Accession Number : AD0606431

Title :   ON THE PRINCIPLE OF INVARIANT IMBEDDING AND NEUTRON TRANSPORT THEORY; I: ONE-DIMENSIONAL CASE,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Bellman,Richard ; Kalaba,Robert ; Wing,G. Milton

Report Date : 11 JUN 1957

Pagination or Media Count : 1

Abstract : Consideration is given to a one-dimensional version of the reflection and transmission of neutrons, and the phenomenon of critical mass. Although the effects of fission, capture and forward and backward scattering are considered, collisions between neutrons are not taken into account. The basic model is stochastic, with standard transport theory derived on the basis of expected values. As the explicit form of the higher moments indicates, an expected value theory yields a quite inadequate view of the distribution of reflected and transmitted neutrons in the neighborhood of critical mass. Some numerical results describing these distributions obtained from the solution of forty simultaneous nonlinear differential equations are presented.

Descriptors :   (*NEUTRON TRANSPORT THEORY, NONLINEAR DIFFERENTIAL EQUATIONS), NEUTRON SCATTERING, CRITICAL ASSEMBLIES, FISSION, NEUTRON CAPTURE, STOCHASTIC PROCESSES, MATHEMATICAL MODELS

Distribution Statement : APPROVED FOR PUBLIC RELEASE