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The transport equation of radiative transfer with isotropic scattering

The solution of the auxiliary equation by a Green's function method

Published online by Cambridge University Press:  24 October 2008

G. E. Hunt
G. E. Hunt
Affiliation:
S.R.C. Atlas Computer Laboratory, Chilton, Didcot, Berks.
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Abstract

The kernel of the integral equation for the source function in a three-dimensional homogeneous atmosphere possesses the properties of a Green's function. These properties are used to transform the integral equation into a singular integral equation for the kernel. The particular case of a homogeneous plane parallel atmosphere is discussed and a solution to the kernel equation is obtained at all points of the atmosphere.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 1 , January 1969 , pp. 199 - 208
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Busbridge, I. W.Mathematics of radiative transfer (Cambridge University Press, 1960).Google Scholar
(2)Busbridge, I. W.On the X and Y functions of Chandrasekhar. Astrophys. J. 122, 2 (1965), 327–348.Google Scholar
(3)Chandrasekhar, S.Radiative transfer (Dover, 1960).Google Scholar
(4)Chandrasekhar, S. and Elbert, D.The X and Y functions for isotropic scattering. Astrophys. J. 115 (1952), 269–278.CrossRefGoogle Scholar
(5)Carlstedt, J. L. and Mullikin, T. W.Chandrasekhar's X and Y functions. Astrophys. J. Supp. Series 12 (1966), 449–586.CrossRefGoogle Scholar
(6)Hunt, G. E.The transport equation of radiative transfer in a three dimensional atmosphere with anisotropic scattering. J. Inst. Math. Appl. 3 (1967), 181–192.Google Scholar
(7)Hunt, G. E.The transport equation of radiative transfer with axial symmetry. J. Soc. Indust. Appl. Math. 16 (1968), 228–237.Google Scholar
(8)Leonard, A. and Mullikin, T. W.Green's functions for one velocity neutron transport in one dimensional slab and sphere. Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 683–688.CrossRefGoogle ScholarPubMed
(9)Mayers, D. F.Calculation of Chandrasekhar's X and Y functions for isotropic scattering. Monthly Notices Roy. Astronm. Soc. 123 (1962), 471–484.Google Scholar
(10)Mullikin, T. W.A complete solution of the X and Y functions of Chandrasekhar. Astrophys. J. 136 (1962), 627–635.Google Scholar
(11)Mullikin, T. W.Non-linear equations of radiative transfer in ‘nonlinear integral equations’, ed. Anselone, P. M. (University of Wisconsin Press, 1964).Google Scholar
(12)Mullikin, T. W.Chandrasekhar's X and Y functions. Trans. Amer. Math. Soc. 113 (1964), 316–332.Google Scholar
(13)Sobolev, V. V.A treatise on radiative transfer (Van Nostrand, 1963).Google Scholar
(14)Sobouti, Y.Scattering and transmission of fluorescent radiation from planetary atmospheres. II. Astrophys. J. 135, (1962), 938.CrossRefGoogle Scholar
(15)Sobouti, Y.Chandrasekhar's X, Y and related functions. Astrophys. J. Suppl. Series. 7 (1963), 411–560.CrossRefGoogle Scholar
(16)Bellman, R., Kagiwada, H., Kalaba, R. and Ueno, S.Numerical results for Chandrasekhar's X and Y functions of radiative transfer. J. Quant. Spectrosc. Radiat. Transfer. 6 (1966), 479–500.Google Scholar