Accession Number : AD0653923
Title : THE INVARIANT IMBEDDING EQUATIONS FOR THE DISSIPATION FUNCTIONS OF AN INHOMOGENEOUS FINITE SLAB WITH ANISOTROPIC SCATTERING,
Corporate Author : RAND CORP SANTA MONICA CALIF
Personal Author(s) : Bellman,R. ; Kagiwada,H. ; Kalaba,R. ; Ueno,S.
Report Date : JUN 1967
Pagination or Media Count : 28
Abstract : This report considers the absorption of photons incident to an atmosphere, to the case of an inhomogeneous atmosphere and anisotropic scattering. By use of the invariant imbedding technique, two complete sets of integro-differential equations are derived--the first for the case of monodirectional illumination of the upper boundary, and the second for monodirectional illumination of the lower boundary--using the equations of transfer and taking into account the polarity of the optical properties of the atmosphere. In both sets, the equations and results for scattering and transmission in the homogeneous case reduce to those given by Chandrasekhar.
Descriptors : (*THERMAL RADIATION, MATHEMATICAL ANALYSIS), (*ATMOSPHERES, OPTICAL PROPERTIES), PHOTONS, BOUNDARY VALUE PROBLEMS, NUMERICAL METHODS AND PROCEDURES, HEAT TRANSFER, SCATTERING, PLANETARY ATMOSPHERES, LIGHT, TRANSPORT PROPERTIES
Subject Categories : Astrophysics
Distribution Statement : APPROVED FOR PUBLIC RELEASE