time series for the period 1900-2008 for Indian and USA stations show that the power spectra and the corresponding probability distributions follow model predicted universal inverse power law form signifying an eddy continuum structure underlying the observed inter-annual variability of rainfall. On a global scale, man-made greenhouse gas related atmospheric warming would result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference
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
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.
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
A Novel Ancient Coin-Like Fractal Multiband Antenna for Wireless Applications
Directory of Open Access Journals (Sweden)
Zhen Yu
2017-01-01
Full Text Available This study proposes a novel square-circle structure fractal multibroadband planar antenna, similar to an ancient Chinese coin-like structure, for second generation (2G, third generation (3G, fourth generation (4G, WLAN, and navigation wireless applications. The device is based on the principles and structural features of conventional monopole antenna elements, combined with the advantages of microstrip antennas and fractal geometry. A fractal method was presented for circular nested square slotted structures, similar to an ancient Chinese copper coin. The proposed antenna adapted five iterations on a fractal structure radiator, which covers more than ten mobile applications in three broad frequency bands with a bandwidth of 70% (1.43–2.97 GHz for DCS1800, TD-SCDMA, WCDMA, CDMA2000, LTE33-41, Bluetooth, GPS (Global Positioning System, BDS (BeiDou Navigation Satellite System, GLONSS (Global Navigation Satellite System, GALILEO (Galileo Satellite Navigation System, and WLAN frequency bands, 16.32% (3.32–3.91 GHz for LTE42, LTE43, and WiMAX frequency bands, and 10.92% (4.85–5.41 GHz for WLAN frequency band. The proposed antenna was fabricated on a 1.6 mm thick G10/FR4 substrate with a dielectric constant of 4.4 and a size of 88.5 × 60 mm2. The measurement results reveal that the omnidirectional radiation patterns achieve a gain of 1.16–3.75 dBi and an efficiency of 40–72%. The good agreement between the measurement results and simulation validates the proposed design approach and satisfies the requirements for various wireless applications.
International Nuclear Information System (INIS)
Chen Yanguang
2009-01-01
A pair of nonlinear programming models is built to explain the fractal structure of systems of cities and those of rivers. The hierarchies of cities can be characterized by a set of exponential functions, which is identical in form to the Horton-Strahler's laws of the river networks. Four power laws can be derived from these exponential functions. The evolution of both systems of cities and rivers are then represented as nonlinear dual programming models: to maximize information entropy subject to a certain energy use or to minimize energy dissipation subject to certain information capacity. The optimal solutions of the programming problems are just the exponential equations associated with scaling relations. By doing so, fractals and the self-organized criticality marked by the power laws are interpreted using the idea from the entropy-maximization principle, which gives further weight to the suggestion that optimality of the system as a whole defines the dynamical origin of fractal forms in both nature and society.
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.
Investigation of the Bose–Einstein condensation based on fractality using fractional mathematics
International Nuclear Information System (INIS)
Şirin, Hüseyin; Ertik, Hüseyin; Büyükkiliç, Fevzi; Demirhan, Doğan
2010-01-01
Although atomic Bose gases are investigated in the dilute gas regime, the physical properties of the Bose–Einstein condensates are affected by interparticle interactions and the fractal nature of the space where the Bose systems are evolving. Theoretical predictions of the traditional Bose–Einstein thermostatistics do not account for the deviations from the experimental results, which are related to internal energy, specific heat, transition temperature, etc. On the other hand, in this study, fractional calculus is introduced where effects of the fractality of space are taken into account. Meanwhile, the order of the fractional derivative α is handled as a measure of the fractality of space. In this content, some improvements which take into account the effects of the fractal nature of the system are made in the standard physical results of the Bose–Einstein condensation phenomena. As an example, for the dilute atomic gas 7 Li, the measured transition temperature of Bose–Einstein condensation could be obtained for the value of α ≈ 0.976, and one could predict that the interparticle interactions have a weak attractive nature consistent with experiment (Bradley et al 1995 Phys. Rev. Lett. 75 1687). Thus, a fractional mathematical theory is established in coherence with experimental results of Bose–Einstein condensation
Lam, Nina Siu-Ngan; Qiu, Hong-Lie; Quattrochi, Dale A.; Emerson, Charles W.; Arnold, James E. (Technical Monitor)
2001-01-01
The rapid increase in digital data volumes from new and existing sensors necessitates the need for efficient analytical tools for extracting information. We developed an integrated software package called ICAMS (Image Characterization and Modeling System) to provide specialized spatial analytical functions for interpreting remote sensing data. This paper evaluates the three fractal dimension measurement methods: isarithm, variogram, and triangular prism, along with the spatial autocorrelation measurement methods Moran's I and Geary's C, that have been implemented in ICAMS. A modified triangular prism method was proposed and implemented. Results from analyzing 25 simulated surfaces having known fractal dimensions show that both the isarithm and triangular prism methods can accurately measure a range of fractal surfaces. The triangular prism method is most accurate at estimating the fractal dimension of higher spatial complexity, but it is sensitive to contrast stretching. The variogram method is a comparatively poor estimator for all of the surfaces, particularly those with higher fractal dimensions. Similar to the fractal techniques, the spatial autocorrelation techniques are found to be useful to measure complex images but not images with low dimensionality. These fractal measurement methods can be applied directly to unclassified images and could serve as a tool for change detection and data mining.
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
Investigation into How 8th Grade Students Define Fractals
Karakus, Fatih
2015-01-01
The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…
Fractal Image Coding with Digital Watermarks
Directory of Open Access Journals (Sweden)
Z. Klenovicova
2000-12-01
Full Text Available In this paper are presented some results of implementation of digitalwatermarking methods into image coding based on fractal principles. Thepaper focuses on two possible approaches of embedding digitalwatermarks into fractal code of images - embedding digital watermarksinto parameters for position of similar blocks and coefficients ofblock similarity. Both algorithms were analyzed and verified on grayscale static images.
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)
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
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.
Constructing and applying the fractal pied de poule (houndstooth)
Feijs, L.M.G.; Toeters, M.J.; Hart, G.; Sarhangi, R.
2013-01-01
Time is ready for a fractal version of pied de poule; it is almost "in the air". Taking inspiration from the Cantor set, and using the analysis of the classical pattern, we obtain a family of elegant new fractal Pied de Poules. We calculate the fractal dimension and develop an attractive fashion
Multirate diversity strategy of fractal modulation
International Nuclear Information System (INIS)
Yuan Yong; Shi Si-Hong; Luo Mao-Kang
2011-01-01
Previous analyses of fractal modulation were carried out mostly from a signle perspective or a subband, but the analyses from the perspective of multiscale synthesis have not been found yet; while multiscale synthesis is just the essence of the mutlirate diversity which is the most important characteristic of fractal modulation. As for the mutlirate diversity of fractal modulation, previous studies only dealt with the general outspread of its concept, lacked the thorough and intensive quantitative comparison and analysis. In light of the above fact, from the perspective of multiscale synthesis, in this paper we provide a comprehensive analysis of the multirate diversity of fractal modulation and corresponding quantitative analysis. The results show that mutlirate diversity, which is a fusion of frequency diversity and time diversity, pays an acceptable price in spectral efficiency in exchange for a significant improvement in bit error rate. It makes fractal modulation particularly suitable for the channels whose bandwidth and duration parameters are unknown or cannot be predicted to the transmitter. Surely it is clearly of great significance for reliable communications. Moreover, we also attain the ability to flexibly make various rate-bandwidth tradeoffs between the transmitter and the receiver, to freely select the reception time and to expediently control the total bandwidth. Furthermore, the acquisitions or improvements of these fine features could provide support of the technical feasibility for the electromagnetic spectrum control technology in a complex electromagnetic environment. (general)
Directory of Open Access Journals (Sweden)
Mirko Ahmadfaraj
2016-06-01
Full Text Available The aim of this study is determination and separation of alteration zones using Concentration-Area (C-A fractal model based on remote sensing data which has been extracted from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER images. The studied area is on the SW part of Saveh, 1:250,000 geological map, which is located in Urumieh-Dokhtar magmatic belt, Central Iran. The pixel values were computed by Principal Component Analysis (PCA method used to determine phyllic, argillic, and propylitic alteration zones. The C-A fractal model is utilized for separation of different parts of alteration zones due to their intensity. The log-log C-A plots reveal multifractal nature for phyllic, argillic, and propylitic alteration zones. The obtained results based on fractal model show that the main trend of the alteration zones is in NW-SE direction. Compared to the geological map of the study area and copper mineralizations, the alteration zones have been detected properly and correlate with the mineral occurrences, intrusive rock, and faults.
Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications
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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.
Vibration modes of 3n-gaskets and other fractals
Energy Technology Data Exchange (ETDEWEB)
Bajorin, N; Chen, T; Dagan, A; Emmons, C; Hussein, M; Khalil, M; Mody, P; Steinhurst, B; Teplyaev, A [Department of Mathematics, University of Connecticut, Storrs CT 06269 (United States)
2008-01-11
We rigorously study eigenvalues and eigenfunctions (vibration modes) on the class of self-similar symmetric finitely ramified fractals, which include the Sierpinski gasket and other 3n-gaskets. We consider the classical Laplacian on fractals which generalizes the usual one-dimensional second derivative, is the generator of the self-similar diffusion process, and has possible applications as the quantum Hamiltonian. We develop a theoretical matrix analysis, including analysis of singularities, which allows us to compute eigenvalues, eigenfunctions and their multiplicities exactly. We support our theoretical analysis by symbolic and numerical computations. Our analysis, in particular, allows the computation of the spectral zeta function on fractals and the limiting distribution of eigenvalues (i.e., integrated density of states). We consider such examples as the level-3 Sierpinski gasket, a fractal 3-tree, and the diamond fractal.
Optical diffraction from fractals with a structural transition
International Nuclear Information System (INIS)
Perez Rodriguez, F.; Canessa, E.
1994-04-01
A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and biharmonic equations and are compared to more 'regular' irreversible clusters such as diffusion limited and Laplacian aggregates. The optical diffraction method enables to identify a decrease of the fractal dimension above the structural point. (author). 19 refs, 6 figs
Bony change of apical lesion healing process using fractal analysis
International Nuclear Information System (INIS)
Lee, Ji Min; Park, Hyok; Jeong, Ho Gul; Kim, Kee Deog; Park, Chang Seo
2005-01-01
To investigate the change of bone healing process after endodontic treatment of the tooth with an apical lesion by fractal analysis. Radiographic images of 35 teeth from 33 patients taken on first diagnosis, 6 months, and 1 year after endodontic treatment were selected. Radiographic images were taken by JUPITER computerized Dental X-ray System. Fractal dimensions were calculated three times at each area by Scion Image PC program. Rectangular region of interest (30 x 30) were selected at apical lesion and normal apex of each image. The fractal dimension at apical lesion of first diagnosis (L 0 ) is 0.940 ± 0.361 and that of normal area (N 0 ) is 1.186 ± 0.727 (p 1 ) is 1.076 ± 0.069 and that of normal area (N 1 ) is 1.192 ± 0.055 (p 2 ) is 1.163 ± 0.074 and that of normal area (N 2 ) is 1.225 ± 0.079 (p<0.05). After endodontic treatment, the fractal dimensions at each apical lesions depending on time showed statistically significant difference. And there are statistically significant different between normal area and apical lesion on first diagnosis, 6 months after, 1 year after. But the differences were grow smaller as time flows. The evaluation of the prognosis after the endodontic treatment of the apical lesion was estimated by bone regeneration in apical region. Fractal analysis was attempted to overcome the limit of subjective reading, and as a result the change of the bone during the healing process was able to be detected objectively and quantitatively.
A study of complexity of oral mucosa using fractal geometry
Directory of Open Access Journals (Sweden)
S R Shenoi
2017-01-01
Full Text Available Background: The oral mucosa lining the oral cavity is composed of epithelium supported by connective tissue. The shape of the epithelial-connective tissue interface has traditionally been used to describe physiological and pathological changes in the oral mucosa. Aim: The aim is to evaluate the morphometric complexity in normal, dysplastic, well-differentiated, and moderately differentiated squamous cell carcinoma (SCC of the oral mucosa using fractal geometry. Materials and Methods: A total of 80 periodic acid–Schiff stained histological images of four groups: normal mucosa, dysplasia, well-differentiated SCC, and moderately differentiated SCC were verified by the gold standard. These images were then subjected to fractal analysis. Statistical Analysis: ANOVA and post hoc test: Bonferroni was applied. Results: Fractal dimension (FD increases as the complexity increases from normal to dysplasia and then to SCC. Normal buccal mucosa was found to be significantly different from dysplasia and the two grades of SCC (P < 0.05. ANOVA of fractal scores of four morphometrically different groups of buccal mucosa was significantly different with F (3,76 = 23.720 and P< 0.01. However, FD of dysplasia was not significantly different from well-differentiated and moderately differentiated SCC (P = 1.000 and P = 0.382, respectively. Conclusion: This study establishes FD as a newer tool in differentiating normal tissue from dysplastic and neoplastic tissue. Fractal geometry is useful in the study of both physiological and pathological changes in the oral mucosa. A new grading system based on FD may emerge as an adjuvant aid in cancer diagnosis.
Directory of Open Access Journals (Sweden)
Tkachuk V.G.
2010-05-01
Full Text Available The features of reactions of the cardiovascular system are considered on the physical loadings in a preparatory period. Researches were conducted before and after championship of Europe 2009 The mathematical analysis of rhythm of heart is resulted. The frequency and fractal methods of research of cardiac rhythm sportsmen the combined team of Ukraine are studied on taekwondo. Informing of some indexes of fractal of cardiac rhythm (coefficient of Khersta is rotined for determination of readiness of sportsman to competition activity.
International Nuclear Information System (INIS)
Fu, Haoran; Xu, Sheng; Rogers, John A.; Xu, Renxiao; Huang, Yonggang; Jiang, Jianqun; Zhang, Yihui
2015-01-01
Fractal-inspired designs for interconnects that join rigid, functional devices can ensure mechanical integrity in stretchable electronic systems under extreme deformations. The bonding configuration of such interconnects with the elastomer substrate is crucial to the resulting deformation modes, and therefore the stretchability of the entire system. In this study, both theoretical and experimental analyses are performed for postbuckling of fractal serpentine interconnects partially bonded to the substrate. The deformation behaviors and the elastic stretchability of such systems are systematically explored, and compared to counterparts that are not bonded at all to the substrate
Fractal analysis of polar bear hairs
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Wang Qing-Li
2015-01-01
Full Text Available Hairs of a polar bear (Ursus maritimus are of superior properties such as the excellent thermal protection. Why do polar bears can resist such cold environment? The paper concludes that its fractal porosity plays an important role, and its fractal dimensions are very close to the golden mean, 1.618, revealing the possible optimal structure of polar bear hair.
Fractal tomography and its application in 3D vision
Trubochkina, N.
2018-01-01
A three-dimensional artistic fractal tomography method that implements a non-glasses 3D visualization of fractal worlds in layered media is proposed. It is designed for the glasses-free 3D vision of digital art objects and films containing fractal content. Prospects for the development of this method in art galleries and the film industry are considered.
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.
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)
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
A short history of fractal-Cantorian space-time
International Nuclear Information System (INIS)
Marek-Crnjac, L.
2009-01-01
The article attempts to give a short historical overview of the discovery of fractal-Cantorian space-time starting from the 17th century up to the present. In the last 25 years a great number of scientists worked on fractal space-time notably Garnet Ord in Canada, Laurent Nottale in France and Mohamed El Naschie in England who gave an exact mathematical procedure for the derivation of the dimensionality and curvature of fractal space-time fuzzy manifold.
Enhancement of critical temperature in fractal metamaterial superconductors
Energy Technology Data Exchange (ETDEWEB)
Smolyaninov, Igor I., E-mail: smoly@umd.edu [Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742 (United States); Smolyaninova, Vera N. [Department of Physics Astronomy and Geosciences, Towson University, 8000 York Road, Towson, MD 21252 (United States)
2017-04-15
Fractal metamaterial superconductor geometry has been suggested and analyzed based on the recently developed theoretical description of critical temperature increase in epsilon near zero (ENZ) metamaterial superconductors. Considerable enhancement of critical temperature has been predicted in such materials due to appearance of large number of additional poles in the inverse dielectric response function of the fractal. Our results agree with the recent observation (Fratini et al. Nature 466, 841 (2010)) that fractal defect structure promotes superconductivity.
International Nuclear Information System (INIS)
Ren Xincheng; Guo Lixin
2008-01-01
A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing. (classical areas of phenomenology)
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.
Fractal Dimension of Fracture Surface in Rock Material after High Temperature
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Z. Z. Zhang
2015-01-01
Full Text Available Experiments on granite specimens after different high temperature under uniaxial compression were conducted and the fracture surfaces were observed by scanning electron microscope (SEM. The fractal dimensions of the fracture surfaces with increasing temperature were calculated, respectively. The fractal dimension of fracture surface is between 1.44 and 1.63. Its value approximately goes up exponentially with the increase of temperature. There is a quadratic polynomial relationship between the rockburst tendency and fractal dimension of fracture surface; namely, a fractal dimension threshold can be obtained. Below the threshold value, a positive correlativity shows between rockburst tendency and fractal dimension; when the fractal dimension is greater than the threshold value, it shows an inverse correlativity.
