Linear Transport in Correlated Stochastic Media

The problem of linear transport in a stationary stochastic medium is examined in the context of stochastic geometry. Boolean models of stochastic media allow calculation of density correlations without use of Markovian assumptions. Most correlation functions are well represented by linear combinations of a few exponentials. Systems of integrodifferential equations are obtained either (a) by a perturbative treatment or (b) by truncation of the hierarchy of moments. The presence of an integral term (i.e., a nonlocal flux) can be avoided by the use of an approximate equivalence between the product of the transport Green function by an exponential with the transport Green function of a modified problem. Introduction of auxiliary unknowns gives rise to a system of coupled Boltzmann equations describing the ensemble average of the flux.