Full Description
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.
Contents
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.