Fu, Yanshu; Qiu, Yaohui; Li, Yulong
2018-05-01
The mechanical anisotropy of an explosive welding composite plate made of 304 stainless steel/245 steel was studied through shear experiments performed on explosively welded wavy interfaces along several orientation angles. The results indicated that the strength and the fracture energy of samples significantly varied with the orientation angles. The fracture surfaces of all samples were observed using a scanning electron microscope and through three-dimensional structure microscopy. The periodic features of all the fracture surfaces were clearly shown in different fracture modes. The fractal dimension of the fracture surfaces was calculated based on the fractal geometry by the box-counting method in MATLAB. The cohesive element model was used to analyze the fracture energy according to the physical dependence of the fractal dimension on thermodynamic entropy and interface separation energy. The fracture energy was an exponential function of the fractal dimension value, which was in good agreement with the experimental results. All results were validated for effective use in the application of anisotropy analysis to the welded interface and structural optimization of explosively welded composite plates.
Evaluation of peri-implant bone using fractal analysis
International Nuclear Information System (INIS)
Jung, Yun Hoa
2005-01-01
The purpose of this study was to investigate whether the fractal dimension of successive panoramic radiographs of bone after implant placement is useful in the characterization of structural change in alveolar bone. Twelve subjects with thirty-five implants were retrospectively followed-up from one week to six months after implantation. Thirty-six panoramic radiographs from twelve patients were classified into 1 week. 1-2 months and 3-6 months after implantation and digitized. The windows of bone apical and mesial or distal to the implant were defined as peri apical region of interest (ROI) and inter dental ROI; the fractal dimension of the image was calculated. There was not a statistically significant difference in fractal dimensions during the period up to 6 months after implantation. The fractal dimensions were higher in 13 and 15 mm than 10 and 11.5 mm implant length at inter dental ROIs in 3-6 months after implantation (p<0.01). Longer fixtures showed the higher fractal dimension of bone around implant. This investigation needs further exploration with large numbers of implants for longer follow-up periods.
Fractal analysis for studying the evolution of forests
International Nuclear Information System (INIS)
Andronache, Ion C.; Ahammer, Helmut; Jelinek, Herbert F.; Peptenatu, Daniel; Ciobotaru, Ana-M.; Draghici, Cristian C.; Pintilii, Radu D.; Simion, Adrian G.
2016-01-01
Highlights: • Legal and illegal deforestation is investigated by fractal analysis. • A new fractal fragmentation index FFI is proposed. • Differences in shapes of forest areas indicate the type of deforestation. • Support of ecological management. - Abstract: Deforestation is an important phenomenon that may create major imbalances in ecosystems. In this study we propose a new mathematical analysis of the forest area dynamic, enabling qualitative as well as quantitative statements and results. Fractal dimensions of the area and the perimeter of a forest were determined using digital images. The difference between fractal dimensions of the area and the perimeter images turned out to be a crucial quantitative parameter. Accordingly, we propose a new fractal fragmentation index, FFI, which is based on this difference and which highlights the degree of compaction or non-compaction of the forest area in order to interpret geographic features. Particularly, this method was applied to forests, where large areas have been legally or illegally deforested. However, these methods can easily be used for other ecological or geographical investigations based on digital images, including deforestation of rainforests.
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
Spatiotemporal Diffusive Evolution and Fractal Structure of Ground Motion
Suwada, Tsuyoshi
2018-02-01
The spatiotemporal diffusive evolution and fractal structure of ground motion have been investigated at the in-ground tunnel of the KEK B-Factory (KEKB) injector linear accelerator (linac). The slow dynamic fluctuating displacements of the tunnel floor are measured in real time with a new remote-controllable sensing system based on a laser-based alignment system. Based on spatiotemporal analyses with linear-regression models, which were applied in both the time and frequency domains to time-series data recorded over a period of approximately 8 months, both coherent and stochastic components in the displacements of the tunnel floor were clearly observed along the entire length of the linac. In particular, it was clearly observed that the stochastic components exhibited characteristic spatiotemporal diffusive evolution with the fractal structure and fractional dimension. This report describes in detail the experimental techniques and analyses of the spatiotemporal diffusive evolution of ground motion observed at the in-ground tunnel of the injector linac using a real-time remote-controllable sensing system.
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 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...
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.
Determining Effective Thermal Conductivity of Fabrics by Using Fractal Method
Zhu, Fanglong; Li, Kejing
2010-03-01
In this article, a fractal effective thermal conductivity model for woven fabrics with multiple layers is developed. Structural models of yarn and plain woven fabric are derived based on the fractal characteristics of macro-pores (gap or channel) between the yarns and micro-pores inside the yarns. The fractal effective thermal conductivity model can be expressed as a function of the pore structure (fractal dimension) and architectural parameters of the woven fabric. Good agreement is found between the fractal model and the thermal conductivity measurements in the general porosity ranges. It is expected that the model will be helpful in the evaluation of thermal comfort for woven fabric in the whole range of porosity.
Modelling, fabrication and characterisation of THz fractal meta-materials
DEFF Research Database (Denmark)
Xiao, S.; Zhou, L.; Malureanu, Radu
2011-01-01
We present theoretical predictions, fabrication procedure and characterisation results of fractal metamaterials for the THz frequency range. The characterisation results match well the predicted response thus validating both the fabrication procedure as well as the simulation one. Such systems sh...
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...
Fractal characteristics of fracture morphology of steels irradiated with high-energy ions
Energy Technology Data Exchange (ETDEWEB)
Xian, Yongqiang; Liu, Juan [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China); University of Chinese Academy of Science, Beijing 100049 (China); Zhang, Chonghong, E-mail: c.h.zhang@impcas.ac.cn [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China); Chen, Jiachao [Paul Scherrer Institute, Villigen PSI (Switzerland); Yang, Yitao; Zhang, Liqing; Song, Yin [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China)
2015-06-15
Highlights: • Fractal dimensions of fracture surfaces of steels before and after irradiation were calculated. • Fractal dimension can effectively describe change of fracture surfaces induced by irradiation. • Correlation of change of fractal dimension with embrittlement of irradiated steels is discussed. - Abstract: A fractal analysis of fracture surfaces of steels (a ferritic/martensitic steel and an oxide-dispersion-strengthened ferritic steel) before and after the irradiation with high-energy ions is presented. Fracture surfaces were acquired from a tensile test and a small-ball punch test (SP). Digital images of the fracture surfaces obtained from scanning electron microscopy (SEM) were used to calculate the fractal dimension (FD) by using the pixel covering method. Boundary of binary image and fractal dimension were determined with a MATLAB program. The results indicate that fractal dimension can be an effective parameter to describe the characteristics of fracture surfaces before and after irradiation. The rougher the fracture surface, the larger the fractal dimension. Correlation of the change of fractal dimension with the embrittlement of the irradiated steels is discussed.
Rheological and fractal characteristics of unconditioned and conditioned water treatment residuals.
Dong, Y J; Wang, Y L; Feng, J
2011-07-01
The rheological and fractal characteristics of raw (unconditioned) and conditioned water treatment residuals (WTRs) were investigated in this study. Variations in morphology, size, and image fractal dimensions of the flocs/aggregates in these WTR systems with increasing polymer doses were analyzed. The results showed that when the raw WTRs were conditioned with the polymer CZ8688, the optimum polymer dosage was observed at 24 kg/ton dry sludge. The average diameter of irregularly shaped flocs/aggregates in the WTR suspensions increased from 42.54 μm to several hundred micrometers with increasing polymer doses. Furthermore, the aggregates in the conditioned WTR system displayed boundary/surface and mass fractals. At the optimum polymer dosage, the aggregates formed had a volumetric average diameter of about 820.7 μm, with a one-dimensional fractal dimension of 1.01 and a mass fractal dimension of 2.74 on the basis of the image analysis. Rheological tests indicated that the conditioned WTRs at the optimum polymer dosage showed higher levels of shear-thinning behavior than the raw WTRs. Variations in the limiting viscosity (η(∞)) of conditioned WTRs with sludge content could be described by a linear equation, which were different from the often-observed empirical exponential relationship for most municipal sludge. With increasing temperature, the η(∞) of the raw WTRs decreased more rapidly than that of the raw WTRs. Good fitting results for the relationships between lgη(∞)∼T using the Arrhenius equation indicate that the WTRs had a much higher activation energy for viscosity of about 17.86-26.91 J/mol compared with that of anaerobic granular sludge (2.51 J/mol) (Mu and Yu, 2006). In addition, the Bingham plastic model adequately described the rheological behavior of the conditioned WTRs, whereas the rheology of the raw WTRs fit the Herschel-Bulkley model well at only certain sludge contents. Considering the good power-law relationships between the
Collisions of ideal gas molecules with a rough/fractal surface. A computational study.
Panczyk, Tomasz
2007-02-01
The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using random deposition technique. By applying various depositions, the roughness of the surface was controlled and, as a measure of the irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in argon (under pressures 2 x 10(3) to 2 x 10(5) Pa) and the numbers of collisions with these surfaces were counted. The calculations were carried out using a simplified molecular dynamics simulation technique (only hard core repulsions were assumed). As a result, it was stated that the frequency of collisions is a linear function of pressure for all fractal dimensions studied (D = 2, ..., 2.5). The frequency per unit pressure is quite complex function of the fractal dimension; however, the changes of that frequency with the fractal dimension are not strong. It was found that the frequency of collisions is controlled by the number of weakly folded sites on the surfaces and there is some mapping between the shape of adsorption energy distribution functions and this number of weakly folded sites. The results for the rough/fractal surfaces were compared with the prediction given by the Langmuir-Hertz equation (valid for smooth surface), generally the departure from the Langmuir-Hertz equation is not higher than 48% for the studied systems (i.e. for the surfaces created using the random deposition technique).
A new numerical approximation of the fractal ordinary differential equation
Atangana, Abdon; Jain, Sonal
2018-02-01
The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.
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.
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
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
Sen, S.; Stebbins, J. F.
1994-07-01
A comparative study of the 29Si spin-lattice relaxation behavior (induced by trace amounts of paramagnetic dopants in the glass) in phase-separated Li2Si4O9 and monophasic Li2Si2O5 and Na2Si2O5 glasses has been made in order to understand the nature of clustering and the resulting intermediate-range ordering. Optically clear tetrasilicate and disilicate glasses were prepared with 500 to 2000 ppm of Gd2O3, a paramagnetic dopant. The constituent structural units (Q3 and Q4 species) in all tetrasilicate glasses show strong differential relaxation following a power-law behavior. This is due to preferential partitioning of Gd3+ into the lower silica (Q3-rich) regions of these glasses, indicating the presence of Q species clusters too small to produce optical opalescence (a few nm to perhaps tens of nm). Preliminary results on 6Li spin-lattice relaxation in these glasses support this hypothesis. Differential relaxation becomes more pronounced on annealing due to growth of such clusters. No such differential relaxation was observed in the monophase disilicate glasses. For spin-lattice relaxation induced by direct dipolar coupling to paramagnetic ions, the recovery of magnetization is proportional to time as M(t)~tα where α is a function of the dimensionality D of mass distribution of the constituent Q species around the Gd3+ paramagnetic centers in the glass. For tetrasilicate glasses D~=2.62+/-0.22 and the system behaves as a mass fractal up to a length scale of 2 to 3 nm. D is thus equal to, within error, the theoretical value of 2.6 for an infinite percolation cluster of one type of Q species in another. For disilicate glasses, D~=3.06+/-0.18 which indicates a three-dimensional (and thus nonfractal) mass distribution of the constituent Q species over the same length scale.
From dendrimers to fractal polymers and beyond
Directory of Open Access Journals (Sweden)
Charles N. Moorefield
2013-01-01
Full Text Available The advent of dendritic chemistry has facilitated materials research by allowing precise control of functional component placement in macromolecular architecture. The iterative synthetic protocols used for dendrimer construction were developed based on the desire to craft highly branched, high molecular weight, molecules with exact mass and tailored functionality. Arborols, inspired by trees and precursors of the utilitarian macromolecules known as dendrimers today, were the first examples to employ predesigned, 1 → 3 C-branched, building blocks; physical characteristics of the arborols, including their globular shapes, excellent solubilities, and demonstrated aggregation, combined to reveal the inherent supramolecular potential (e.g., the unimolecular micelle of these unique species. The architecture that is a characteristic of dendritic materials also exhibits fractal qualities based on self-similar, repetitive, branched frameworks. Thus, the fractal design and supramolecular aspects of these constructs are suggestive of a larger field of fractal materials that incorporates repeating geometries and are derived by complementary building block recognition and assembly. Use of terpyridine-M2+-terpyridine (where, M = Ru, Zn, Fe, etc connectivity in concert with mathematical algorithms, such as forms the basis for the Seirpinski gasket, has allowed the beginning exploration of fractal materials construction. The propensity of the fractal molecules to self-assemble into higher order architectures adds another dimension to this new arena of materials and composite construction.
Paper-based inkjet-printed ultra-wideband fractal antennas
Maza, Armando Rodriguez; Cook, Benjamin Stassen; Jabbour, Ghassan E.; Shamim, Atif
2012-01-01
For the first time, paper-based inkjet-printed ultra-wideband (UWB) fractal antennas are presented. Two new designs, a miniaturised UWB monopole, which utilises a fractal matching network and is the smallest reported inkjet-printed UWB printed
Assessment of textural differentiations in forest resources in Romania using fractal analysis
DEFF Research Database (Denmark)
Andronache, Ion; Fensholt, Rasmus; Ahammer, Helmut
2017-01-01
regions in Romania affected by both deforestation and reforestation using a non-Euclidean method based on fractal analysis.We calculated four fractal dimensions of forest areas: the fractal box-counting dimension of the forest areas, the fractal box-counting dimension of the dilated forest areas......, the fractal dilation dimension and the box-counting dimension of the border of the dilated forest areas. Fractal analysis revealed morpho-structural and textural differentiations of forested, deforested and reforested areas in development regions with dominant mountain relief and high hills (more forested...... and compact organization) in comparison to the development regions dominated by plains or low hills (less forested, more fragmented with small and isolated clusters). Our analysis used the fractal analysis that has the advantage of analyzing the entire image, rather than studying local information, thereby...
Band structures in Sierpinski triangle fractal porous phononic crystals
International Nuclear Information System (INIS)
Wang, Kai; Liu, Ying; Liang, Tianshu
2016-01-01
In this paper, the band structures in Sierpinski triangle fractal porous phononic crystals (FPPCs) are studied with the aim to clarify the effect of fractal hierarchy on the band structures. Firstly, one kind of FPPCs based on Sierpinski triangle routine is proposed. Then the influence of the porosity on the elastic wave dispersion in Sierpinski triangle FPPCs is investigated. The sensitivity of the band structures to the fractal hierarchy is discussed in detail. The results show that the increase of the hierarchy increases the sensitivity of ABG (Absolute band gap) central frequency to the porosity. But further increase of the fractal hierarchy weakens this sensitivity. On the same hierarchy, wider ABGs could be opened in Sierpinski equilateral triangle FPPC; whilst, a lower ABG could be opened at lower porosity in Sierpinski right-angled isosceles FPPCs. These results will provide a meaningful guidance in tuning band structures in porous phononic crystals by fractal design.
Band structures in Sierpinski triangle fractal porous phononic crystals
Energy Technology Data Exchange (ETDEWEB)
Wang, Kai; Liu, Ying, E-mail: yliu5@bjtu.edu.cn; Liang, Tianshu
2016-10-01
In this paper, the band structures in Sierpinski triangle fractal porous phononic crystals (FPPCs) are studied with the aim to clarify the effect of fractal hierarchy on the band structures. Firstly, one kind of FPPCs based on Sierpinski triangle routine is proposed. Then the influence of the porosity on the elastic wave dispersion in Sierpinski triangle FPPCs is investigated. The sensitivity of the band structures to the fractal hierarchy is discussed in detail. The results show that the increase of the hierarchy increases the sensitivity of ABG (Absolute band gap) central frequency to the porosity. But further increase of the fractal hierarchy weakens this sensitivity. On the same hierarchy, wider ABGs could be opened in Sierpinski equilateral triangle FPPC; whilst, a lower ABG could be opened at lower porosity in Sierpinski right-angled isosceles FPPCs. These results will provide a meaningful guidance in tuning band structures in porous phononic crystals by fractal design.
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
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
An efficient fractal image coding algorithm using unified feature and DCT
International Nuclear Information System (INIS)
Zhou Yiming; Zhang Chao; Zhang Zengke
2009-01-01
Fractal image compression is a promising technique to improve the efficiency of image storage and image transmission with high compression ratio, however, the huge time consumption for the fractal image coding is a great obstacle to the practical applications. In order to improve the fractal image coding, efficient fractal image coding algorithms using a special unified feature and a DCT coder are proposed in this paper. Firstly, based on a necessary condition to the best matching search rule during fractal image coding, the fast algorithm using a special unified feature (UFC) is addressed, and it can reduce the search space obviously and exclude most inappropriate matching subblocks before the best matching search. Secondly, on the basis of UFC algorithm, in order to improve the quality of the reconstructed image, a DCT coder is combined to construct a hybrid fractal image algorithm (DUFC). Experimental results show that the proposed algorithms can obtain good quality of the reconstructed images and need much less time than the baseline fractal coding algorithm.
