Pattern Formation and Dynamics in Nonequilibrium Systems PDF Download

Author: Michael Cross
Publisher: Cambridge University Press
ISBN: 0521770505
Category : Mathematics
Languages : en
Pages : 547

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Book Description
An account of how complex patterns form in sustained nonequilibrium systems; for graduate students in biology, chemistry, engineering, mathematics, and physics.

Author: J. A. Scott Kelso
Publisher: MIT Press
ISBN: 9780262611312
Category : Behavior
Languages : en
Pages : 368

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Book Description
foreword by Hermann Haken For the past twenty years Scott Kelso's research has focused on extending the physical concepts of self- organization and the mathematical tools of nonlinear dynamics to understand how human beings (and human brains) perceive, intend, learn, control, and coordinate complex behaviors. In this book Kelso proposes a new, general framework within which to connect brain, mind, and behavior.Kelso's prescription for mental life breaks dramatically with the classical computational approach that is still the operative framework for many newer psychological and neurophysiological studies. His core thesis is that the creation and evolution of patterned behavior at all levels--from neurons to mind--is governed by the generic processes of self-organization. Both human brain and behavior are shown to exhibit features of pattern-forming dynamical systems, including multistability, abrupt phase transitions, crises, and intermittency. Dynamic Patterns brings together different aspects of this approach to the study of human behavior, using simple experimental examples and illustrations to convey essential concepts, strategies, and methods, with a minimum of mathematics. Kelso begins with a general account of dynamic pattern formation. He then takes up behavior, focusing initially on identifying pattern-forming instabilities in human sensorimotor coordination. Moving back and forth between theory and experiment, he establishes the notion that the same pattern-forming mechanisms apply regardless of the component parts involved (parts of the body, parts of the nervous system, parts of society) and the medium through which the parts are coupled. Finally, employing the latest techniques to observe spatiotemporal patterns of brain activity, Kelso shows that the human brain is fundamentally a pattern forming dynamical system, poised on the brink of instability. Self-organization thus underlies the cooperative action of neurons that produces human behavior in all its forms.

Author: M. I. Rabinovich
Publisher: World Scientific
ISBN: 9789810240561
Category : Science
Languages : en
Pages : 340

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Book Description
"This beautifully illustrated book brings together a remarkable array of pattern-forming phenomena The authors have assembled an impressive collection of striking photographs and computer-generated images, and the book would be worth buying for this alone the Appendix describing key experiments is a highlight. Here the authors outline the historical development of experiments in parametrically-excited patterns, thermal convection and diffusive chemical reactions." UK Nonlinear News, 2002

Author: M I Rabinovich
Publisher: World Scientific
ISBN: 9814494356
Category : Science
Languages : en
Pages : 336

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Book Description
Spirals, vortices, crystalline lattices, and other attractive patterns are prevalent in Nature. How do such beautiful patterns appear from the initial chaos? What universal dynamical rules are responsible for their formation? What is the dynamical origin of spatial disorder in nonequilibrium media? Based on the many visual experiments in physics, hydrodynamics, chemistry, and biology, this invaluable book answers those and related intriguing questions. The mathematical models presented for the dynamical theory of pattern formation are nonlinear partial differential equations. The corresponding theory is not so accessible to a wide audience. Consequently, the authors have made every attempt to synthesize long and complex mathematical calculations to exhibit the underlying physics. The book will be useful for final year undergraduates, but is primarily aimed at graduate students, postdoctoral fellows, and others interested in the puzzling phenomena of pattern formation. Contents:Patterns: Prelude to a Dynamical DescriptionLinear Stage of Pattern FormationModel EquationsThe Ginzburg–Landau Equation‘Crystal’ FormationQuasicrystalsBreaking of OrderLocalized PatternsSpiralsPatterns in Oscillating Soap FilmsPatterns in Colonies of MicroorganismsSpatial DisorderPatterns in Chaotic MediaEpilogue: Living Matter and Dynamic FormsA Short Guide to Nonlinear DynamicsKey Experiments in Pattern Formation Readership: Graduate students of mathematical physics and nonlinear science. Keywords:Quasicrystals;Disordered Patterns;Defects;Spirals;Turbulence;Synchronization;Convection;Capillary Waves;Chaotic Dynamics;Biological PatternsReviews: “This beautifully illustrated book brings together a remarkable array of pattern-forming phenomena … The authors have assembled an impressive collection of striking photographs and computer-generated images, and the book would be worth buying for this alone … the Appendix describing key experiments is a highlight. Here the authors outline the historical development of experiments in parametrically-excited patterns, thermal convection and diffusive chemical reactions.” UK Nonlinear News “This book contains a very impressive account of key ideas and results in nonlinear dynamics and an equally excellent description of important experiments in pattern formation … readers can gain quite comprehensive knowledge about all possible patterns and their mathematical theories by reading a single chapter, coupled with Appendix I.” Mathematical Reviews

Author: Muthusamy Lakshmanan
Publisher: Springer Science & Business Media
ISBN: 3642556884
Category : Mathematics
Languages : en
Pages : 628

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Book Description
This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Author: Igor S. Aranson
Publisher: Springer
ISBN: 3319536737
Category : Technology & Engineering
Languages : en
Pages : 336

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Book Description
This book focuses on recent progress in complexity research based on the fundamental nonlinear dynamical and statistical theory of oscillations, waves, chaos, and structures far from equilibrium. Celebrating seminal contributions to the field by Prof. M. I. Rabinovich of the University of California at San Diego, this volume brings together perspectives on both the fundamental aspects of complexity studies, as well as in applications in different fields ranging from granular patterns to understanding of the cognitive brain and mind dynamics. The slate of world-class authors review recent achievements that together present a broad and coherent coverage of modern research in complexity greater than the sum of its parts.

