By Valery I. Klyatskin

ISBN-10: 0444517960

ISBN-13: 9780444517968

Fluctuating parameters seem in numerous actual structures and phenomena. they often come both as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, and so on. the well-known instance of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the root for contemporary stochastic calculus and statistical physics. different vital examples comprise turbulent shipping and diffusion of particle-tracers (pollutants), or non-stop densities (''oil slicks''), wave propagation and scattering in randomly inhomogeneous media, for example gentle or sound propagating within the turbulent atmosphere.

Such versions evidently render to statistical description, the place the enter parameters and ideas are expressed through random techniques and fields.

The primary challenge of stochastic dynamics is to spot the basic features of process (its country and evolution), and relate these to the enter parameters of the approach and preliminary data.

This increases a number of hard mathematical concerns. you can actually infrequently remedy such platforms precisely (or nearly) in a closed analytic shape, and their strategies count in a sophisticated implicit demeanour at the initial-boundary info, forcing and system's (media) parameters . In mathematical phrases such resolution turns into a classy "nonlinear functional" of random fields and processes.

Part I offers mathematical formula for the fundamental actual versions of delivery, diffusion, propagation and develops a few analytic tools.

Part II units up and applies the suggestions of variational calculus and stochastic research, like Fokker-Plank equation to these versions, to supply particular or approximate options, or in worst case numeric techniques. The exposition is encouraged and confirmed with various examples.

Part III takes up concerns for the coherent phenomena in stochastic dynamical platforms, defined via usual and partial differential equations, like wave propagation in randomly layered media (localization), turbulent advection of passive tracers (clustering).

Each bankruptcy is appended with difficulties the reader to resolve by means of himself (herself), as a way to be a superb education for autonomous investigations.

· This ebook is translation from Russian and is finished with new significant result of fresh research.

· The ebook develops mathematical instruments of stochastic research, and applies them to a variety of actual types of debris, fluids, and waves.

· available to a large viewers with common historical past in mathematical physics, yet no designated services in stochastic research, wave propagation or turbulence