Markovian binary mixtures: benchmarks for the albedo problem

Accurately predicting the linear transport of waves or particles in stochastic media is a challenging and important problem that has applications in radiation shielding issues. We present new albedo-problem benchmarks for three-dimensional stochastic media. We use an unbiased Monte Carlo method to estimate the law of diffuse reflection for a binary Markov stochastic half-space with plane-parallel illumination at the boundary. These gold-standard quenched-disorder benchmarks are compared to four annealed-disorder models: the atomic-mix (AM) approximation, the standard Chord-Length Sampling (CLS) method, and two distinct proposals of Generalized Radiative Transfer (GRT) that apply the generalized linear Boltzmann equation in bounded domains. Across nine benchmarks (using isotropic scattering) we observe that memory effects can lead to significant errors in all four annealed models. For non-stochastic albedo, the reciprocal formulation of GRT is universally more accurate than the alternative proposal