Linear kinetic theory in stochastic media

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Abstract
Linear kinetic particle transport in stochastic heterogeneous media is discussed. The analysis includes scattering in a three-dimensional setting and deals with arbitrary time-dependent statistics. Ensemble-average operators are used to derive two independent complete descriptions for the ensemble-averaged angular flux. The first description consists of an infinite system of integral, renewal-like equations for averaged flux values over spatially dependent, increasingly smaller sets. The second approach results in an infinite system of kinetic, balancelike equations for locally averaged flux values. Both types of equations include averagings over transitional sets of states that change locally of physical properties. Previous results are recovered from the limit form of these equations for no-memory statistics and purely absorbing media. Also, the Levermore–Pomraning–Wong proposed models are shown to correspond to truncated forms of these equations.

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