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Fractals in Physics

By L. Pietronero, E. Tosatti
Publisher: Elsevier, 2012-12-02
Pages: 489
Language: en
ISBN_13:9780444598417
ISBN_10:0444598413
Subject: Science

$This lovely little book will take off and fly on its own power, but the author has asked me to write a few words, and one should not say no to a friend. Specific topics in fractal geometry and its applications have already benefited from several excellent surveys of moderate length, and gossip and preliminary drafts tell us that we shall soon see several monographic treatments of broader topics. For the teacher, however, these surveys and monographs are not enough, and an urgent need for more helpful books has been widely recognized. To write such a book is no easy task, but Jens Feder meets the challenge head on. His approach combines the old Viking's willingness to attack many difficulties at the same time, and the modern Norwegian's ability to achieve fine balance between diverging needs. lowe him special gratitude for presenting the main facts about R/ S analysis of long-run dependence; now a wide scientific public will have access to a large group of papers of mine that had until this day remained fairly confidential. Last but not least, we are all grateful to Jens for not having allowed undue personal modesty to deprive us of accounts of his own group's varied and excellent work. He did not attempt to say everything, but what he said is just fine. Benoit B. Mandelbrot Physics Department, IBM Thomas J.$

جزئیات و درخواست

By Jens Feder
Publisher: Springer Science & Business Media, 2013-11-11
Pages: 305
Language: en
ISBN_13:9781489921246
ISBN_10:1489921249
Subject: Science

Fractals in Physics

Proceedings of the Sixth Trieste International Symposium on ...

$The concepts of self-similarity and scale invariance have arisen independently in several areas. One is the study of the critical properties of phase transitions; another is fractal geometry, which involves the concept of (non-integer) fractal dimension. These two areas have now come together, and their methods have extended to various fields of physics. The purpose of this Symposium was to provide an overview of the physical phenomena that manifest scale invariance and fractal properties with the aim of bringing out the common mathematical features. The emphasis was on theoretical and experimental work related to well defined physical phenomena.$

جزئیات و درخواست

By Luciano Pietronero, Erio Tosatti
Publisher: North Holland, 1986
Pages: 504
Language: en
OTHER:UOM:39015016061627
Subject: Science

Fractals, Chaos, Power Laws

Minutes from an Infinite Paradise

$This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author -- hailed by Publishers Weekly as a modern Lewis Carroll -- conveys memorable insights in the form of puns and puzzles. 1992 edition.$

جزئیات و درخواست

By Manfred Schroeder
Publisher: Courier Corporation, 2009-08-21
Pages: 450
Language: en
ISBN_13:9780486472041
ISBN_10:0486472043
Subject: Science

Fractal Concepts in Condensed Matter Physics

$Concisely and clearly written by two foremost scientists, this book provides a self-contained introduction to the basic concepts of fractals and demonstrates their use in a range of topics. The authors’ unified description of different dynamic problems makes the book extremely accessible.$

جزئیات و درخواست

By Tsuneyoshi Nakayama, Kousuke Yakubo
Publisher: Springer Science & Business Media, 2013-06-29
Pages: 216
Language: en
ISBN_13:9783662051931
ISBN_10:3662051931
Subject: Science

Physics and Fractal Structures

جزئیات و درخواست

By Jean-François Gouyet
Publisher: Elsevier Masson, 1996
Pages: 260
Language: en
OTHER:UOM:39015038157502
Subject: Mathematics

Fractals in the Physical Sciences

جزئیات و درخواست

By Hideki Takayasu
Publisher: Manchester University Press, 1990
Pages: 196
Language: en
ISBN_10:0719034345
ISBN_13:9780719034343
Subject: Mathematics

