Noise in Nonlinear Dynamical Systems: Volume 2, Theory of Noise Induced Processes in Special Applications


Book Description

Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The second volume applies the theory of Volume 1 to the calculation of the influence of noise in a variety of contexts. These include quantum mechanics, condensed matter, noise induced transitions, escape processes and transition probabilities, systems with periodic potentials, discrete nonlinear systems, symmetry-breaking transition, and optics.







Noise in Nonlinear Dynamical Systems


Book Description

Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The second volume applies the theory of Volume 1 to the calculation of the influence of noise in a variety of contexts. These include quantum mechanics, condensed matter, noise induced transitions, escape processes and transition probabilities, systems with periodic potentials, discrete nonlinear systems, symmetry-breaking transition, and optics.




Noise in Nonlinear Dynamical Systems


Book Description

A specially written review of all areas of noise and nonlinear in natural environments.




Nonlinear Dynamics of Chaotic and Stochastic Systems


Book Description

We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the ?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kinetic equations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.




IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics


Book Description

This book presents the latest research results in the area of applied nonlinear dynamics and chaos theory. Papers by three academic generations address new applications of nonlinear dynamics to mechanics, including fluid-structure interaction, machining and mechanics of solids, and many other applications.




Nanoelectronics: A Molecular View


Book Description

'This is one of the best available graduate-level textbooks on electronic transport at the nanoscale. Its unique feature is providing a thorough and completely self-contained treatment of several theoretical formalisms for treating the transport problem. As such, the book is useful not only for the graduate students working in the field of nanoscale electrical transport, but also for the researchers who wish to expand their knowledge of various fundamental issues associated with this rapidly developing field. Of particular note are deep physical insights accompanying the rigorous mathematical derivations in each of the chapters, as well as the clear statement of all the approximations involved in a particular theoretical formalism. This winning combination makes the book very accessible to a reader with basic knowledge of quantum mechanics, solid state theory and thermodynamics/statistical mechanics. I give this book the highest recommendation.' [Read Full Review]Serfei A EgorovUniveristy of Virginia, USAThis book is aimed at senior undergraduates, graduate students and researchers interested in quantitative understanding and modeling of nanomaterial and device physics. With the rapid slow-down of semiconductor scaling that drove information technology for decades, there is a pressing need to understand and model electron flow at its fundamental molecular limits. The purpose of this book is to enable such a deconstruction needed to design the next generation memory, logic, sensor and communication elements. Through numerous case studies and topical examples relating to emerging technology, this book connects 'top down' classical device physics taught in electrical engineering classes with 'bottom up' quantum and many-body transport physics taught in physics and chemistry. The book assumes no more than a nodding acquaintance with quantum mechanics, in addition to knowledge of freshman level mathematics. Segments of this book are useful as a textbook for a course in nano-electronics.




Mathematical Tools for Physicists


Book Description

Mathematical Tools for Physicists is a unique collection of 18 carefully reviewed articles, each one written by a renowned expert working in the relevant field. The result is beneficial to both advanced students as well as scientists at work; the former will appreciate it as a comprehensive introduction, while the latter will use it as a ready reference. The contributions range from fundamental methods right up to the latest applications, including: - Algebraic/ analytic / geometric methods - Symmetries and conservation laws - Mathematical modeling - Quantum computation The emphasis throughout is ensuring quick access to the information sought, and each article features: - an abstract - a detailed table of contents - continuous cross-referencing - references to the most relevant publications in the field, and - suggestions for further reading, both introductory as well as highly specialized. In addition, a comprehensive index provides easy access to the vast number of key words extending beyond the range of the headlines.







Effective Dynamics of Stochastic Partial Differential Equations


Book Description

Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors’ experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations Solutions or hints to all Exercises