Characterisation of human non-proliferativediabetic retinopathy using the fractal analysis
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Carmen Alina Lupaşcu
2015-08-01
Full Text Available AIM:To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method.METHODS:This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding to both normal (24 images and pathological (148 images states of the retina were examined. An automatic unsupervised method for retinal vessel segmentation was applied before fractal analysis. The fractal analyses of the retinal digital images were performed using the fractal analysis software ImageJ. Statistical analyses were performed for these groups using Microsoft Office Excel 2003 and GraphPad InStat software.RESULTS:It was found that subtle changes in the vascular network geometry of the human retina are influenced by diabetic retinopathy (DR and can be estimated using the fractal geometry. The average of fractal dimensions D for the normal images (segmented and skeletonized versions is slightly lower than the corresponding values of mild non-proliferative DR (NPDR images (segmented and skeletonized versions. The average of fractal dimensions D for the normal images (segmented and skeletonized versions is higher than the corresponding values of moderate NPDR images (segmented and skeletonized versions. The lowest values were found for the corresponding values of severe NPDR images (segmented and skeletonized versions.CONCLUSION:The fractal analysis of fundus photographs may be used for a more complete undeTrstanding of the early and basic pathophysiological mechanisms of diabetes. The architecture of the retinal microvasculature in diabetes can be quantitative quantified by means of the fractal dimension. Microvascular abnormalities on retinal imaging may elucidate early mechanistic pathways for microvascular complications and distinguish patients with
Fractal dimension evolution and spatial replacement dynamics of urban growth
International Nuclear Information System (INIS)
Chen Yanguang
2012-01-01
Highlights: ► The fractal dimension growth can be modeled by Boltzmann’s equation. ► Boltzmann’s model suggests urban spatial replacement dynamics. ► If the rate of urban growth is too high, periodic oscillations or chaos will arise. ► Chaos is associated with fractals by the fractal dimension evolution model. ► The fractal dimension of urban form implies the space-filling ratio of a city. - Abstract: This paper presents a new perspective of looking at the relation between fractals and chaos by means of cities. Especially, a principle of space filling and spatial replacement is proposed to interpret the fractal dimension of urban form. The fractal dimension evolution of urban growth can be empirically modeled with Boltzmann’s equation. For the normalized data, Boltzmann’s equation is just equivalent to the logistic function. The logistic equation can be transformed into the well-known 1-dimensional logistic map, which is based on a 2-dimensional map suggesting spatial replacement dynamics of city development. The 2-dimensional recurrence relations can be employed to generate the nonlinear dynamical behaviors such as bifurcation and chaos. A discovery is thus made in this article that, for the fractal dimension growth following the logistic curve, the normalized dimension value is the ratio of space filling. If the rate of spatial replacement (urban growth) is too high, the periodic oscillations and chaos will arise. The spatial replacement dynamics can be extended to general replacement dynamics, and bifurcation and chaos mirror a process of complex replacement.
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.
Feature extraction algorithm for space targets based on fractal theory
Tian, Balin; Yuan, Jianping; Yue, Xiaokui; Ning, Xin
2007-11-01
In order to offer a potential for extending the life of satellites and reducing the launch and operating costs, satellite servicing including conducting repairs, upgrading and refueling spacecraft on-orbit become much more frequently. Future space operations can be more economically and reliably executed using machine vision systems, which can meet real time and tracking reliability requirements for image tracking of space surveillance system. Machine vision was applied to the research of relative pose for spacecrafts, the feature extraction algorithm was the basis of relative pose. In this paper fractal geometry based edge extraction algorithm which can be used in determining and tracking the relative pose of an observed satellite during proximity operations in machine vision system was presented. The method gets the gray-level image distributed by fractal dimension used the Differential Box-Counting (DBC) approach of the fractal theory to restrain the noise. After this, we detect the consecutive edge using Mathematical Morphology. The validity of the proposed method is examined by processing and analyzing images of space targets. The edge extraction method not only extracts the outline of the target, but also keeps the inner details. Meanwhile, edge extraction is only processed in moving area to reduce computation greatly. Simulation results compared edge detection using the method which presented by us with other detection methods. The results indicate that the presented algorithm is a valid method to solve the problems of relative pose for spacecrafts.
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.
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.
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
Speculations on self-avoiding surfaces in fractals. A mean field treatment
International Nuclear Information System (INIS)
Pandey, R.B.; Kumar, N.; Stauffer, D.
1984-08-01
We estimate the exponents characterizing the self-avoiding surfaces using an approximation in the framework of a Flory-type theory. We find for planar self-avoiding surfaces embedded randomly in a fractal of dimensionality D':theta=3/(4+D'); for random surfaces of fractal dimension D embedded in a Euclidian space of dimensionality d:theta=3/(2D+d-2); and for fractal surfaces embedded in a structure of fractal dimensionality D':theta=3/(2D+D'-2). (author)
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.
Determination of fish gender using fractal analysis of ultrasound images
DEFF Research Database (Denmark)
McEvoy, Fintan J.; Tomkiewicz, Jonna; Støttrup, Josianne
2009-01-01
The gender of cod Gadus morhua can be determined by considering the complexity in their gonadal ultrasonographic appearance. The fractal dimension (DB) can be used to describe this feature in images. B-mode gonadal ultrasound images in 32 cod, where gender was known, were collected. Fractal...... by subjective analysis alone. The mean (and standard deviation) of the fractal dimension DB for male fish was 1.554 (0.073) while for female fish it was 1.468 (0.061); the difference was statistically significant (P=0.001). The area under the ROC curve was 0.84 indicating the value of fractal analysis in gender...... result. Fractal analysis is useful for gender determination in cod. This or a similar form of analysis may have wide application in veterinary imaging as a tool for quantification of complexity in images...
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.
Insulator Contamination Forecasting Based on Fractal Analysis of Leakage Current
Directory of Open Access Journals (Sweden)
Bing Luo
2012-07-01
Full Text Available In this paper, an artificial pollution test is carried out to study the leakage current of porcelain insulators. Fractal theory is adopted to extract the characteristics hidden in leakage current waveforms. Fractal dimensions of the leakage current for the security, forecast and danger zones are analyzed under four types of degrees of contamination. The mean value and the standard deviation of the fractal dimension in the forecast zone are calculated to characterize the differences. The analysis reveals large differences in the fractal dimension of leakage current under different contamination discharge stages and degrees. The experimental and calculation results suggest that the fractal dimension of a leakage current waveform can be used as a new indicator of the discharge process and contamination degree of insulators. The results provide new methods and valid indicators for forecasting contamination flashovers.
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.
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
A New Fractal Multiband Antenna for Wireless Power Transmission Applications
Directory of Open Access Journals (Sweden)
Taoufik Benyetho
2018-01-01
Full Text Available The Microwave Power Transmission (MPT is the possibility of feeding a system without contact by using microwave energy. The challenge of such system is to increase the efficiency of transmitted energy from the emitter to the load. This can be achieved by rectifying the microwave energy using a rectenna system composed of an antenna of a significant gain associated with a rectifier with a good input impedance matching. In this paper, a new multiband antenna using the microstrip technology and fractal geometry is developed. The fractal antenna is validated into simulation and measurement in the ISM (industrial, scientific, and medical band at 2.45 GHz and 5.8 GHz and it presents a wide aperture angle with an acceptable gain for both bands. The final antenna is printed over an FR4 substrate with a dimension of 60 × 30 mm2. These characteristics make the antenna suitable for a multiband rectenna circuit use.
Hybrid 3D Fractal Coding with Neighbourhood Vector Quantisation
Directory of Open Access Journals (Sweden)
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.
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.
International Nuclear Information System (INIS)
Pyun, Su-Il; Rhee, Chang-Kyu
2004-01-01
Fractal characteristics of mesoporous carbon electrodes were investigated with various pore structures using the N 2 gas adsorption method and the transmission electron microscopy (TEM) image analysis method. The mesoporous carbons with various pore structures were prepared by imprinting mesophase pitch used as a carbonaceous precursor with different colloidal silica particles. All imprinted mesoporous carbons were composed of two groups of pores produced from the carbonisation of mesophase pitch and from the silica imprinting. The overall surface fractal dimensions of the carbon specimens were determined from the analyses of the N 2 gas adsorption isotherms. In order to distinguish the surface fractal dimension of the carbonisation-induced pore surface from that fractal dimension of the silica-imprinted pore surface, the individual surface fractal dimensions were determined from the image analyses of the TEM images. From the comparison of the overall surface fractal dimension with the individual surface fractal dimensions, it was recognised that the overall surface fractal dimension is crucially influenced by the individual surface fractal dimension of the silica-imprinted pore surface. Moreover, from the fact that the silica-imprinted pore surface with broad relative pore size distribution (PSD) gave lower value of the individual surface fractal dimension than that pore surface with narrow relative PSD, it is concluded that as the silica-imprinted pores comprising the carbon specimen agglomerate, the individual surface fractal dimension of that pore surface decreases
FRACTAL IMAGE FEATURE VECTORS WITH APPLICATIONS IN FRACTOGRAPHY
Directory of Open Access Journals (Sweden)
Hynek Lauschmann
2011-05-01
Full Text Available The morphology of fatigue fracture surface (caused by constant cycle loading is strictly related to crack growth rate. This relation may be expressed, among other methods, by means of fractal analysis. Fractal dimension as a single numerical value is not sufficient. Two types of fractal feature vectors are discussed: multifractal and multiparametric. For analysis of images, the box-counting method for 3D is applied with respect to the non-homogeneity of dimensions (two in space, one in brightness. Examples of application are shown: images of several fracture surfaces are analyzed and related to crack growth rate.
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.
Fractal Dimension and Maximum Sunspot Number in Solar Cycle
Directory of Open Access Journals (Sweden)
R.-S. Kim
2006-09-01
Full Text Available The fractal dimension is a quantitative parameter describing the characteristics of irregular time series. In this study, we use this parameter to analyze the irregular aspects of solar activity and to predict the maximum sunspot number in the following solar cycle by examining time series of the sunspot number. For this, we considered the daily sunspot number since 1850 from SIDC (Solar Influences Data analysis Center and then estimated cycle variation of the fractal dimension by using Higuchi's method. We examined the relationship between this fractal dimension and the maximum monthly sunspot number in each solar cycle. As a result, we found that there is a strong inverse relationship between the fractal dimension and the maximum monthly sunspot number. By using this relation we predicted the maximum sunspot number in the solar cycle from the fractal dimension of the sunspot numbers during the solar activity increasing phase. The successful prediction is proven by a good correlation (r=0.89 between the observed and predicted maximum sunspot numbers in the solar cycles.
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
Dubuc, Serge
1991-01-01
This ASI- which was also the 28th session of the Seminaire de mathematiques superieures of the Universite de Montreal - was devoted to Fractal Geometry and Analysis. The present volume is the fruit of the work of this Advanced Study Institute. We were fortunate to have with us Prof. Benoit Mandelbrot - the creator of numerous concepts in Fractal Geometry - who gave a series of lectures on multifractals, iteration of analytic functions, and various kinds of fractal stochastic processes. Different foundational contributions for Fractal Geometry like measure theory, dy namical systems, iteration theory, branching processes are recognized. The geometry of fractal sets and the analytical tools used to investigate them provide a unifying theme of this book. The main topics that are covered are then as follows. Dimension Theory. Many definitions of fractional dimension have been proposed, all of which coincide on "regular" objects, but often take different values for a given fractal set. There is ample discussion ...
Extremal dynamics: A unifying physical explanation of fractals, 1/f noise, and activated processes
International Nuclear Information System (INIS)
Miller, S.L.; Miller, W.M.; McWhorter, P.J.
1993-01-01
The properties of physical systems whose observable properties depend upon random exceedances of critical parameters are quantitatively examined. Using extreme value theory, the dynamical behavior of this broad class of systems is derived. This class of systems can exhibit two characteristic signatures: generalized activation when far from equilibrium and noise with a characteristic power spectrum (including 1/f ) when in quasiequilibrium. Fractal structures can also arise from these systems. It is thus demonstrated that generalized activation, noise, and fractals, in some cases, are simply different manifestations of a single common dynamical principle, which is termed ''extremal dynamics.'' Examples of physical processes governed by extremal dynamics are discussed, including data loss of nonvolatile memories and dielectric breakdown
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.
Griscom, David L.
2001-11-01
Formalisms have been developed to express the time evolution of bimolecular processes taking place in fractal spaces. These ``stretched-second-order'' solutions are specifically applicable to radiation-induced electron-hole pairs and/or vacancy-interstitial pairs in insulating glasses. Like the analogous Kohlrausch-type (stretched-first-order) expressions, the present solutions are functions of (kt)β, where 0the new second-order formalism and the familiar Kohlrausch approach have been used to fit experimental data (induced optical absorptions in silica-based glasses monitored at selected wavelengths) that serve as proxies for the numbers of color centers created by γ irradiation and/or destroyed by processes involving thermal, optical, or γ-ray activation. Two material systems were investigated: (1) optical fibers with Ge-doped-silica cores and (2) fibers with low-OH/low-chloride pure-silica cores. Successful fits of the growth curves for the Ge-doped-silica-core fibers at four widely separated dose rates were accomplished using solutions for color-center concentrations, N[(kt)β], which approach steady-state values, Nsat, as t-->∞. The parametrization of these fits reveals some unexpected, and potentially useful, empirical rules regarding the dose-rate dependences of β, k, and Nsat in the fractal regime (0the pure-silica-core fibers as well. In both material systems, there appear to be fractal classical phase transitions at certain threshold values of dose rate, below which the dose-rate dependencies of k and Nsat revert to those specified by classical (β=1) first- or second-order kinetics. For ktthe first- and second-order fractal kinetic growth curves become identical, i.e., N((kt)β)~Atβ, where the coefficient A depends on dose rate but not kinetic order. It is found empirically that A depends on the 3β/2 power of dose rate in both first- and second-order kinetics, thus ``accidentally'' becoming linearly proportional to dose rate in cases where β~2
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...
Anisotropic fractal media by vector calculus in non-integer dimensional space
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)
2014-08-15
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
Anisotropic fractal media by vector calculus in non-integer dimensional space
Tarasov, Vasily E.
2014-08-01
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
Anisotropic fractal media by vector calculus in non-integer dimensional space
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2014-01-01
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media
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 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.
Return to axi-symmetry for pipe flows generated after a fractal orifice
Energy Technology Data Exchange (ETDEWEB)
Nicolleau, F C G A, E-mail: F.Nicolleau@Sheffield.ac.uk [SFMG, Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD (United Kingdom)
2013-12-15
We present experimental results obtained from pipe flows generated by fractal shaped orifices or openings. We compare different fractal orifices and their efficiencies to re-generate axi-symmetric flows and to return to the standard flow generated by a perforated plate or a circular orifice plate. We consider two families of fractal openings: mono-orifice and complex orifice and emphasize the differences between the two fractal families. For the Reynolds number we used, we found that there is an optimum iteration for the fractal level above which no improvement for practical applications such as flowmetering is to be expected. The main parameters we propose for the characterization of the fractal orifice are the connexity parameter, the symmetry angle and the gap to the wall {delta}*{sub g}. The results presented here are among the first for flows forced through fractal openings and will serve as a reference for future studies and benchmarks for numerical applications. (paper)
Return to axi-symmetry for pipe flows generated after a fractal orifice
International Nuclear Information System (INIS)
Nicolleau, F C G A
2013-01-01
We present experimental results obtained from pipe flows generated by fractal shaped orifices or openings. We compare different fractal orifices and their efficiencies to re-generate axi-symmetric flows and to return to the standard flow generated by a perforated plate or a circular orifice plate. We consider two families of fractal openings: mono-orifice and complex orifice and emphasize the differences between the two fractal families. For the Reynolds number we used, we found that there is an optimum iteration for the fractal level above which no improvement for practical applications such as flowmetering is to be expected. The main parameters we propose for the characterization of the fractal orifice are the connexity parameter, the symmetry angle and the gap to the wall δ* g . The results presented here are among the first for flows forced through fractal openings and will serve as a reference for future studies and benchmarks for numerical applications. (paper)
Turbulent premixed flames on fractal-grid-generated turbulence
Energy Technology Data Exchange (ETDEWEB)
Soulopoulos, N; Kerl, J; Sponfeldner, T; Beyrau, F; Hardalupas, Y; Taylor, A M K P [Mechanical Engineering Department, Imperial College London, London SW7 2AZ (United Kingdom); Vassilicos, J C, E-mail: ns6@ic.ac.uk [Department of Aeronautics, Imperial College London, London SW7 2AZ (United Kingdom)
2013-12-15
A space-filling, low blockage fractal grid is used as a novel turbulence generator in a premixed turbulent flame stabilized by a rod. The study compares the flame behaviour with a fractal grid to the behaviour when a standard square mesh grid with the same effective mesh size and solidity as the fractal grid is used. The isothermal gas flow turbulence characteristics, including mean flow velocity and rms of velocity fluctuations and Taylor length, were evaluated from hot-wire measurements. The behaviour of the flames was assessed with direct chemiluminescence emission from the flame and high-speed OH-laser-induced fluorescence. The characteristics of the two flames are considered in terms of turbulent flame thickness, local flame curvature and turbulent flame speed. It is found that, for the same flow rate and stoichiometry and at the same distance downstream of the location of the grid, fractal-grid-generated turbulence leads to a more turbulent flame with enhanced burning rate and increased flame surface area. (paper)
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.
