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 and III 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 IV 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), wave propagation in disordered 2D and 3D media.
For the sake of reader I provide several appendixes (Part V) that
give many technical mathematical details needed in the book.
For scientists dealing with stochastic dynamic systems in different
areas, such as hydrodynamics, acoustics, radio wave physics,
theoretical and mathematical physics, and applied mathematics
the theory of stochastic in terms of the functional analysis
Referencing those papers, which are used or discussed in this book
and also recent review papers with extensive bibliography on the
subject.
General
Imprint: |
Elsevier Science Ltd
|
Country of origin: |
United Kingdom |
Release date: |
May 2005 |
First published: |
August 2005 |
Authors: |
Valery I. Klyatskin
|
Dimensions: |
240 x 165 x 35mm (L x W x T) |
Format: |
Hardcover
|
Pages: |
556 |
ISBN-13: |
978-0-444-51797-5 |
Categories: |
Books >
Science & Mathematics >
Physics >
General
|
LSN: |
0-444-51797-9 |
Barcode: |
9780444517975 |
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