Ambartsumian’s methods in the theory of radiative transfer |
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| Authors: | A G Nikoghossian |
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| Institution: | (1) V. A. Ambartsumian Byurakan Astrophysical Observatory, Byurakan, Armenia |
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| Abstract: | The purpose of this article is to provide some insight into Ambartsumian’s methods in the theory of radiative transfer, their
applications, and further development. Two of these methods are emphasized--the invariance principle and the method of addition
of layers, proposed by Ambartsumian in the 1940’s. The difference between these methods and the classical approach for solving
radiative transfer problems is discussed. We discuss only a small portion of the subsequent work by others that we believe
reveals, in a more intuitive way, the essence and significance of Ambartsumian’s methods and their efficiency for applications.
Thus, for example, a separate section is devoted to applications of the Lagrangian formalism to radiative transfer and it
is shown that the invariance principle is a special case of a more general variational principle that reflects an invariance
with respect to translational transformation of the optical depth. Our discussion of the method of addition of layers points
out its generality and the major role it has played in the later creation of such methods as Bellman’s invariant imbedding
method and the method for solving radiative transfer problems in inhomogeneous media. The latter method has yielded a number
of new analytic results. The concluding section is a brief summary of Ambartsumian’s results in the nonlinear theory of radiative
transfer, where he was a pioneer in the study of the class of multilevel problems. This article also sets out to demonstrate
the place and role of Ambartsumian’s methods in the theory of radiative transfer, which, to a great extent, set the path along
which this theory developed for many years to come.
Translated from Astrofizika, Vol. 52, No. 1, pp. 5–27 (February 2009). |
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| Keywords: | radiative transfer theory invariance principle the method of addition of layers variational formalism |
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