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
Self-stabilized Fractality of Sea-coasts Through Damped Erosion
Sapoval, B.; Baldassari, A.; Gabrielli, A.
2004-05-01
Coastline morphology is of current interest in geophysical research and coastline erosion has important economic consequences. At the same time, although the geometry of seacoasts is often used as an introductory archetype of fractal morphology in nature there has been no explanation about which physical mechanism could justify that empirical observation. The present work propose a minimal, but robust, model of evolution of rocky coasts towards fractality. The model describes how a stationary fractal geometry arises spontaneously from the mutual self-stabilization of a rocky coast morphology and sea eroding power. If, on one hand, erosion generally increases the geometrical irregularity of the coast, on the other hand this increase creates a stronger damping of the sea and a consequent diminution of its eroding power. The increased damping argument relies on the studies of fractal acoustical cavities, which have shown that viscous damping is augmented on a longer, irregular, surface. A minimal two-dimensional model of erosion is introduced which leads to the through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with dimension close to 4/3. Fractal geometry plays here the role of a morphological attractor directly related to percolation geometry. The model reproduces at least qualitatively some of the features of real coasts using only simple ingredients: the randomness of the lithology and the decrease of the erosion power of the sea. B. Sapoval, Fractals (Aditech, Paris, 1989). B. Sapoval, O. Haeberlé, and S.Russ, J. Acoust. Soc. Am., 2014 (1997). B. Hébert B., B. Sapoval, and S.Russ, J. Acoust. Soc. Am., 1567 (1999).
Fractal Geometry in the Arts: AN Overview across the Different Cultures
Sala, Nicoletta
Fractal, in mathematics, is a geometric shape that is complex and detailed in structure at any level of magnification. The word "fractal" was coined less than thirty years ago by one of history's most creative and mathematicians, Benoit Mandelbrot, whose work, The Fractal Geometry of Nature, first introduced and explained concepts underlying this new vision of the geometry. Although other mathematical thinkers like Georg Cantor (1845-1918), Felix Hausdorff (1868-1942), Gaston Julia (1893-1978), Helge von Koch (1870-1924), Giuseppe Peano (1858-1932), Lewis Richardson (1891-1953), Waclaw Sierpinski (1882-1969) and others had attained isolated insights of fractal understanding, such ideas were largely ignored until Mandelbrot's genius forged them at a single blow into a gorgeously coherent and fascinating discipline. Fractal geometry is applied in different field now: engineering, physics, chemistry, biology, and architecture. The aim of this paper is to introduce an approach where the arts are analysed using a fractal point of view.
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)...
International Nuclear Information System (INIS)
Schmidt, P.W.; Tang, Y.; Roell, A.; Steiner, M.; Hoehr, A.; Neumann, H.B.
1990-01-01
Small-angle x-ray and neutron scattering are useful methods for investigating the structure of materials on a scale from about 10 to 2000 A. Some experimental procedures and methods of data analysis for small-angle scattering are outlined, and the use of small-angle scattering for studies of polydisperse systems (i.e., systems of particles of different size) of independently scattering particles is reviewed. Some general properties of the small-angle scattering from mass and surface fractals are discussed, and some applications of these concepts in recent experimental studies are presented. Results obtained in calculations of the small-angle scattering from a model of a surface are summarized. (author) 3 figs., 18 refs
Study on Conversion Between Momentum and Contrarian Based on Fractal Game
Wu, Xu; Song, Guanghui; Deng, Yan; Xu, Lin
2015-06-01
Based on the fractal game which is performed by the majority and the minority, the fractal market theory (FMT) is employed to describe the features of investors' decision-making. Accordingly, the process of fractal games is formed in order to analyze the statistical features of conversion between momentum and contrarian. The result shows that among three fractal game mechanisms, the statistical feature of simulated return rate series is much more similar to log returns on actual series. In addition, the conversion between momentum and contrarian is also extremely similar to real situation, which can reflect the effectiveness of using fractal game in analyzing the conversion between momentum and contrarian. Moreover, it also provides decision-making reference which helps investors develop effective investment strategy.
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.
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.
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.
Two and Three-Phases Fractal Models Application in Soil Saturated Hydraulic Conductivity Estimation
Directory of Open Access Journals (Sweden)
ELNAZ Rezaei abajelu
2017-03-01
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
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.
Fractal Dimension analysis for seismicity spatial and temporal ...
Indian Academy of Sciences (India)
23
The research can further promote the application of fractal theory in the study ... spatial-temporal propagation characteristics of seismic activities, fractal theory is not ... provide a theoretical basis for the prevention and control of earthquakes. 2. ... random self-similar structure of the earthquake in the time series and the spatial.
Experiencia en el aula de secundaria con fractales
Gallardo, Sandra; Martínez-Santaolalla, Manuel José; Molina, Marta; Peñas, María; Cañadas, María C.; Crisóstomo, Edson
2006-01-01
Presentamos una experiencia docente en un aula de 2º ESO en la que trabajamos los fractales mediante el uso de material de carácter manipulativo. La metodología seguida se basa en la construcción de casos particulares con el fin de llegar al concepto de fractal.
A fractal view of Chernobyl fallout in Northern Italy and Europe
International Nuclear Information System (INIS)
Salvadori, G.; Ratti, S.P.; Belli, G.; Quinto, E.
1996-01-01
Fractals are associated with irregularity and represent a powerful tool for investigating phenomena featuring a complex behaviour, as it is the case of the atmospheric processes playing a role in spreading the radioactive pollution of Chernobyl in the environment. The introduction of fractals in environmental sciences is quite recent. Fractals may account for the presence of strong fluctuations and for the high variability characterising the natural events involved in the Chernobyl fallout: the geographical sparseness of pollutant and the presence of 'hot spots' make it advisable to use fractals as a theoretical framework for modelling
A family of fractal sets with Hausdorff dimension 0.618
Energy Technology Data Exchange (ETDEWEB)
Zhong Ting [Information Management and Engineering Institute, Jishou University, Zhangjiajie 427000, Hunan (China)], E-mail: zhongting_2005@126.com
2009-10-15
In this paper, we introduce a class of fractal sets, which can be recursively constructed by two sequences {l_brace}n{sub k}{r_brace}{sub k{>=}}{sub 1} and {l_brace}c{sub k}{r_brace}{sub k{>=}}{sub 1}. We obtain the exact Hausdorff dimensions of these types of fractal sets using the continued fraction map. Connection of continued fraction with El Naschie's fractal spacetime is also illustrated. Furthermore, we restrict one sequence {l_brace}c{sub k}{r_brace}{sub k{>=}}{sub 1} to make every irrational number {alpha} element of (0, 1) correspond to only one of the above fractal sets called {alpha}-Cantor sets, and we found that almost all {alpha}-Cantor sets possess a common Hausdorff dimension of 0.618, which is also the Hausdorff dimension of the one-dimensional random recursive Cantor set and it is the foundation stone of E-infinity fractal spacetime theory.
Formation of fractals by the self-assembly of interpolymer adducts of ...
Indian Academy of Sciences (India)
Polycarboxylic acids form self-organized poly- ... observation of the formation of fractal patterns in self- organizing polyacrylic acid systems in films driven by hydrogen bonding .... various positions, the SEM and EDX studies are car- ried out.
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
Fractal dimension and image statistics of anal intraepithelial neoplasia
International Nuclear Information System (INIS)
Ahammer, H.; Kroepfl, J.M.; Hackl, Ch.; Sedivy, R.
2011-01-01
Research Highlights: → Human papillomaviruses cause anal intraepithelial neoplasia (AIN). → Digital image processing was carried out to classify the grades of AIN quantitatively. → The fractal dimension as well as grey value statistics was calculated. → Higher grades of AIN yielded higher values of the fractal dimension. → An automatic detection system is feasible. - Abstract: It is well known that human papillomaviruses (HPV) induce a variety of tumorous lesions of the skin. HPV-subtypes also cause premalignant lesions which are termed anal intraepithelial neoplasia (AIN). The clinical classification of AIN is of growing interest in clinical practice, due to increasing HPV infection rates throughout human population. The common classification approach is based on subjective inspections of histological slices of anal tissues with all the drawbacks of depending on the status and individual variances of the trained pathologists. Therefore, a nonlinear quantitative classification method including the calculation of the fractal dimension and first order as well as second order image statistical parameters was developed. The absolute values of these quantitative parameters reflected the distinct grades of AIN very well. The quantitative approach has the potential to decrease classification errors significantly and it could be used as a widely applied screening technique.
Form in the Natural Environment: Fractal Computer Graphics and Wassily Kandinsky.
Geake, John; Porter, Jim
1992-01-01
Reports on study of use of fractal geometry in a computer graphics program to improve the perception of intermediate grade level students in their paintings. Finds that students are more likely to use changing shapes and colors after viewing slides of fractal computer graphics. Concludes that fractal computer graphics would make highly engaging…
International Nuclear Information System (INIS)
Ogura, Tatsuo; Miyamoto, Masanori; Budiyono, Agung; Nakamura, Katsuhiro
2007-01-01
Fractal magnetoconductance fluctuations are often observed in experiments on ballistic quantum dots. Although the analysis of the exact self-affine fractal has been given by the semiclassical theory using self-similar periodic orbits in systems with a soft-walled potential with a saddle, there has been no corresponding quantum mechanical investigation. We numerically calculate the quantum conductance with use of the recursive Green's function method applied to open cavities characterized by a Henon-Heiles type potential. The conductance fluctuations show exact self-affinity just as in some of the experimental observations. The enlargement factor for the horizontal axis can be explained by the scaling factor of the area of self-similar periodic orbits, and therefore be attributed to the curvature of the saddle in the cavity potential. The fractal dimension obtained through the box counting method agrees with those evaluated with use of the Hurst exponent, and coincides with the semiclassical prediction. We further investigate the variation of the fractal dimension by changing the control parameters between the classical and quantum domains. (fast track communication)
Prediction of pork quality parameters by applying fractals and data mining on MRI
DEFF Research Database (Denmark)
Caballero, Daniel; Pérez-Palacios, Trinidad; Caro, Andrés
2017-01-01
This work firstly investigates the use of MRI, fractal algorithms and data mining techniques to determine pork quality parameters non-destructively. The main objective was to evaluate the capability of fractal algorithms (Classical Fractal algorithm, CFA; Fractal Texture Algorithm, FTA and One...... Point Fractal Texture Algorithm, OPFTA) to analyse MRI in order to predict quality parameters of loin. In addition, the effect of the sequence acquisition of MRI (Gradient echo, GE; Spin echo, SE and Turbo 3D, T3D) and the predictive technique of data mining (Isotonic regression, IR and Multiple linear...... regression, MLR) were analysed. Both fractal algorithm, FTA and OPFTA are appropriate to analyse MRI of loins. The sequence acquisition, the fractal algorithm and the data mining technique seems to influence on the prediction results. For most physico-chemical parameters, prediction equations with moderate...
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.
Fractal study of Ni-Cr-Mo alloy for dental applications: effect of beryllium
Energy Technology Data Exchange (ETDEWEB)
Eftekhari, Ali
2003-12-30
Different Ni-based alloys with various compositions were prepared by varying the amounts of beryllium. Effect of the amount of beryllium added to the alloy on its corrosion in an electrolyte solution of artificial saliva was investigated. Fractal dimension was used as a quantitative factor for surface analysis of the alloys before and after storage in the artificial salvia. The fractal dimensions of the electrode surfaces were determined by means of the most reliable method in this context viz. time dependency of the diffusion-limited current for a system involving 'diffusion towards electrode surface'. The results showed that increase of the beryllium amount in the alloy composition significantly increases the alloy corrosion. It is accompanied by increase of the fractal dimension and roughness of the electrode surface, whereas a smooth and shiny surface is required for dentures. From the methodology point of view, the approach utilized for fractal analysis of the alloy surfaces (Au-masking of metallic surfaces) is a novel and efficient method for study of denture surfaces. Generally, this approach is of interest for corrosion studies of different metals and alloys, particularly where changes in surface structure have a significant importance.
Plot-slope soil erosion using 7Be measurement and rill fractal dimension
International Nuclear Information System (INIS)
Zhang Fengbao; Yang Mingyi
2010-01-01
In this study, we intended to use 7 Be measurement and fractal theory to quantify soil erosion process on slope. The results showed that contribution rate of inter rill erosion was more than that of rill erosion during early stage of rainfall. When it rained, contribution rate of rill erosion began to be higher than inter rill erosion and become the main part of erosion during medium stage of rainfall. The trend of contribution rate of inter rill erosion was growing and the rill erosion was lowering during late stage of rainfall. Rill fractal dimension on the plot slope was almost growing larger during rainfall,growing quickly during early stage of rainfall and slowly during the late stage. Correlations was positive between rill fractal dimension and total erosion amount, also positive between rill fractal dimension and rill erosion. The correlations was positive between rill fractal dimension variation and total erosion amount, also was positive between rill fractal dimension variation and rill erosion amount. The best correlation was observed between rill fractal dimension and rill erosion amount. These results indicated that the rill fractal dimension on the plot slope could represent the development process of rill,the complex degree of rill and the variation of soil erosion intensity on the entire slope. (authors)
Fractal dimension of the fractured surface of materials
International Nuclear Information System (INIS)
Lung, C.W.; Zhang, S.Z.
1989-05-01
Fractal dimension of the fractured surface of materials is discussed to show that the origin of the negative correlation between D F and toughness lies in the method of fractal dimension measurement with perimeter-area relation and also in the physical mechanism of crack propagation. (author). 8 refs, 4 figs, 1 tab
A variable-order fractal derivative model for anomalous diffusion
Directory of Open Access Journals (Sweden)
Liu Xiaoting
2017-01-01
Full Text Available This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.
Moisture diffusivity in structure of random fractal fiber bed
Energy Technology Data Exchange (ETDEWEB)
Zhu, Fanglong, E-mail: zhufanglong_168@163.com [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); The Chinese People' s Armed Police Forces Academy, Langfan City (China); Zhou, Yu; Feng, Qianqian [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); Xia, Dehong [School of Mechanical Engineering, University of Science and Technology, Beijing (China)
2013-11-08
A theoretical expression related to effective moisture diffusivity to random fiber bed is derived by using fractal theory and considering both parallel and perpendicular channels to diffusion flow direction. In this Letter, macroporous structure of hydrophobic nonwoven material is investigated, and Knudsen diffusion and surface diffusion are neglected. The effective moisture diffusivity predicted by the present fractal model are compared with water vapor transfer rate (WVTR) experiment data and calculated values obtained from other theoretical models. This verifies the validity of the present fractal diffusivity of fibrous structural beds.
An Efficient Computational Technique for Fractal Vehicular Traffic Flow
Directory of Open Access Journals (Sweden)
Devendra Kumar
2018-04-01
Full Text Available In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.
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
Fractal corrections of BaTiO3-ceramic sintering parameters
Directory of Open Access Journals (Sweden)
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
Exploring the relationship between fractal features and bacterial essential genes
International Nuclear Information System (INIS)
Yu Yong-Ming; Yang Li-Cai; Zhao Lu-Lu; Liu Zhi-Ping; Zhou Qian
2016-01-01
Essential genes are indispensable for the survival of an organism in optimal conditions. Rapid and accurate identifications of new essential genes are of great theoretical and practical significance. Exploring features with predictive power is fundamental for this. Here, we calculate six fractal features from primary gene and protein sequences and then explore their relationship with gene essentiality by statistical analysis and machine learning-based methods. The models are applied to all the currently available identified genes in 27 bacteria from the database of essential genes (DEG). It is found that the fractal features of essential genes generally differ from those of non-essential genes. The fractal features are used to ascertain the parameters of two machine learning classifiers: Naïve Bayes and Random Forest. The area under the curve (AUC) of both classifiers show that each fractal feature is satisfactorily discriminative between essential genes and non-essential genes individually. And, although significant correlations exist among fractal features, gene essentiality can also be reliably predicted by various combinations of them. Thus, the fractal features analyzed in our study can be used not only to construct a good essentiality classifier alone, but also to be significant contributors for computational tools identifying essential genes. (paper)
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)
Bouguer correction density determination from fractal analysis using ...
African Journals Online (AJOL)
In this work, Bouguer density is determined using the fractal approach. This technique was applied to the gravity data of the Kwello area of the Basement Complex, north-western Nigeria. The density obtained using the fractal approach is 2500 kgm which is lower than the conventional value of 2670 kgm used for average ...
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
Fractal sets generated by chemical reactions discrete chaotic dynamics
International Nuclear Information System (INIS)
Gontar, V.; Grechko, O.