Fractals in Science

$A deeply detailed discussion of fractals in biology, heterogeneous chemistry, polymers, and the earth sciences. Beginning with a general introduction to fractal geometry it continues with eight chapters on self-organized criticality, rough surfaces and interfaces, random walks, chemical reactions, and fractals in chemisty, biology, and medicine. A special chapter entitled "Computer Exploration of Fractals, Chaos, and Cooperativity" presents computer demonstrations of fractal models: 14 programs are included on a 3 1/2" MS-DOS diskette which run on any PC with at least 1 MB RAM and a EGA or VGA graphics card, 16 colors.$

جزئیات و درخواست

By Armin Bunde, Shlomo Havlin
Publisher: Springer, 2013-12-21
Pages: 317
Language: en
ISBN_13:9783642779534
ISBN_10:3642779530
Subject: Science

Thinking in Patterns

Fractals and Related Phenomena in Nature

$Fractal geometry, together with the broader fields of nonlinear dynamics and complexity, represented a large segment of modern science at the end of the 20th century. Penetration of the resulting new paradigms into practically all academic disciplines has confirmed the fundamental assertion of universal formalism common to a wide range of human endeavors.This book contains an extended article by B B Mandelbrot, reviewing his contribution to fractal geometry and outlining some unsolved problems, with illustrations especially of finance and physics. It covers a range of multidisciplinary topics ? from the biology of aging, through the self-similar shape of plants, image decompression and solar magnetic fields, to sound reflection in the street. The book is a treasure trove for innovative researchers working in fields related to fractal geometry.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings? (ISTP? / ISI Proceedings)? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences$

جزئیات و درخواست

By Miroslav Michal Novak
Publisher: World Scientific, 2004
Pages: 336
Language: en
ISBN_13:9789812388223
ISBN_10:9812388222
Subject: Science

Physics of Fractal Operators

$This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials.$

جزئیات و درخواست

By Bruce West, Mauro Bologna, Paolo Grigolini
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 355
Language: en
ISBN_13:9780387217468
ISBN_10:0387217460
Subject: Science

Fractal Analysis

Applications in Physics, Engineering and Technology

$Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: "Part I: Petroleum Industry and Numerical Analysis"; "Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure"; and "Part III: Scattering Theory, Porosity, and Turbulence." It's impossible to picture today's research without fractal analysis.$

جزئیات و درخواست

By Fernando Brambila
Publisher: BoD – Books on Demand, 2017-06-14
Pages: 296
Language: en
ISBN_13:9789535131915
ISBN_10:9535131915
Subject: Mathematics

Fractals and Disordered Systems

$Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In ten chapters written by leading experts in the field, the reader is introduced to basic concepts and techniques in disordered systems and is led to the forefront of current research. This second edition has been substantially revised and updates the literature in this important field.$

جزئیات و درخواست

By Armin Bunde, Shlomo Havlin
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 428
Language: en
ISBN_13:9783642848681
ISBN_10:3642848680
Subject: Science

Applying Fractals in Astronomy

$'Fractal geometry addressesitselfto questions that many people have been asking themselves. It con cerns an aspect of Nature that almost everybody had been conscious of, but could not address in a formal fashion. ' 'Fractal geometry seems to be the proper language to describe the complezity of many very compli cated shapes around us. ' (Mandelbrot, 1990a) 'I believe that fractals respond to a profound un easiness in man. ' (Mandelbrot, 1990b) The catchword fractal, ever since it was coined by Mandelbrot (1975) to refer to a class of abstract mathematical objects that were already known at the turn ofthe 19th century, has found an unprecedented resonance both inside and outside the scientific community. Fractal concepts, far more than the concepts of catastrophe theory introduced a few years earlier, are currently being applied not only in the physical sciences, but also in biology and medicine (Goldberger and West 1987). In the mid-eighties, Kadanoff (1986) asked the question: 'Why all the fuss about /ractals'! '. He offered a twofold answer: in the first place, it is 'because of the practical, technological importance of fractal objects'. Indeed he emphasised the relevance of these structures for materials scientists and oil drilling engineers, in search of structures with novel properties, or models for the flow of oil through the soil. His second answer was: 'Because of the intellectual interest of fractals '.$

