THE VARIANCE IN STOCHASTIC TRANSPORT PROBLEMS WITH MARKOVIAN MIXING

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