2007-01-01
Fractal sets composed by the parameters values of difference equations derived from chemical reactions discrete chaotic dynamics (DCD) and corresponding to the sequences of symmetrical patterns were obtained in this work. Examples of fractal sets with the corresponding symmetrical patterns have been presented
Ghezelbash, Reza; Maghsoudi, Abbas
2018-05-01
The delineation of populations of stream sediment geochemical data is a crucial task in regional exploration surveys. In this contribution, uni-element stream sediment geochemical data of Cu, Au, Mo, and Bi have been subjected to two reliable anomaly-background separation methods, namely, the concentration-area (C-A) fractal and the U-spatial statistics methods to separate geochemical anomalies related to porphyry-type Cu mineralization in northwest Iran. The quantitative comparison of the delineated geochemical populations using the modified success-rate curves revealed the superiority of the U-spatial statistics method over the fractal model. Moreover, geochemical maps of investigated elements revealed strongly positive correlations between strong anomalies and Oligocene-Miocene intrusions in the study area. Therefore, follow-up exploration programs should focus on these areas.
Analysis of fractal dimensions of rat bones from film and digital images
Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Yamauchi, M.
2001-01-01
OBJECTIVES: (1) To compare the effect of two different intra-oral image receptors on estimates of fractal dimension; and (2) to determine the variations in fractal dimensions between the femur, tibia and humerus of the rat and between their proximal, middle and distal regions. METHODS: The left femur, tibia and humerus from 24 4-6-month-old Sprague-Dawley rats were radiographed using intra-oral film and a charge-coupled device (CCD). Films were digitized at a pixel density comparable to the CCD using a flat-bed scanner. Square regions of interest were selected from proximal, middle, and distal regions of each bone. Fractal dimensions were estimated from the slope of regression lines fitted to plots of log power against log spatial frequency. RESULTS: The fractal dimensions estimates from digitized films were significantly greater than those produced from the CCD (P=0.0008). Estimated fractal dimensions of three types of bone were not significantly different (P=0.0544); however, the three regions of bones were significantly different (P=0.0239). The fractal dimensions estimated from radiographs of the proximal and distal regions of the bones were lower than comparable estimates obtained from the middle region. CONCLUSIONS: Different types of image receptors significantly affect estimates of fractal dimension. There was no difference in the fractal dimensions of the different bones but the three regions differed significantly.
Integration of Fractal Biosensor in a Digital Microfluidic Platform
Mashraei, Yousof
2016-06-08
The digital microfluidic (DMF) platform introduces many applications in biomedical assays. If it is to be commercially available to the public, it needs to have the essential features of smart sensing and a compact size. In this work, we report on a fractal electrode biosensor that is used for both droplet actuation and sensing C-reactive protein (CRP) concentration levels to assess cardiac disease risk. Our proposed electrode is the first two-terminal electrode design to be integrated into DMF platforms. A simulation of the electrical field distribution shows reduced peak intensities and uniform distribution of the field. When compared to a V-notch square electrode, the fractal electrode shows a superior performance in both aspects, i.e. field uniformity and intensity. These improvements are translated into a successful and responsive actuation of a water droplet with 100V. Likewise, the effective dielectric strength is improved by a 33% increase in the fractal electrode breakdown voltage. Additionally, the capability of the fractal electrode to work as a capacitive biosensor is evaluated with CRP quantification test. Selected fractal electrodes undergo a surface treatment to immobilize anti-CRP antibodies on their surface. The measurement shows a response to the added CRP in capacitance within three minutes. When the untreated electrodes were used for quantification, there was no significant change in capacitance, and this suggested that immobilization was necessary. The electrodes configuration in the fabricated DMF platform allows the fractal electrodes to be selectively used as biosensors, which means the device could be integrated into point-of-care applications.
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
Assessment of Textural Differentiations in Forest Resources in Romania Using Fractal Analysis
Directory of Open Access Journals (Sweden)
Ion Andronache
2017-02-01
Full Text Available Deforestation and forest degradation have several negative effects on the environment including a loss of species habitats, disturbance of the water cycle and reduced ability to retain CO2, with consequences for global warming. We investigated the evolution of forest resources from development regions in Romania affected by both deforestation and reforestation using a non-Euclidean method based on fractal analysis. We calculated four fractal dimensions of forest areas: the fractal box-counting dimension of the forest areas, the fractal box-counting dimension of the dilated forest areas, the fractal dilation dimension and the box-counting dimension of the border of the dilated forest areas. Fractal analysis revealed morpho-structural and textural differentiations of forested, deforested and reforested areas in development regions with dominant mountain relief and high hills (more forested and compact organization in comparison to the development regions dominated by plains or low hills (less forested, more fragmented with small and isolated clusters. Our analysis used the fractal analysis that has the advantage of analyzing the entire image, rather than studying local information, thereby enabling quantification of the uniformity, fragmentation, heterogeneity and homogeneity of forests.
Solving fractal steady heat-transfer problems with the local fractional Sumudu transform
Directory of Open Access Journals (Sweden)
Wang Yi
2015-01-01
Full Text Available In this paper the linear oscillator problem in fractal steady heat-transfer is studied within the local fractional theory. In particular, the local fractional Sumudu transform (LFST will be used to solve both the homogeneous and the non-homogeneous local fractional oscillator equations (LFOEs under fractal steady heat-transfer. It will be shown that the obtained non-differentiable solutions characterize the fractal phenomena with and without the driving force in fractal steady heat transfer at low excess temperatures.
Inspecting plastic deformation of Pd by means of fractal geometry
International Nuclear Information System (INIS)
Eftekhari, Ali
2007-01-01
The influence of phase transformation-induced plastic deformation in Pd|H system on the electrode surface was investigated. Since the Pd surface is subject of severe plastic deformation during this process, the structure and roughness of the electrode surface significantly change. Quantitative analysis of the electrode surfaces for comparative study of such changes is a valuable tool to inspect the plastic deformation induced. Fractal dimension can be used as a quantitative measure for this purpose. Since inappropriate methods may lead to significant errors, an appropriate approach was proposed for the determination of fractal dimensions in such systems. It was demonstrated that the surface roughness generated is mainly due to the plastic deformation induced, not the other side processes, as the electrodes were coated with a uniform layer of gold with thickness smaller than 10 nm. Since plastic deformation is due to hydrogen insertion/extraction and occurs in atomic-scale, it is necessary to divide structural changes appeared in nano- and micro-scale
Evaluation of surface quality by Fractal Dimension and Volume ...
African Journals Online (AJOL)
Experimental and simulation results have enabled to show than the large diameter ball under low loads and medium feed speeds, favors the elimination of peaks and reduction of fractal dimension whence quality improvement of surface. Keywords: burnishing, volume parameters, fractal dimension, experimental designs ...
Growth of fractal structures in flames with silicon admixture
Smirnov, B. M.; Dutka, M.; van Essen, V. M.; Gersen, S.; Visser, P.; Vainchtein, D.; De Hosson, J. Th. M.; Levinsky, H. B.; Mokhov, A. V.
Transmission electron microscopy (TEM) measurements and theoretical analysis are combined to construct the physical picture of formation of SiO2 fractal aggregates in a methane/hexamethyldisiloxane/air atmospheric pressure flame. The formation of SiO2 fractal aggregates is described as a multistage
Efficient fractal-based mutation in evolutionary algorithms from iterated function systems
Salcedo-Sanz, S.; Aybar-Ruíz, A.; Camacho-Gómez, C.; Pereira, E.
2018-03-01
In this paper we present a new mutation procedure for Evolutionary Programming (EP) approaches, based on Iterated Function Systems (IFSs). The new mutation procedure proposed consists of considering a set of IFS which are able to generate fractal structures in a two-dimensional phase space, and use them to modify a current individual of the EP algorithm, instead of using random numbers from different probability density functions. We test this new proposal in a set of benchmark functions for continuous optimization problems. In this case, we compare the proposed mutation against classical Evolutionary Programming approaches, with mutations based on Gaussian, Cauchy and chaotic maps. We also include a discussion on the IFS-based mutation in a real application of Tuned Mass Dumper (TMD) location and optimization for vibration cancellation in buildings. In both practical cases, the proposed EP with the IFS-based mutation obtained extremely competitive results compared to alternative classical mutation operators.
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.
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.
Directory of Open Access Journals (Sweden)
Jian Xiong
2015-01-01
Full Text Available We mainly focus on the Permian, Lower Cambrian, Lower Silurian, and Upper Ordovician Formation; the fractal dimensions of marine shales in southern China were calculated using the FHH fractal model based on the low-pressure nitrogen adsorption analysis. The results show that the marine shales in southern China have the dual fractal characteristics. The fractal dimension D1 at low relative pressure represents the pore surface fractal characteristics, whereas the fractal dimension D2 at higher relative pressure describes the pore structure fractal characteristics. The fractal dimensions D1 range from 2.0918 to 2.718 with a mean value of 2.4762, and the fractal dimensions D2 range from 2.5842 to 2.9399 with a mean value of 2.8015. There are positive relationships between fractal dimension D1 and specific surface area and total pore volume, whereas the fractal dimensions D2 have negative correlation with average pore size. The larger the value of the fractal dimension D1 is, the rougher the pore surface is, which could provide more adsorption sites, leading to higher adsorption capacity for gas. The larger the value of the fractal dimension D2 is, the more complicated the pore structure is, resulting in the lower flow capacity for gas.
Fractal Dimension Analysis of Texture Formation of Whey Protein-Based Foods
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Robi Andoyo
2018-01-01
Full Text Available Whey protein in the form of isolate or concentrate is widely used in food industries due to its functionality to form gel under certain condition and its nutritive value. Controlling or manipulating the formation of gel aggregates is used often to evaluate food texture. Many researchers made use of fractal analysis that provides the quantitative data (i.e., fractal dimension for fundamentally and rationally analyzing and designing whey protein-based food texture. This quantitative analysis is also done to better understand how the texture of whey protein-based food is formed. Two methods for fractal analysis were discussed in this review: image analysis (microscopy and rheology. These methods, however, have several limitations which greatly affect the accuracy of both fractal dimension values and types of aggregation obtained. This review therefore also discussed problem encountered and ways to reduce the potential errors during fractal analysis of each method.
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)
Three-dimensional fractal geometry for gas permeation in microchannels
Malankowska, Magdalena; Schlautmann, Stefan; Berenschot, Erwin J.W.; Tiggelaar, Roald M.; Pina, Maria Pilar; Mallada, Reyes; Tas, Niels R.; Gardeniers, Han
2018-01-01
The novel concept of a microfluidic chip with an integrated three-dimensional fractal geometry with nanopores, acting as a gas transport membrane, is presented. The method of engineering the 3D fractal structure is based on a combination of anisotropic etching of silicon and corner lithography. The
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.
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Le Wang
2015-11-01
Full Text Available Based on phase space reconstruction and fractal dynamics in nonlinear dynamics, a method is proposed to extract and analyze the dynamics of the rotating stall in the impeller of centrifugal compressor, and some numerical examples are given to verify the results as well. First, the rotating stall of an existing low speed centrifugal compressor (LSCC is numerically simulated, and the time series of pressure in the rotating stall is obtained at various locations near the impeller outlet. Then, the phase space reconstruction is applied to these pressure time series, and a low-dimensional dynamical system, which the dynamics properties are included in, is reconstructed. In phase space reconstruction, C–C method is used to obtain the key parameters, such as time delay and the embedding dimension of the reconstructed phase space. Further, the fractal characteristics of the rotating stall are analyzed in detail, and the fractal dimensions are given for some examples to measure the complexity of the flow in the post-rotating stall. The results show that the fractal structures could reveal the intrinsic dynamics of the rotating stall flow and could be considered as a characteristic to identify the rotating stall.
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.
Fractal Image Coding Based on a Fitting Surface
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Sheng Bi
2014-01-01
Full Text Available A no-search fractal image coding method based on a fitting surface is proposed. In our research, an improved gray-level transform with a fitting surface is introduced. One advantage of this method is that the fitting surface is used for both the range and domain blocks and one set of parameters can be saved. Another advantage is that the fitting surface can approximate the range and domain blocks better than the previous fitting planes; this can result in smaller block matching errors and better decoded image quality. Since the no-search and quadtree techniques are adopted, smaller matching errors also imply less number of blocks matching which results in a faster encoding process. Moreover, by combining all the fitting surfaces, a fitting surface image (FSI is also proposed to speed up the fractal decoding. Experiments show that our proposed method can yield superior performance over the other three methods. Relative to range-averaged image, FSI can provide faster fractal decoding process. Finally, by combining the proposed fractal coding method with JPEG, a hybrid coding method is designed which can provide higher PSNR than JPEG while maintaining the same Bpp.
Vector calculus in non-integer dimensional space and its applications to fractal media
Tarasov, Vasily E.
2015-02-01
We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.
Fractal apertures in waveguides, conducting screens and cavities analysis and design
Ghosh, Basudeb; Kartikeyan, M V
2014-01-01
This book deals with the design and analysis of fractal apertures in waveguides, conducting screens and cavities using numerical electromagnetics and field-solvers. The aim is to obtain design solutions with improved accuracy for a wide range of applications. To achieve this goal, a few diverse problems are considered. The book is organized with adequate space dedicated for the design and analysis of fractal apertures in waveguides, conducting screens, and cavities, microwave/millimeter wave applications followed by detailed case-study problems to infuse better insight and understanding of the subject. Finally, summaries and suggestions are given for future work. Fractal geometries were widely used in electromagnetics, specifically for antennas and frequency selective surfaces (FSS). The self-similarity of fractal geometry gives rise to a multiband response, whereas the space-filling nature of the fractal geometries makes it an efficient element in antenna and FSS unit cell miniaturization. Until now, no e...
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)
Retinal vascular fractals predict long-term microvascular complications in type 1 diabetes mellitus
DEFF Research Database (Denmark)
Broe, Rebecca; Rasmussen, Malin L; Frydkjaer-Olsen, Ulrik
2014-01-01
: We included 180 patients with type 1 diabetes in a 16 year follow-up study. In baseline retinal photographs (from 1995), all vessels in a zone 0.5-2.0 disc diameters from the disc margin were traced using Singapore Institute Vessel Assessment-Fractal image analysis software. Artefacts were removed......AIMS/HYPOTHESIS: Fractal analysis of the retinal vasculature provides a global measure of the complexity and density of retinal vessels summarised as a single variable: the fractal dimension. We investigated fractal dimensions as long-term predictors of microvasculopathy in type 1 diabetes. METHODS....... Retinal fractal analysis therefore is a potential tool for risk stratification in type 1 diabetes....
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
Microfluidic immunomagnetic separation for enhanced bacterial detection
DEFF Research Database (Denmark)
Hoyland, James; Kunstmann-Olsen, Casper; Ahmed, Shakil
A combined lab-on-a-chip approach combining immunomagnetic separation (IMS) and flow cytometry was developed for the enrichment and detection of salmonella contamination in food samples. Immunomagnetic beads were immobilized in chips consisting of long fractal meanders while contaminated samples...... to obtain maximum capturing efficiency. The effects of channel volume, path length and number of bends of microfluidic chip on IMS efficiency were also determined....
Fractal dimension algorithms and their application to time series associated with natural phenomena
International Nuclear Information System (INIS)
La Torre, F Cervantes-De; González-Trejo, J I; Real-Ramírez, C A; Hoyos-Reyes, L F
2013-01-01
Chaotic invariants like the fractal dimensions are used to characterize non-linear time series. The fractal dimension is an important characteristic of systems, because it contains information about their geometrical structure at multiple scales. In this work, three algorithms are applied to non-linear time series: spectral analysis, rescaled range analysis and Higuchi's algorithm. The analyzed time series are associated with natural phenomena. The disturbance storm time (Dst) is a global indicator of the state of the Earth's geomagnetic activity. The time series used in this work show a self-similar behavior, which depends on the time scale of measurements. It is also observed that fractal dimensions, D, calculated with Higuchi's method may not be constant over-all time scales. This work shows that during 2001, D reaches its lowest values in March and November. The possibility that D recovers a change pattern arising from self-organized critical phenomena is also discussed
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 ...
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.
