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Öğe Case’s method for Anlı-Güngör Scattering Formula(2022) Türeci, Recep Gökhan; Bülbül, AhmetCase method is a powerful method in solving one-speed neutron transport equation. The method can be applied to one-speed neutron transport problems and pseudo- geometry problems. The method basis on the usage of Case’s eigenfunctions and the orthogonality relations with the certain boundary conditions according to the interested problem. The scattering effects can be investigated via Mika scattering formula and also İnönü’s scattering formula. In this study Case method’s formalism is derived by using Anlı-Güngör scattering formula as an analogue of Mika’s scattering function. This study is about the Case’s eigenfunctions, normalization relation and the orthogonality properties among these eigenfunctions and, moreover; Case’s eigenfunctions and the orthogonality properties must be rewritten according to the studied scattering order as the number of scattering order increase in Anlı-Güngör scattering formula.Öğe Lineer-Kuadratik Anizotropik Saçılma için Kritiklik Probleminde Yansıtıcı Özdeğerleri(2019) Türeci, Recep GökhanTek-hızlı nötron transport teoride son zamanlarda çalışılan lineer-kuadratik anizotropik saçılma fonksiyonu belirli kritik levha kalınlıkları için yansıtıcı öz değerlerini çözmek amacıyla kullanılır. Lineer-kuadratik anizotropik saçılma özelliği gösteren nükleer materyale sahip bir düzlem reaktör göz önüne alınmıştır ve problem yansıtıcı sınır koşullarını içermektedir. Amaç belirli ikincil nötron sayılarına ve belirli reaktör kalınlıklarına göre yansıtıcı katsayılarını bulmaktır. Sayısal sonuçlar Modified FN yöntemi kullanılarak bulunmuştur.Öğe Machine Learning Applications to the One-speed Neutron Transport Problems(2022) Türeci, Recep GökhanMachine learning is a branch of artificial intelligence and computer science. The purpose of machine learning is to predict new data by using the existing data. In this study, two different machine learning methods which are Polynomial Regression (PR) and Artificial Neural Network (ANN) are applied to the neutron transport problems which are albedo problem, the Milne problem, and the criticality problem. ANN applications contain two different activation functions, Leaky Relu and Elu. The training data set is calculated by using the HN method. PR and ANN results are compared with the literature data. The study is only based on the existing data; therefore, the study could be thought only data mining on the one-speed neutron transport problems for isotropic scattering.Öğe Singüler Özfonksiyonlar Yöntemi ile Lineer-Kuadratik Anizotropik Saçılmalı Yarı-Uzay Albedo Hesaplamaları(2018) Türeci, Recep GökhanBu çalışmada tek-hızlı nötron transport teoride çalışılan lineer-kuadratik anizotropik saçılma fonksiyonu için sonsuz ortam Green fonksyionu elde edilmiş ve yarı-uzay albedo hesaplamaları için Singüler özfonksiyonlar yönteminde kullanılmıştır. Elde edilen sayısal sonuçlar Modified FN (HN) yöntemi sonuçları ile tamamen uyumludur.Öğe Some Numerical Results of the Albedo Problem in Spherical Geometry with Linearly Anisotropic Scattering(Taylor & Francis Inc, 2024) Bozkır, A. Z.; Türeci, Recep Gökhan; 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 Milne Problem for Linear-Triplet Anisotropic Scattering with HN Method(Taylor & Francis Inc, 2022) Gülderen, D.; Şahni, D. C.; Türeci, Recep Gökhan; Aydın, AbdullahThe 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 Milne Problem with the Anli-Gungor Scattering(Taylor & Francis Inc, 2022) Türeci, Recep GökhanRecently developed the Anli-Gungor scattering function is applied to the Milne problem in this study. It is the function of Legendre polynomials with t parameter which can be called as scattering parameter. The extrapolation distance values are calculated for varying t parameters and varying secondary neutron numbers with the H-N method. The numerical results are calculated by 40th approximation in order to get high precision results. The calculated extrapolation distance results are very convergence. Since there is no a similar study for the Milne problem with the Anli-Gungor scattering in the literature, the interpolation technique is applied to the H-N method results. Thus, the isotropic scattering results could be determined by t -> 0 limit.Öğe The singular eigenfunction method: the critical slab problem for linearly anisotropic scattering(Carl Hanser Verlag, 2005) Türeci, Recep Gökhan; Güleçyüz, Mustafa Çetin; Kaskas, A.; Tezcan, C.The critical slab problem for linearly anisotropic scattering is investigated using the singular eigenfunction method. The third form of the transport equation is considered. The singular eigenfunctions for linearly anisotropic scattering are inserted into the Green's function. This Green's function with the full range orthogonality relations of the singular eigenfunctions together with the appropriate boundary conditions provide the criticality equation. This equation is exact and leads as shown in tables to fast converging numerical results.Öğe The Slab Albedo problem with the Anli-Gungor scattering function(Indian Assoc Cultivation Science, 2023) Türeci, Recep GökhanThe 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.
