Statistics
Scientific paper
Jun 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996jqsrt..55..771p&link_type=abstract
Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 55, issue 6, pp. 771-785
Statistics
2
Radiative Transfer: Scattering
Scientific paper
This paper considers planar symmetry, steady-state, energy dependent, linear transport of a normally incident radiation beam through a scattering/absorbing thin slab, composed of a stochastic mixture of two immiscible materials. The scattering process is assumed sufficiently peaked in both energy and angle so that the Fokker-Planck description is valid. If the material mixing obeys Markovian statistics, and if particle backscattering can be ignored, this situation is a joint Markov process. As such, the stochastic Liouville master equation is valid, and the author obtains a set of two coupled linear transport equations describing exactly the ensemble-averaged solution for the particle intensity. He develops the small correlation length asymptotic limit of this set of two equations, which results in a single renormalized equation. The two-equation set is treated by an angular moments method, exploiting the assumed peakedness of the solution in angle. In a separate development, an explicit result is obtained for the spatial profile of the particle density in the case of monoenergetic, purely scattering transport through a layered statistical mixture.
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