Dissipative Structures And Chaos

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Dissipative Structures and Chaos

Hazime Mori,Yoshiki Kuramoto
Dissipative Structures and Chaos Book PDF

Author : Hazime Mori,Yoshiki Kuramoto
Publisher : Springer Science & Business Media
Page : 306 pages
File Size : 44,8 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783642803765

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Dissipative Structures and Chaos by Hazime Mori,Yoshiki Kuramoto Pdf

This book consists of two parts, the first dealing with dissipative structures and the second with the structure and physics of chaos. The first part was written by Y. Kuramoto and the second part by H. Mori. Throughout the book, emphasis is laid on fundamental concepts and methods rather than applications, which are too numerous to be treated here. Typical physical examples, however, including nonlinear forced oscilla tors, chemical reactions with diffusion, and Benard convection in horizontal fluid layers, are discussed explicitly. Our consideration of dissipative structures is based on a phenomenolog ical reduction theory in which universal aspects of the phenomena under consideration are emphasized, while the theory of chaos is developed to treat transport phenomena, such as the mixing and diffusion of chaotic orbits, from the viewpoint of the geometrical phase space structure of chaos. The title of the original, Japanese version of the book is Sanitsu Kozo to Kaosu (Dissipative Structures and Chaos). It is part of the Iwanami Koza Gendai no Butsurigaku (Iwanami Series on Modern Physics). The first Japanese edition was published in March 1994 and the second in August 1997. We are pleased that this book has been translated into English and that it can now have an audience outside of Japan. We would like to express our gratitude to Glenn Paquette for his English translation, which has made this book more understandable than the original in many respects.

Elementary Symbolic Dynamics and Chaos in Dissipative Systems

Bai-Lin Hao
Elementary Symbolic Dynamics and Chaos in Dissipative Systems Book PDF

Author : Bai-Lin Hao
Publisher : World Scientific
Page : 488 pages
File Size : 42,5 Mb
Release : 1989
Category : Mathematics
ISBN : 997150698X

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Elementary Symbolic Dynamics and Chaos in Dissipative Systems by Bai-Lin Hao Pdf

This book is a monograph on chaos in dissipative systems written for those working in the physical sciences. Emphasis is on symbolic description of the dynamics and various characteristics of the attractors, and written from the view-point of practical applications without going into formal mathematical rigour. The author used elementary mathematics and calculus, and relied on physical intuition whenever possible. Substantial attention is paid to numerical techniques in the study of chaos. Part of the book is based on the publications of Chinese researchers, including those of the author's collaborators.

Dissipative Structures and Weak Turbulence

Anonim
Dissipative Structures and Weak Turbulence Book PDF

Author : Anonim
Publisher : Academic Press
Page : 505 pages
File Size : 42,6 Mb
Release : 2014-06-28
Category : Science
ISBN : 9780080924458

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Dissipative Structures and Weak Turbulence by Anonim Pdf

Dissipative Structure and Weak Turbulence provides an understanding of the emergence and evolution of structures in macroscopic systems. This book discusses the emergence of dissipative structures. Organized into 10 chapters, this book begins with an overview of the stability of a fluid layer with potentially unstable density stratification in the field of gravity. This text then explains the theoretical description of the dynamics of a given system at a formal level. Other chapters consider several examples of how such simplified models can be derived, complicating the picture progressively to account for other phenomena. This book discusses as well the theory and experiments on plain Rayleigh–Bénard convection by setting first the theoretical frame and deriving the analytical solution of the marginal stability problem. The final chapter deals with building a bridge between chaos as studied in weakly confined systems and more advanced turbulence in the most conventional sense. This book is a valuable resource for physicists.

