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.
- A comprehensive update of Dynamics of Stochastic Systems
- Develops mathematical tools of stochastic analysis and applies them to a wide range of physical models of particles, fluids and waves
- Includes problems for the reader to solve
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
Lecture 8. Approximation of Gaussian random field delta-correlated
Lecture 9. Methods for solving and analyzing the Fokker-Planck
Lecture 10. Some other approximate approaches to the problems of
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
Born in 1940 in Moscow, USSR, Valery I. Klyatskin received his secondary education at school in Tbilisi, Georgia, finishing in 1957. Seven years later he graduated from Moscow Institute of Physics and Technology (FIZTEX), whereupon he took up postgraduate studies at the Institute of Atmospheric Physics USSR Academy of Sciences, Moscow gaining the degree of Candidate of Physical and Mathematical Sciences (Ph.D) in 1968. He then continued at the Institute as a researcher, until 1978, when he was appointed as Head of the Wave Process Department at the Pacific Oceanological Institute of the USSR Academy of Sciences, based in Vladivostok. In 1992 Valery I. Klyatskin returned to Institute of Atmospheric Physics Russian Academy of Sciences, Moscow when he was appointed to his present position as Chief Scientist. At the same time he is Chief Scientific Consultant of Pacific Oceanological Institute Russian Academy of Sciences, Vladivostok. In 1977 he obtained a doctorate in Physical and Mathematical Sciences and in 1988 became Research Professor of Theoretical and Mathematical Physics, Russian Academy of Science.