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    Half-Space Albedo Problem with Pure-Triplet Scattering and Legendre Polynomial Outgoing Flux
    (Taylor & Francis Inc, 2022) Bozkir, A. Z.; Sahni, D. C.; Tureci, R. G.
    In this study, the albedo problem is investigated with three different methods, HN method, FN method, and SVD method. The first two methods are used for the comparison of the SVD method results. Therefore, the main aim of this study is to study of the SVD method for albedo problem. The recently improved method is based on usage of the transformation of the integral part to a sum in the one-speed, source free, and homogeneous medium neutron transport equation. This sum term is written with two different ways. One of them is to use midpoint approximation and the second is to use linear approximation. The numerical results of the SVD method are compared with both the HN method and the FN method results. Another different situation of this study is to use a series of the Legendre polynomials for the outgoing flux over the surface.
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    Partial Range Completeness of Case Eigenfunctions and Numerical Solution of Singular Integral Equations of Particle Transport Problems
    (TAYLOR & FRANCIS INC, 2020) Sahni, D. C.; Tureci, R. G.; Bozkir, A. Z.
    We study numerical solution of Singular Integral Equations (SIE) of particle transport theory. We convert them into matrix equations by standard discretization process. It is found that the matrices are highly ill-conditioned and can be solved by Singular Value Decomposition (SVD) method. One expects that matrices resulting from expansions over Partial Range will not be ill-conditioned. We find this is not true though their ill-conditioning is an order of magnitude less than those of full or half range. Reasons for this phenomenon are explained.
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    The Criticality Problem for the Anisotropic Scattering with Two Discrete Eigenvalues
    (Taylor & Francis Inc, 2024) Türeci, R. Gökhan; Bozkir, A. Z.; Sahni, D. C.
    In a recent study, the eigenvalue numbers of Case eigenfunctions were investigated for the situation of anisotropic scattering. The results of this study is applied to the criticality problem. The investigation is performed with two different methods: the singular value decomposition (SVD) method and the HN method. The former was recently improved using the SVD to solve the matrix of the problem, and the latter is based on the usage of the Case method for proper boundary conditions. We have two different eigenvalues for the given number of secondary neutrons and the scattering parameter. Either these eigenvalues are both complex, or one is complex and one is real. The investigation is to show the effect of the second eigenvalues over the critical thickness values.