Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010ap.....53..268d&link_type=abstract
Astrophysics, Volume 53, Issue 2, pp.268-283
Astronomy and Astrophysics
Astrophysics
Radiative Transfer Theory, Analytical Solutions
Scientific paper
The basic concepts for developing a system of analytic solutions for the standard problems of radiative transfer theory are discussed. These solutions, which are found using Ambartsumyan’s layer addition method in Sobolev’s probabilistic interpretation for radiative diffusion problems, are maximally compact and easily used in numerical computations. New expressions are obtained for the resolvents and the resolvent functions, as well as a unified structure for the form of an integral representation for solving different radiative transfer problems in semi-infinite media and in finite layers. Block diagrams of the sequence of stages for solving these problems are provided, where the Ambartsumyan function φ(η) (more precisely, 1/φ(η)) plays a fundamental role in the case of semi-infinite media while the functions a(η, τ0 ) and b(η, τ0) play an analogous role for finite layers.
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