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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November 1989
Research Article|
November 01 1989
Linear kinetic theory in stochastic media
Richard Sanchez
Richard Sanchez
Service d’Etudes de Réacteurs et de Mathématiques Appliquées, Centre d’ Etudes Nucléaires de Saclay, 91191 Gif sur Yvette Cedex, France
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Richard Sanchez
Service d’Etudes de Réacteurs et de Mathématiques Appliquées, Centre d’ Etudes Nucléaires de Saclay, 91191 Gif sur Yvette Cedex, France
J. Math. Phys. 30, 2498–2511 (1989)
Article history
Received:
February 01 1989
Accepted:
July 12 1989
Citation
Richard Sanchez; Linear kinetic theory in stochastic media. J. Math. Phys. 1 November 1989; 30 (11): 2498–2511. https://doi.org/10.1063/1.528530
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