Gc. Pomraning, THE PLANAR SYMMETRY BEAM PROBLEM IN STOCHASTIC MEDIA, Journal of quantitative spectroscopy & radiative transfer, 55(6), 1996, pp. 771-785
This paper considers planar symmetry, steady-state, energy dependent,
linear transport of a normally incident radiation beam through a scatt
ering/absorbing thin slab, composed of a stochastic mixture of two imm
iscible materials. The scattering process is assumed sufficiently peak
ed in both energy and angle so that the Fokker-Planck description is v
alid. If the material mixing obeys Markovian statistics, and if partic
le backscattering can be ignored, this situation is a joint Markov pro
cess. As such, the stochastic Liouville master equation is valid, and
we obtain a set of two coupled linear transport equations describing e
xactly the ensemble-averaged solution for the particle intensity. We d
evelop the small correlation length asymptotic limit of this set of tw
o equations, which results in a single renormalized equation. The two-
equation set is treated by an angular moments method, exploiting the a
ssumed peakedness of the solution in angle. In a separate development,
an explicit result is obtained for the spatial profile of the particl
e density in the case of monoenergetic, purely scattering transport th
rough a layered statistical mixture. Copyright (C) 1996 Elsevier Scien
ce Ltd