Publications Details

THEORY AND GENERATION METHODS FOR N-ARY STOCHASTIC MIXTURES WITH MARKOVIAN MIXING STATISTICS

Olson, Aaron J.; Pautz, Shawn D.; Bolintineanu, Dan S.; Vu, Emily

Work on radiation transport in stochastic media has tended to focus on binary mixing with Markovian mixing statistics. However, although some real-world applications involve only two materials, others involve three or more. Therefore, we seek to provide a foundation for ongoing theoretical and numerical work with “N-ary” stochastic media comprised of discrete material phases with spatially homogenous Markovian mixing statistics. To accomplish this goal, we first describe a set of parameters and relationships that are useful to characterize such media. In doing so, we make a noteworthy observation: media that are frequently called Poisson media only comprise a subset of those that have Markovian mixing statistics. Since the concept of correlation length (as it has been used in stochastic media transport literature) and the hyperplane realization generation method are both tied to the Poisson property of the media, we argue that not all media with Markovian mixing statistics have a correlation length in this sense or are realizable with the traditional hyperplane generation method. Second, we describe methods for generating realizations of N-ary media with Markovian mixing. We generalize the chord- and hyperplane-based sampling methods from binary to N-ary mixing and propose a novel recursive hyperplane method that can generate a broader class of material structures than the traditional, non-recursive hyperplane method. Finally, we perform numerical studies that provide validation to the proposed N-ary relationships and generation methods in which statistical quantities are observed from realizations of ternary and quaternary media and are shown to agree with predicted values.