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Présentation Lectures On Dynamics Of Stochastic Systems de Valery I. Klyatskin
- Livre Sciences de la vie et de la terre
Résumé : Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics is to identify the essential characteristics of the system (its state and evolution), and relate those to the input parameters of the system and initial data. This book is a revised and more comprehensive version of Dynamics of Stochastic Systems. Part I provides an introduction to the topic. Part II is devoted to the general theory of statistical analysis of dynamic systems with fluctuating parameters described by differential and integral equations. Part III deals with the analysis of specific physical problems associated with coherent phenomena.
Sommaire: Introduction Part I: Dynamical description of stochastic systems Lecture 1. Examples, basic problems, peculiar features of solutions Lecture 2. Solution dependence on problem type, medium parameters, and initial data Lecture 3. Indicator function and Liouville Part II: Statistical description of stochastic systems Lecture 4. Random quantities, processes, and fields Lecture 5. Correlation splitting Lecture 6. General approaches to analyzing stochastic systems Lecture 7. Stochastic equations with the Markovian fluctuations of parameters Lecture 8. Approximation of Gaussian random field delta-correlated in time Lecture 9. Methods for solving and analyzing the Fokker-Planck equation Lecture 10. Some other approximate approaches to the problems of statistical hydrodynamics Part III: Examples of coherent phenomena in stochastic dynamic systems 269 Lecture 11. Passive tracer clustering and diffusion in random hydrodynamic and magnetohydrodynamic flows Lecture 12. Wave localization in randomly layered media Lecture 13. Caustic structure of wavefield in random media Bibliography
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