Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T16:59:45.888Z Has data issue: false hasContentIssue false
  • English
  • Français

On Combined Operational Method for Transfer Problems in Homogeneous, Spherical Media

Published online by Cambridge University Press:  12 April 2016

T. H. Kho  and
K. K. Sen
T. H. Kho
Affiliation:
Department of Mathematics, University of Singapore, Singapore
K. K. Sen
Affiliation:
Department of Mathematics, University of Singapore, Singapore

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, the Combined Operational Method developed by Busbridge (1961) in connection with the radiative transfer problems in plane-parallel atmospheres has been extended to similar problems in isotropic scattering, homogeneous spherical media. The relevant auxiliary equation has been formulated, the scattering function defined and the integro-differential equation for such function deduced. For a medium having radial distribution of source in addition to the incident flux at the outer surface, the integro-differential equations for source function and emergent intensity have been established.

Type
Research Article
Information
International Astronomical Union Colloquium , Volume 10: Gravitational N-Body Problem , November 1971 , pp. 223 - 242
Copyright
Copyright © Reidel 1971

References

Bailey, P. B.: 1964, J. Math. Anal. Appl. 8, 144.CrossRefGoogle Scholar
Bailey, P. B. and Wing, G. M.: 1964, J. Math. Anal. Appl. 8, 170.CrossRefGoogle Scholar
Bellman, R. and Kalaba, R.: 1956, Proc. Nat. Acad. Sci. 42, 629.CrossRefGoogle Scholar
Bellman, R., Kalaba, R., and Prestrud, M.: 1963, Invariant Imbedding and Radiative Transfer in Slabs of Finite Thickness American Elsevier Publ. Co., New York.Google Scholar
Bellman, R., Kagiwada, H., Kalaba, R., and Ueno, S.: 1966, RM-5402-PR-RAND External Publ. Google Scholar
Bellman, R., Kagiwada, H., Kalaba, R., and Ueno, S.: 1968, J. Math. Rhys. 9, 909.CrossRefGoogle Scholar
Bellman, R., Kagiwada, H., Kalaba, R., and Ueno, S.: 1969, Icarus 11, 417.CrossRefGoogle Scholar
Busbridge, I. W.: 1955, Quart. J. Math., Oxford 2, 6, 218.CrossRefGoogle Scholar
Busbridge, I. W.: 1955, Monthly Notices Roy. Astron. Soc. 115, 521; 1956, Monthly Notices Roy. Astron. Soc. 116, 304; 1957, Monthly Notices Roy. Astron. Soc. 117, 516.CrossRefGoogle Scholar
Busbridge, I. W.: 1960, The Mathematics of Radiative Transfer, Cambridge University Press, Cambridge.Google Scholar
Busbridge, I. W.: 1961, Astrophys. J. 133, 198.CrossRefGoogle Scholar
Cuperman, S., Engelmann, F., and Oxenius, J.: 1963, Phys. Fluids, 6, 108.CrossRefGoogle Scholar
Germogenova, T. A.: 1966, Astrophyzika 2, 251.Google Scholar
Hopf, E.: 1934, Mathematical Problems of Radiative Equilibrium (Cambridge Tracts, No. 31).Google Scholar
Kourganoff, V., and Busbridge, I. W.: 1952, Basic Methods of Transfer Problem, Oxford.Google Scholar
Leong, T. K. and Sen, K. K.: 1968, Ann. Astrophys. 31, 467.Google Scholar
Leong, T. K. and Sen, K. K.: 1969, Publ. Astron. Soc. Japan 21, 167.Google Scholar
Leong, T. K. and Sen, K. K.: 1970, Publ. Astron. Soc. Japan 22, 57.Google Scholar
Rybicki, G. B.: 1970, J. Comp. Phys. 6, 131.CrossRefGoogle Scholar
Sobolev, V. V.: 1963, A Treatise of Radiative Transfer, Van Nostrand, New York.Google Scholar
Tsujita, J.: 1967, Publ. Astron. Soc. Japan 19, 468.Google Scholar
Ueno, S.: 1957, Astrophys. J. 126, 413.CrossRefGoogle Scholar
Ueno, S.: 1958, J. Math. Mech. 7, 629.Google Scholar
Ueno, S.: 1959, Ann. Astron. 22, 468 and 484.Google Scholar
Ueno, S.: 1960, Astrophys. J. 132, 729.CrossRefGoogle Scholar
Ueno, S., Kagiwada, H., and Kalaba, R.: 1969, The Rand Corporation Research Memorandum, RM-6061-PR.Google Scholar
Uesugi, A., and Tsujita, J.: 1969, Publ. Astron. Soc. Japan 21, 370.Google Scholar