Jordi Garcia-Ojalvo, Jose Sancho

Noise in Spatially Extended Systems (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 307
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461215363
• Artikelnr.: 44052149

Inhaltsangabe

Introduction: Fluctuations; phase transitions; pattern formation.- Fundamentals and Tools: Stochastic partial differential equations; analytical techniques; numerical techniques.- Noise-induced Phase Transitions: additive and multiplicative noise.- Dynamics of Phase Transitions with Fluctuations: internal noise; noise-induced phase separation.- Pattern Formation Under Multiplicative Noise.- Front Dynamics and External Fluctuations.- 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.

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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 Stochastic 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.

Rezensionen

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