Transport Theory in Discrete Stochastic Mixtures

The flow of neutral particles which interact with a background material but not with themselves is described in some generality by a linear kinetic, or transport, equation. This equation, while algebraically complex, has a very simple physical content; it is simply the mathematical statement of particle conservation in phase space. Applications of such transport descriptions are numerous. They include neutron migration in nuclear reactors, radiative transfer (thermal photon flow), neutrino flow in astrophysical problems, neutral particle transport in plasmas, gamma ray transport in shielding considerations, and Knudsen flow arising in the kinetic theory of gases. A vast literature exists on the formulation and solution methods, both analytical and numerical, of such transport problems, but generally only in the nonstochastic area. The author uses the terms stochastic and nonstochastic throughout this article in a special sense. That is, particle transport is in itself a stochastic process, but this is not the stochasticity or lack thereof that is meant when the terms {open_quotes}stochastic transport{close_quotes} and {open_quotes}nonstochastic transport{close_quotes} are used. In this use of the word, nonstochastic means that the properties, as functions of space and time, of the background material with which the particles interact are either specified or can conceptually bemore » computed in a deterministic fashion.« less