Non-classical transport with angular-dependent path-length distributions. 1: Theory

This paper extends a recently introduced theory describing particle transport for random statistically homogeneous systems in which the distribution function p(s) for chord lengths between scattering centers is non-exponential. Here, we relax the previous assumption that p(s) does not depend on the direction of flight \Omega; this leads to an extended generalized linear Boltzmann equation that includes angular-dependent cross sections, and to an extended generalized diffusion equation that accounts for anisotropic behavior resulting from the statistics of the system.