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Mathematical Aspects of the Plane-parallel Transfer Equation by G.V Efimov; W von Waldenfels; R Wehrse is a Engineering article available to read on EtoBox.

What is Mathematical Aspects of the Plane-parallel Transfer Equation about?

The modelling of high-quality spectra from laboratory experiments or astronomical observations often requires the consideration, for example, of media with strong density inhomogeneities that can be treated only statistically, of complicated redistribution functions and/or of very many lines. Since the numerical methods available for solution of the corresponding radiative transfer equations are not efficient enough to deal with such situations, basically new methods have to be deviced. In order to provide a sound foundation for such algorithms, the relevant mathematical properties of the radiative transfer equation for static, plane-parallel media with coherent, isotropic scattering are investigated in this paper. The starting point is the solution in terms of the matrix tangent hyperbolic function. It is shown that this operator is the sum of a diagonal operator plus the difference between two positive operators of finite trace, which have the completely unexpected property that the highest eigenvalue practically coincides with the trace so that, in a zeroth approximation, the other eigenvalues can be neglected and the operators can be represented in the form &,,..I V,,.)( V&I. T

Who reads Mathematical Aspects of the Plane-parallel Transfer Equation?

Author

G.V Efimov; W von Waldenfels; R Wehrse

Publisher

Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0022-4073)

Published

1997

Language

EN

Field

Engineering (Physical Sciences)