Dynamics of stochastic systems:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Elsevier
2005
|
| Ausgabe: | 1st ed |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | 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 scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere. Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields. The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of the system and initial data. This raises a host of challenging mathematical issues. One could rarely solve such systems exactly (or approximately) in a closed analytic form, and their solutions depend in a complicated implicit manner on the initial-boundary data, forcing and system's (media) parameters . In mathematical terms such solution becomes a complicated "nonlinear functional" of random fields and processes. Part I gives mathematical formulation for the basic physical models of transport, diffusion, propagation and develops some analytic tools. Part II sets up and applies the techniques of variational calculus and stochastic analysis, like Fokker-Plank equation to those models, to produce exact or approximate solutions, or in worst case numeric procedures. The exposition is motivated and demonstrated with numerous examples. Part III takes up issues for the coherent phenomena in stochastic dynamical systems, described by ordinary and partial differential equations, like wave propagation in randomly layered media (localization), turbulent advection of passive tracers (clustering). Each chapter is appended with problems the reader to solve by himself (herself), which will be a good training for independent investigations. This book is translation from Russian and is completed with new principal results of recent research. The book develops mathematical tools of stochastic analysis, and applies them to a wide range of physical models of particles, fluids, and waves. Accessible to a broad audience with general background in mathematical physics, but no special expertise in stochastic analysis, wave propagation or turbulence Contents -- Preface -- Introduction -- I Dynamical description of stochastic systems -- 1 Examples, basic problems, peculiar features of solutions -- 2 Indicator function and Liouville equation -- 3 Random quantities, processes and fields -- 4 Correlation splitting -- 5 General approaches to analyzing stochastic dynamic systems -- 6 Stochastic equations with the Markovian fluctuations of parameters -- 7 Gaussian random field delta-correlated in time (ordinary differential equations) -- 8 Methods for solving and analyzing the Fokker-Planck equation -- 9 Gaussian delta-correlated random field (causal integral equations) -- 10 Diffusion approximation -- 11 Passive tracer clustering and diffusion in random hydrodynamic flows -- 12 Wave localization in randomly layered media -- 13 Wave propagation in random inhomogeneous medium -- 14 Some problems of statistical hydrodynamics -- V Appendix -- A Variation (functional) derivatives -- B Fundamental solutions of wave problems in empty and layered media -- C Imbedding method in boundary-value wave problems 380 -- Bibliography -- Index Includes bibliographical references (p. 200-203) and index |
| Beschreibung: | 1 Online-Ressource (205 p.) |
| ISBN: | 008050485X 0444517960 9780080504858 9780444517968 |
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| 500 | |a 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 scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere. Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields. | ||
| 500 | |a The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of the system and initial data. This raises a host of challenging mathematical issues. One could rarely solve such systems exactly (or approximately) in a closed analytic form, and their solutions depend in a complicated implicit manner on the initial-boundary data, forcing and system's (media) parameters . In mathematical terms such solution becomes a complicated "nonlinear functional" of random fields and processes. Part I gives mathematical formulation for the basic physical models of transport, diffusion, propagation and develops some analytic tools. Part II sets up and applies the techniques of variational calculus and stochastic analysis, like Fokker-Plank equation to those models, to produce exact or approximate solutions, or in worst case numeric procedures. | ||
| 500 | |a The exposition is motivated and demonstrated with numerous examples. Part III takes up issues for the coherent phenomena in stochastic dynamical systems, described by ordinary and partial differential equations, like wave propagation in randomly layered media (localization), turbulent advection of passive tracers (clustering). Each chapter is appended with problems the reader to solve by himself (herself), which will be a good training for independent investigations. This book is translation from Russian and is completed with new principal results of recent research. The book develops mathematical tools of stochastic analysis, and applies them to a wide range of physical models of particles, fluids, and waves. Accessible to a broad audience with general background in mathematical physics, but no special expertise in stochastic analysis, wave propagation or turbulence | ||
| 500 | |a Contents -- Preface -- Introduction -- I Dynamical description of stochastic systems -- 1 Examples, basic problems, peculiar features of solutions -- 2 Indicator function and Liouville equation -- 3 Random quantities, processes and fields -- 4 Correlation splitting -- 5 General approaches to analyzing stochastic dynamic systems -- 6 Stochastic equations with the Markovian fluctuations of parameters -- 7 Gaussian random field delta-correlated in time (ordinary differential equations) -- 8 Methods for solving and analyzing the Fokker-Planck equation -- 9 Gaussian delta-correlated random field (causal integral equations) -- 10 Diffusion approximation -- 11 Passive tracer clustering and diffusion in random hydrodynamic flows -- 12 Wave localization in randomly layered media -- 13 Wave propagation in random inhomogeneous medium -- 14 Some problems of statistical hydrodynamics -- V Appendix -- A Variation (functional) derivatives -- B Fundamental solutions of wave problems in empty and layered media -- C Imbedding method in boundary-value wave problems 380 -- Bibliography -- Index | ||
