Noise in Spatially Extended Systems
By: by Jordi García-Ojalvo, José M. Sancho
Contributors: Sancho, José M.
Series: Institute for Nonlinear Science; Institute for Nonlinear Science
Publisher: Springer New York
Published: 1999
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 307
ISBN-13: 9781461271826; 9781461215363
Subjects: Distribution (Probability theory); Physics
Description: 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.
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Table of contents: title: Introduction: Fluctuations; phase transitions; pattern formation; title: Fundamentals and Tools: Stochastic partial differential equations; analytical techniques; numerical techniques; title: Noise-induced Phase Transitions: additive and multiplicative noise; title: Dynamics of Phase Transitions with Fluctuations: internal noise; noise-induced phase separation; title: Pattern Formation Under Multiplicative Noise; title: Front Dynamics and External Fluctuations; title: Conclusions. A. Continuum and Discrete Space Descriptions. B. Fourier Transforms. C. Fokker-Planck Equations for Additive Colored Noise. D. Colored Noise in a Linear Model. E. Fokker-Planck Equation for Multiplicative Noise.