Dynamics of stochastic systems
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...
Main Author:  

Format:  eBook 
Language:  English 
Published: 
Amsterdam
Elsevier
2005, 2005

Edition:  1st ed 
Subjects:  
Online Access:  
Collection:  Elsevier ScienceDirect eBooks  Collection details see MPG.ReNa 
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 particletracers (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 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 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 initialboundary 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 FokkerPlank equation to those models, to produce exact or approximate solutions, or in worst case numeric procedures. 

Physical Description:  online resource (205 p.) ill 
ISBN:  008050485X 9780444517968 0444517960 9780080504858 