Nonlinear Dynamics and Chaotic Phenomena

B.K Shivamoggi
Nonlinear Dynamics and Chaotic Phenomena Book PDF

Author : B.K Shivamoggi
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 47,7 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401724425

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Nonlinear Dynamics and Chaotic Phenomena by B.K Shivamoggi Pdf

FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasize their geometrical character. Poincare and Liapunov successfuIJy developed analytical mechanics further along these lines. In this approach, one represents the evolution of all possible states (positions and momenta) by the flow in phase space, or more efficiently, by mappings on manifolds with a symplectic geometry, and tries to understand qualitative features of this problem, rather than solving it explicitly. One important outcome of this line of inquiry is the discovery that vastly different physical systems can actually be abstracted to a few universal forms, like Mandelbrot's fractal and Smale's horse-shoe map, even though the underlying processes are not completely understood. This, of course, implies that much of the observed diversity is only apparent and arises from different ways of looking at the same system. Thus, modern nonlinear dynamics 1 is very much akin to classical thermodynamics in that the ideas and results appear to be applicable to vastly different physical systems. Chaos theory, which occupies a central place in modem nonlinear dynamics, refers to a deterministic development with chaotic outcome. Computers have contributed considerably to progress in chaos theory via impressive complex graphics. However, this approach lacks organization and therefore does not afford complete insight into the underlying complex dynamical behavior. This dynamical behavior mandates concepts and methods from such areas of mathematics and physics as nonlinear differential equations, bifurcation theory, Hamiltonian dynamics, number theory, topology, fractals, and others.

Instabilities, Chaos and Turbulence

Paul Manneville
Instabilities Chaos and Turbulence Book PDF

Author : Paul Manneville
Publisher : World Scientific
Page : 456 pages
File Size : 44,5 Mb
Release : 2010
Category : Science
ISBN : 9781848163928

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Instabilities, Chaos and Turbulence by Paul Manneville Pdf

This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.

Collapse of Tori and Genesis of Chaos in Dissipative Systems

K Kaneko
Collapse of Tori and Genesis of Chaos in Dissipative Systems Book PDF

Author : K Kaneko
Publisher : World Scientific Publishing Company
Page : 276 pages
File Size : 53,7 Mb
Release : 1986-05-01
Category : Science
ISBN : 9789813104204

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Collapse of Tori and Genesis of Chaos in Dissipative Systems by K Kaneko Pdf

This book provides a good coverage of the recent developments and future directions in the study of dissipative systems. The primary thrust here is in exposing the reader to the frontiers of chaos, pointing out clues for further work in nonlinear science. With the aid of various types of mappings, the collapse of tori is investigated. The book contains much valuable introductory material and copious reference lists. Some notes on the historical development of the subject are interspersed in this volume. Request Inspection Copy

Order Out of Chaos

Ilya Prigogine,Isabelle Stengers
Order Out of Chaos Book PDF

Author : Ilya Prigogine,Isabelle Stengers
Publisher : Verso Books
Page : 384 pages
File Size : 54,8 Mb
Release : 2018-01-23
Category : Science
ISBN : 9781786631022

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Order Out of Chaos by Ilya Prigogine,Isabelle Stengers Pdf

A pioneering book that shows how the two great themes of classic science, order and chaos, are being reconciled in a new and unexpected synthesis Order Out of Chaos is a sweeping critique of the discordant landscape of modern scientific knowledge. In this landmark book, Nobel Laureate Ilya Prigogine and acclaimed philosopher Isabelle Stengers offer an exciting and accessible account of the philosophical implications of thermodynamics. Prigogine and Stengers bring contradictory philosophies of time and chance into a novel and ambitious synthesis. Since its first publication in France in 1978, this book has sparked debate among physicists, philosophers, literary critics and historians.

