Gaussian Self Affinity And Fractals
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Gaussian Self Affinity And Fractals
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Author : Benoit Mandelbrot
language : en
Publisher: Springer Science & Business Media
Release Date : 2002
Gaussian Self Affinity And Fractals written by Benoit Mandelbrot 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 2002 with Mathematics categories.
The book contributes to their development and will therefore be of use in diverse scientific communities."--BOOK JACKET.
Fractals And Chaos
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Author : Benoit Mandelbrot
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Fractals And Chaos written by Benoit Mandelbrot 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 Mathematics categories.
It has only been a couple of decades since Benoit Mandelbrot published his famous picture of what is now called the Mandelbrot set. That picture, now seeming graphically primitive, has changed our view of the mathematical and physical universe. The properties and circumstances of the discovery of the Mandelbrot Set continue to generate much interest in the research community and beyond. This book contains the hard-to-obtain original papers, many unpublished illustrations dating back to 1979 and extensive documented historical context showing how Mandelbrot helped change our way of looking at the world.
Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Ii
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Author : David Carfi
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-10-24
Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Ii written by David Carfi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-24 with Mathematics categories.
This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.
Fractal Geometry And Applications A Jubilee Of Benoit Mandelbrot
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Author : Michel Laurent Lapidus
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Fractal Geometry And Applications A Jubilee Of Benoit Mandelbrot written by Michel Laurent Lapidus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.
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.
Digital Wood Design
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Author : Fabio Bianconi
language : en
Publisher: Springer
Release Date : 2019-02-24
Digital Wood Design written by Fabio Bianconi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-24 with Technology & Engineering categories.
This book explores various digital representation strategies that could change the future of wooden architectures by blending tradition and innovation. Composed of 61 chapters, written by 153 authors hailing from 5 continents, 24 countries and 69 research centers, it addresses advanced digital modeling, with a particular focus on solutions involving generative models and dynamic value, inherent to the relation between knowing how to draw and how to build. Thanks to the potential of computing, areas like parametric design and digital manufacturing are opening exciting new avenues for the future of construction. The book’s chapters are divided into five sections that connect digital wood design to integrated approaches and generative design; to model synthesis and morphological comprehension; to lessons learned from nature and material explorations; to constructive wisdom and implementation-related challenges; and to parametric transfigurations and morphological optimizations.
An Invitation To Fractal Geometry
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Author : Michel L. Lapidus
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-30
An Invitation To Fractal Geometry written by Michel L. Lapidus and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-30 with Mathematics categories.
This book offers a comprehensive exploration of fractal dimensions, self-similarity, and fractal curves. Aimed at undergraduate and graduate students, postdocs, mathematicians, and scientists across disciplines, this text requires minimal prerequisites beyond a solid foundation in undergraduate mathematics. While fractal geometry may seem esoteric, this book demystifies it by providing a thorough introduction to its mathematical underpinnings and applications. Complete proofs are provided for most of the key results, and exercises of different levels of difficulty are proposed throughout the book. Key topics covered include the Hausdorff metric, Hausdorff measure, and fractal dimensions such as Hausdorff and Minkowski dimensions. The text meticulously constructs and analyzes Hausdorff measure, offering readers a deep understanding of its properties. Through emblematic examples like the Cantor set, the Sierpinski gasket, the Koch snowflake curve, and the Weierstrass curve, readers are introduced to self-similar sets and their construction via the iteration of contraction mappings. The book also sets the stage for the advanced theory of complex dimensions and fractal drums by gently introducing it via a variety of classical examples, including well-known fractal curves. By intertwining historical context with rigorous mathematical exposition, this book serves as both a stand-alone resource and a gateway to deeper explorations in fractal geometry.
Multiscale Coupling Of Sun Earth Processes
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Author : A.T.Y. Lui
language : en
Publisher: Elsevier
Release Date : 2005-07-06
Multiscale Coupling Of Sun Earth Processes written by A.T.Y. Lui and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-06 with Science categories.
