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Titlebook: Noise in Spatially Extended Systems; Jordi García-Ojalvo,José M. Sancho Book 1999 Springer Science+Business Media New York 1999 Fokker-Pla

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书目名称Noise in Spatially Extended Systems
编辑Jordi García-Ojalvo,José M. Sancho
视频video
丛书名称Institute for Nonlinear Science
图书封面Titlebook: Noise in Spatially Extended Systems;  Jordi García-Ojalvo,José M. Sancho Book 1999 Springer Science+Business Media New York 1999 Fokker-Pla
描述Intended for graduate students 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 offers a practical introduction to 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. The text begins with a general introduction to noise-induced phenomena in dynamical systems followed by an extensive discussion of analytical and numerical tools needed to get information from stochastic partial differential equations. It then turns to particular problems described by stochastic partial differential equations, 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.
出版日期Book 1999
关键词Fokker-Planck equation; dynamics; functional analysis; mathematics; partial differential equation
版次1
doihttps://doi.org/10.1007/978-1-4612-1536-3
isbn_softcover978-1-4612-7182-6
isbn_ebook978-1-4612-1536-3Series ISSN 1431-4673
issn_series 1431-4673
copyrightSpringer Science+Business Media New York 1999
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Introduction,, with a particular emphasis on phase transitions. Section 1.4 briefly reviews the phenomenology associated with a particularly relevant type of spatially extended phenomena, namely, pattern formation out of equilibrium. Finally, some features not studied further in this book are commented upon in Section 1.5.
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Front Dynamics and External Fluctuations, framework, along with the achievements accomplished so far in relation to it, will be used as a starting point in this study. Section 6.2, on the other hand, analyzes the propagation of fronts . induced by noise. Finally, Section 6.3 studies the influence of the noise spectrum on front propagation dynamics in turbulent media.
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Noise-Induced Phase Transitions,itive and multiplicative noises, and pure multiplicative noise. There is evidence enough in favor of most of these transitions being second-order. However, a comment will also be made on noise effects on first-order phase transitions.
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Pattern Formation Under Multiplicative Noise,t show in Section 5.1 that multiplicative noise can induce order by advancing the appearance of a deterministic pattern-forming bifurcation in the Swift—Hohenberg model. In a second kind of model, presented in Section 5.2, noise can be seen to induce . stochastic patterns, which do not exist in the absence of fluctuations.
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Noise in Spatially Extended Systems978-1-4612-1536-3Series ISSN 1431-4673
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