Fractal dimensions of silica gels generated using reactive molecular dynamics simulations
International Nuclear Information System (INIS)
Bhattacharya, Sudin; Kieffer, John
2005-01-01
We have used molecular dynamics simulations based on a three-body potential with charge transfer to generate nanoporous silica aerogels. Care was taken to reproduce the sol-gel condensation reaction that forms the gel backbone as realistically as possible and to thereby produce credible gel structures. The self-similarity of aerogel structures was investigated by evaluating their fractal dimension from geometric correlations. For comparison, we have also generated porous silica glasses by rupturing dense silica and computed their fractal dimension. The fractal dimension of the porous silica structures was found to be process dependent. Finally, we have determined that the effect of supercritical drying on the fractal nature of condensed silica gels is not appreciable
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
Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review
Energy Technology Data Exchange (ETDEWEB)
Michallek, Florian; Dewey, Marc [Humboldt-Universitaet zu Berlin, Freie Universitaet Berlin, Charite - Universitaetsmedizin Berlin, Medical School, Department of Radiology, Berlin (Germany)
2014-01-15
To provide an overview of recent research in fractal analysis of tissue perfusion imaging, using standard radiological and nuclear medicine imaging techniques including computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, positron emission tomography (PET) and single-photon emission computed tomography (SPECT) and to discuss implications for different fields of application. A systematic review of fractal analysis for tissue perfusion imaging was performed by searching the databases MEDLINE (via PubMed), EMBASE (via Ovid) and ISI Web of Science. Thirty-seven eligible studies were identified. Fractal analysis was performed on perfusion imaging of tumours, lung, myocardium, kidney, skeletal muscle and cerebral diseases. Clinically, different aspects of tumour perfusion and cerebral diseases were successfully evaluated including detection and classification. In physiological settings, it was shown that perfusion under different conditions and in various organs can be properly described using fractal analysis. Fractal analysis is a suitable method for quantifying heterogeneity from radiological and nuclear medicine perfusion images under a variety of conditions and in different organs. Further research is required to exploit physiologically proven fractal behaviour in the clinical setting. (orig.)
Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review
International Nuclear Information System (INIS)
Michallek, Florian; Dewey, Marc
2014-01-01
To provide an overview of recent research in fractal analysis of tissue perfusion imaging, using standard radiological and nuclear medicine imaging techniques including computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, positron emission tomography (PET) and single-photon emission computed tomography (SPECT) and to discuss implications for different fields of application. A systematic review of fractal analysis for tissue perfusion imaging was performed by searching the databases MEDLINE (via PubMed), EMBASE (via Ovid) and ISI Web of Science. Thirty-seven eligible studies were identified. Fractal analysis was performed on perfusion imaging of tumours, lung, myocardium, kidney, skeletal muscle and cerebral diseases. Clinically, different aspects of tumour perfusion and cerebral diseases were successfully evaluated including detection and classification. In physiological settings, it was shown that perfusion under different conditions and in various organs can be properly described using fractal analysis. Fractal analysis is a suitable method for quantifying heterogeneity from radiological and nuclear medicine perfusion images under a variety of conditions and in different organs. Further research is required to exploit physiologically proven fractal behaviour in the clinical setting. (orig.)
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.
Aqueous synthesis of LiFePO4 with Fractal Granularity
Cabán-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P.; Gómez-Romero, Pedro
2016-06-01
Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes.
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.
FCC riser quick separation system: a review
Directory of Open Access Journals (Sweden)
Zhi Li
2016-10-01
Full Text Available Abstract The riser reactor is the key unit in the fluid catalytic cracking (FCC process. As the FCC feedstocks become heavier, the product mixture of oil, gas and catalysts must be separated immediately at the outlet of the riser to avoid excessive coking. The quick separation system is the core equipment in the FCC unit. China University of Petroleum (Beijing has developed many kinds of separation system including the fender-stripping cyclone and circulating-stripping cyclone systems, which can increase the separation efficiency and reduce the pressure drop remarkably. For the inner riser system, a vortex quick separation system has been developed. It contains a vortex quick separator and an isolated shell. In order to reduce the separation time, a new type of separator called the short residence time separator system was developed. It can further reduce the separation time to less than 1 s. In this paper, the corresponding design principles, structure and industrial application of these different kinds of separation systems are reviewed. A system that can simultaneously realize quick oil gas separation, quick oil gas extraction and quick pre-stripping of catalysts at the end of the riser is the trend in the future.
Computer Security: The dilemma of fractal defence
Stefan Lueders, Computer Security Team
2015-01-01
Aren’t mathematical fractals just beautiful? The Mandelbrot set and the Julia set, the Sierpinski gasket, the Menger sponge, the Koch curve (see here)… Based on very simple mathematical rules, they quickly develop into a mosaic of facets slightly different from each other. More and more features appear the closer you zoom into a fractal and expose similar but not identical features of the overall picture. Computer security is like these fractals, only much less pretty: simple at first glance, but increasingly complex and complicated when you look more closely at the details. The deeper you dig, the more and more possibilities open up for malicious people as the attack surface grows, just like that of “Koch’s snowflakes”, where the border length grows exponentially. Consequently, the defensive perimeter also increases when we follow the bits and bytes layer by layer from their processing in the CPU, trickling up the software stack thro...
Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.
Quodbach, Julian; Moussavi, Amir; Tammer, Roland; Frahm, Jens; Kleinebudde, Peter
2014-11-20
An efficient disintegrant is capable of breaking up a tablet in the smallest possible particles in the shortest time. Until now, comparative data on the efficacy of different disintegrants is based on dissolution studies or the disintegration time. Extending these approaches, this study introduces a method, which defines the evolution of fractal dimensions of tablets as surrogate parameter for the available surface area. Fractal dimensions are a measure for the tortuosity of a line, in this case the upper surface of a disintegrating tablet. High-resolution real-time MRI was used to record videos of disintegrating tablets. The acquired video images were processed to depict the upper surface of the tablets and a box-counting algorithm was used to estimate the fractal dimensions. The influence of six different disintegrants, of different relative tablet density, and increasing disintegrant concentration was investigated to evaluate the performance of the novel method. Changing relative densities hardly affect the progression of fractal dimensions, whereas an increase in disintegrant concentration causes increasing fractal dimensions during disintegration, which are also reached quicker. Different disintegrants display only minor differences in the maximal fractal dimension, yet the kinetic in which the maximum is reached allows a differentiation and classification of disintegrants. Copyright © 2014 Elsevier B.V. All rights reserved.
24-GHz LTCC Fractal Antenna Array SoP With Integrated Fresnel Lens
Ghaffar, Farhan A.
2012-09-30
A novel 24-GHz mixed low-temperature co-fired ceramic (LTCC) tape based system-on-package (SoP) is presented, which incorporates a fractal antenna array with an integrated grooved Fresnel lens. The four-element fractal array employs a relatively low dielectric constant substrate (CT707, εr = 6.4), whereas the lens has been realized on a high-dielectric-constant superstrate (CT765, εr = 68.7 ). The two (substrate and superstrate) are integrated through four corner posts to realize the required air gap (focal distance). The fractal array alone provides a measured gain of 8.9 dBi. Simulations predict that integration of this array with the lens increases the gain by 6 dB. Measurements reveal that the design is susceptible to LTCC fabrication tolerances. In addition to high gain, the SoP provides a bandwidth of 8%. The high performance and compact size (24 × 24 × 4.8 mm3 ) of the design makes it highly suitable for emerging wireless applications such as automotive radar front end.
Fractal Information by Means of Harmonic Mappings and Some Physical Implications
Directory of Open Access Journals (Sweden)
Maricel Agop
2016-04-01
Full Text Available Considering that the motions of the complex system structural units take place on continuous, but non-differentiable curves, in the frame of the extended scale relativity model (in its Schrödinger-type variant, it is proven that the imaginary part of a scalar potential of velocities can be correlated with the fractal information and, implicitly, with a tensor of “tensions”, which is fundamental in the construction of the constitutive laws of material. In this way, a specific differential geometry based on a Poincaré-type metric of the Lobachevsky plane (which is invariant to the homographic group of transformations and also a specific variational principle (whose field equations represent an harmonic map from the usual space into the Lobachevsky plane are generated. Moreover, fractal information (which is made explicit at any scale resolution is produced, so that the field variables define a gravitational field. This latter situation is specific to a variational principle in the sense of Matzner–Misner and to certain Ernst-type field equations, the fractal information being contained in the material structure and, thus, in its own space associated with it.
Afzal, Peyman; Mirzaei, Misagh; Yousefi, Mahyar; Adib, Ahmad; Khalajmasoumi, Masoumeh; Zarifi, Afshar Zia; Foster, Patrick; Yasrebi, Amir Bijan
2016-07-01
Recognition of significant geochemical signatures and separation of geochemical anomalies from background are critical issues in interpretation of stream sediment data to define exploration targets. In this paper, we used staged factor analysis in conjunction with the concentration-number (C-N) fractal model to generate exploration targets for prospecting Cr and Fe mineralization in Balvard area, SE Iran. The results show coexistence of derived multi-element geochemical signatures of the deposit-type sought and ultramafic-mafic rocks in the NE and northern parts of the study area indicating significant chromite and iron ore prospects. In this regard, application of staged factor analysis and fractal modeling resulted in recognition of significant multi-element signatures that have a high spatial association with host lithological units of the deposit-type sought, and therefore, the generated targets are reliable for further prospecting of the deposit in the study area.
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.
Directory of Open Access Journals (Sweden)
Rodríguez Velásquez, Javier Oswaldo
2014-01-01
Full Text Available Background: Pathological interpretation of cellular form in cervical cytology is very important for preven- tion of cervical cancer. The methods most frequently used for assessment of this test have reproducibility and inter-observer variability problems. Objective: To make fractal and Euclidean measure- ments to mathematically diagnose normal and pre- malignant cells of cervical squamous epithelium. Methodology: 21 cells with normal, ASCUS or LSIL diagnosis according to the Bethesda system were assessed. Fractal and Euclidean geometric measures of three mathematical objects were calculated: cyto- plasm, nucleus and whole cell. Mathematical propor- tions between these measurements were calculated in order to compare them with conventional classification methods. Results: It was found that the nuclear border measures calculated with the 2-pixel grill and the surface measures could mathematically and objectively differentiate normal cells from the pre-malignant ones (ASCUS and LSIL. Conclusions: An objective and reproducible diagnos- tic method was developed; it allows to identify the evolution towards malignant cellular states based on simultaneous fractal and Euclidean measures, estab- lishing the severity level of ASCUS and LSIL cells.
Multi-fractal analysis of highway traffic data
Institute of Scientific and Technical Information of China (English)
Shang Peng-Jian; Shen Jin-Sheng
2007-01-01
The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwise H(o)lder exponent of a function is calculated by developing an algorithm for the numerical evaluation of H(o)lder exponent of time series. The traffic time series observed on the Beijing Yuquanying highway are analysed. The results from all these methods indicate that the traffic data exhibit the multi-fractal behaviour.
Fractal Theory for Permeability Prediction, Venezuelan and USA Wells
Aldana, Milagrosa; Altamiranda, Dignorah; Cabrera, Ana
2014-05-01
Inferring petrophysical parameters such as permeability, porosity, water saturation, capillary pressure, etc, from the analysis of well logs or other available core data has always been of critical importance in the oil industry. Permeability in particular, which is considered to be a complex parameter, has been inferred using both empirical and theoretical techniques. The main goal of this work is to predict permeability values on different wells using Fractal Theory, based on a method proposed by Pape et al. (1999). This approach uses the relationship between permeability and the geometric form of the pore space of the rock. This method is based on the modified equation of Kozeny-Carman and a fractal pattern, which allows determining permeability as a function of the cementation exponent, porosity and the fractal dimension. Data from wells located in Venezuela and the United States of America are analyzed. Employing data of porosity and permeability obtained from core samples, and applying the Fractal Theory method, we calculated the prediction equations for each well. At the beginning, this was achieved by training with 50% of the data available for each well. Afterwards, these equations were tested inferring over 100% of the data to analyze possible trends in their distribution. This procedure gave excellent results in all the wells in spite of their geographic distance, generating permeability models with the potential to accurately predict permeability logs in the remaining parts of the well for which there are no core samples, using even porority logs. Additionally, empirical models were used to determine permeability and the results were compared with those obtained by applying the fractal method. The results indicated that, although there are empirical equations that give a proper adjustment, the prediction results obtained using fractal theory give a better fit to the core reference data.
The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction.
Najafi, Elham; Darooneh, Amir H
2015-01-01
A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction.
The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction
Najafi, Elham; Darooneh, Amir H.
2015-01-01
A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction. PMID:26091207
Directory of Open Access Journals (Sweden)
Geoff Boeing
2016-11-01
Full Text Available Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Systems of nonlinear equations are difficult to solve analytically, and scientists have relied heavily on visual and qualitative approaches to discover and analyze the dynamics of nonlinearity. Indeed, few fields have drawn as heavily from visualization methods for their seminal innovations: from strange attractors, to bifurcation diagrams, to cobweb plots, to phase diagrams and embedding. Although the social sciences are increasingly studying these types of systems, seminal concepts remain murky or loosely adopted. This article has three aims. First, it argues for several visualization methods to critically analyze and understand the behavior of nonlinear dynamical systems. Second, it uses these visualizations to introduce the foundations of nonlinear dynamics, chaos, fractals, self-similarity and the limits of prediction. Finally, it presents Pynamical, an open-source Python package to easily visualize and explore nonlinear dynamical systems’ behavior.
Model to estimate fractal dimension for ion-bombarded materials
Energy Technology Data Exchange (ETDEWEB)
Hu, A., E-mail: hu77@purdue.edu; Hassanein, A.
2014-03-15
Comprehensive fractal Monte Carlo model ITMC-F (Hu and Hassanein, 2012 [1]) is developed based on the Monte Carlo ion bombardment simulation code, i.e., Ion Transport in Materials and Compounds (ITMC) code (Hassanein, 1985 [2]). The ITMC-F studies the impact of surface roughness on the angular dependence of sputtering yield. Instead of assuming material surfaces to be flat or composed of exact self-similar fractals in simulation, we developed a new method to describe the surface shapes. Random fractal surfaces which are generated by midpoint displacement algorithm and support vector machine algorithm are combined with ITMC. With this new fractal version of ITMC-F, we successfully simulated the angular dependence of sputtering yield for various ion-target combinations, with the input surface roughness exponent directly depicted from experimental data (Hu and Hassanein, 2012 [1]). The ITMC-F code showed good agreement with the experimental data. In advanced, we compare other experimental sputtering yield with the results from ITMC-F to estimate the surface roughness exponent for ion-bombarded material in this research.
[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.
Sea floor separation system; Havbunnsseparasjonssystem
Energy Technology Data Exchange (ETDEWEB)
Hatlo, Andreas; Skaranger, Jon
1998-07-01
This presentation describes work done by an alliance of Kongsberg Offshore a.s. (KOS) and Aker Maritime (AMA). The alliance comprises the development and delivery of seafloor separation systems. The alliance was established as an answer to the identified need of seafloor separation and processing in the oil industry. In several fields on the Norwegian shelf there is defined a potential need for seafloor separation and pumping. The same trend can be seen in international waters as well, especially on deeper waters. Calculation of the economic potential for the relevant applications is based on a large number of variables, including both OPEX and CAPEX assessments. In order to be able to identify and analyse this potential in a better way, KOS and AMA are developing a tool for cost-benefit evaluations of such a seafloor separation and pumping system. PROSERNAT (France) and ALSTOME (UK) are important subcontractors in the development of seafloor separation and pumping systems. PROSERNAT will supply the separation tank and internal arrangement, ALSTOME will supply the power electronics for the distribution of seafloor power distribution.
Evaluation of bridge instability caused by dynamic scour based on fractal theory
International Nuclear Information System (INIS)
Lin, Tzu-Kang; Shian Chang, Yu; Wu, Rih-Teng; Chang, Kuo-Chun
2013-01-01
Given their special structural characteristics, bridges are prone to suffer from the effects of many hazards, such as earthquakes, wind, or floods. As most of the recent unexpected damage and destruction of bridges has been caused by hydraulic issues, monitoring the scour depth of bridges has become an important topic. Currently, approaches to scour monitoring mainly focus on either installing sensors on the substructure of a bridge or identifying the physical parameters of a bridge, which commonly face problems of system survival or reliability. To solve those bottlenecks, a novel structural health monitoring (SHM) concept was proposed by utilizing the two dominant parameters of fractal theory, including the fractal dimension and the topothesy, to evaluate the instability condition of a bridge structure rapidly. To demonstrate the performance of this method, a series of experiments has been carried out. The function of the two parameters was first determined using data collected from a single bridge column scour test. As the fractal dimension gradually decreased, following the trend of the scour depth, it was treated as an alternative to the fundamental frequency of a bridge structure in the existing methods. Meanwhile, the potential of a positive correlation between the topothesy and the amplitude of vibration data was also investigated. The excellent sensitivity of the fractal parameters related to the scour depth was then demonstrated in a full-bridge experiment. Moreover, with the combination of these two parameters, a safety index to detect the critical scour condition was proposed. The experimental results have demonstrated that the critical scour condition can be predicted by the proposed safety index. The monitoring system developed greatly advances the field of bridge scour health monitoring and offers an alternative choice to traditional scour monitoring technology. (paper)
Evolution of fractality in space plasmas of interest to geomagnetic activity
Muñoz, Víctor; Domínguez, Macarena; Alejandro Valdivia, Juan; Good, Simon; Nigro, Giuseppina; Carbone, Vincenzo
2018-03-01
We studied the temporal evolution of fractality for geomagnetic activity, by calculating fractal dimensions from the Dst data and from a magnetohydrodynamic shell model for turbulent magnetized plasma, which may be a useful model to study geomagnetic activity under solar wind forcing. We show that the shell model is able to reproduce the relationship between the fractal dimension and the occurrence of dissipative events, but only in a certain region of viscosity and resistivity values. We also present preliminary results of the application of these ideas to the study of the magnetic field time series in the solar wind during magnetic clouds, which suggest that it is possible, by means of the fractal dimension, to characterize the complexity of the magnetic cloud structure.
