Time-dependent transport process

✍ Scribed by Alan Ping-I Wang

• Publisher: Elsevier Science
• Year: 1969
• Tongue: English
• Weight: 763 KB
• Volume: 287
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(69)00218-3

✦ Synopsis

A compact and unified derivation of transport theory in the time-dependent case is presented. The development is based on the "star-product" which is an extension of that used by Redheffer (2). A "state form" and a corresponding "linearized system" are derived.

The former is a system of non-linear integral equations which correspond to the invariant imbedding formulations of Bellman and Kalaba (1). The latter shows that such a system can be linearized. We also show that the right and left linearized equations can be derived from each other. This result is a generalization of a theorem given by Reid ( ). The boundary effects on time-dependent transport equations are discussed. The general results are applicable to problems of transmission-line theory, radiative tra,nsfer, and neutron transfer in slab geometry. A speci$c example of the time-dependent problem for particles moving in a rod is given. S(X>Y; T,T,) = W', T,) 0 o W', T,) ' (3) we write X(x, y; T, T,) = E(T, T,) and E(T, T) = E. The equation X(x,x; T,T) = E, which, we assume, indicates that an infinitely thin medium produces no disturbance.