Dynamical Systems, Plasmas and Gravitation

Published in honour of Marc Feix this book tries to give a thorough overview of mathematical methods, analytical and numerical techniques and simulations applied to a variety of problems from physics and engineering. The book addresses graduate students, researchers and especially engineers. The main emphasis is to apply the generality of methods to form a coherent and stimulating approach to practical investigations.

Includes supplementary material: sn.pub/extras

Inhalt
General introduction.- Honouring marc feix.- Interaction of a ultra-high-intensity electromagnetic pulse with an overdense plasma.- Plasma accelerator simulations using semi-lagrangian 1D and 2D Vlasov code.- 2D vlasov-eulerian simulations: Extension to the relativistic case.- A limiting case of averaging compactness lemmas motivated by the kinetic formulation of some classical systems of fluid mechanics.- Expansion of a negative ion plasma into vacuum.- A presentation of the diffusion velocity method.- Finite-difference schemes for the diffusion equation.- 1, 2, 3 plasmas!.- The notion of integrability for time-dependent Hamiltonian systems: Illustration from the relativistic motion of a charged particle in an electromagnetic field.- Stochastisation of phases in four-wave interaction.- Light bullets propagation in saturating nonlinear optical medium.- The dynamics of some quantum open systems with short-range nonlinearities.- Global dynamics of fusion plasmas.- The Jeans' criterion and the gravitational instability.- Recent progress in studies of one-dimensional gravitating systems.- Fluctuations of the kinetic energy and stability of coherent structures in a one-dimensional gravitating gas: Numerical simulation.- Structure formation in the one-dimensional gravitational gas.- Interaction forces and space symmetry.- Cellular automaton explosion models.- Acoustic earth imaging by seismic migration.- Integrability and alegbraic solutions for the 2-D lotka-Volterra system.- Isochronous centers of cubic reversible systems.- On the polynomial first integrals of the (a, b, c) Lotka-Volterra system.- Local integrability for nilpotent critical point.- Lie symmetries of generalized Ermakov systems.- Hamilton's principal function and integration by quadratures for anN-degree-of-freedom non - autonomous system given N invertible invariants in involution.- Hierarchies of similarity symmetries and singularity analysis.- Area preserving flows on compact connected surfaces.- A lattice model for tropical rain forests.- Periodic solutions and associated limit cycle for the generalised Chazy equation.- A branch and bound algorithm for the flow-shop scheduling problem.- On the linear third-order differential equation.- Telecommunication network optimisation and statistical physics.- A study of the analytical and local semiclassical Wigner distribution.- Quantum transition and irreversibility.- Pioneering in plasma simulation.