Effective mean free paths in absorbing and scattering media: direct numerical simulation

The transport of particles (photons, neutrons, charged particles, neutrinos, etc) in a random medium is a very challenging problem that arises in a wide variety of applications. In order to understand the limitations of the theoretical models better and hopefully gain some insight into the problem of transport in a random medium, the goal of the work presented here is to develop a phenomenological picture based on direct numerical simulation. We show the usefulness of this approach by considering a 3-dimensional pure absorption problem. Using optical depth distributions constructed from the direct numerical simulation (DNS), we numerically arrive at effective mean free paths (MFP) through the random medium. We validate this approach by constructing the analytic solution for the effective MFP of a random medium consisting of single size inclusions. We then apply DNS to 1-dimensional scattering in a random medium. We construct a response surface that represents the variability of the mean free path as a function of input variations. Using non-linear regression analysis, we construct approximate relations between the effective mean free path and such input variables as volume fraction and absorption and scattering opacity. (authors)