جزئیات و درخواست

By Andre HECK, Jean M. Perdang
Publisher: Springer Science & Business Media, 2008-09-11
Pages: 217
Language: en
ISBN_13:9783540475828
ISBN_10:3540475826
Subject: Science

Analysis, Probability And Mathematical Physics On Fractals

$In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.$

جزئیات و درخواست

By Patricia Alonso Ruiz, Joe Po-chou Chen, Luke G Rogers, Alexander Teplyaev
Publisher: World Scientific, 2020-02-26
Pages: 594
Language: en
ISBN_13:9789811215544
ISBN_10:9811215545
Subject: Mathematics

Fractal Growth Phenomena (2nd Edition)

$The investigation of phenomena involving fractals has gone through a spectacular development in the last decade. Many physical, technological and biological processes have been shown to be related to and described by objects with non-integer dimensions. The physics of far-from-equilibrium growth phenomena represents one of the most important fields in which fractal geometry is widely applied. During the last couple of years considerable experimental, numerical and theoretical information has accumulated concerning such processes.This book, written by a well-known expert in the field, summarizes the basic concepts born in the studies of fractal growth and also presents some of the most important new results for more specialized readers. It also contains 15 beautiful color plates demonstrating the richness of the geometry of fractal patterns. Accordingly, it may serve as a textbook on the geometrical aspects of fractal growth and it treats this area in sufficient depth to make it useful as a reference book. No specific mathematical knowledge is required for reading this book which is intended to give a balanced account of the field.$

جزئیات و درخواست

By Tamas Vicsek
Publisher: World Scientific, 1992-06-25
Pages: 531
Language: en
ISBN_13:9789814506199
ISBN_10:9814506192
Subject: Science

Fractal Geometry, Complex Dimensions and Zeta Functions

Geometry and Spectra of Fractal Strings

$Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary. Throughout Geometry, Complex Dimensions and Zeta Functions, Second Edition, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition.$

جزئیات و درخواست

By Michel Lapidus, Machiel van Frankenhuijsen
Publisher: Springer Science & Business Media, 2012-09-20
Pages: 583
Language: en
ISBN_13:9781461421757
ISBN_10:1461421756
Subject: Mathematics

Fractals

$What are fractals? Why are they such fun? How do you make one? Why is a dripping tap not as random as it seems? What is chaos? Is the Mandelbrot Set really the most complex object in mathematics? In this beautifully illustrated book, fractal-hunter Oliver Linton takes us on a fascinating journey into the mathematics of fractals and chaos, diving into many kinds of self- similar structures to reveal some of the most recently discovered and intriguing patterns in science and nature. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.$

جزئیات و درخواست

By Oliver Linton
Publisher: eBook Partnership, 2021-05-20
Pages: 66
Language: en
ISBN_13:9781912706136
ISBN_10:191270613X
Subject: Mathematics

Critical Phenomena in Natural Sciences

Chaos, Fractals, Selforganization and Disorder: Concepts and...

جزئیات و درخواست

By Didier Sornette
Publisher: Springer Science & Business Media, 2013-04-17
Pages: 445
Language: en
ISBN_13:9783662041741
ISBN_10:366204174X
Subject: Science

Chaos, Noise and Fractals

$The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.$

جزئیات و درخواست

By E. Roy Pike, L .A. Lugiato
Publisher: CRC Press, 1987-01-01
Pages: 282
Language: en
ISBN_10:0852743645
ISBN_13:9780852743645
Subject: Science

Chaotic Dynamics

An Introduction Based on Classical Mechanics

جزئیات و درخواست

By Tamás Tél, Márton Gruiz
Publisher: Cambridge University Press, 2006-08-24
Pages: 440
Language: en
ISBN_10:0521547830
ISBN_13:9780521547833
Subject: Mathematics

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