The Dynamics Of Pattern
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The Dynamics Of Pattern
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Author : Alexander B Ezersky
language : en
Publisher: World Scientific
Release Date : 2000-10-31
The Dynamics Of Pattern written by Alexander B Ezersky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-31 with Science categories.
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.
The Dynamics Of Patterns
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Author : M. I. Rabinovich
language : en
Publisher: World Scientific
Release Date : 2000
The Dynamics Of Patterns written by M. I. Rabinovich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.
"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
Pattern Formation And Dynamics In Nonequilibrium Systems
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Author : Michael Cross
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-16
Pattern Formation And Dynamics In Nonequilibrium Systems written by Michael Cross and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-16 with Mathematics categories.
An account of how complex patterns form in sustained nonequilibrium systems; for graduate students in biology, chemistry, engineering, mathematics, and physics.
Patterns In Excitable Media
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Author : Sitabhra Sinha
language : en
Publisher: CRC Press
Release Date : 2014-12-13
Patterns In Excitable Media written by Sitabhra Sinha and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-13 with Mathematics categories.
Excitable media comprise a class of models for a wide range of physical, chemical, and biological systems that exhibit spontaneous formation of spatial patterns. Patterns in Excitable Media: Genesis, Dynamics, and Control explores several aspects of the dynamics of such patterns—in particular their evolution upon interaction with structural and functional heterogeneities in the system. The book provides readers with an introduction to recent developments in the interdisciplinary field of dynamics and control of patterns in nonlinear biological systems described by excitable media models. It also discusses low-amplitude control schemes for eliminating such patterns from an excitable medium which has direct clinical relevance in view of the close connection to life-threatening cardiac arrhythmia.
Dynamic Patterns
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Author : J. A. Scott Kelso
language : en
Publisher: MIT Press
Release Date : 1995
Dynamic Patterns written by J. A. Scott Kelso and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Medical categories.
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.
Neural Fields
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Author : Stephen Coombes
language : en
Publisher: Springer
Release Date : 2014-06-17
Neural Fields written by Stephen Coombes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-17 with Mathematics categories.
Neural field theory has a long-standing tradition in the mathematical and computational neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan, Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Robinson, Bressloff, Wright and Haken. Since then, much progress has been made in both, the development of mathematical and numerical techniques and in physiological refinement und understanding. In contrast to large-scale neural network models described by huge connectivity matrices that are computationally expensive in numerical simulations, neural field models described by connectivity kernels allow for analytical treatment by means of methods from functional analysis. Thus, a number of rigorous results on the existence of bump and wave solutions or on inverse kernel construction problems are nowadays available. Moreover, neural fields provide an important interface for the coupling of neural activity to experimentally observable data, such as the electroencephalogram (EEG) or functional magnetic resonance imaging (fMRI). And finally, neural fields over rather abstract feature spaces, also called dynamic fields, found successful applications in the cognitive sciences and in robotics. Up to now, research results in neural field theory have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. There is no comprehensive collection of results or reviews available yet. With our proposed book Neural Field Theory, we aim at filling this gap in the market. We received consent from some of the leading scientists in the field, who are willing to write contributions for the book, among them are two of the founding-fathers of neural field theory: Shun-ichi Amari and Jack Cowan.
Nonlinear Dynamics And Pattern Formation In The Natural Environment
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Author : A Doelman
language : en
Publisher: Taylor & Francis
Release Date : 2022-09-16
Nonlinear Dynamics And Pattern Formation In The Natural Environment written by A Doelman and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-16 with Mathematics categories.
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.
Food Webs
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Author : Gary A. Polis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Food Webs written by Gary A. Polis 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 2013-04-17 with Science categories.
Reflecting the recent surge of activity in food web research fueled by new empirical data, this authoritative volume successfully spans and integrates the areas of theory, basic empirical research, applications, and resource problems. Written by recognized leaders from various branches of ecological research, this work provides an in-depth treatment of the most recent advances in the field and examines the complexity and variability of food webs through reviews, new research, and syntheses of the major issues in food web research. Food Webs features material on the role of nutrients, detritus and microbes in food webs, indirect effects in food webs, the interaction of productivity and consumption, linking cause and effect in food webs, temporal and spatial scales of food web dynamics, applications of food webs to pest management, fisheries, and ecosystem stress. Three comprehensive chapters synthesize important information on the role of indirect effects, productivity and consumer regulation, and temporal, spatial and life history influences on food webs. In addition, numerous tables, figures, and mathematical equations found nowhere else in related literature are presented in this outstanding work. Food Webs offers researchers and graduate students in various branches of ecology an extensive examination of the subject. Ecologists interested in food webs or community ecology will also find this book an invaluable tool for understanding the current state of knowledge of food web research.
Dynamics Of Self Organized And Self Assembled Structures
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Author : Rashmi C. Desai
language : en
Publisher: Cambridge University Press
Release Date : 2009-03-26
Dynamics Of Self Organized And Self Assembled Structures written by Rashmi C. Desai and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-26 with Mathematics categories.
Describes pattern formation processes and how they can be modeled for graduate-level courses.
An Introduction To Nonlinear Chemical Dynamics
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Author : Irving R. Epstein
language : en
Publisher: Oxford University Press
Release Date : 1998-10-22
An Introduction To Nonlinear Chemical Dynamics written by Irving R. Epstein and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-22 with Science categories.
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.