Fractal Dimension For Fractal Structures
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Fractal Dimension For Fractal Structures
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Author : Manuel Fernández-Martínez
language : en
Publisher: Springer
Release Date : 2019-04-23
Fractal Dimension For Fractal Structures written by Manuel Fernández-Martínez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-23 with Mathematics categories.
This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts. In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithms for properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes. This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.
A Random Walk Through Fractal Dimensions
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Author : Brian H. Kaye
language : en
Publisher: John Wiley & Sons
Release Date : 2008-07-11
A Random Walk Through Fractal Dimensions written by Brian H. Kaye and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-11 with Technology & Engineering categories.
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
Physics And Fractal Structures
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Author : Jean-François Gouyet
language : en
Publisher: Elsevier Masson
Release Date : 1996
Physics And Fractal Structures written by Jean-François Gouyet and has been published by Elsevier Masson this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Fractals Physical Origin And Properties
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Author : Luciano Pietronero
language : en
Publisher: Springer
Release Date : 2013-12-19
Fractals Physical Origin And Properties written by Luciano Pietronero and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-19 with Medical categories.
This volume contains the Proceedings of the Special Seminar on: FRAGTALS held from October 9-15, 1988 at the Ettore Majorana Centre for Scientific Culture, Erice (Trapani), Italy. The concepts of self-similarity and scale invariance have arisen independently in several areas. One is the study of critical properites of phase transitions; another is fractal geometry, which involves the concept of (non-integer) fractal dimension. These two areas have now come together, and their methods have extended to various fields of physics. The purpose of this Seminar was to provide an overview of the recent developments in the field. Most of the contributions are theoretical, but some experimental work is also included. Du:cing the past few years two tendencies have emerged in this field: one is to realize that many phenomena can be naturally modelled by fractal structures. So one can use this concept to define simple modele and study their physical properties. The second point of view is more microscopic and tries to answer the question: why nature gives rise to fractal structures. This implies the formulation of fractal growth modele based on physical concepts and their theoretical understanding in the same sense as the Renormalization Group method has allowed to understand the critical properties of phase transitions.
A Random Walk Through Fractal Dimensions
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Author : Brian Howard Kaye
language : en
Publisher:
Release Date : 1989
A Random Walk Through Fractal Dimensions written by Brian Howard Kaye and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Fractals categories.
The aim of this book is both to stimulate interest in fractal geometry and to be useful as a first text to those who use fractal geometry in their work. It contains many suggestions for experiments, and tends to rely on graphic examples, rather than swamping the reader with equations and symbols.
Applying Fractals In Astronomy
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Author : Andre HECK
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-11
Applying Fractals In Astronomy written by Andre HECK and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-11 with Science categories.
'Fractal geometry addressesitselfto questions that many people have been asking themselves. It con cerns an aspect of Nature that almost everybody had been conscious of, but could not address in a formal fashion. ' 'Fractal geometry seems to be the proper language to describe the complezity of many very compli cated shapes around us. ' (Mandelbrot, 1990a) 'I believe that fractals respond to a profound un easiness in man. ' (Mandelbrot, 1990b) The catchword fractal, ever since it was coined by Mandelbrot (1975) to refer to a class of abstract mathematical objects that were already known at the turn ofthe 19th century, has found an unprecedented resonance both inside and outside the scientific community. Fractal concepts, far more than the concepts of catastrophe theory introduced a few years earlier, are currently being applied not only in the physical sciences, but also in biology and medicine (Goldberger and West 1987). In the mid-eighties, Kadanoff (1986) asked the question: 'Why all the fuss about /ractals'! '. He offered a twofold answer: in the first place, it is 'because of the practical, technological importance of fractal objects'. Indeed he emphasised the relevance of these structures for materials scientists and oil drilling engineers, in search of structures with novel properties, or models for the flow of oil through the soil. His second answer was: 'Because of the intellectual interest of fractals '.
Fractal Frontiers Fractals In The Natural And Applied Sciences
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Author : Miroslav M Novak
language : en
Publisher: World Scientific
Release Date : 1997-03-29
Fractal Frontiers Fractals In The Natural And Applied Sciences written by Miroslav M Novak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03-29 with categories.
Historically, science has developed by reducing complex situations to simple ones, analyzing the components and synthesizing the original situation. While this 'reductionist' approach has been extremely successful, there are phenomena of such complexity that one cannot simplify them without eliminating the problem itself. Recently, attention has turned to such problems in a wide variety of fields. This is in part due to the development of fractal geometry. Fractal geometry provides the mathematical tools for handling complexity. The present volume is a collection of papers that deal with the application of fractals in both traditional scientific disciplines and in applied fields. This volume shows the advance of our understanding of complex phenomena across a spectrum of disciplines. While these diverse fields work on very different problems, fractals provide a unifying formalism for approaching these problems.
Fractals In Natural Science
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Author : M Matsushita
language : en
Publisher: World Scientific
Release Date : 1994-10-26
Fractals In Natural Science written by M Matsushita and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-26 with Science categories.
During the last couple of years, fractals have been shown to represent the common aspects of many complex processes occurring in an unusually diverse range of fields including biology, chemistry, earth sciences, physics and technology. Using fractal geometry as a language, it has become possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iteractive functions, colloidal aggregation, biological pattern formation and inhomogenous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality.This volume contains a selection of high quality papers that discuss the latest developments in the research of fractals. It is divided into 5 sections and contains altogether 64 papers. Each paper is written by a well known author or authors in the field. Beginning each section is a short introduction, written by a prominent author, which gives a brief overview of the topics discussed in the respective sections.
Fractal Analysis
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Author : Fernando Brambila
language : en
Publisher: BoD – Books on Demand
Release Date : 2017-06-14
Fractal Analysis written by Fernando Brambila and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-14 with Mathematics categories.
Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: "Part I: Petroleum Industry and Numerical Analysis"; "Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure"; and "Part III: Scattering Theory, Porosity, and Turbulence." It's impossible to picture today's research without fractal analysis.
Fractals In Chemistry Geochemistry And Biophysics
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Author : K.S. Birdi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Fractals In Chemistry Geochemistry And Biophysics written by K.S. Birdi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
In this introductory text, Dr. Birdi demonstrates experimental methods and analyses of fractal dimensions in natural processes. In addition to a general overview, he discusses in detail problems in the fields of chemistry, geochemistry, and biophysics. Both students and professionals with a minimum of mathematics or physical science training will learn to find and model shapes and patterns from their own everyday observations.