On the master equation approach to transport in discrete random media in the presence of scattering

The master equation approach to transport in binary statistical media is revisited to examine the role of scattering in this formalism. We show that it is possible to generalize this approach to rigorously incorporate scattering events, but a unique closure problem is encountered arising from scattering induced correlations in the angular flux. We further show that these correlations do not play a role in the equations for the conditional mean angular flux. That is, the well-known standard model for the mean is recovered. However, all moment equations higher than the mean are afflicted with this closure, indicating in particular that a standard model for the variance will perforce be less accurate than that for the mean.