The variance in stochastic transport problems with Markovian mixing.

Details The variance in stochastic transport problems with Markovian mixing. The variance in stochastic transport problems with Markovian mixing.

Nov 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996jqsrt..56..629p&link_type=abstract

Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 56, issue 5, pp. 629-646

Statistics

2

Radiative Transfer

Scientific paper

This paper considers steady-state particle transport and radiative transfer through a stochastic mixture consisting of two immiscible materials. The mixing of these two components of the medium is assumed to be described by Markovian statistics. In the absence of scattering, exact 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 description is obtained in the asymptotic limit of a small amount of opaque 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 variance. An asymptotic equivalence argument is used to ensure robustness of the renormalized variance equation.

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