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On the Green's function for heterogeneous media in one-speed transport theory

Published online by Cambridge University Press:  24 October 2008

A. K. Prinja
A. K. Prinja
Affiliation:
U.C.L.A., Los Angeles, California
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Abstract

The Green's functions for semi-infinite and adjacent semi-infinite media are considered in one-speed transport theory. Chandrasekhar's Principles of Invariance are used to formulate integral equations that describe the emergent and interface angular distributions. It is shown that mathematically these are equivalent to subtracting from the transport equation known solutions to related, simpler problems. Duplication of effort is avoided in this way. For adjacent semi-infinite media, a difficulty encountered in the solutions of the integral equations necessitates the application of a Laplace transform for its resolution. Some virtues of using the transform are explored, e.g. in the determination of the internal distribution where it yields concise expressions for the Green's function.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 1 , January 1981 , pp. 181 - 192
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

(1)Auerbach, T. B. N. L. 676 (T-225) (1961).CrossRefGoogle Scholar
(2)Burkhart, A. R., Ishiguro, Y. and Siewert, C. E.Nuclear Sci. Eng. 61 (1976), 72.CrossRefGoogle Scholar
(3)Busbridge, I. W.The mathematics of radiative transfer (Cambridge, University Press, 1960).Google Scholar
(4)Case, K. M.Rev. Modern Phys. 29 (1957) no. 4, 651.CrossRefGoogle Scholar
(5)Case, K. M., De Hoffman, F. and Placzek, G.Introduction to the theory of neutron diffusion (U.S. Government Printing Office, 1953).Google Scholar
(6)Case, K. M. and Zweifel, P. F.Linear transport theory (Addison-Wesley, London, 1967).Google Scholar
(7)Chandrasekhar, S.Canad. J. Phys. A 29 (1951), 14.CrossRefGoogle Scholar
(8)Chandrasekhar, S.Radiative transfer (Dover, New York, 1960).Google Scholar
(9)Davison, B.Neutron transport theory (Clarendon Press, Oxford, 1957).Google Scholar
(10)Noble, B.Methods based on the Wiener–Hopf technique (Pergamon Press, London, 1958).Google Scholar
(11)Siewert, C. E. and Burkhart, A. R.Nuclear Sci. Eng. 58 (1975), 253.CrossRefGoogle Scholar
(12)Williams, M. M. R.Mathematical methods in particle transport theory (Butterworth, London, 1971).Google Scholar