A generalized Fokker-Planck equation for particle transport in random media

David C. Swailes and Kirsty F.F. Darbyshire

Physica A: Statistical Mechanics and its Applications, 1997, vol. 242, issue 1, 38-48

Abstract: A transport equation is derived for the probability density function (pdf) that gives the phase-space distribution of a particle moving in a random medium: the motion of the particle is determined by a general second-order stochastic differential equation that models transport in a medium exhibiting correlated fluctuations in both space and time. The derivation makes use of cumulant expansions and functional calculus. The most general form of the transport equation requires closure, and a simple closure approximation is discussed. No closure approximation is necessary when the stochastic component of the particle equation of motion is a correlated Gaussian process, and results for transport in an unbounded medium are derived for this exact case. These results are consistent with other studies and serve to validate the model.

Keywords: Stochastic processes; Fokker-Planck equation; Particle transport (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:242:y:1997:i:1:p:38-48

DOI: 10.1016/S0378-4371(97)00195-7

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