Dynamics of Stochastic Systems

Nonfiction, Science & Nature, Science, Physics, General Physics, Mathematics
Cover of the book Dynamics of Stochastic Systems by Valery I. Klyatskin, Elsevier Science
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Valery I. Klyatskin ISBN: 9780080504858
Publisher: Elsevier Science Publication: March 17, 2005
Imprint: Elsevier Science Language: English
Author: Valery I. Klyatskin
ISBN: 9780080504858
Publisher: Elsevier Science
Publication: March 17, 2005
Imprint: Elsevier Science
Language: English

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

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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

More books from Elsevier Science

Cover of the book Wildlife Demography by Valery I. Klyatskin
Cover of the book Thermal Design of Nuclear Reactors by Valery I. Klyatskin
Cover of the book Biochemistry for Materials Science by Valery I. Klyatskin
Cover of the book Emerging Membrane Technology for Sustainable Water Treatment by Valery I. Klyatskin
Cover of the book Intelligent Vehicular Networks and Communications by Valery I. Klyatskin
Cover of the book Physiology and Biochemistry by Valery I. Klyatskin
Cover of the book Nutrient Metabolism by Valery I. Klyatskin
Cover of the book Gene Therapy of Cancer by Valery I. Klyatskin
Cover of the book New and Future Developments in Microbial Biotechnology and Bioengineering by Valery I. Klyatskin
Cover of the book Electronics Calculations Data Handbook by Valery I. Klyatskin
Cover of the book Academic Libraries in the US and China by Valery I. Klyatskin
Cover of the book Ion Channel Factsbook by Valery I. Klyatskin
Cover of the book Waste Minimization and Cost Reduction for the Process Industries by Valery I. Klyatskin
Cover of the book Basic Neurochemistry by Valery I. Klyatskin
Cover of the book Computational Systems Biology by Valery I. Klyatskin
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy