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Öğe Albedo and constant source problems for extremely anisotropic scattering(Carl Hanser Verlag, 2013) Kocmen, M. A.; Tegmen, A.; Tureci, D.; Gulecyuz, M. C.; Tureci, R. G.The half-space albedo problem and the constant source problem have been solved for a combination of the linearly anisotropic scattering and Inonu's scattering functions. The linear transport equation for extremely anisotropic scattering kernel can be converted into an equivalent equation with a linearly anisotropic scattering kernel and the modified F-N method can be used for albedo calculations.Öğe The critical slab problem for pure-triplet anisotropic scattering by singular eigenfunction method(Carl Hanser Verlag, 2017) Tureci, R. G.; Tureci, D.The infinite medium Green function can be written by using the jump condition, found Case's eigenfunctions. Thus, any reactor theory problem which is inplane geometry such the criticality problem as can be investigated by using the proper boundary conditions and suggested flux definitions. By using the criticality equation the critical thicknesses can be calculated as numerically. The selected numerical results can be tabulated.Öğe Discrete Eigenvalues of Case Spectrum with Anisotropic Scattering(Taylor & Francis Inc, 2018) Sahni, D. C.; Tureci, R. G.Discrete eigenvalues of a one-speed linear transport equation with anisotropic scattering are studied. It is shown that there is only one pair of real discrete eigenvalues for linear, quadratic, or triplet scattering for a nonmultiplicative medium. For a multiplicative medium there is one imaginary pair of eigenvalues or at most four eigenvalues. These can form one real and one imaginary pair, two imaginary pairs, or a quartet. The range of parameters for these different situations is derived analytically. These are then supported by numerical results that are tabulated in tables for each type of scattering.Öğe Half-space albedo problem for Inonu, linear and quadratic anisotropic scattering(Korean Nuclear Soc, 2020) Tureci, R. G.This study is concerned with the investigation of the half-space albedo problem for "Inonu-linearquadratic anisotropic scattering" by the usage of Modified FN method. The method is based on Case's method. Therefore, Case's eigenfunctions and its orthogonality properties are derived for anisotropic scattering of interest. Albedo values are calculated for various linear, quadratic and inonu anisotropic scattering coefficients and tabulated in Tables. (C) 2019 Korean Nuclear Society, Published by Elsevier Korea LLC.Öğe Half-space albedo problem with modified F-N' method for linear and quadratic anisotropic scattering(Carl Hanser Verlag, 2017) Tureci, R. G.; Tureci, D.One speed, time independent and homogeneous medium neutron transport equation can be solved with the anisotropic scattering which includes both the linear anisotropic and the quadratic anisotropic scattering properties. Having solved Case's eigenfunctions and the orthogonality relations among these eigenfunctions, some neutron transport problems such as albedo problem can be calculated as numerically by using numerical or semi-analytic methods. In this study the half-space albedo problem is investigated by using the modified F-N method.Öğe 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.Öğe Original The critical slab problem with the Anli-Gungor scattering function(Korean Nuclear Soc, 2023) Tureci, R. G.The criticality problem in this study is studied with the recently investigated the Anli-Gungoeuror scattering function. The scattering function depends on the Legendre polynomials as the Mika scattering function, but it includes only one scattering parameter, t, and its orders. Both Mika and Anli-Gungoeuror scattering are the same for only linear anisotropic scattering. The difference appears for the quadratic scattering and further. The analytical calculations are performed with the HN method, and the numerical results are calculated with Wolfram Mathematica. Interpolation technique in Mathematica is also used to approx-imate the isotropic scattering results when t parameter goes to zero. Thus, the calculated results could be compared with the literature data for isotropic scattering. (c) 2023 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Öğe 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.Öğe Slab albedo for linearly and quadratically anisotropic scattering kernel with modified F-N method(Carl Hanser Verlag, 2017) Tureci, R. G.; Tureci, D.One speed, time independent and homogeneous medium neutron transport equation is solved with the anisotropic scattering which includes both the linearly and the quadratically anisotropic scattering kernel. Having written Case's eigenfunctions and the orthogonality relations among of these eigenfunctions, slab albedo problem is investigated as numerically by using Modified F-N method. Selected numerical results are pesented in tables.Öğe The Slab Albedo Problem for Pure-Triplet Anisotropic Scattering by Singular Eigenfunction Method(Amer Inst Physics, 2017) Tureci, D.; Tureci, R. G.One-speed, time independent and homogenous medium neutron transport equation can be solved by using pure-triplet anisotropic scattering. This solution bases on finding the Case's eigenfunctions and the orthogonality relations of these eigenfunctions. The infinite medium Green function can be written by using the jump condition after finding Case's eigenfunctions. The slab albedo problem can be investigated as numerical by using suggested solutions over surfaces with the singular eigentimetion method which bases on the infinite medium Green function. The selected numerical results can be tabulated.Öğe Some Numerical Results of the Albedo Problem in Spherical Geometry with Linearly Anisotropic Scattering(Taylor & Francis Inc, 2024) Bozkir, A. Z.; Tureci, R. G.; Sahni, D. C.We examine the effect of linear anisotropic scattering on the solution of spherical geometry transport problems. We consider the albedo problem of a solid homogeneous sphere with linearly anisotropic scattering and write two matrix equations to solve the albedo problem with the HN and SVD methods in pseudo slab geometry. These methods are based on Case method of singular eigenfunctions. The numerical results of both methods are in agreement with each other.Öğe The Criticality Problem for the Anisotropic Scattering with Two Discrete Eigenvalues(Taylor & Francis Inc, 2024) Tureci, R. G.; 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.Öğe The Milne Problem for Linear-Triplet Anisotropic Scattering with HN Method(Taylor & Francis Inc, 2022) Gulderen, D.; Sahni, D. C.; Tureci, R. G.; Aydin, A.The Milne problem is investigated for the linear-triplet anisotropic scattering with H-N method in this study. The scattering function is the linear combination of linear anisotropic scattering and triplet anisotropic scattering in Mika's scattering. The positivity condition is needed to find physical results since the scattering function defines the scattering probabilities. It defines the relationship between the scattering coefficients. H-N method is based on using the Case method. Therefore, properties of the Case method should be derived for the scattering function. The linear anisotropic scattering is the dominant scattering according to the calculated results.Öğe The Slab Albedo problem with the Anli-Gungor scattering function(Indian Assoc Cultivation Science, 2023) Tureci, R. G.The slab albedo problem is investigated here for the Anli-Gungor scattering function with its quadratic term. The scattering is the function of Legendre polynomials, and it includes t scattering parameter. The analytical calculations are performed with HN method, and the numerical results are calculated using Wolfram Mathematica software. The interpolation technique is applied to the calculated results in this study. Thus, the results are compared with the literature data when t parameter goes to zero. A second comparison is performed for the linear-quadratic Mika anisotropic scattering function and the quadratic Anli-Gu spexpressioncing diexpressioneresis ngo spexpressioncing diexpressioneresis r scattering function. Both scattering functions give the same results under the certain situations. These situations are also investigated.
