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On eigensolutions of the one-speed neutron transport equation in plane geometry

Published online by Cambridge University Press:  17 February 2009

Nassar H. S. Haidar
Nassar H. S. Haidar
Affiliation:
Lebanese NCSR Nuclear Research Centre and Department of Mathematics, American University of Beirut, Lebanon.
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Abstract

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We revisit the singular eigensolution to the steady state one-speed transport equation for an isotropically scattering and multiplying heterogeneous slab. It is proved that this solution is a sum of Stieltjes integrals over the resolvent set of only the operator of multiplication by the angular variable.

Type
Research Article
Information
The ANZIAM Journal , Volume 32 , Issue 2 , October 1990 , pp. 223 - 230
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Bartle, R. G., The elements of real analysis (Wiley, New York, 1964).Google Scholar
[2]Bell, G. I. and Glasstone, S., Nuclear reactor theory (Van Nostrand Reinhold, New York, 1970).Google Scholar
[3]Bilenko, V. I., “Applying summator operators to the computer solution of integrodiffer-ential equation of radiation transfer” Sov. J. Atom. Energy 53 (1982) 800–803.CrossRefGoogle Scholar
[4]Case, K. M. and Zweifel, P. F., Linear transport theory (Addison-Wesley, Massachusetts, 1967).Google Scholar
[5]Garabedian, P. R., Partial differential equations (Wiley, New York, 1964).Google Scholar
[6]Garcia, R. D. M. and Siewert, C. E., “Multislab multigroup transport theory with Lth order anisotropic scattering”, J. Comput. Phys. 50 (1983) 181–192.CrossRefGoogle Scholar
[7]Haidar, N. H. S., “A coordinate transform method for one-speed neutron transport in composite slabs”, J. Phys. D: Appl. Phys 21 (1988) 1543–1549.CrossRefGoogle Scholar
[8]Kaper, H. G., Lekkerkerker, C. G. and Hejtmanek, J., Spectral methods in linear transport theory (Birkhauser Verlag, Basel, 1982).Google Scholar
[9]Kikuta, T., “Extensions of variational methods, I. Super-stationary variational method”, Prog. Theor. Phys. 14 (1955) 457–472.CrossRefGoogle Scholar
[10]Kriese, J. T., Siewert, C. E. and Yener, Y., “Two-group critical problems for slabs and spheres in neutron-transport theory”, Nucl. Sci. Eng. 50 (1973) 3–9.CrossRefGoogle Scholar
[11]Lemanska, M., “On the analytic solutions of the monoenergetic neutron transport equation for slab geometry”, J. Appl. Math. Phys. 30 (1979) 655–661.Google Scholar
[12]Pahor, S. and Shultis, J. K., “Half-space general multigroup transport theory”, J. Nucl. Energy 23 (1969) 477–493.CrossRefGoogle Scholar
[13]Smirnov, V. I., A course of higher mathematics, Vol. 5 (Pergamon Press, Oxford, 1964).Google Scholar
[14]Siewert, C. E. and Benoit, P., “Multigroup transport theory, I. Basic analysis”, Nucl. Sci. Eng. 78 (1981) 311–314.CrossRefGoogle Scholar
[15]Weinberger, H. F., Variational methods for eigenvalue approximation (SIAM, Philadelphia, 1974).CrossRefGoogle Scholar
[16]Williams, M. M. R., Mathematical methods in particle transport theory (Wiley Inter-science, London, 1971).Google Scholar