A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique

Details A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique

Aug 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976apj...207..808c&link_type=abstract

Astrophysical Journal, vol. 207, Aug. 1, 1976, pt. 1, p. 808-819.

Mathematics

2

Anisotropic Media, Radiative Transfer, Scattering Functions, Variational Principles, Electromagnetic Scattering, Integral Equations, Kernel Functions, Linear Equations, Operators (Mathematics), Rayleigh-Ritz Method

Scientific paper

The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.

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