Download or read book Pattern Formation and Dynamics in Nonequilibrium Systems written by Michael Cross and published by Cambridge University Press. This book was released on 2009-07-16 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: An account of how complex patterns form in sustained nonequilibrium systems; for graduate students in biology, chemistry, engineering, mathematics, and physics.
Download or read book Dynamic Patterns written by J. A. Scott Kelso and published by MIT Press. This book was released on 1995 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Dynamics of Patterns written by M. I. Rabinovich and published by World Scientific. This book was released on 2000 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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
Download or read book The Dynamics of Patterns written by M I Rabinovich and published by World Scientific. This book was released on 2000-10-31 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Nonlinear Dynamics written by Muthusamy Lakshmanan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advances in Dynamics Patterns Cognition written by Igor S. Aranson and published by Springer. This book was released on 2017-05-02 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Dynamics and Patterns in Complex Fluids written by Akira Onuki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Patterns and Interfaces in Dissipative Dynamics written by L.M. Pismen and published by Springer Science & Business Media. This book was released on 2006-07-07 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Dynamics and Pattern Formation in the Natural Environment written by A. Van Harten and published by Taylor & Francis. This book was released on 2022-09-16 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Nonlinear Chemical Dynamics written by Irving R. Epstein and published by Oxford University Press. This book was released on 1998-10-22 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fractal Patterns in Nonlinear Dynamics and Applications written by Santo Banerjee and published by CRC Press. This book was released on 2020-03-27 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most books on fractals focus on deterministic fractals as the impact of incorporating randomness and time is almost absent. Further, most review fractals without explaining what scaling and self-similarity means. This book introduces the idea of scaling, self-similarity, scale-invariance and their role in the dimensional analysis. For the first time, fractals emphasizing mostly on stochastic fractal, and multifractals which evolves with time instead of scale-free self-similarity, are discussed. Moreover, it looks at power laws and dynamic scaling laws in some detail and provides an overview of modern statistical tools for calculating fractal dimension and multifractal spectrum.
Download or read book Spatial Dynamics and Pattern Formation in Biological Populations written by Ranjit Kumar Upadhyay and published by Chapman & Hall/CRC. This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to deterministic (and some stochastic) modeling of spatiotemporal phenomena in ecology, epidemiology, and neural systems. A survey of the classical models in the fields with up to date applications is given. The book begins with detailed description of how spatial dynamics/diffusive processes influence the dynamics of biological populations. These processes play a key role in understanding the outbreak and spread of pandemics which help us in designing the control strategies from the public health perspective. A brief discussion on the functional mechanism of the brain (single neuron models and network level) with classical models of neuronal dynamics in space and time is given. Relevant phenomena and existing modeling approaches in ecology, epidemiology and neuroscience are introduced, which provide examples of pattern formation in these models. The analysis of patterns enables us to study the dynamics of macroscopic and microscopic behaviour of underlying systems and travelling wave type patterns observed in dispersive systems. Moving on to virus dynamics, authors present a detailed analysis of different types models of infectious diseases including two models for influenza, five models for Ebola virus and seven models for Zika virus with diffusion and time delay. A Chapter is devoted for the study of Brain Dynamics (Neural systems in space and time). Significant advances made in modeling the reaction-diffusion systems are presented and spatiotemporal patterning in the systems is reviewed. Development of appropriate mathematical models and detailed analysis (such as linear stability, weakly nonlinear analysis, bifurcation analysis, control theory, numerical simulation) are presented. Key Features Covers the fundamental concepts and mathematical skills required to analyse reaction-diffusion models for biological populations. Concepts are introduced in such a way that readers with a basic knowledge of differential equations and numerical methods can understand the analysis. The results are also illustrated with figures. Focuses on mathematical modeling and numerical simulations using basic conceptual and classic models of population dynamics, Virus and Brain dynamics. Covers wide range of models using spatial and non-spatial approaches. Covers single, two and multispecies reaction-diffusion models from ecology and models from bio-chemistry. Models are analysed for stability of equilibrium points, Turing instability, Hopf bifurcation and pattern formations. Uses Mathematica for problem solving and MATLAB for pattern formations. Contains solved Examples and Problems in Exercises. The Book is suitable for advanced undergraduate, graduate and research students. For those who are working in the above areas, it provides information from most of the recent works. The text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.
Download or read book Pattern Formations and Oscillatory Phenomena written by Shuichi Kinoshita and published by Elsevier Inc. Chapters. This book was released on 2013-05-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present examples of familiar phenomena found in nonequilibrium systems, including oscillatory phenomena, order-formation processes, and pattern formation. In particular, we introduce commonly used mathematical methods to analyze their characteristics. First, we present oscillations described by the Lotka–Volterra and van der Pol equations, the Brusselator, the Oregonator, and relaxation oscillations as examples of oscillatory phenomena. Second, we investigate the order-formation process in colloidal crystals and present an experimental observation of 2D array formation. Third, we demonstrate pattern formation in crystals on the basis of the Mullins–Sekerka instability, and in chemical and biological systems on the basis of the Turing instability. In particular, we describe the optical properties and development of sophisticated structural patterns that directly interact with light. Finally, we briefly describe a theoretical phase-transition analogy that might clarify the concept of order formation in nonequilibrium systems.
Download or read book Patterns in Excitable Media written by Sitabhra Sinha and published by CRC Press. This book was released on 2014-12-13 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 fun
Download or read book Historical Dynamics written by Peter Turchin and published by Princeton University Press. This book was released on 2018-05-08 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many historical processes are dynamic. Populations grow and decline. Empires expand and collapse. Religions spread and wither. Natural scientists have made great strides in understanding dynamical processes in the physical and biological worlds using a synthetic approach that combines mathematical modeling with statistical analyses. Taking up the problem of territorial dynamics--why some polities at certain times expand and at other times contract--this book shows that a similar research program can advance our understanding of dynamical processes in history. Peter Turchin develops hypotheses from a wide range of social, political, economic, and demographic factors: geopolitics, factors affecting collective solidarity, dynamics of ethnic assimilation/religious conversion, and the interaction between population dynamics and sociopolitical stability. He then translates these into a spectrum of mathematical models, investigates the dynamics predicted by the models, and contrasts model predictions with empirical patterns. Turchin's highly instructive empirical tests demonstrate that certain models predict empirical patterns with a very high degree of accuracy. For instance, one model accounts for the recurrent waves of state breakdown in medieval and early modern Europe. And historical data confirm that ethno-nationalist solidarity produces an aggressively expansive state under certain conditions (such as in locations where imperial frontiers coincide with religious divides). The strength of Turchin's results suggests that the synthetic approach he advocates can significantly improve our understanding of historical dynamics.
Download or read book Becoming an Agent written by Larry Cochran and published by SUNY Press. This book was released on 1994-01-01 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about individuals who have made dramatic changes in their lives. In the beginning, these people were living as patients or victims of circumstance. In the end, they were living as agents, free to shape the courses of their lives, to choose, set goals, plan--to make things happen, rather than to experience life as events happening to them. The authors describe what is involved in such remarkable transformations. They identify a common structure of transformation involving four distinguishable phases. They also clarify a progressive dialectic between living the plot of a patient and living the plot of an agent, and show how an old plot is destroyed or deconstructed and a new plot is constructed.
Download or read book Food Webs written by Gary A. Polis and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
