Dissipative Solitons In Reaction Diffusion Systems

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Dissipative Solitons In Reaction Diffusion Systems

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Author : Andreas Liehr
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-27

Dissipative Solitons In Reaction Diffusion Systems written by Andreas Liehr 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 2013-03-27 with Science categories.

Why writing a book about a specialized task of the large topic of complex systems? And who will read it? The answer is simple: The fascination for a didactically valuable point of view, the elegance of a closed concept and the lack of a comprehensive disquisition. The fascinating part is that field equations can have localized solutions exhibiting the typical characteristics of particles. Regarding the field equations this book focuses on, the field phenomenon of localized solutions can be described in the context of a particle formalism, which leads to a set of ordinary differential equations covering the time evolution of the position and the velocity of each particle. Moreover, starting from these particle dynamics and making the transition to many body systems, one considers typical phenomena of many body systems as shock waves and phase transitions, which themselves can be described as field phenomena. Such transitions between different level of modelling are well known from conservative systems, where localized solutions of quantum field theory lead to the mechanisms of elementary particle interaction and from this to field equations describing the properties of matter. However, in dissipative systems such transitions have not been considered yet, which is adjusted by the presented book. The elegance of a closed concept starts with the observation of self-organized current filaments in a semiconductor gas discharge system. These filaments move on random paths and exhibit certain particle features like scattering or the formation of bound states. Neither the reasons for the propagation of the filaments nor the laws of the interaction between the filaments can be registered by direct observations. Therefore a model is established, which is phenomenological in the first instance due to the complexity of the experimental system. This model allows to understand the existence of localized structures, their mechanisms of movement, and their interaction, at least, on a qualitative level. But this model is also the starting point for developing a data analysis method that enables the detection of movement and interaction mechanisms of the investigated localized solutions. The topic is rounded of by applying the data analysis to real experimental data and comparing the experimental observations to the predictions of the model. A comprehensive publication covering the interesting topic of localized solutions in reaction diffusion systems in its width and its relation to the well known phenomena of spirals and patterns does not yet exist, and this is the third reason for writing this book. Although the book focuses on a specific experimental system the model equations are as simple as possible so that the discussed methods should be adaptable to a large class of systems showing particle-like structures. Therefore, this book should attract not only the experienced scientist, who is interested in self-organization phenomena, but also the student, who would like to understand the investigation of a complex system on the basis of a continuous description.

Dissipative Solitons

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Author : Nail Akhmediev
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-04-25

Dissipative Solitons written by Nail Akhmediev 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 2005-04-25 with Technology & Engineering categories.

This volume is devoted to the exciting topic of dissipative solitons, i.e. pulses or spatially localised waves in systems exhibiting gain and loss. Examples are laser systems, nonlinear resonators and optical transmission lines. The physical principles and mathematical concepts are explained in a clear and concise way, suitable for students and young researchers. The similarities and differences in the notion of a soliton between dissipative systems and Hamiltonian and integrable systems are discussed, and many examples are given. The contributions are written by the world's leading experts in the field, making it a unique exposition of this emerging topic.

Dissipative Solitons From Optics To Biology And Medicine

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Author : Nail Akhmediev
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-26

Dissipative Solitons From Optics To Biology And Medicine written by Nail Akhmediev 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 2008-08-26 with Technology & Engineering categories.

The dissipative soliton concept is a fundamental extension of the concept of solitons in conservative and integrable systems. It includes ideas from three major sources, namely standard soliton theory developed since the 1960s; nonlinear dynamics theory; and Prigogine's ideas of systems far from equilibrium. These three sources also correspond to the three component parts of this novel paradigm. This book explains the above principles in detail and gives the reader various examples.

Recent Progress On Reaction Diffusion Systems And Viscosity Solutions

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Author : Yihong Du
language : en
Publisher: World Scientific
Release Date : 2009

Recent Progress On Reaction Diffusion Systems And Viscosity Solutions written by Yihong Du and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

This book consists of survey and research articles expanding on the theme of the OC International Conference on Reaction-Diffusion Systems and Viscosity SolutionsOCO, held at Providence University, Taiwan, during January 3OCo6, 2007. It is a carefully selected collection of articles representing the recent progress of some important areas of nonlinear partial differential equations. The book is aimed for researchers and postgraduate students who want to learn about or follow some of the current research topics in nonlinear partial differential equations. The contributors consist of international experts and some participants of the conference, including Nils Ackermann (Mexico), Chao-Nien Chen (Taiwan), Yihong Du (Australia), Alberto Farina (France), Hitoshi Ishii (Japan), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin Lo (Taiwan), Peter Polacik (USA), Kunimochi Sakamoto (Japan), Richard Tsai (USA), Mingxin Wang (China), Yoshio Yamada (Japan), Eiji Yanagida (Japan), and Xiao-Qiang Zhao (Canada).

Synergetic Phenomena In Active Lattices

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Author : Vladimir I. Nekorkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Synergetic Phenomena In Active Lattices written by Vladimir I. Nekorkin 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 2012-12-06 with Science categories.

In recent years there has been growing interest in the study of the nonlinear spatio-temporal dynamics of problems appearing in various ?elds of science and engineering. In a wide class of such systems an important place is - cupied by active lattice dynamical systems. Active lattice systems are, e. g. , networks of identical or almost identical interacting units ordered in space. The activity of lattices is provided by the activity of units in them that possess energy or matter sources. In real (1D, 2D or 3D) space, processes develop by means of various types of connections, the simplest being di?usion. The uniqueness of lattice systems is that they represent spatially extended systems while having a ?nite-dimensional phase space. Therefore, active lattice s- tems are of interest for the study of multidimensional dynamical systems and the theory of nonlinear waves and dissipative structures of extended systems as well. The theory of nonlinear waves and dissipative structures of spatially distributed systems demands using theoretical methods and approaches of the qualitative theory of dynamical systems, bifurcation theory, and numerical methods or computer experiments. In other words, the investigation of spat- temporal dynamics in active lattice systems demands a multitool, synergetic approach, which we shall use in this book.