Application of chaos and fractals to computer vision
Farmer, Michael E
2014-01-01
This book provides a thorough investigation of the application of chaos theory and fractal analysis to computer vision. The field of chaos theory has been studied in dynamical physical systems, and has been very successful in providing computational models for very complex problems ranging from weather systems to neural pathway signal propagation. Computer vision researchers have derived motivation for their algorithms from biology and physics for many years as witnessed by the optical flow algorithm, the oscillator model underlying graphical cuts and of course neural networks. These algorithm
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...
Fractal scattering of Gaussian solitons in directional couplers with logarithmic nonlinearities
Energy Technology Data Exchange (ETDEWEB)
Teixeira, Rafael M.P.; Cardoso, Wesley B., E-mail: wesleybcardoso@gmail.com
2016-08-12
In this paper we study the interaction of Gaussian solitons in a dispersive and nonlinear media with log-law nonlinearity. The model is described by the coupled logarithmic nonlinear Schrödinger equations, which is a nonintegrable system that allows the observation of a very rich scenario in the collision patterns. By employing a variational approach and direct numerical simulations, we observe a fractal-scattering phenomenon from the exit velocities of each soliton as a function of the input velocities. Furthermore, we introduce a linearization model to identify the position of the reflection/transmission window that emerges within the chaotic region. This enables us the possibility of controlling the scattering of solitons as well as the lifetime of bound states. - Highlights: • We study the interaction of Gaussian solitons in a system with log-law nonlinearity. • The model is described by the coupled logarithmic nonlinear Schrödinger equations. • We observe a fractal-scattering phenomenon of the solitons.
Effect of exposure time and image resolution on fractal dimension
International Nuclear Information System (INIS)
An, Byung Mo; Heo, Min Suk; Lee, Seung Pyo; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won; Kim, Jong Dae
2002-01-01
To evaluate the effect of exposure time and image resolution on fractal dimension calculations for determining the optimal range of these two variances. Thirty-one radiographs of the mandibular angle area of sixteen human dry mandibles were taken at different exposure times (0.01, 0.08, 0.16, 0.25, 0.40, 0.64, and 0.80 s). Each radiograph was digitized at 1200 dpi, 8 bit, 256 gray level using a film scanner. We selected an Region of Interest (ROI) that corresponded to the same region as in each radiograph, but the resolution of ROI was degraded to 1000, 800, 600, 500, 400, 300, 200, and 100 dpi. The fractal dimension was calculated by using the tile-counting method for each image, and the calculated values were then compared statistically. As the exposure time and the image resolution increased, the mean value of the fractal dimension decreased, except the case where exposure time was set at 0.01 seconds (alpha = 0.05). The exposure time and image resolution affected the fractal dimension by interaction (p<0.001). When the exposure time was set to either 0.64 seconds or 0.80 seconds, the resulting fractal dimensions were lower, irrespective of image resolution, than at shorter exposure times (alpha = 0.05). The optimal range for exposure time and resolution was determined to be 0.08-0.40 seconds and from 400-1000 dpi, respectively. Adequate exposure time and image resolution is essential for acquiring the fractal dimension using tile-counting method for evaluation of the mandible.
Fractal-Based Analysis of the Influence of Music on Human Respiration
Reza Namazi, H.
An important challenge in respiration related studies is to investigate the influence of external stimuli on human respiration. Auditory stimulus is an important type of stimuli that influences human respiration. However, no one discovered any trend, which relates the characteristics of the auditory stimuli to the characteristics of the respiratory signal. In this paper, we investigate the correlation between auditory stimuli and respiratory signal from fractal point of view. We found out that the fractal structure of respiratory signal is correlated with the fractal structure of the applied music. Based on the obtained results, the music with greater fractal dimension will result in respiratory signal with smaller fractal dimension. In order to verify this result, we benefit from approximate entropy. The results show the respiratory signal will have smaller approximate entropy by choosing the music with smaller approximate entropy. The method of analysis could be further investigated to analyze the variations of different physiological time series due to the various types of stimuli when the complexity is the main concern.
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...
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....
Fractal dynamics in self-evaluation reveal self-concept clarity.
Wong, Alexander E; Vallacher, Robin R; Nowak, Andrzej
2014-10-01
The structural account of self-esteem and self-evaluation maintains that they are distinct constructs. Trait self-esteem is stable and is expressed over macro timescales, whereas state self-evaluation is unstable and experienced on micro timescales. We compared predictions based on the structural account with those derived from a dynamical systems perspective on the self, which maintains that self-esteem and self-evaluation are hierarchically related and share basic dynamic properties. Participants recorded a 3-minute narrative about themselves, then used the mouse paradigm (Vallacher, Nowak, Froehlich, & Rockloff, 2002) to track the momentary self-evaluation in their narrative. Multiple methods converged to reveal fractal patterns in the resultant temporal patterns, indicative of nested timescales that link micro and macro selfevaluation and thus supportive of the dynamical account. The fractal dynamics were associated with participants' self-concept clarity, suggesting that the hierarchical relation between macro self-evaluation (self-esteem) and momentary self-evaluation is predicted by the coherence of self-concept organization.
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.
Terahertz response of fractal meta-atoms based on concentric rectangular square resonators
Energy Technology Data Exchange (ETDEWEB)
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.
Davarpanah, A.; Babaie, H. A.
2012-12-01
The interaction of the thermally induced stress field of the Yellowstone hotspot (YHS) with existing Basin and Range (BR) fault blocks, over the past 17 m.y., has produced a new, spatially and temporally variable system of normal faults around the Snake River Plain (SRP) in Idaho and Wyoming-Montana area. Data about the trace of these new cross faults (CF) and older BR normal faults were acquired from a combination of satellite imageries, DEM, and USGS geological maps and databases at scales of 1:24,000, 1:100,000, 1:250,000, 1:1000, 000, and 1:2,500, 000, and classified based on their azimuth in ArcGIS 10. The box-counting fractal dimension (Db) of the BR fault traces, determined applying the Benoit software, and the anisotropy intensity (ellipticity) of the fractal dimensions, measured with the modified Cantor dust method applying the AMOCADO software, were measured in two large spatial domains (I and II). The Db and anisotropy of the cross faults were studied in five temporal domains (T1-T5) classified based on the geologic age of successive eruptive centers (12 Ma to recent) of the YHS along the eastern SRP. The fractal anisotropy of the CF system in each temporal domain was also spatially determined in the southern part (domain S1), central part (domain S2), and northern part (domain S3) of the SRP. Line (fault trace) density maps for the BR and CF polylines reveal a higher linear density (trace length per unit area) for the BR traces in the spatial domain I, and a higher linear density of the CF traces around the present Yellowstone National Park (S1T5) where most of the seismically active faults are located. Our spatio-temporal analysis reveals that the fractal dimension of the BR system in domain I (Db=1.423) is greater than that in domain II (Db=1.307). It also shows that the anisotropy of the fractal dimension in domain I is less eccentric (axial ratio: 1.242) than that in domain II (1.355), probably reflecting the greater variation in the trend of the BR
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...
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 Analysis of Stealthy Pathfinding Aesthetics
Directory of Open Access Journals (Sweden)
Ron Coleman
2009-01-01
Full Text Available This paper uses a fractal model to analyze aesthetic values of a new class of obstacle-prone or “stealthy” pathfinding which seeks to avoid detection, exposure, openness, and so forth in videogames. This study is important since in general the artificial intelligence literature has given relatively little attention to aesthetic outcomes in pathfinding. The data we report, according to the fractal model, suggests that stealthy paths are statistically significantly unique in relative aesthetic value when compared to control paths. We show furthermore that paths generated with different stealth regimes are also statistically significantly unique. These conclusions are supported by statistical analysis of model results on experimental trials involving pathfinding in randomly generated, multiroom virtual worlds.
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.
Random a-adic groups and random net fractals
Energy Technology Data Exchange (ETDEWEB)
Li Yin [Department of Mathematics, Nanjing University, Nanjing 210093 (China)], E-mail: Lyjerry7788@hotmail.com; Su Weiyi [Department of Mathematics, Nanjing University, Nanjing 210093 (China)], E-mail: suqiu@nju.edu.cn
2008-08-15
Based on random a-adic groups, this paper investigates the relationship between the existence conditions of a positive flow in a random network and the estimation of the Hausdorff dimension of a proper random net fractal. Subsequently we describe some particular random fractals for which our results can be applied. Finally the Mauldin and Williams theorem is shown to be very important example for a random Cantor set with application in physics as shown in E-infinity theory.
Application of fractal theory to top-coal caving
International Nuclear Information System (INIS)
Xie, H.; Zhou, H.W.
2008-01-01
The experiences of underground coal mining in China show that coal in a thick hard coal seam with a hard roof, the so-called 'double hard coal seam', is difficult to be excavated by top-coal caving technique. In order to solve the problem, a top-coal weakening technique is proposed in this paper. In the present study, fractal geometry provides a new description of the fracture mechanism for blasting. By means of theoretical analysis of the relationship between the fractal dimension of blasting fragments and the dynamite specific energy, a mechanical model for describing the size distribution of top-coal and the dissipation of blasting energy is proposed. The theoretical results are in agreement with laboratory and in situ test results. Moreover, it is shown that the fractal dimension of coal fragments can be used as an index for optimizing the blasting parameters for a top-coal weakening technique
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.
Effective Thermal Conductivity of Open Cell Polyurethane Foam Based on the Fractal Theory
Directory of Open Access Journals (Sweden)
Kan Ankang
2013-01-01
Full Text Available Based on the fractal theory, the geometric structure inside an open cell polyurethane foam, which is widely used as adiabatic material, is illustrated. A simplified cell fractal model is created. In the model, the method of calculating the equivalent thermal conductivity of the porous foam is described and the fractal dimension is calculated. The mathematical formulas for the fractal equivalent thermal conductivity combined with gas and solid phase, for heat radiation equivalent thermal conductivity and for the total thermal conductivity, are deduced. However, the total effective heat flux is the summation of the heat conduction by the solid phase and the gas in pores, the radiation, and the convection between gas and solid phase. Fractal mathematical equation of effective thermal conductivity is derived with fractal dimension and vacancy porosity in the cell body. The calculated results have good agreement with the experimental data, and the difference is less than 5%. The main influencing factors are summarized. The research work is useful for the enhancement of adiabatic performance of foam materials and development of new materials.
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.
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.
Field and electric potential of conductors with fractal geometry
Energy Technology Data Exchange (ETDEWEB)
Assis, Thiago A de; Mota, Fernando de B; Miranda, Jose G V; Andrade, Roberto F S; Castilho, Caio M C de [Instituto de Fisica, Universidade Federal da Bahia, Campus Universitario da Federacao, 40210-340, Salvador (Brazil)
2007-11-28
In this study, the behavior of the electric field and its potential are investigated in a region bounded by a rough fractal surface and a distant plane. Both boundaries, maintained at distinct potential values, are assumed to be conductors and, as such, the electric potential is obtained by numerically solving Laplace's equation subject to the appropriate Dirichlet's condition. The rough boundaries, generated by the ballistic deposition and fractal Brownian motion methods, are characterized by the values of the surface roughness W and the local fractal dimension df = 3-{alpha}, where {alpha} is the usual roughness exponent. The equipotential surfaces, obtained from Laplace's equation, are characterized by these same parameters. Results presented show how df depends on the potential value, on the method used to generate the boundary and on W. The behavior of the electric field with respect to the equipotential surface is also considered. Its average intensity was found to increase as a function of the average distance from the equipotential to the fractal boundary; however, its intensity reaches a maximum before decreasing towards an asymptotic constant value, an effect that increases as the value of W increases.
Field and electric potential of conductors with fractal geometry
International Nuclear Information System (INIS)
Assis, Thiago A de; Mota, Fernando de B; Miranda, Jose G V; Andrade, Roberto F S; Castilho, Caio M C de
2007-01-01
In this study, the behavior of the electric field and its potential are investigated in a region bounded by a rough fractal surface and a distant plane. Both boundaries, maintained at distinct potential values, are assumed to be conductors and, as such, the electric potential is obtained by numerically solving Laplace's equation subject to the appropriate Dirichlet's condition. The rough boundaries, generated by the ballistic deposition and fractal Brownian motion methods, are characterized by the values of the surface roughness W and the local fractal dimension df = 3-α, where α is the usual roughness exponent. The equipotential surfaces, obtained from Laplace's equation, are characterized by these same parameters. Results presented show how df depends on the potential value, on the method used to generate the boundary and on W. The behavior of the electric field with respect to the equipotential surface is also considered. Its average intensity was found to increase as a function of the average distance from the equipotential to the fractal boundary; however, its intensity reaches a maximum before decreasing towards an asymptotic constant value, an effect that increases as the value of W increases
Can fractal objects operate as efficient inline mixers?
Laizet, Sylvain; Vassilicos, John; Turbulence, Mixing; Flow Control Group Team
2011-11-01
Recently, Hurst & Vassilicos, PoF 2007, Seoud & Vassilicos, PoF 2007, Mazellier & Vassilicos, PoF, 2010 used different multiscale grids to generate turbulence in a wind tunnel and have shown that complex multiscale boundary/initial conditions can drastically influence the behaviour of a turbulent flow, but that the detailled specific nature of the multiscale geometry matters too. Multiscale (fractal) objects can be designed to be immersed in any fluid flow where there is a need to control and design the turbulence generated by the object. Different types of multiscale objects can be designed as different types of energy-efficient mixers with varying degrees of high turbulent intensities, small pressure drop and downstream distance from the grid where the turbulence is most vigorous. Here, we present a 3D DNS study of the stirring and mixing of a passive scalar by turbulence generated with either a fractal square grid or a regular grid in the presence of a mean scalar gradient. The results show that: (1) there is a linear increase for the passive scalar variance for both grids, (2) the passive scalar variance is ten times bigger for the fractal grid, (3) the passive scalar flux is constant after the production region for both grids, (4) the passive scalar flux is enhanced by an order of magnitude for the fractal grid. We acknowledge support from EPSRC, UK.
Random fractal structures in North American energy markets
Energy Technology Data Exchange (ETDEWEB)
Serletis, Apostolos [Calgary Univ., Dept. of Economics, Calgary, AB (Canada); Andreadis, Ioannis [European Univ. of the Hague, Center of Management Studies, The Hague (Netherlands)
2004-05-01
This paper uses daily observations on West Texas Intermediate (WTI) crude oil prices at Chicago and Henry Hub natural gas prices at LA (over the deregulated period of the 1990s) and various tests from statistics and dynamical systems theory to support a random fractal structure for North American energy markets. In particular, this evidence is supported by the Vassilicos et al. (1993) multifractal structure test and the Ghashghaie et al. [Nature 381 (1996) 767] turbulent behavior test. (Author)
Efficiency analysis of diffusion on T-fractals in the sense of random walks.
Peng, Junhao; Xu, Guoai
2014-04-07
Efficiently controlling the diffusion process is crucial in the study of diffusion problem in complex systems. In the sense of random walks with a single trap, mean trapping time (MTT) and mean diffusing time (MDT) are good measures of trapping efficiency and diffusion efficiency, respectively. They both vary with the location of the node. In this paper, we analyze the effects of node's location on trapping efficiency and diffusion efficiency of T-fractals measured by MTT and MDT. First, we provide methods to calculate the MTT for any target node and the MDT for any source node of T-fractals. The methods can also be used to calculate the mean first-passage time between any pair of nodes. Then, using the MTT and the MDT as the measure of trapping efficiency and diffusion efficiency, respectively, we compare the trapping efficiency and diffusion efficiency among all nodes of T-fractal and find the best (or worst) trapping sites and the best (or worst) diffusing sites. Our results show that the hub node of T-fractal is the best trapping site, but it is also the worst diffusing site; and that the three boundary nodes are the worst trapping sites, but they are also the best diffusing sites. Comparing the maximum of MTT and MDT with their minimums, we find that the maximum of MTT is almost 6 times of the minimum of MTT and the maximum of MDT is almost equal to the minimum for MDT. Thus, the location of target node has large effect on the trapping efficiency, but the location of source node almost has no effect on diffusion efficiency. We also simulate random walks on T-fractals, whose results are consistent with the derived results.
Sandwich type plasmonic platform for MEF using silver fractals
DEFF Research Database (Denmark)
Raut, Sangram L.; Rich, Ryan; Shtoyko, Tanya
2015-01-01
was studied with the N-methyl-azadioxatriangulenium chloride salt (Me-ADOTA·Cl) in PVA films made from 0.2% PVA (w/v) solution spin-coated on a clean glass coverslip. The Plasmonic Platforms (PP) were assembled by pressing together silver fractals on one glass slide and a separate glass coverslip spin-coated...... with a uniform Me-ADOTA·Cl in PVA film. In addition, we also tested ADOTA labeled human serum albumin (HSA) deposited on a glass slide for potential PP bioassay applications. Using the new PP, we could achieve more than a 20-fold fluorescence enhancement (bright spots) accompanied by a decrease...... of PP can be a convenient approach for constructing assays utilizing metal enhanced fluorescence (MEF) without the need for depositing the material directly on metal structures platforms....