Unifying Themes in Complex Systems IV

Ali A. Minai,Yaneer Bar-Yam
Unifying Themes in Complex Systems IV Book PDF

Author : Ali A. Minai,Yaneer Bar-Yam
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 40,5 Mb
Release : 2008-11-05
Category : Science
ISBN : 9783540738497

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Unifying Themes in Complex Systems IV by Ali A. Minai,Yaneer Bar-Yam Pdf

In June of 2002, over 500 professors, students and researchers met in Boston, Massachusetts for the Fourth International Conference on Complex Systems. The attendees represented a remarkably diverse collection of fields: biology, ecology, physics, engineering, computer science, economics, psychology and sociology, The goal of the conference was to encourage cross-fertilization between the many disciplines represented and to deepen understanding of the properties common to all complex systems. This volume contains 43 papers selected from the more than 200 presented at the conference. Topics include: cellular automata, neurology, evolution, computer science, network dynamics, and urban planning. About NECSI: For over 10 years, The New England Complex Systems Institute (NECSI) has been instrumental in the development of complex systems science and its applications. NECSI conducts research, education, knowledge dissemination, and community development around the world for the promotion of the study of complex systems and its application for the betterment of society. NECSI hosts the International Conference on Complex Systems and publishes the NECSI Book Series in conjunction with Springer Publishers. ALI MINAI is an Affiliate of the New England Complex Systems Institute and an Associate Professor in the Department of Electrical and Computer Engineering and Computer Science at the University of Cincinnati. YANEER BAR-YAM is President and founder of the New England Complex Systems Institute. He is the author of Dynamics of Complex Systems and Making Things Work: Solving Complex Problems in a Complex World.

Chaotic Behaviour of Deterministic Dissipative Systems

Milos Marek,Igor Schreiber
Chaotic Behaviour of Deterministic Dissipative Systems Book PDF

Author : Milos Marek,Igor Schreiber
Publisher : Cambridge University Press
Page : 384 pages
File Size : 50,7 Mb
Release : 1995-07-20
Category : Science
ISBN : 0521438306

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Chaotic Behaviour of Deterministic Dissipative Systems by Milos Marek,Igor Schreiber Pdf

This graduate text surveys both the theoretical and experimental aspects of deterministic chaotic behaviour.

An Exploration of Dynamical Systems and Chaos

John H. Argyris,Gunter Faust,Maria Haase,Rudolf Friedrich
An Exploration of Dynamical Systems and Chaos Book PDF

Author : John H. Argyris,Gunter Faust,Maria Haase,Rudolf Friedrich
Publisher : Springer
Page : 865 pages
File Size : 47,7 Mb
Release : 2015-04-24
Category : Technology & Engineering
ISBN : 9783662460429

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An Exploration of Dynamical Systems and Chaos by John H. Argyris,Gunter Faust,Maria Haase,Rudolf Friedrich Pdf

This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlarged second edition which comprises recently obtained research results of topical interest, and has been extended to include a new section on the basic concepts of probability theory. A completely new chapter on fully developed turbulence presents the successes of chaos theory, its limitations as well as future trends in the development of complex spatio-temporal structures. "This book will be of valuable help for my lectures" Hermann Haken, Stuttgart "This text-book should not be missing in any introductory lecture on non-linear systems and deterministic chaos" Wolfgang Kinzel, Würzburg “This well written book represents a comprehensive treatise on dynamical systems. It may serve as reference book for the whole field of nonlinear and chaotic systems and reports in a unique way on scientific developments of recent decades as well as important applications.” Joachim Peinke, Institute of Physics, Carl-von-Ossietzky University Oldenburg, Germany

Elementary Symbolic Dynamics and Chaos in Dissipative Systems

Hao Bailin
Elementary Symbolic Dynamics and Chaos in Dissipative Systems Book PDF

Author : Hao Bailin
Publisher : World Scientific
Page : 476 pages
File Size : 50,6 Mb
Release : 1989-09-01
Category : Science
ISBN : 9789814520010

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Elementary Symbolic Dynamics and Chaos in Dissipative Systems by Hao Bailin Pdf

