Dynamics of stochastic systems / V.I. Klyatskin.

Format:

Book

Author/Creator:

Klyatskin, V. I.

Language:

English

Subjects (All):

Stochastic analysis.

Statistical physics.

Stochastic processes.

Physical Description:

1 online resource (211 p.)

Edition:

1st ed.

Place of Publication:

Amsterdam ; San Diego : Elsevier, 2005.

Language Note:

English

Summary:

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. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''oil slicks''), wave propagation and scatteri

Contents:

Cover; DYNAMICS OF STOCHASTIC SYSTEMS; Copyright Page; Preface; Contents; Introduction; Part I: Dynamical description of stochastic systems; Chapter 1. Examples, basic problems, peculiar features of solutions; 1.1 Ordinary differential equations: initial value problems; 1.2 Boundary-value problems for linear ordinary differential equations (plane waves in layered media); 1.3 Partial differential equations; Chapter 2. Solution dependence on problem type, medium parameters, and initial data; 2.1 Functional representation of problem solution; 2.2 Solution dependence on problem's parameters

ProblemsChapter 3. Indicator function and Liouville equation; 3.1 Ordinary differential equations; 3.2 First-order partial differential equations; 3.3 Higher-order partial differential equations; Problems; Part II: Statistical description of stochastic systems; Chapter 4. Random quantities, processes and fields; 4.1 Random quantities and their characteristics; 4.2 Random processes, fields, and their characteristics; 4.3 Markovian processes; Problems; Chapter 5. Correlation splitting; 5.1 General remarks; 5.2 Gaussian process; 5.3 Poisson process; 5.4 Telegrapher's random process

5.5 Delta-correlated random processesProblems; Chapter 6. General approaches to analyzing stochastic dynamic systems; 6.1 Ordinary differential equations; 6.2 Completely solvable stochastic dynamic systems; 6.3 Delta-correlated fields and processes; Problems; Chapter 7. Stochastic equations with the Markovian fluctuations of parameters; 7.1 Telegrapher's processes; 7.2 Gaussian Markovian processes; Problems; Chapter 8. Gaussian delta-correlated random field (ordinary differential equations); 8.1 The Fokker-Planck equation; 8.2 Transition probability distributions

8.3 Applicability range of the Fokker-Planck equationProblems; Chapter 9. Methods for solving and analyzing the Fokker-Planck equation; 9.1 Wiener random process; 9.2 Logarithmic-normal random process; 9.3 Integral transformations; 9.4 Steady-state solutions of the Fokker-Planck equation; 9.5 Boundary-value problems for the Fokker-Planck equation (transfer phenomena); 9.6 Method of fast oscillation averaging; Problems; Chapter 10. Gaussian delta-correlated random field (causal integral equations); Problems; Part III: Examples of coherent phenomena in stochastic dynamic systems

Chapter 11. Passive tracer clustering and diffusion in random hydrodynamic flows11.1 Lagrangian description (particle diffusion); 11.2 Diffusion of passive tracer concentration in random velocity field; 11.3 Effect of molecular diffusion; Problems; Chapter 12. Wave localization in randomly layered media; 12.1 Statistics of scattered field at layer boundaries; 12.2 Statistical theory of radiative transfer; 12.3 Numerical simulation; Problems; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-281-03671-4

9786611036713

0-08-050485-X

OCLC:

469608542