We will go from the general mathematical theory to specific equations and then to their applications. There is an intimate relationship between new insights in the mathematical aspects of nonlinear pattern formation and the comprehension of such phenomena. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. They give examples of self-organization phenomena on micro- and nano-scale as well as examples of the interplay between phenomena on nano- and macro-scales leading to complex behavior in various physical, chemical and biological systems. They are also intended to discuss why certain subjects are currently exciting and worthy of additional research. Each chapter includes a tutorial and background information, as well as a survey of each area's main results and state of the art. The book dicusses exciting discoveries, with special emphasis on transverse effects such as spatial soliton formation and interaction, spontaneous pattern formation and pattern competition in active feedback systems.
New scenarios have emerged for spatio-temporal structures in dynamical systems far from equilibrium. Self-organization and pattern formation play crucial role on nano-scales and promise new, effective routes to control various nano-scales processes. They give examples of self-organization phenomena on micro- and nano-scale as well as examples of the interplay between phenomena on nano- and macro-scales leading to complex behavior in various physical, chemical and biological systems. Handsomely produced with high resolution color graphics for enhanced readability, this book has been carefully written at a high level of exposition and is somewhat self-contained. Nonlinear Dynamics and Chaos in Semiconductors is the first book to concentrate on specific physical and experimental situations in semiconductors as well as examine how to use chaos theory to explain semiconductor phenomena. It also describes spatial and spatiotemporal evolution of the current density filament formed by the impact ionization avalanche.
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. Pattern formation has been studied intensively for most of this century by both experimentalists and theoreticians. Recent mathematical developments concern the study of the nonlinear stability of systems at near-critical conditions by an appropriate system of modulation equations. Basic models for domain coarsening and pattern formation. The authors of these lecture notes are the leading experts in the field of self-organization, pattern formation and nonlinear dynamics in non-equilibrium, complex systems. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids.
Self-organization and pattern formation play crucial role on nano-scales and promise new, effective routes to control various nano-scales processes. Moreover, it provides unifying point of view for a wide range of problems. Nano-science and nano-technology are rapidly developing scientific and technological areas that deal with physical, chemical and biological processes that occur on nano-meter scale — one millionth of a millimeter. Basic topics and foundations are always linked to concrete and precise examples. Further, the theory describing the macroscopic dynamics of fluids is well established and contains only very few parameters, all of which have well-known values. It has been painstakingly researched and written by leading scientists and eminent expositors, including L Shilnikov, R Seydel, I Prigogine, W Porod, C Mira, M Lakshmanan, W Lauterborn, A Holden, H Haken, C Grebogi, E Doedel and L Chua; each chapter addresses a current and intensively researched area of nonlinear science and chaos, including nonlinear dynamics, mathematics, numerics and technology.
These and many other applications are described by reaction-diffusion equations. The authors of those lecture notes are the top specialists within the box of self-organization, trend formation and nonlinear dynamics in non-equilibrium, complicated systems. They give examples of self-organization phenomena on micro- and nano-scale as well as examples of the interplay between phenomena on nano- and macro-scales leading to complex behavior in various physical, chemical and biological systems. The authors of these lecture notes are the leading experts in the field of self-organization, pattern formation and nonlinear dynamics in non-equilibrium, complex systems. Research has been focused on a variety of problems, such as the characteristics of regular and chaotic motion in Hamiltonian dynamics, the problem of quantum chaos, the forma tion and properties of solitary spatio-temporal structures, the occurrence of strange attractors in dissipative systems, and the bifurcation scenarios leading to complex time behaviour. The complexity of the original problem can be reduced drastically by this approximation.
Until recently, predictions of the theory have been tested predominantly on insta bilities in hydrodynamic systems, where many interesting experiments have provided valuable input and have led to a fruitful interaction between experiment and theory. The classical theory of reaction-diffusion equations and new topics such as nonlocal equations and multi-scale models in biology will be considered. Papers cover the fundamental properties of hot carrier transport and the associated instabilities and light emission in 2-dimensional semiconductors dealing with both theory and experiment. The book addresses systems including both singlemode and multimode lasers, bistable and multistable devices, optical fibers, counter-propagating beam interactions, nonlinear mixing, and related optical phenomena. Discussing both theory and experiment, the author shows how this powerful combination has lead to real progress with difficult nonlinear problems in this technologically important field. Nano-science and nano-technology are quickly constructing medical and technological components that take care of actual, chemical and organic strategies that happen on nano-meter scale — one millionth of a millimeter.
In this treatise we focus on a detailed theoretical understanding of devices of the kind that can be made unstable against circuit oscillations, large amplitude switching events, and in some cases, internal rearrangement of the electric field or current density distribution. The goals were to continue communication between these groups, and to familiarize a larger audience with some of the newer directions in the field. A review of general features of all pattern forming systems is also given. The text applies and exploits this knowledge to propose devices which operate more efficiently and cheaply, while affording the promise of much better performance. This workshop focused on new directions in the patterns literature. Furthermore, we have geared the book to device engineers and physicists desirous of obtaining an understanding substantially deeper than that associated with a small signal equivalent circuit approach. Written by a well-respected researcher of chaos in semiconductors, Nonlinear Dynamics and Chaos in Semiconductors provides a rich and detailed account of progress in research on nonlinear effects in semiconductor physics.
The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work. A review of general features of all pattern forming systems is also given. In recent decades there has been significant progress in the theory of nonlinear phenomena, but there are comparatively few devices that actually take this rich behavior into account. The theory of reaction-diffusion equations appeared in the first half of the last century. In the last decade there has been considerable progress in this field, both from a theoretical and a practical point of view.
General aspects of pattern formation; A. A Category: Mathematics Page: 276 View: 8567 Release On This is the first introductory monograph exclusively devoted to the dynamic properties of lasers. A review of general features of all pattern forming systems is also given. A assessment of normal gains of all trend forming platforms is additionally given. With its numerous case studies and clear illustrations, the volume is also suitable as a textbook. The book explores impact ionization models, linear stability analysis, bifurcation theory, fractal dimensions, and various analytical methods in chaos theory. The duality of fundamental and applied research is a focal point of its main attractivity and fascination.