This book is a monograph on chaos in dissipative systems written for those working in the physical sciences. Emphasis is on symbolic description of the dynamics and various characteristics of the attractors, and written from the view-point of practical applications without going into formal mathematical rigour. The author used elementary mathematics and calculus, and relied on physical intuition whenever possible. Substantial attention is paid to numerical techniques in the study of chaos. Part of the book is based on the publications of Chinese researchers, including those of the author's collaborators. Contents:Mathematical Models Exhibiting ChaosOne Dimensional MappingsElementary Symbolic DynamicsCircle Mappings and Two-Dimensional MapsChaos in Ordinary Differential EquationsCharacterization of Chaotic AttractorsTransient Behaviour Readership: Condensed matter physicists, applied mathematicians and computer scientists. Keywords:Symbolic Dynamics;One Dimensional Mappings;Circle Mapping;Two-Dimensional Maps;Chaotic Attractors;Transient Behaviour

Chaos

Angelo Vulpiani
Chaos Book PDF

Author : Angelo Vulpiani
Publisher : World Scientific
Page : 482 pages
File Size : 53,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814277662

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Chaos by Angelo Vulpiani Pdf

Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.

Dissipative Structures in Transport Processes and Combustion

Dirk Meinköhn
Dissipative Structures in Transport Processes and Combustion Book PDF

Author : Dirk Meinköhn
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642842306

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Dissipative Structures in Transport Processes and Combustion by Dirk Meinköhn Pdf

Any description of the workings of nature by means of measurements and ob servations is beset with the problem of how to cope with an immense amount of information. In physics, it is an established approach to derive basic equations which then serve as cornerstones of what is called a theory of the phenomena. This derivation is based on certain characteristics of the phenomena, the refine ment of which results from a reduction of the amount of empirical information, with the reduction leading to an enhancement of the very characteristics that are sought for in the otherwise seemingly amorphous wealth of data. If physics is mainly concerned with the derivation of equations, lately there has emerged a conceptually different approach, which in a way is equivalent to a reversal of the line of attack: here, the basic equations serve as the point of departure and the aim is to demonstrate that the equations are capable of de to represent the essence of the scribing certain characteristics which are thought phenomenon under investigation. By definition, this variant approach must tran scend the realm of pure physics and could possibly be termed "applied mathe matics" in a broader sense. The phenomena it strives to characterize arise from a range of influences such that a combination of theoretical concepts from physics, chemistry, engineering, biology, etc. , is called for.

Dynamics of Dissipation

Piotr Garbaczewski,Robert Olkiewicz
Dynamics of Dissipation Book PDF

Author : Piotr Garbaczewski,Robert Olkiewicz
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 42,6 Mb
Release : 2007-08-04
Category : Science
ISBN : 9783540461227

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Dynamics of Dissipation by Piotr Garbaczewski,Robert Olkiewicz Pdf

This collection of lectures treats the dynamics of open systems with a strong emphasis on dissipation phenomena related to dynamical chaos. This research area is very broad, covering topics such as nonequilibrium statistical mechanics, environment-system coupling (decoherence) and applications of Markov semi-groups to name but a few. The book addresses not only experienced researchers in the field but also nonspecialists from related areas of research, postgraduate students wishing to enter the field and lecturers searching for advanced textbook material.

Collapse of Tori and Genesis of Chaos in Dissipative Systems

Kunihiko Kaneko
Collapse of Tori and Genesis of Chaos in Dissipative Systems Book PDF

Author : Kunihiko Kaneko
Publisher : World Scientific
Page : 284 pages
File Size : 41,5 Mb
Release : 1986
Category : Science
ISBN : 997197861X

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Collapse of Tori and Genesis of Chaos in Dissipative Systems by Kunihiko Kaneko Pdf

This book provides a good coverage of the recent developments and future directions in the study of dissipative systems. The primary thrust here is in exposing the reader to the frontiers of chaos, pointing out clues for further work in nonlinear science. With the aid of various types of mappings, the collapse of tori is investigated. The book contains much valuable introductory material and copious reference lists. Some notes on the historical development of the subject are interspersed in this volume.