Klyatskin Lectures on Dynamics of Stochastic Systems

1. Auflage 2010
ISBN: 978-0-12-384967-0
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 410 Seiten

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

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.

Autoren/Hrsg.

Klyatskin, Valery I.

Inhaltsverzeichnis

1;Front cover;1
2;Lectures on Dynamics of Stochastic Systems;4
3;Copyright page;5
4;Table of contents;6
5;Preface;10
6;Introduction;12
7;Part I: Dynamical Description of Stochastic Systems;16
7.1;Lecture 1. Examples, Basic Problems, Peculiar Features of Solutions;18
7.1.1;1.1. Ordinary Differential Equations: Initial-Value Problems;18
7.1.2;1.2. Boundary-Value Problems for Linear Ordinary Differential Equations (Plane Waves in Layered Media);35
7.1.3;1.3. Partial Differential Equations;39
7.1.4;Problem;65
7.2;Lecture 2. Solution Dependence on Problem Type, Medium Parameters, and Initial Data;68
7.2.1;2.1. Functional Representation of Problem Solution;68
7.2.2;2.2. Solution Dependence on Problem's Parameters;75
7.2.3;Problems;80
7.3;Lecture 3. Indicator Function and Liouville Equation;84
7.3.1;3.1. Ordinary Differential Equations;84
7.3.2;3.2. First-Order Partial Differential Equations;87
7.3.3;3.3. Higher-Order Partial Differential Equations;95
7.3.4;Problems;100
8;Part II: Statistical Description of Stochastic Systems;102
8.1;Lecture 4. Random Quantities, Processes, and Fields;104
8.1.1;4.1. Random Quantities and their Characteristics;104
8.1.2;4.2. Random Processes, Fields, and their Characteristics;110
8.1.3;4.3. Markovian Processes;130
8.1.4;Problems;134
8.2;Lecture 5. Correlation Splitting;138
8.2.1;5.1. General Remarks;138
8.2.2;5.2. Gaussian Process;140
8.2.3;5.3. Poisson's Process;142
8.2.4;5.4. Telegrapher's Random Process;143
8.2.5;5.5. Delta-Correlated Random Processes;145
8.2.6;Problems;150
8.3;Lecture 6. General Approaches to Analyzing Stochastic Systems;156
8.3.1;6.1. Ordinary Differential Equations;156
8.3.2;6.2. Completely Solvable Stochastic Dynamic Systems;159
8.3.3;6.3. Delta-Correlated Fields and Processes;175
8.3.4;Problems;181
8.4;Lecture 7. Stochastic Equations with the Markovian Fluctuations of Parameters;198
8.4.1;7.1. Telegrapher's Processes;199
8.4.2;7.2. Gaussian Markovian Processes;202
8.4.3;Problems;203
8.5;Lecture 8. Approximations of Gaussian Random Field Delta-Correlated in Time;206
8.5.1;8.1. The Fokker–Planck Equation;206
8.5.2;8.2. Transition Probability Distributions;209
8.5.3;8.3. The Simplest Markovian Random Processes;211
8.5.4;8.4. Applicability Range of the Fokker–Planck Equation;226
8.5.5;8.5. Causal Integral Equations;230
8.5.6;8.6. Diffusion Approximation;233
8.5.7;Problems;235
8.6;Lecture 9. Methods for Solving and Analyzing the Fokker–Planck Equation;244
8.6.1;9.1. Integral Transformations;244
8.6.2;9.2. Steady-State Solutions of the Fokker–Planck Equation;245
8.6.3;9.3. Boundary-Value Problems for the Fokker–Planck Equation (Hopping Phenomenon);257
8.6.4;9.4. Method of Fast Oscillation Averaging;260
8.6.5;Problems;262
8.7;Lecture 10. Some Other Approximate Approaches to the Problems of Statistical Hydrodynamics;268
8.7.1;10.1. Quasi-Elastic Properties of Isotropic and Stationary Noncompressible Turbulent Media;269
8.7.2;10.2. Sound Radiation by Vortex Motions;273
9;Part III: Examples of Coherent Phenomena in
Stochastic Dynamic Systems;284
9.1;Lecture 11. Passive Tracer Clustering and Diffusion in Random Hydrodynamic and

Magnetohydrodynamic Flows;286
9.1.1;11.1. General Remarks;286
9.1.2;11.2. Particle Diffusion in Random Velocity Field;291
9.1.3;11.3. Probabilistic Description of Density Field in Random Velocity Field;299
9.1.4;11.4. Probabilistic Description of Magnetic Field and Magnetic Energy in Random Velocity Field;306
9.1.5;11.5. Integral One-Point Statistical Characteristics of Passive Vector Fields;313
9.1.6;Problems;334
9.2;Lecture 12. Wave Localization in Randomly Layered Media;340
9.2.1;12.1. General Remarks;340
9.2.2;12.2. Statistics of Scattered Field at Layer Boundaries;345
9.2.3;12.3. Statistical Theory of Radiative Transfer;354
9.2.4;12.4. Numerical Simulation;365
9.2.5;Problems;367
9.3;Lecture 13. Caustic Structure of Wavefield in Random Media;370
9.3.1;13.1. Input Stochastic Equations and Their Implications;370
9.3.2;13.2. Wavefield Amplitude–Phase Fluctuations. Rytov's Smooth Perturbation Method;376
9.3.3;13.3. Method of Path Integral;382
9.3.4;13.4 Elements of Statistical Topography of Random Intensity Field;396
9.3.5;Problems;403
10;References;408