Pierre-Louis Sulem – författare

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.

This book covers a variety of topics related to kinetic theory in neutral gases and magnetized plasmas, with extensions to other systems such as quantum plasmas and granular flows. A comprehensive presentation is given for the Boltzmann equations and other kinetic equations for a neutral gas, together with the derivations of compressible and incompressible fluid dynamical systems, and their rigorous justification. Several contributions are devoted to collisionless magnetized plasmas. Rigorous results concerning the well-posedness of the Vlasov-Maxwell system are presented. Special interest is devoted to asymptotic regimes where the scales of variation of the electromagnetic field are clearly separated from those associated with the gyromotion of the particles. This volume collects lectures given at the Short Course and Workshop on Kinetic Theory organized at the Fields Institute of Mathematical Sciences in Toronto during the Spring of 2004.

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.