Overview

This book provides an interdisciplinary presentation of the current knowledge of pattern formation in complex system, with sufficiently many details, tools, and concrete examples to be useful for the graduate student or scientist entering this area of research.

Full Product Details

Author:   Daniel Walgraef
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1997 ed.
Dimensions:   Width: 15.50cm , Height: 1.90cm , Length: 23.50cm
Weight:   1.390kg
ISBN:  

9780387948577

ISBN 10:   0387948570
Pages:   306
Publication Date:   13 December 1996
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Introduction.- 2 Instabilities and Patterns in Hydrodynamical Systems.- 2.1 Rayleigh-Bénard instability.- 2.2 Taylor-Couette instability.- 2.3 Liquid crystal instabilities.- 3 Instabilities and Patterns in Reaction-Diffusion Systems.- 3.1 Chemical instabilities.- 3.2 Defect microstructures in irradiated materials.- 3.3 Plastic deformation and dislocation patterns.- 4 Generic Aspects of Pattern-Forming Instabilities.- 4.1 Phenomenology.- 4.2 Reaction-diffusion dynamics and stability.- 4.3 Reduced dynamics and amplitude equations.- 4.4 Spatial patterns: selection and stability.- 4.5 Phase dynamics of periodic patterns.- 5 The Hopf Bifurcation and Related Spatio-Temporal Patterns.- 5.1 The generic aspects of oscillatory media.- 5.2 Real chemical systems and the complex Ginzburg-Landau equation.- 5.3 The effect of natural forcings on chemical oscillators.- 5.4 Conclusions.- 6 The Turing Instability and Associated Spatial Structures.- 6.1 The Turing mechanism.- 6.2 The search for Turing structures.- 6.3 At last, genuine Turing structures?.- 6.4 The interaction between Turing and Hopf instabilities.- 7 Defects and Defect Bifurcations.- 7.1 Generic existence of defects.- 7.2 Examples of defects.- 7.3 Defects and disorder.- 7.4 Bifurcation of defects.- 8 The Effect of External Fields.- 8.1 Spatial forcing of stationary patterns.- 8.2 Temporal forcing of a Hopf bifurcation.- 8.3 Temporal forcing of one-dimensional wave patterns.- 8.4 Temporal forcing of two-dimensional wave patterns.- 8.5 Spatial forcing of wave patterns.- 8.6 Flow field effects on pattern forming instabilities.- 8.7 The effect of noise on wave patterns.- 8.8 Conclusions.- 9 Fronts.- 9.1 One-dimensional aspects.- 9.2 Two-dimensional aspects.- 10 Pattern Formation: Generic versus Nongeneric Aspects.- 10.1Kinetic coefficients.- 10.2 Nongradient dynamics.- 10.3 Experimental set-ups.- 11 Microstructures in Irradiated Materials.- 11.1 Particle irradiation of metals and alloys.- 11.2 Laser induced deformation of surfaces.- 12 Plastic Instabilities.- 12.1 Dislocation dynamics and rate equations.- 12.2 Stability analysis and bifurcations.- 12.3 Nonlinear analysis.- 12.4 Multiple slip.- 13 Afterword.- 14 Appendices.- 14.1 Bifurcations and normal forms.- 14.2 More about dynamical models.- 14.3 The Brusselator: A toy model for pattern formation in RD systems.- 14.4 Resonant forcings of nonlinear oscillators.

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