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Intended for graduates and researchers in physics, chemistry, biology, and applied mathematics, this book provides an up-to-date introduction to current research in fluctuations in spatially extended systems. It covers the theory of stochastic partial differential equations and gives an overview of the effects of external noise on dynamical systems with spatial degrees of freedom. Starting with a general introduction to noise-induced phenomena in dynamical systems, the text moves on to an extensive discussion of analytical and numerical tools needed to gain information from stochastic partial differential equations. It then turns to particular problems described by stochastic PDEs, covering a wide part of the rich phenomenology of spatially extended systems, such as nonequilibrium phase transitions, domain growth, pattern formation, and front propagation. The only prerequisite is a minimal background knowledge of the Langevin and Fokker-Planck equations.
This book investigates the impact of noise upon the emergence and sustenance of patterns. ?Patterns? loosely refers to coherent spatial structures, including fronts, as well as temporal patterns. The crucial role of nonlinearities is highlighted and expanded upon in the context of dynamical system frameworks. The author's familiarity with chaos theory, statistical physics and nonlinear science is reflected in the highly interdisciplinary character of the text. Model equations and experiments taken from fluid dynamics, semiconductor devices, biophysics and statistical mechanics complement theoretical concepts.It should be of great value to researchers and graduate students who desire a quick introduction to the subject. Excursions into emerging fields such as traffic flow simulations and game theory serve to broaden the scope and to encourage the exploration of sundry topics.
A specially written review of all areas of noise and nonlinear in natural environments.
Noise in physical systems - as a consequence of the corpuscular nature of matter - conveys information about microscopic mechanisms determining the macroscopic behavior of the system. Besides being a source of information, noise also represents a source of annoying disturbances which affect information transMission along a physical system. Therefore, noise analysis can promote our insight into the behavior of a physical system, as well as our knowledge of the natural constraints imposed upon physical-information transmission channels and devices. In recent years the continuous scientific and technical interest in noise problems has led to a remarkable progress in the understanding of noise phenomena. This progress is reflected by the rich material presented at the Fifth International Conference on Noise in Physical Systems. The conference papers originally published in these proceedings cover the various aspects of today's noise research in the fields of solid-state devices, l/f-noise, magnetic and superconducting materials, measuring methods, and theory of fluctuations. Each session of the conference was introduced by one or two invited review lectures which are included in these proceedings in full length. The 12 invited papers and more than 40 contributed papers on specific topics (only three of them have been omitted from the proceedings since they will be published elsewhere) provide a comprehensive survey of the current state-of-the-art and recent advances of noise analysis.
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.