Browsing by Author "Sancaktar, Selim"

Now showing 1 - 5 of 5
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    Extension of Case formulas to Lp. Application to half and full space problems
    Larsen, E. W.; Sancaktar, Selim; Zweifel, Paul F. (AIP Publishing, 1975-05)
    The singular eigenfunction expansions originally applied by Case to solutions of the transport equation are extended from the space of Hölder‐continuous functions to the function spaces X p = {f‖μf (μ) ‐ L p }, where the expansions are now to be interpreted in the X p norm. The spectral family for the transport operator is then obtained explicitly, and is used to solve transport problems with X p sources and incident distributions.
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    A functional analytic approach to multigroup transport theory
    Sancaktar, Selim (Virginia Polytechnic Institute and State University, 1975)
    A functional Analytic method which was first introduced by Larsen and Habetler for the one-speed isotropic case in 1973 is applied to full and half-space multigroup problems in one dimension with a constant and invertible transfer matrix. The Case-type eigenfunction expansion formulas for the solutions of these problems are explicitly obtained. For the half-space case, the formulas are expressed in terms of two matrices X and Y which provide the Wiener-Hopf factorization of the dispersion matrix. The method applied yields compact results avoiding the calculation of adjoint solutions and normalization integrals to determine the expansion coefficients. Since the method proves to be amenable to further generalization, the case of a degenerate transfer kernel is also considered along the same lines, yielding the expansion formulas for that problem in the full and half-space cases. The expansion formulas are shown to be valid at least for subcritical media, but an extension to critical problems is expected.
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    Multigroup neutron transport. I. Full range
    Bowden, Robert L.; Sancaktar, Selim; Zweifel, Paul F. (AIP Publishing, 1976-01)
    A functional analytic approach to the N_group, isotropic scattering, particle transport problem is presented. A full_range eigenfunction expansion is found in a particularly compact way, and the stage is set for the determination of the half_range expansion, which is discussed in a companion paper. The method is an extension of the work of Larsen and Habetler for the one_group case.
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    Multigroup neutron transport. II. Half range
    Bowden, Robert L.; Sancaktar, Selim; Zweifel, Paul F. (AIP Publishing, 1976-01)
    This paper accompanies a preceding one in which a functional analytic method was used to obtain the full_range expansion in multigoup neutron transport. In the present paper the analysis is extended to obtain the half_range expansion. The method used is an extension of the work of Larsen and Habetler for the one_group case. The results are given in terms of certain matrices which are solutions of coupled integral equations and which factor the dispersion matrix.
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    Solution of multigroup transport equation in Lp spaces
    Greenberg, William; Sancaktar, Selim (AIP Publishing, 1976-11)
    The isotropic multigroup transport equation is solved in L p , p_1, for both half range and full range problems, using resolvent integration techniques. The connection between these techniques and a spectral decomposition of the transport operator is indicated.