On new understanding with radiative transfer in purely absorbing binary stochastic mixtures

We revisit radiative transfer in purely absorbing binary stochastic mixtures. To this end, benchmark results of the ensemble-averaged specific radiation intensity for one-dimensional (1D) arbitrary mixtures are presented based on the renewal theory, which can quantitatively reproduce high-accuracy numerical simulation data. We are for the first time to derive the analytical solutions for periodic statistics, which precisely follow the benchmarks in cases considered. Furthermore, we propose a delta-function expansion method to approximate the statistical distributions for non-Markovian mixtures, which successfully explains the remarkable transition of oscillating structures from periodic to block statistics. The accuracy of present approximate method is compared to the Markov-based correction approach and benchmark solutions in several typical cases. Our results provide new understanding on absorption-dominated radiative transfer in binary stochastic mixtures.