Large Scale Structures in Nonlinear Physics: Proceedings of a Workshop Held in Villefranche-sur-Mer, France 13–18 January 1991

T. Passot, A. C. Newell (auth.), Jean-Daniel Fournier, Pierre-Louis Sulem (eds.)3540548998, 9783540548997, 0387548998

This book collects together recent results on large-scale structures in non-linear science. Coherent states, convective and turbulent patterns, inverse cascades, interfaces and cooperative phenomena in fluids and plasmas are discussed, together with the implementation of concepts of statistical mechanics to particle physics and nuclear matter. Special attention is devoted to phenomena, such as mixing, which display macroscopicfeatures, even though generated by small-scale dynamical processes. In this context, homoclinic structure, the KAM theorem, Lyapunov stability,and singularities are addressed. A new perturbative technique for classical and quantum fields and new results concerning the analysis of hierarchially organized objects are presented. The book should be attractive for a large audience including engineers, mathematicians and physicists.

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Table of contents :
The phase-diffusion equation and its regularization for natural convective patterns….Pages 1-20
Asymptotic time behavior of nonlinear classical field equations….Pages 21-36
Nonlinear waves and the KAM theorem: Nonlinear degeneracies….Pages 37-49
Homoclinic structures in open flows….Pages 50-72
Large scale structures in kinetic plasma turbulence….Pages 73-104
Supersonic homogeneous turbulence….Pages 105-125
Large-scale instabilities and inverse cascades in ordinary and MHD flows at low Reynolds numbers….Pages 126-146
From quantum fields to fractal structures: Intermittency in particle physics….Pages 147-160
Hot QCD and the quark-gluon plasma….Pages 161-189
New approach to the solution of nonlinear problems….Pages 190-210
Numerical study of the transition to chaotic convection inside spherical shells….Pages 211-221
Direct numerical simulations of natural and controlled transition of three-dimensional mixing layers….Pages 222-231
Organized vortices as maximum entropy structures….Pages 232-241
Spectral degeneracy and hydrodynamic stability….Pages 242-251
Non-linear stability of plane Couette flow….Pages 252-261
Continued-function solutions and eikonal approximations….Pages 262-266
Quantum chaos and Sabine’s law of reverberation in ergodic rooms….Pages 267-274
Self-organized criticality, earthquakes and plate tectonics….Pages 275-277
Psi-series and their summability for nonintegrable dynamical systems….Pages 278-287
Bound solitons in the nonlinear Schrödinger/Ginzburg-Landau equation….Pages 288-294
The colour of the force in the renormalized Navier-Stokes equation : A free parameter?….Pages 295-302
Structure of homogeneous turbulence observed in a direct numerical simulation….Pages 303-311
New results on the fine scale structure of fully developed turbulence….Pages 312-312
On fast dynamo action in steady chaotic flows….Pages 313-317
Magnetic structures in fast dynamo….Pages 318-319
Rigorous wavelet analysis for multifractal sets….Pages 320-328
Eigenfunction analysis of turbulent mixing phenomena….Pages 329-339
Wavelets and the analysis of astronomical objects….Pages 340-347