| Titre : | Dynamics of stochastic systems |
| Auteurs : | Valery I. (1940-) Klyatskin, Auteur |
| Type de document : | texte imprimé |
| Editeur : | Amsterdam : Elsevier, 2005 |
| ISBN/ISSN/EAN : | 978-0-444-51796-8 |
| Format : | 205 p. / ill. / 25 cm |
| Note générale : | Bibliogr. p. 200-203. - Index |
| Langues : | Anglais |
| Index. décimale : | 531.21 (Loi statiques en générale.Processus statiques) |
| Tags : | Analyse stochastique Physique statistique Processus stochastiques Stochastic analysis Statistical physics Stochastic processes |
| Résumé : | 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. |
| Note de contenu : |
Summary :
Part I: Dynamical description of stochastic systems Chapter 1. Examples, basic problems, peculiar features of solutions Chapter 2. Solution dependence on problem type, medium parameters, and initial data Part II: Statistical description of stochastic systems Chapter 3. Indicator function and Liouville equation Chapter 4. Random quantities, processes and fields Chapter 5. Correlation splitting Chapter 6. General approaches to analyzing stochastic dynamic systems Chapter 7. Stochastic equations with the Markovian fluctuations of parameters Chapter 8. Gaussian delta-correlated random field (ordinary differential equations) Chapter 9. Methods for solving and analyzing the Fokker-Planck equation Chapter 10. Gaussian delta-correlated random field (causal integral equations) Part III: Examples of coherent phenomena in stochastic dynamic systems Chapter 11. Passive tracer clustering and diffusion in random hydrodynamic flows Chapter 12 - Wave localization in randomly layered media |
Exemplaires (1)
| Cote | Support | Localisation | Section | Disponibilité | Etat_Exemplaire |
|---|---|---|---|---|---|
| 531.21 KLY | Papier | Bibliothèque Centrale | Physique | Disponible | Consultation sur place |
