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.
Fractal Dimension For Fractal Structures A Middle Definition Between Hausdorff And Box Dimensions
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Author : Manuel Fernández-Martínez
language : en
Publisher:
Release Date : 2019
Fractal Dimension For Fractal Structures A Middle Definition Between Hausdorff And Box Dimensions written by Manuel Fernández-Martínez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Finance 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
Biophysical Chemistry Of Fractal Structures And Processes In Environmental Systems
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Author : Nicola Senesi
language : en
Publisher: John Wiley & Sons
Release Date : 2008-09-15
Biophysical Chemistry Of Fractal Structures And Processes In Environmental Systems written by Nicola Senesi 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 2008-09-15 with Science categories.
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 contrasted with the more classical approaches. The book will provide the fundamental knowledge necessary for solving practical environmental problems. Furthermore, it examinea how the fractal approach has been applied in order to understand the structure and reactivity of natural, environmental systems including flocs, sediments, soils, microorganisms and humic substances.
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.
A Random Walk Through Fractal Dimensions
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Author : Brian Howard Kaye
language : en
Publisher: Wiley-VCH
Release Date : 1989
A Random Walk Through Fractal Dimensions written by Brian Howard Kaye and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics 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
The Structural Stabilization Of Polymers Fractal Models
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Author : Kozlov
language : en
Publisher: CRC Press
Release Date : 2006-07-01
The Structural Stabilization Of Polymers Fractal Models written by Kozlov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-01 with Science categories.
This monograph deals with the structural aspects of transport processes of gases, physical ageing and thermo-oxidative degradation of polymers in detail. Fractal analysis, cluster models of the polymer structurea ‘s amorphous state as well as irreversible aggregation models are used as main structural models. It is shown that the polymer structure
Synergetics And Fractals In Tribology
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Author : Ahad Kh Janahmadov
language : en
Publisher: Springer
Release Date : 2016-01-29
Synergetics And Fractals In Tribology written by Ahad Kh Janahmadov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-29 with Science categories.
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.
Frontier Computing
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Author : Jason C. Hung
language : en
Publisher: Springer Nature
Release Date : 2023-05-24
Frontier Computing written by Jason C. Hung and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-24 with Technology & Engineering categories.
This book gathers the proceedings of the 12th International Conference on Frontier Computing, held in Tokyo, Japan, on July 12–15, 2022, and provides comprehensive coverage of the latest advances and trends in information technology, science, and engineering. It addresses a number of broad themes, including communication networks, business intelligence and knowledge management, Web intelligence, and related fields that inspire the development of information technology. The respective contributions cover a wide range of topics: database and data mining, networking and communications, Web and Internet of things, embedded systems, soft computing, social network analysis, security and privacy, optical communication, and ubiquitous/pervasive computing. Many of the papers outline promising future research directions, and the book benefits students, researchers, and professionals alike. Further, it offers a useful reference guide for newcomers to the field.
Optical Properties Of Low Dimensional Materials Vol 2
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Author : Tetsuo Ogawa
language : en
Publisher: World Scientific
Release Date : 1998-08-06
Optical Properties Of Low Dimensional Materials Vol 2 written by Tetsuo Ogawa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-06 with Science categories.
This book surveys recent theoretical and experimental studies of optical properties of low-dimensional materials. As an extended version of Optical Properties of Low-Dimensional Materials (Volume 1, published in 1995 by World Scientific), Volume 2 covers a wide range of interesting low-dimensional materials including both inorganic and organic systems, such as disordered polymers, deformable molecular crystals, dilute magnetic semiconductors, SiGe/Si short-period superlattices, GaAs quantum wires, semiconductor microcavities, and photonic crystals. There are excellent review articles by promising researchers in each field. All the materials introduced in this book yield new optical phenomena originating from their mesoscopic and low-dimensional electronic characters and electron-lattice couplings, which offer a new research field of materials science as well as condensed-matter and optical physics. Volumes 1 and 2 are interrelated but can be read independently. They are pitched at the level of graduate students and are useful to both students and scientists.