Author: L.M. Pismen
Publisher: Springer Science & Business Media
ISBN: 3540304312
Category : Science
Languages : en
Pages : 383

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Book Description
Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. This book explores the forefront of current research, describing in-depth the analytical methods that elucidate the complex evolution of nonlinear dissipative systems.

Author: Akira Onuki
Publisher: Springer Science & Business Media
ISBN: 3642760082
Category : Science
Languages : en
Pages : 231

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Book Description
The fourth Nishinomiya-Yukawa Memorial Symposium, devoted to the topic of dynamics and patterns in complex fluids, was held on October 26 and 27, 1989, in Nishinomiya City, Japan, where ten invited speakers gave their lectures. A one-day meeting, comprising short talks and poster sessions, was then held on the same topic on October 28 at the Research Institute for Fundamental Physics, Kyoto University. The present volume contains the 10 invited papers and 38 contributed papers presented at these two meetings. The symposium was sponsored by Nishinomiya City, where Prof. Hideki Yukawa once lived and where he wrote the celebrated paper describing the work that was later honored by a Nobel prize. The topic of the fourth symposium was chosen from one of the most vigorously evolving and highly interdisciplinary fields in condensed matter physics. The field of complex fluids is very diverse and still in its infancy and, as a result, the definition of a complex fluid varies greatly from one researcher to the next. One of the objectives of the symposium was to clarify its definition by explicitly posing a number of potentially rich problems waiting to be explored. Indeed, experimentalists are disclosing a variety of intriguing dynamical phenomena in complex systems such as polymers, liquid crystals, gels, colloids, and surfactant systems. We, the organizers, hope that the symposium will contribute to the increasing importance of the field in the coming years.

Author: A. Van Harten
Publisher: Taylor & Francis
ISBN: 1351428276
Category : Mathematics
Languages : en
Pages : 344

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Book Description
This Research Note aims to provide an insight into recent developments in the theory of pattern formation. In the last decade there has been considerable progress in this field, both from a theoretical and a practical point of view. Recent mathematical developments concern the study of the nonlinear stability of systems at near-critical conditions by an appropriate system of modulation equations. The complexity of the original problem can be reduced drastically by this approximation. Moreover, it provides unifying point of view for a wide range of problems. New applications of the theory arise in a multitude of scientific areas such as hydrodynamics, reaction-diffusion problems, oceanography, meteorology, combustion, geophysical and biological morphodynamics and semi-conductors.This book is intended to show the interactions between the mathematical theory of nonlinear dynamics and the study of pattern generating phenomena in the natural environment. There is an intimate relationship between new insights in the mathematical aspects of nonlinear pattern formation and the comprehension of such phenomena. Therefore there are two partly overlapping main themes: one in which the emphasis is on generally applicable mathematical theories and techniques and one in which the phenomenology of pattern evolution in various areas is discussed.The book comprises 19 contributions by experts in the field. Although the emphasis changes considerably from paper to paper, in each contribution the same two themes are present; all the authors have aimed to achieve a suitable balance between the mathematical theory and the physical phenomena.

Author: Irving R. Epstein
Publisher: Oxford University Press
ISBN: 0198025661
Category : Science
Languages : en
Pages : 407

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Book Description
Just a few decades ago, chemical oscillations were thought to be exotic reactions of only theoretical interest. Now known to govern an array of physical and biological processes, including the regulation of the heart, these oscillations are being studied by a diverse group across the sciences. This book is the first introduction to nonlinear chemical dynamics written specifically for chemists. It covers oscillating reactions, chaos, and chemical pattern formation, and includes numerous practical suggestions on reactor design, data analysis, and computer simulations. Assuming only an undergraduate knowledge of chemistry, the book is an ideal starting point for research in the field. The book begins with a brief history of nonlinear chemical dynamics and a review of the basic mathematics and chemistry. The authors then provide an extensive overview of nonlinear dynamics, starting with the flow reactor and moving on to a detailed discussion of chemical oscillators. Throughout the authors emphasize the chemical mechanistic basis for self-organization. The overview is followed by a series of chapters on more advanced topics, including complex oscillations, biological systems, polymers, interactions between fields and waves, and Turing patterns. Underscoring the hands-on nature of the material, the book concludes with a series of classroom-tested demonstrations and experiments appropriate for an undergraduate laboratory.