Many approaches exist for scientific investigations and space research is no exception. The early approach during which each space plasma region within the Sun-Earth system was investigated separately with physics-based tools has now progressed to encompass investigations on coupling between these regions. Ample evidence now exists indicating the dynamic processes in these regions exhibit disturbances over a wide range of scales both in time and space. This new reckoning naturally leads to an emerging perspective of probing these natural phenomena with concepts and tools developed in modern statistical mechanics for physical processes governing the evolution of out-of-equilibrium and complex systems.These new developments have prompted a topical conference on Sun-Earth connection, held on February 9-13, 2004 at Kailua-Kona, Hawaii, USA, with the goal of promoting interactions among scientists practicing the traditional physics-based approach and those utilizing modern statistical techniques.This monograph is a product of this conference, a compilation of thirty-nine articles assembled into seven chapters: (1) multiscale features in complexity dynamics, (2) space storms, (3) magnetospheric substorms, (4) turbulence and magnetic reconnection, (5) modeling and coupling of space phenomena, (6) techniques for multiscale space plasma problems, and (7) present and future multiscale space missions. These articles show a diversity of space phenomena exhibiting scale free characteristics, intermittency, and non-Gaussian distributions of probability density function of fluctuations in the physical parameters of the Sun-Earth system. The scope covers the latest observations, theories, simulations, and techniques on the multiscale nature of Sun-Earth phenomena and underscores the usefulness in cross-disciplinary exchange needed to unravel the underlying physical processes, which may eventually lead to a possible unified description and prediction for space disturbances.* Extensive collection of state-of-the-art papers on multiscale coupling of Sun-Earth Processes* Present and future multiscale space missions* New techniques and models for performing multiscale analysis
Natural Time Analysis The New View Of Time
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Author : Panayiotis Varotsos
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-14
Natural Time Analysis The New View Of Time written by Panayiotis Varotsos 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 2011-08-14 with Nature categories.
This book deals with the theory and the applications of a new time domain, termed natural time domain, that has been forwarded by the authors almost a decade ago (P.A. Varotsos, N.V. Sarlis and E.S. Skordas, Practica of Athens Academy 76, 294-321, 2001; Physical Review E 66, 011902, 2002). In particular, it has been found that novel dynamical features hidden behind time series in complex systems can emerge upon analyzing them in this new time domain, which conforms to the desire to reduce uncertainty and extract signal information as much as possible. The analysis in natural time enables the study of the dynamical evolution of a complex system and identifies when the system enters a critical stage. Hence, natural time plays a key role in predicting impending catastrophic events in general. Relevant examples of data analysis in this new time domain have been published during the last decade in a large variety of fields, e.g., Earth Sciences, Biology and Physics. The book explains in detail a series of such examples including the identification of the sudden cardiac death risk in Cardiology, the recognition of electric signals that precede earthquakes, the determination of the time of an impending major mainshock in Seismology, and the analysis of the avalanches of the penetration of magnetic flux into thin films of type II superconductors in Condensed Matter Physics. In general, this book is concerned with the time-series analysis of signals emitted from complex systems by means of the new time domain and provides advanced students and research workers in diverse fields with a sound grounding in the fundamentals of current research work on detecting (long-range) correlations in complex time series. Furthermore, the modern techniques of Statistical Physics in time series analysis, for example Hurst analysis, the detrended fluctuation analysis, the wavelet transform etc., are presented along with their advantages when natural time domain is employed.
Mathematical Principle And Fractal Analysis Of Mesoscale Eddy
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Author : Shu-Tang Liu
language : en
Publisher: Springer Nature
Release Date : 2021-06-29
Mathematical Principle And Fractal Analysis Of Mesoscale Eddy written by Shu-Tang Liu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-29 with Technology & Engineering categories.
This book focuses on universal nonlinear dynamics model of mesoscale eddies. The results of this book are not only the direct-type applications of pure mathematical limit cycle theory and fractal theory in practice but also the classic combination of nonlinear dynamic systems in mathematics and the physical oceanography. The universal model and experimental verification not only verify the relevant results that are obtained by Euler's form but also, more importantly, are consistent with observational numerical statistics. Due to the universality of the model, the consequences of the system are richer and more complete. The comprehensive and systematic mathematical modeling of mesoscale eddies is one of the major features of the book, which is particularly suited for readers who are interested to learn fractal analysis and prediction in physical oceanography. The book benefits researchers, engineers, and graduate students in the fields of mesoscale eddies, fractal, chaos, and other applications, etc.