An Exploration Of Dynamical Systems And Chaos

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Author : John H. Argyris
language : en
Publisher: Springer
Release Date : 2015-04-24

An Exploration Of Dynamical Systems And Chaos written by John H. Argyris and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-24 with Technology & Engineering categories.

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

Reaction Diffusion Computers

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Author : Andrew Adamatzky
language : en
Publisher: Elsevier
Release Date : 2005-10-05

Reaction Diffusion Computers written by Andrew Adamatzky and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-05 with Mathematics categories.

The book introduces a hot topic of novel and emerging computing paradigms and architectures -computation by travelling waves in reaction-diffusion media. A reaction-diffusion computer is a massively parallel computing device, where the micro-volumes of the chemical medium act as elementary few-bit processors, and chemical species diffuse and react in parallel. In the reaction-diffusion computer both the data and the results of the computation are encoded as concentration profiles of the reagents, or local disturbances of concentrations, whilst the computation per se is performed via the spreading and interaction of waves caused by the local disturbances. The monograph brings together results of a decade-long study into designing experimental and simulated prototypes of reaction-diffusion computing devices for image processing, path planning, robot navigation, computational geometry, logics and artificial intelligence. The book is unique because it gives a comprehensive presentation of the theoretical and experimental foundations, and cutting-edge computation techniques, chemical laboratory experimental setups and hardware implementation technology employed in the development of novel nature-inspired computing devices.Key Features:- Non-classical and fresh approach to theory of computation.- In depth exploration of novel and emerging paradigms of nature-inspired computing.- Simple to understand cellular-automata models will help readers/students to design their own computational experiments to advance ideas and concepts described in the book .- Detailed description of receipts and experimental setups of chemical laboratory reaction-diffusion processors will make the book an invaluable resource in practical studies of non-classical and nature-inspired computing architectures .- Step by step explanations of VLSI reaction-diffusion circuits will help students to design their own types of wave-based processors.Key Features:- Non-classical and fresh approach to theory of computation.- In depth exploration of novel and emerging paradigms of nature-inspired computing.- Simple to understand cellular-automata models will help readers/students to design their own computational experiments to advance ideas and concepts described in the book .- Detailed description of receipts and experimental setups of chemical laboratory reaction-diffusion processors will make the book an invaluable resource in practical studies of non-classical and nature-inspired computing architectures .- Step by step explanations of VLSI reaction-diffusion circuits will help students to design their own types of wave-based processors.

High Performance Computing In Science And Engineering 02

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Author : Egon Krause
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

High Performance Computing In Science And Engineering 02 written by Egon Krause 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 2012-12-06 with Mathematics categories.

This book presents the state-of-the-art in modeling and simulation on supercomputers. Leading German research groups present their results achieved on high-end systems of the High Performance Computing Center Stuttgart (HLRS) for the year 2002. Reports cover all fields of supercomputing simulation ranging from computational fluid dynamics to computer science. Special emphasis is given to industrially relevant applications. Moreover, by presenting results for both vector sytems and micro-processor based systems the book allows to compare performance levels and usability of a variety of supercomputer architectures. It therefore becomes an indispensable guidebook to assess the impact of the Japanese Earth Simulator project on supercomputing in the years to come.

Nonlinear Optical Cavity Dynamics

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Author : Philippe Grelu
language : en
Publisher: John Wiley & Sons
Release Date : 2015-12-23

Nonlinear Optical Cavity Dynamics written by Philippe Grelu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-23 with Science categories.

By recirculating light in a nonlinear propagation medium, the nonlinear optical cavity allows for countless options of light transformation and manipulation. In passive media, optical bistability and frequency conversion are central figures. In active media, laser light can be generated with versatile underlying dynamics. Emphasizing on ultrafast dynamics, the vital arena for the information technology, the soliton is a common conceptual keyword, thriving into its modern developments with the closely related denominations of dissipative solitons and cavity solitons. Recent technological breakthroughs in optical cavities, from micro-resonators to ultra-long fiber cavities, have entitled the exploration of nonlinear optical dynamics over unprecedented spatial and temporal orders of magnitude. By gathering key contributions by renowned experts, this book aims at bridging the gap between recent research topics with a view to foster cross-fertilization between research areas and stimulating creative optical engineering design.

High Performance Computing In Science And Engineering 03

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Author : Egon Krause
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

High Performance Computing In Science And Engineering 03 written by Egon Krause 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 2012-12-06 with Mathematics categories.

This book presents the state of the art in modeling and simulation on supercomputers. Leading German research groups present their results achieved on high-end systems of the High Performance Computing Center Stuttgart (HLRS) for the year 2003. The reports cover all fields of computational science and engineering ranging from computational fluid dynamics via computational physics and chemistry to computer science. Special emphasis is given to industrially relevant applications. Presenting results for both vector-systems and micro-processor based systems, the book allows the reader to compare performance levels and usability of a variety of supercomputer architectures. In the light of the success of the Japanese Earth-Simulator, this book may serve as a guide book for a US response. The book covers the main methods in high performance computing. Its outstanding results in achieving highest performance for production codes are of particular interest for both the scientist and the engineer. The book comes with a wealth of color illustrations and tables of results.