Noise in Spatially Extended Systems / Edition 1

by Jordi Garcia-Ojalvo, Jose Sancho

Overview

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 shastic 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 shastic partial differential equations. It then turns to particular problems described by shastic 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.

Product Details

ISBN-13:	9780387988559
Publisher:	Springer New York
Publication date:	06/22/1999
Series:	Institute for Nonlinear Science
Edition description:	1999
Pages:	307
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1 Introduction.- 1.1 Fluctuations in a Macroscopic World.- 1.2 Transitions in Zero-Dimensional Systems.- 1.3 Phase Transitions in d-Dimensional Systems.- 1.4 Pattern Formation.- 1.5 Other Effects of Noise in Extended Media.- 2 Fundamentals and Tools.- 2.1 Introduction to Shastic Partial Differential Equations.- 2.2 Analytical Techniques.- 2.3 Numerical Techniques.- 3 Noise-Induced Phase Transitions.- 3.1 Additive Noise.- 3.2 Additive and Multiplicative Noise.- 3.3 Multiplicative Noise.- 4 Dynamics of Phase Transitions with Fluctuations.- 4.1 Internal Multiplicative Noise.- 4.2 Noise-Induced Phase Separation.- 5 Pattern Formation Under Multiplicative Noise.- 5.1 Multiplicative Noise in the Swift-Hohenberg Model.- 5.2 Pure Noise-Induced Patterns.- 6 Front Dynamics and External Fluctuations.- 6.1 External Fluctuations in Deterministic Fronts.- 6.2 Noise-Induced Fronts.- 6.3 Reactive Fronts under Turbulent Advection.- 7 Conclusions.- 7.1 What Has Been Done.- 7.2 What Needs to Be Done.- A Continuum and Discrete Space Descriptions.- A.1 Coarse Graining.- A.2 Continuum Limit and Functional Analysis.- B Fourier Transforms.- B.1 Continuum Fourier Transforms.- B.2 Discrete Fourier Transforms.- B.3 Discrete Fourier Transform of a Real Uncorrelated Field.- C Fokker—Planck Equation for an Additive Colored Noise.- D Colored Noise in a Linear Model.- E Fokker—Planck Equation for a Multiplicative Noise.- References.

Editorial Reviews

From the reviews

"... this book is a valuable contribution, focused on mathematical and computational techniques to solve shastic partial differential equations." (PHYSICS TODAY)

From the Publisher