Pierre-Louis Sulem - Böcker

This monograph aims to fill the gap between the mathematical literature which significantly contributed during the last decade to the understanding of the collapse phenomenon, and applications to domains like plasma physics and nonlinear optics where this process provides a fundamental mechanism for small scale formation and wave dissipation. This results in a localized heating of the medium and in the case of propagation in a dielectric to possible degradation of the material. For this purpose, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal asymptotic expansions and numerical simulations.

Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.

This book is of interest to researchers in astrophysics and the planetary sciences. It surveys the current knowledge on the propagation of nonlinear waves and the development of a turbulent dynamics in magnetohydrodynamic flows. The authors emphasize how the theoretical understanding of MHD waves and turbulence is related to the description of media where the presence of an ambient magnetic field is known to play an essential role. These effects are important in the physics of various space plasmas such as the magnetosphere, the solar wind, the solar corona, the interplanetary and interstellar media, etc. The authors treat fundamental aspects as revealed by asymptotic analysis, numerical simulations, and observations in the solar wind.

This book is of interest to researchers in astrophysics and the planetary sciences. It surveys the current knowledge on the propagation of nonlinear waves and the development of a turbulent dynamics in magnetohydrodynamic flows. The authors emphasize how the theoretical understanding of MHD waves and turbulence is related to the description of media where the presence of an ambient magnetic field is known to play an essential role. These effects are important in the physics of various space plasmas such as the magnetosphere, the solar wind, the solar corona, the interplanetary and interstellar media, etc. The authors treat fundamental aspects as revealed by asymptotic analysis, numerical simulations, and observations in the solar wind.

This book collects together recent results on large-scalestructures in non-linear science. Coherent states,convective and turbulent patterns, inverse cascades,interfaces and cooperative phenomena in fluids and plasmasare discussed, together with the implementation of conceptsof statistical mechanics to particle physics and nuclearmatter. Special attention is devoted to phenomena, such asmixing, which display macroscopicfeatures, even thoughgenerated by small-scale dynamical processes. In thiscontext, homoclinic structure, the KAM theorem, Lyapunovstability,and singularities are addressed. A newperturbative technique for classical and quantum fields andnew results concerning the analysis of hierarchiallyorganized objects are presented.The book should be attractive for a large audience includingengineers, mathematicians and physicists.