Invariant Imbedding and Variational Principles in Transport Theory

Journal Article · Sat Jul 01 04:00:00 EDT 1961 · Bulletin of the American Mathematical Society (U.S.)

DOI:https://doi.org/10.1090/S0002-9904-1961-10638-1· OSTI ID:4837545

Bellman, R; Kalaba, R; Wing, G M

A single variational problem is derived which yields the linear equations of conventional transport theory when treated by means of the calculus of variations, and which yields the nonlinear equations of invariant imbedding when approached by means of the functional equation techniques of dynamic programming. The problem considered is a steady-state transport process, involving absorption, fission and scattering, taking place in a one-dimensional rod. For the sake of simplicity, the rod is homogeneous and isotropic. At the conceptual level, the results provide a unified approach to the treatment of internal and external fluxes along classical and modern lines. At the analytic and computational levels, the results enable the calculation of various inequalities for the reflected fluxes and the application of the Rayleigh-Ritz techniques to the determination of fluxes and critical lengths. (N.W.R.)

• Research Organization: RAND Corp., Santa Monica, Calif.
• Sponsoring Organization: USDOE
• NSA Number: NSA-15-032708
• OSTI ID: 4837545
• Report Number(s): SCR-402; 0002-9904
• Journal Information: Bulletin of the American Mathematical Society (U.S.), Journal Name: Bulletin of the American Mathematical Society (U.S.) Vol. Vol: 67: No. 4; ISSN BAMOA
• Country of Publication: United States
• Language: English

Related Subjects

ABSORPTION
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
FISSION
HOMOGENEOUS REACTORS
MATHEMATICS
NEUTRON FLUX
NEUTRONS
NUMERICALS
PHYSICS
RODS
SCATTERING
TRANSPORT THEORY
VARIATIONAL METHOD