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Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 1

Basic Concepts, Exact Results, and Asymptotic Approximations

  • Book
  • © 2015

Overview

Authors:
  1. Valery I. Klyatskin

    1. Russian Academy of Sciences, A.M. Obukhov Institute of Atmospheric Physics, Moscow, Russia

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  • Presents a consistent framework of stochastic dynamic systems with maximal possible completeness
  • The present Volume 2 presents Coherent Phenomena in Stochastic Dynamic Systems
  • Studies specific problems of the stochastic structure formation in random media not published elsewhere before
  • With illustrative applications from acoustics, hydrodynamics, magnetohydrodynamics, wave dynamics, and radiophysics

Part of the book series: Understanding Complex Systems (UCS)

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Table of contents (13 chapters)

  1. Front Matter

    Pages 1-16
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  2. Dynamical Description of Stochastic Systems

    1. Front Matter

      Pages 1-1
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    2. Examples, Basic Problems, Peculiar Features of Solutions

      • Valery I. Klyatskin
      Pages 3-80

    3. Solution Dependence on Problem Type, Medium Parameters, and Initial Data

      • Valery I. Klyatskin
      Pages 81-93

    4. Indicator Function and Liouville Equation

      • Valery I. Klyatskin
      Pages 95-114

  3. Random Quantities, Processes, and Fields

    1. Front Matter

      Pages 115-115
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    2. Random Quantities and Their Characteristics

      • Valery I. Klyatskin
      Pages 117-123

    3. Random Processes and Their Characteristics

      • Valery I. Klyatskin
      Pages 125-154

    4. Random Fields

      • Valery I. Klyatskin
      Pages 155-164

    5. Correlation Splitting

      • Valery I. Klyatskin
      Pages 165-189

  4. Stochastic Equations

    1. Front Matter

      Pages 191-191
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    2. General Approaches to Analyzing Stochastic Dynamic Systems

      • Valery I. Klyatskin
      Pages 193-260

    3. Stochastic Equations with the Markovian Fluctuations of Parameters

      • Valery I. Klyatskin
      Pages 261-301

  5. Asymptotic and Approximate Methods for Analyzing Stochastic Equations

    1. Front Matter

      Pages 303-303
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    2. Gaussian Random Field Delta-Correlated in Time (Ordinary Differential Equations)

      • Valery I. Klyatskin
      Pages 305-340

    3. Methods for Solving and Analyzing the Fokker-Planck Equation

      • Valery I. Klyatskin
      Pages 341-375

    4. Diffusion and Higher Approximations

      • Valery I. Klyatskin
      Pages 377-389

    5. Some Other Approximate Approaches to the Problems of Statistical Hydrodynamics

      • Valery I. Klyatskin
      Pages 391-405

  6. Back Matter

    Pages 407-417
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Keywords

About this book

This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. Volume 1 presents the basic concepts, exact results, and asymptotic approximations of the theory of stochastic equations on the basis of the developed functional approach. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings. Ideas of statistical topography are used to discuss general issues of generating coherent structures from chaos with probability one, i.e., almost in every individual realization of random parameters. The general theory is illustrated with certain problems and applications of stochastic mathematical physics in various fields such as mechanics, hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics.

Reviews

“The book represents a comprehensive and very well-written study of stochastic equations and their applications to acoustics, hydrodynamics, and other branches of physics. … The book may be recommended to all interested in the subject; it is really a pleasant read! The book may be also recommended as a textbook for graduate students in both stochastic analysis and diverse areas of applied mathematics.” (B. Belinskiy, Mathematical Reviews, August, 2015)

Authors and Affiliations

  • Russian Academy of Sciences, A.M. Obukhov Institute of Atmospheric Physics, Moscow, Russia

    Valery I. Klyatskin

Bibliographic Information

  • Book Title: Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 1

  • Book Subtitle: Basic Concepts, Exact Results, and Asymptotic Approximations

  • Authors: Valery I. Klyatskin

  • Series Title: Understanding Complex Systems

  • DOI: https://doi.org/10.1007/978-3-319-07587-7

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-07586-0Published: 29 July 2014

  • Softcover ISBN: 978-3-319-35775-1Published: 10 September 2016

  • eBook ISBN: 978-3-319-07587-7Published: 14 July 2014

  • Series ISSN: 1860-0832

  • Series E-ISSN: 1860-0840

  • Edition Number: 1

  • Number of Pages: XX, 418

  • Number of Illustrations: 45 b/w illustrations

  • Topics: Complexity, Data-driven Science, Modeling and Theory Building, Dynamical Systems and Ergodic Theory, Engineering Fluid Dynamics

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