Large Scale Structures in Nonlinear Physics

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.

Inhalt
The phase-diffusion equation and its regularization for natural convective patterns.- Asymptotic time behavior of nonlinear classical field equations.- Nonlinear waves and the KAM theorem: Nonlinear degeneracies.- Homoclinic structures in open flows.- Large scale structures in kinetic plasma turbulence.- Supersonic homogeneous turbulence.- Large-scale instabilities and inverse cascades in ordinary and MHD flows at low Reynolds numbers.- From quantum fields to fractal structures: Intermittency in particle physics.- Hot QCD and the quark-gluon plasma.- New approach to the solution of nonlinear problems.- Numerical study of the transition to chaotic convection inside spherical shells.- Direct numerical simulations of natural and controlled transition of three-dimensional mixing layers.- Organized vortices as maximum entropy structures.- Spectral degeneracy and hydrodynamic stability.- Non-linear stability of plane Couette flow.- Continued-function solutions and eikonal approximations.- Quantum chaos and Sabine's law of reverberation in ergodic rooms.- Self-organized criticality, earthquakes and plate tectonics.- Psi-series and their summability for nonintegrable dynamical systems.- Bound solitons in the nonlinear Schrödinger/Ginzburg-Landau equation.- The colour of the force in the renormalized Navier-Stokes equation : A free parameter?.- Structure of homogeneous turbulence observed in a direct numerical simulation.- New results on the fine scale structure of fully developed turbulence.- On fast dynamo action in steady chaotic flows.- Magnetic structures in fast dynamo.- Rigorous wavelet analysis for multifractal sets.- Eigenfunction analysis of turbulent mixing phenomena.- Wavelets and the analysis of astronomical objects.