We consider particle transport in a spatially random medium, the transport governed by the traditional, linear, time- and space-dependent transport equation for “host and guest.” The scattering is elastic and isotropic; there is no absorption. If the host medium has uniform density we know that an initial burst will, in time, approach the solution to the time-dependent diffusion equation. In the case of random medium we find that for a large class of such media the asymptotic behavior is unchanged by the stochasticity; there is neither renormalization of the equation nor the diffusion co-efficient.The nature of the correlation between fluctuations of density at large separation plays an important role in the analysis.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. C. Pomraning (1991) Linear Kinetic Theory and Particle Transport in Stochastic Mixtures World Scientific Press Singapore
A. V. Stepanov (1971) ArticleTitleNeutron Transfer Theory for Inhomogeneous Media Proc. P.N. Lebedev. Inst 44 193
A. Z. Akcasu M. M. R. Williams (2004) ArticleTitleAn analytical study of particle transport in spatially random media in one dimension: mean and variance calculations Nucl. Sci. Eng 148 1–11
E. W. Larsen, Asymptotic derivation....for a 1-D random diffusive medium. Proc. 18th ICTT, Rio de Janeiro, 2003.
A. K. Prinja (2004) ArticleTitleOn the master equation approach to transport in discrete random media in the presence of scattering Ann. Nucl. Energy 31 2005–2016 Occurrence Handle10.1016/j.anucene.2004.08.003
M.M.R. Williams (2000) ArticleTitleSome aspects of neutron transport in spatially random media Nucl. Sci. Eng 136 34–58
H. Beijeren Particlevan (1982) ArticleTitleTransport properties of stochastic lorentz models Rev. Modern Phys. 54 195–234 Occurrence Handle10.1103/RevModPhys.54.195
H. Spohn (1980) ArticleTitleKinetic equations from Hamiltonian dynamics: Markovian limits Rev. Modern Phys 53 569–615 Occurrence Handle10.1103/RevModPhys.52.569
J. B. Keller (1960) ArticleTitleStochastic equations and wave propagation in random media Proc. Sympos. Appl. Math. Amer. Math. Soc. 13 145–170
R. W. Zwanzig (1961) Statistical mechanics of irreversibility. Lectures in Theoretical Physics, Vol. 3 Interscience New York
J. J. Duderstadt W. R. Martin (1979) Transport Theory John Wiley and Sons New York
B. Davison (1955) Neutron Transport Theory Oxford University Press Oxford
G. B. Whitham (1974) Linear and Nonlinear Waves John Wiley and Sons New York
L. E. Reichl (1987) A Modern Course in Statistical Physics University of Texas Press Austin
R. H. Terwiel (1974) ArticleTitleprojection operator methods applied to stochastic linear differential equations Physica 74 248–265 Occurrence Handle10.1016/0031-8914(74)90123-2
U. Frisch, in Probabilistic Methods in Applied Mathematics, A. T. Bharucha-Reid, ed. (Academic Press, New York 1968.)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Corngold, N. Transport and Diffusion in a Random Medium. J Stat Phys 120, 521–541 (2005). https://doi.org/10.1007/s10955-005-6801-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-005-6801-z