Factorial moment and fractal analysis of γ families
International Nuclear Information System (INIS)
Kalmakhelidze, M.Eh.; Roinishvili, N.N.; Svanidze, M.S.; Khizanishvili, L.A.; Chadranyan, L.Kh.
1997-01-01
Factorial and fractal methods were applied to nuclear-electromagnetic cascades in the atmosphere (γ families) to find sensitivity of these methods to multiparticle fluctuations in γ families. Averaged parameters of factorial and fractal methods of the real families were compared with the same quantities for the statistical set of random families. The correlations between the same parameters for families divided into sectors and into rings are studied. The correlations between different parameters for the same families divided into sectors are investigated
Directory of Open Access Journals (Sweden)
Cai Lin
2017-01-01
Full Text Available This paper describes a numerical analysis of a heat transfer enhancement technique that introduces fractal-shaped design for impingement cooling. Based on the gas turbine combustion chamber cooling, a fractal-shaped nozzle is designed for the constant flow area in a single impingement cooling model. The incompressible Reynolds-averaged Navier-Stokes equations are applied to the system using CFD software. The numerical results are compared with the experiment results for array impingement cooling.
Magnetic separation in microfluidic systems
DEFF Research Database (Denmark)
Smistrup, Kristian
2007-01-01
to facilitate real-time monitoring of the experiments. The set-up and experimental protocol are described in detail. Results are presented for ’active’ magnetic bead separators, where on-chip microfabricated electromagnets supply the magnetic field and field gradients necessary for magnetic bead separation....... It is shown conceptually how such a system can be applied for parallel biochemical processing in a microfluidic system. ’Passive’ magnetic separators are presented, where on-chip soft magnetic elements are magnetized by an external magnetic field and create strong magnetic fields and gradients inside...
Fractality and growth of He bubbles in metals
Kajita, Shin; Ito, Atsushi M.; Ohno, Noriyasu
2017-08-01
Pinholes are formed on surfaces of metals by the exposure to helium plasmas, and they are regarded as the initial process of the growth of fuzzy nanostructures. In this study, number density of the pinholes is investigated in detail from the scanning electron microscope (SEM) micrographs of tungsten and tantalum exposed to the helium plasmas. A power law relation was identified between the number density and the size of pinholes. From the slope and the region where the power law was satisfied, the fractal dimension D and smin, which characterize the SEM images, are deduced. Parametric dependences and material dependence of D and smin are revealed. To explain the fractality, simple Monte-Carlo simulations including random walks of He atoms and absorption on bubble was introduced. It is shown that the initial position of the random walk is one of the key factors to deduce the fractality. The results indicated that new nucleations of bubbles are necessary to reproduce the number-density distribution of bubbles.
Labelling Of Coolant Flow Anomaly Using Fractal Structure
International Nuclear Information System (INIS)
Djainal, Djen Djen
1996-01-01
This research deals with the instrumentation of the detection and characterization of vertical two-phase flow coolant. This type of work is particularly intended to find alternative method for the detection and identification of noise in vertical two-phase flow in a nuclear reactor environment. Various new methods have been introduced in the past few years, an attempt to developed an objective indicator off low patterns. One of new method is Fractal analysis which can complement conventional methods in the description of highly irregular fluctuations. In the present work, Fractal analysis was applied to analyze simulated boiling coolant signal. This simulated signals were built by sum random elements in small subchannels of the coolant channel. Two modes are defined and both are characterized by their void fractions. In the case of uni modal -PDF signals, the difference between these modes is relatively small. On other hand, bimodal -PDF signals have relative large range. In this research, Fractal dimension can indicate the characters of that signals simulation
Energy Technology Data Exchange (ETDEWEB)
Wei, Wei, E-mail: weiw2015@gmail.com [Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074 (China); Cai, Jianchao, E-mail: caijc@cug.edu.cn [Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074 (China); Hu, Xiangyun, E-mail: xyhu@cug.edu.cn [Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074 (China); Han, Qi, E-mail: hanqi426@gmail.com [Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074 (China); Liu, Shuang, E-mail: lius@cug.edu.cn [Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074 (China); Zhou, Yingfang, E-mail: yingfang.zhou@abdn.ac.uk [School of Engineering, University of Aberdeen, FN 264, King' s College, Aberdeen, AB24 3UE (United Kingdom)
2016-08-26
A theoretical effective thermal conductivity model for nanofluids is derived based on fractal distribution characteristics of nanoparticle aggregation. Considering two different mechanisms of heat conduction including particle aggregation and convention, the model is expressed as a function of the fractal dimension and concentration. In the model, the change of fractal dimension is related to the variation of aggregation shape. The theoretical computations of the developed model provide a good agreement with the experimental results, which may serve as an effective approach for quantitatively estimating the effective thermal conductivity of nanofluids. - Highlights: • A thermal conductivity model is derived based on fractal aggregation distribution. • The relationship between aggregation shape and fractal dimension is analyzed. • Predictions of the proposed model show good agreement with experimental data.
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.
The Validity of Dimensional Regularization Method on Fractal Spacetime
Directory of Open Access Journals (Sweden)
Yong Tao
2013-01-01
Full Text Available Svozil developed a regularization method for quantum field theory on fractal spacetime (1987. Such a method can be applied to the low-order perturbative renormalization of quantum electrodynamics but will depend on a conjectural integral formula on non-integer-dimensional topological spaces. The main purpose of this paper is to construct a fractal measure so as to guarantee the validity of the conjectural integral formula.
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.
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.
FRACTAL ANALYSIS OF PHYSICAL ADSORPTION ON SURFACES OF ACID ACTIVATED BENTONITES FROM SERBIA
Directory of Open Access Journals (Sweden)
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.
An extended fractal growth regime in the diffusion limited aggregation including edge diffusion
Directory of Open Access Journals (Sweden)
Aritra Ghosh
2016-01-01
Full Text Available We have investigated on-lattice diffusion limited aggregation (DLA involving edge diffusion and compared the results with the standard DLA model. For both cases, we observe the existence of a crossover from the fractal to the compact regime as a function of sticking coefficient. However, our modified DLA model including edge diffusion shows an extended fractal growth regime like an earlier theoretical result using realistic growth models and physical parameters [Zhang et al., Phys. Rev. Lett. 73 (1994 1829]. While the results of Zhang et al. showed the existence of the extended fractal growth regime only on triangular but not on square lattices, we find its existence on the square lattice. There is experimental evidence of this growth regime on a square lattice. The standard DLA model cannot characterize fractal morphology as the fractal dimension (Hausdorff dimension, DH is insensitive to morphology. It also predicts DH = DP (the perimeter dimension. For the usual fractal structures, observed in growth experiments on surfaces, the perimeter dimension can differ significantly (DH ≠ DP depending on the morphology. Our modified DLA model shows minor sensitivity to this difference.
Radiologic assessment of bone healing after orthognathic surgery using fractal analysis
Energy Technology Data Exchange (ETDEWEB)
Park, Kwang Soo; Heo, Min Suk; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won [College of Dentistry, Seoul National University, Seoul (Korea, Republic of); Jeon, In Seong [Department of Dentistry, Inje University Sanggyepaik Hospital, Seoul (Korea, Republic of); Kim, Jong Dae [Division of Information and Communication Engineering, Hallym university, Chuncheon (Korea, Republic of)
2002-12-15
To evaluate the radiographic change of operation sites after orthognathic surgery using the digital image processing and fractal analysis. A series of panoramic radiographs of thirty-five randomly selected patients who had undergone mandibular orthognathic surgery (bilateral sagittal split ramus osteotomy) without clinical complication for osseous healing, were taken. The panoramic radiographs of each selected patient were taken at pre-operation (stage 0), 1 or 2 days after operation (stage 1), 1 month after operation (stage 2), 6 months after operation (stage 3), and 12 months after operation (stage 4). The radiographs were digitized at 600 dpi, 8 bit, and 256 gray levels. The region of interest, centered on the bony gap area of the operation site, was selected and the fractal dimension was calculated by using the tile-counting method. The mean values and standard deviations of fractal dimension for each stage were calculated and the differences among stage 0, 1, 2, 3, and 4 were evaluated through repeated measures of the ANOVA and paired t-test. The mean values and standard deviations of the fractal dimensions obtained from stage 0, 1, 2, 3, and 4 were 1.658 {+-} 0.048, 1.580 {+-} 0.050, 1.607 {+-} 0.046, 1.624 {+-} 0.049, and 1.641 {+-} 0.061, respectively. The fractal dimensions from stage 1 to stage 4 were shown to have a tendency to increase (p<0.05). The tendency of the fractal dimesion to increase relative to healing time may be a useful means of evaluating post-operative bony healing of the osteotomy site.
Radiologic assessment of bone healing after orthognathic surgery using fractal analysis
International Nuclear Information System (INIS)
Park, Kwang Soo; Heo, Min Suk; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won; Jeon, In Seong; Kim, Jong Dae
2002-01-01
To evaluate the radiographic change of operation sites after orthognathic surgery using the digital image processing and fractal analysis. A series of panoramic radiographs of thirty-five randomly selected patients who had undergone mandibular orthognathic surgery (bilateral sagittal split ramus osteotomy) without clinical complication for osseous healing, were taken. The panoramic radiographs of each selected patient were taken at pre-operation (stage 0), 1 or 2 days after operation (stage 1), 1 month after operation (stage 2), 6 months after operation (stage 3), and 12 months after operation (stage 4). The radiographs were digitized at 600 dpi, 8 bit, and 256 gray levels. The region of interest, centered on the bony gap area of the operation site, was selected and the fractal dimension was calculated by using the tile-counting method. The mean values and standard deviations of fractal dimension for each stage were calculated and the differences among stage 0, 1, 2, 3, and 4 were evaluated through repeated measures of the ANOVA and paired t-test. The mean values and standard deviations of the fractal dimensions obtained from stage 0, 1, 2, 3, and 4 were 1.658 ± 0.048, 1.580 ± 0.050, 1.607 ± 0.046, 1.624 ± 0.049, and 1.641 ± 0.061, respectively. The fractal dimensions from stage 1 to stage 4 were shown to have a tendency to increase (p<0.05). The tendency of the fractal dimesion to increase relative to healing time may be a useful means of evaluating post-operative bony healing of the osteotomy site.
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
Fractal analysis of the spatial distribution of earthquakes along the Hellenic Subduction Zone
Papadakis, Giorgos; Vallianatos, Filippos; Sammonds, Peter
2014-05-01
The Hellenic Subduction Zone (HSZ) is the most seismically active region in Europe. Many destructive earthquakes have taken place along the HSZ in the past. The evolution of such active regions is expressed through seismicity and is characterized by complex phenomenology. The understanding of the tectonic evolution process and the physical state of subducting regimes is crucial in earthquake prediction. In recent years, there is a growing interest concerning an approach to seismicity based on the science of complex systems (Papadakis et al., 2013; Vallianatos et al., 2012). In this study we calculate the fractal dimension of the spatial distribution of earthquakes along the HSZ and we aim to understand the significance of the obtained values to the tectonic and geodynamic evolution of this area. We use the external seismic sources provided by Papaioannou and Papazachos (2000) to create a dataset regarding the subduction zone. According to the aforementioned authors, we define five seismic zones. Then, we structure an earthquake dataset which is based on the updated and extended earthquake catalogue for Greece and the adjacent areas by Makropoulos et al. (2012), covering the period 1976-2009. The fractal dimension of the spatial distribution of earthquakes is calculated for each seismic zone and for the HSZ as a unified system using the box-counting method (Turcotte, 1997; Robertson et al., 1995; Caneva and Smirnov, 2004). Moreover, the variation of the fractal dimension is demonstrated in different time windows. These spatiotemporal variations could be used as an additional index to inform us about the physical state of each seismic zone. As a precursor in earthquake forecasting, the use of the fractal dimension appears to be a very interesting future work. Acknowledgements Giorgos Papadakis wish to acknowledge the Greek State Scholarships Foundation (IKY). References Caneva, A., Smirnov, V., 2004. Using the fractal dimension of earthquake distributions and the
Correlation of optical properties with the fractal microstructure of black molybdenum coatings
Energy Technology Data Exchange (ETDEWEB)
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.
Analysis of MRI by fractals for prediction of sensory attributes: A case study in loin
DEFF Research Database (Denmark)
Caballero, Daniel; Antequera, Teresa; Caro, Andrés
2018-01-01
This study investigates the use of fractal algorithms to analyse MRI of meat products, specifically loin, in order to determine sensory parameters of loin. For that, the capability of different fractal algorithms was evaluated (Classical Fractal Algorithm, CFA; Fractal Texture Algorithm, FTA...... was analysed. Results on this study firstly demonstrate the capability of fractal algorithms to analyse MRI from meat product. Different combinations of the analysed techniques can be applied for predicting most sensory attributes of loins adequately (R > 0.5). However, the combination of SE, OPFTA and MLR...... offered the most appropriate results. Thus, it could be proposed as an alternative to the traditional food technology methods....
Fractal mechanism for characterizing singularity of mode shape for damage detection
Energy Technology Data Exchange (ETDEWEB)
Cao, M. S. [Department of Engineering Mechanics, Hohai University, Nanjing 210098 (China); Ostachowicz, W. [Institute of Fluid-Flow Machinery, Polish Academy of Sciences, ul. Fiszera 14, 80-952 Gdansk (Poland); Faculty of Automotive and Construction Machinery, Warsaw University of Technology, Narbutta 84, 02-524 Warsaw (Poland); Bai, R. B., E-mail: bairunbo@gmail.com [Department of Engineering Mechanics, Shandong Agricultural University, Taian 271000 (China); Radzieński, M. [Institute of Fluid-Flow Machinery, Polish Academy of Sciences, ul. Fiszera 14, 80-952 Gdansk (Poland)
2013-11-25
Damage is an ordinary physical phenomenon jeopardizing structural safety; damage detection is an ongoing interdisciplinary issue. Waveform fractal theory has provided a promising resource for detecting damage in plates while presenting a concomitant problem: susceptibility to false features of damage. This study proposes a fractal dimension method based on affine transformation to address this problem. Physical experiments using laser measurement demonstrate that this method can substantially eliminate false features of damage and accurately identify complex cracks in plates, providing a fundamental mechanism that brings the merits of waveform fractal theory into full play in structural damage detection applications.
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 ...
Directory of Open Access Journals (Sweden)
Leandro Redin Vestena
2010-08-01
Full Text Available Os objetivos deste trabalho foram estimar e avaliar a dimensão fractal da rede de drenagem da bacia hidrográfica do Caeté, em Alfredo Wagner, SC, a partir de diferentes métodos, com o propósito de caracterizar as formas geomorfológicas irregulares. A rede de drenagem apresenta propriedades multifractais. As dimensões fractais para os segmentos individuais (df e para a rede de drenagem inteira (Df foram determinadas por métodos que se fundamentaram nas razões de Horton e pelo método da contagem de caixas (Box-Counting. A rede de drenagem tem característica de autoafinidade. A dimensão fractal proveniente da relação de parâmetros obtidos pelas Leis de Horton apresentou resultados dentro dos limiares da teoria da geometria fractal.The objective of the present work was to evaluate the fractal dimensions of the drainage network of the Caeté river watershed, Alfredo Wagner/SC, with different methods in order to characterize the irregular geomorphologic forms. The drainage network possesses multi-fractal properties. That is why the fractal dimensions for the individual segments (df and for the entire network (Df were evaluated with Horton's Laws and the Box-Counting method. The drainage network has self-affinity characteristics. The fractal dimension obtained through the parameters relationship of Horton's Laws showed the results within the thresholds of the fractal geometry theory.
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.
The virtual education fractality: nature and organization
Directory of Open Access Journals (Sweden)
Osbaldo Turpo Gebera
2013-04-01
Full Text Available The potential generated by ICT in education raises reflect on the underlying frameworks. In this sense, the fractal is an opportunity to explain how it organizes and manages virtual education.This approach recognizes that educational dynamics are recursive and iterative processes instituted as progressive sequences, by way of fractals. This understanding enables becoming as mediated and articulated successive levels. In each dimension are embodied own activities and in turn, involves the recurrence of subsequent levels as possible solving of problem situations. Thus, the knowledge built in response to a collaborative action, participation in networks, ranging from autonomous to the cultural level or conversely.
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.
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...
Fractal modeling of fluidic leakage through metal sealing surfaces
Zhang, Qiang; Chen, Xiaoqian; Huang, Yiyong; Chen, Yong
2018-04-01
This paper investigates the fluidic leak rate through metal sealing surfaces by developing fractal models for the contact process and leakage process. An improved model is established to describe the seal-contact interface of two metal rough surface. The contact model divides the deformed regions by classifying the asperities of different characteristic lengths into the elastic, elastic-plastic and plastic regimes. Using the improved contact model, the leakage channel under the contact surface is mathematically modeled based on the fractal theory. The leakage model obtains the leak rate using the fluid transport theory in porous media, considering that the pores-forming percolation channels can be treated as a combination of filled tortuous capillaries. The effects of fractal structure, surface material and gasket size on the contact process and leakage process are analyzed through numerical simulations for sealed ring gaskets.