The transit-length distribution for a binary Markovian mixture is the telegraph-process occupation-time distribution; the paper adds a stable high-mixing asymptotic form that converges to atomic mix and improves porous-slab transmission estimates.
A Reciprocal Formulation of Nonexponential Radiative Transfer. 3: Binary Mixtures
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We derive the form of reciprocal generalized radiative transfer (RGRT) that includes the Levermore-Pomraning attenuation law for paths leaving a deterministic origin. The resulting model describes linear transport within multi-dimensional stochastic binary mixtures with Markovian mixing statistics and nonstochastic albedo and phase function. The derivation includes a new attenuation law and related free-path distribution between collisions, which was previously estimated using a Monte Carlo approach. We also show that previous stationary descriptions of binary mixtures with binomial mixing statistics reduce to exponential attenuations and, thus, have an exact homogenization within classical radiative transfer.
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Transit-Length Distribution for Particle Transport in Binary Markovian Mixed Media
The transit-length distribution for a binary Markovian mixture is the telegraph-process occupation-time distribution; the paper adds a stable high-mixing asymptotic form that converges to atomic mix and improves porous-slab transmission estimates.