The problem of 1-D radiation transport in a stochastic medium is analyzed using a multiple length-scale asymptotic analysis. The analysis shows that when the chunk sizes of the different materials are O(1) in optical thickness, one obtains -- as the leading-order approximation to the transport equation -- a diffusion approximation with spatially-averaged (atomic mix) cross sections. To our knowledge, this is the first time that the atomic mix approximation for particle transport has been shown to be valid for problems in which the chunk sizes are not optically thin.
We also show that the "Standard" or "Levermore-Pomraning" model of particle transport in stochastic media does not limit to the correct asymptotic result in the "same" asymptotic limit. (A diffusion equation is obtained, but with an un-physically large diffusion coefficient. This un-physically "flattens" the solutions.)Finally, we present numerical simulations that validate the theoretical predictions.
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