Accession Number : AD0287114

Title :   UNIQUENESS PROBLEMS IN THE MATHEMATICS OF MULTIPLE SCATTERING

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : MULLIKIN,T.W.

Report Date : OCT 1962

Pagination or Media Count : 1

Abstract : Some recent mathematical studies concerning the uniqueness of solutions to Chandrasekhar's mathematical formulation of principles of invariance in the theory of radiative transfer are reported. It is shown that the X and Y equations and the psi(m) sub l and phi(m) sub l equations of Chandrasekhar have a multiplicity of solutions for many phase functions describing local scattering, the extent of this nonuniqueness having been only partially explored by Chandrasekhar. The desired solution to the X and Y equations is selected by imposing two additional linear constraints, which differ in the conservative case from those imposed by Chandrasekhar. An extension will later be made of these results to the psi(m) sub l and phi(m) sub l equations. A new formulation of all this theory is being worked out in terms of linear equations which are particularly well suited to numerical computation for thick atmospheres. (Author)

Descriptors :   *ATMOSPHERES, *COSMIC RAYS, *SCATTERING, DIFFERENTIAL EQUATIONS, ELECTROMAGNETIC WAVE REFLECTIONS, EQUATIONS, FUNCTIONS(MATHEMATICS), INTEGRAL EQUATIONS, INTENSITY, MATHEMATICAL ANALYSIS, NONLINEAR DIFFERENTIAL EQUATIONS, POLYNOMIALS, SERIES(MATHEMATICS), THEORY, WAVE PROPAGATION

Distribution Statement : APPROVED FOR PUBLIC RELEASE