| 500 | |a Includes bibliographical references (p. 200-203) and index | ||
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Datensatz im Suchindex
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| author | Kli͡at͡skin, Valeriĭ Isaakovich |
| author_facet | Kli͡at͡skin, Valeriĭ Isaakovich |
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| bvnumber | BV043043851 |
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| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1st ed |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:15:49Z |
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| spelling | Kli͡at͡skin, Valeriĭ Isaakovich Verfasser aut Dynamics of stochastic systems V.I. Klyatskin 1st ed Amsterdam Elsevier 2005 1 Online-Ressource (205 p.) txt rdacontent c rdamedia cr rdacarrier 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 scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere. Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields. The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of the system and initial data. This raises a host of challenging mathematical issues. One could rarely solve such systems exactly (or approximately) in a closed analytic form, and their solutions depend in a complicated implicit manner on the initial-boundary data, forcing and system's (media) parameters . In mathematical terms such solution becomes a complicated "nonlinear functional" of random fields and processes. Part I gives mathematical formulation for the basic physical models of transport, diffusion, propagation and develops some analytic tools. Part II sets up and applies the techniques of variational calculus and stochastic analysis, like Fokker-Plank equation to those models, to produce exact or approximate solutions, or in worst case numeric procedures. The exposition is motivated and demonstrated with numerous examples. Part III takes up issues for the coherent phenomena in stochastic dynamical systems, described by ordinary and partial differential equations, like wave propagation in randomly layered media (localization), turbulent advection of passive tracers (clustering). Each chapter is appended with problems the reader to solve by himself (herself), which will be a good training for independent investigations. This book is translation from Russian and is completed with new principal results of recent research. The book develops mathematical tools of stochastic analysis, and applies them to a wide range of physical models of particles, fluids, and waves. Accessible to a broad audience with general background in mathematical physics, but no special expertise in stochastic analysis, wave propagation or turbulence Contents -- Preface -- Introduction -- I Dynamical description of stochastic systems -- 1 Examples, basic problems, peculiar features of solutions -- 2 Indicator function and Liouville equation -- 3 Random quantities, processes and fields -- 4 Correlation splitting -- 5 General approaches to analyzing stochastic dynamic systems -- 6 Stochastic equations with the Markovian fluctuations of parameters -- 7 Gaussian random field delta-correlated in time (ordinary differential equations) -- 8 Methods for solving and analyzing the Fokker-Planck equation -- 9 Gaussian delta-correlated random field (causal integral equations) -- 10 Diffusion approximation -- 11 Passive tracer clustering and diffusion in random hydrodynamic flows -- 12 Wave localization in randomly layered media -- 13 Wave propagation in random inhomogeneous medium -- 14 Some problems of statistical hydrodynamics -- V Appendix -- A Variation (functional) derivatives -- B Fundamental solutions of wave problems in empty and layered media -- C Imbedding method in boundary-value wave problems 380 -- Bibliography -- Index Includes bibliographical references (p. 200-203) and index MATHEMATICS / Probability & Statistics / General bisacsh Statistical physics fast Stochastic analysis fast Stochastic processes fast Stochastic analysis Statistical physics Stochastic processes Dynamisches System (DE-588)4013396-5 gnd rswk-swf Stochastisches System (DE-588)4057635-8 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastisches System (DE-588)4057635-8 s Dynamisches System (DE-588)4013396-5 s 1\p DE-604 Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=199119 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kli͡at͡skin, Valeriĭ Isaakovich Dynamics of stochastic systems MATHEMATICS / Probability & Statistics / General bisacsh Statistical physics fast Stochastic analysis fast Stochastic processes fast Stochastic analysis Statistical physics Stochastic processes Dynamisches System (DE-588)4013396-5 gnd Stochastisches System (DE-588)4057635-8 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4057635-8 (DE-588)4057621-8 |
| title | Dynamics of stochastic systems |
| title_auth | Dynamics of stochastic systems |
| title_exact_search | Dynamics of stochastic systems |
| title_full | Dynamics of stochastic systems V.I. Klyatskin |
| title_fullStr | Dynamics of stochastic systems V.I. Klyatskin |
| title_full_unstemmed | Dynamics of stochastic systems V.I. Klyatskin |
| title_short | Dynamics of stochastic systems |
| title_sort | dynamics of stochastic systems |
| topic | MATHEMATICS / Probability & Statistics / General bisacsh Statistical physics fast Stochastic analysis fast Stochastic processes fast Stochastic analysis Statistical physics Stochastic processes Dynamisches System (DE-588)4013396-5 gnd Stochastisches System (DE-588)4057635-8 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | MATHEMATICS / Probability & Statistics / General Statistical physics Stochastic analysis Stochastic processes Dynamisches System Stochastisches System Stochastische Differentialgleichung |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=199119 |
| work_keys_str_mv | AT kliatskinvaleriiisaakovich dynamicsofstochasticsystems |