Gc. Pomraning, THE VARIANCE IN STOCHASTIC TRANSPORT PROBLEMS WITH MARKOVIAN MIXING, Journal of quantitative spectroscopy & radiative transfer, 56(5), 1996, pp. 629-646
This paper considers steady-state particle transport and radiative tra
nsfer through a stochastic mixture consisting of two immiscible materi
als. The mixing of these two components of the medium is assumed to be
described by Markovian statistics. In the absence of scattering, exac
t equations are developed for the ensemble average of any power of the
stochastic intensity field. Particular attention is paid to the first
and second powers, which yield algorithms for computing the ensemble-
averaged intensity as well as the associated variance. A simplified de
scription is obtained in the asymptotic limit of a small amount of opa
que material admired with a large amount of transparent material. This
description is in the form of renormalized transport equations, with
effective coefficients, for the ensemble-averaged intensity and varian
ce. An asymptotic equivalence argument is used to ensure robustness of
the renormalized variance equation. Copyright (C) 1996 Elsevier Scien
ce Ltd