Papers by mustafa güleçyüz
Indian Journal of Physics, 2019
The solution of the Milne problem is studied by one-speed neutron transport equation in plane geo... more The solution of the Milne problem is studied by one-speed neutron transport equation in plane geometry with I ˙no ¨nu ¨'s scattering kernel, which is known as a linear combination of the forward, backward and isotropic scattering kernel (FBIS kernel). The solution of the neutron transport equation with I ˙no ¨nu ¨'s scattering kernel can be written in terms of the solution of the neutron transport equation for isotropic scattering case. The extrapolation distance is calculated with modified F N (or H N ) method. The numerical values of the extrapolation distance are obtained depending on the secondary neutron numbers and anisotropy coefficients and compared with the available data in the literature values.
TURKISH JOURNAL OF PHYSICS, 2017
The Milne problem, known as one of the classical problems of radiative transfer and neutron trans... more The Milne problem, known as one of the classical problems of radiative transfer and neutron transport theory, is solved using the P N method for a nonabsorbing medium (c = 1) with a linearly anisotropic scattering kernel. Specular and diffuse reflection boundary conditions are taken into account. The numerical results are listed for different selected parameters. Some results are also compared with the literature.
DergiPark (Istanbul University), Aug 1, 2017
The Milne problem, known as one of the classical problems of radiative transfer and neutron trans... more The Milne problem, known as one of the classical problems of radiative transfer and neutron transport theory, is solved using the P N method for a nonabsorbing medium (c = 1) with a linearly anisotropic scattering kernel. Specular and diffuse reflection boundary conditions are taken into account. The numerical results are listed for different selected parameters. Some results are also compared with the literature.
Journal of Quantitative Spectroscopy and Radiative Transfer, 1996
In a new approach of solving the third form of the transport equation, one should consider and co... more In a new approach of solving the third form of the transport equation, one should consider and compare the two methods C, and FN. Both of the methods depend on the use of Green's function. In C, method the Green's function obtained by the Fourier-transform technique is used to solve the system of integral equations which is provided at the boundary of the various media. In FN method which is a modified version of C, method. The Green's function in terms of singular eigenfunctions is used to solve the integro-differential form of the Boltzmann equation. In our approach we use the Green's function of FN method to solve C, equations. That is Green's function in terms of singular eigenfunctions is used to solve the system of integral equations of C, method. As in FN method this approach yields simple analytical equations that can be solved numericaly even more efficiently than the C, method and the convergence of the numerical results is faster than the numerical results of FN method.
Journal of Quantitative Spectroscopy and Radiative Transfer, 2004
The recently developed HN method is used to solve the critical slab problem for a slab which is s... more The recently developed HN method is used to solve the critical slab problem for a slab which is surrounded by a reflector. In the special case for R=0 (the reflection coefficient) the problem reduces to the one under vacuum boundary conditions. It is shown that the method is concise and leads to fast converging numerical results. The presented numerical results
Journal of Quantitative Spectroscopy and Radiative Transfer, 1999
ABSTRACT The albedo and the transmission factor for slabs for extremely anisotropic scattering ar... more ABSTRACT The albedo and the transmission factor for slabs for extremely anisotropic scattering are calculated. The solution of the problem is obtained using a new approach; that is the solution of the third form of the transport equation using the singular eigenfunctions of the method of elementary solutions. This approach leads simple equations for solving numerically when compared with CN method and also leads the convergence of the numerical results to be faster than that of the other methods in literature (i.e. FN-method).
Indian Journal of Physics, 2017
The Milne problem is studied in one speed neutron transport theory using the linearly anisotropic... more The Milne problem is studied in one speed neutron transport theory using the linearly anisotropic scattering kernel which combines forward and backward scatterings (extremely anisotropic scattering) for a non-absorbing medium with specular and diffuse reflection boundary conditions. In order to calculate the extrapolated endpoint for the Milne problem, Legendre polynomial approximation (P N method) is applied and numerical results are tabulated for selected cases as a function of different degrees of anisotropic scattering. Finally, some results are discussed and compared with the existing results in literature.
... [34] C. Tezcan and C. Yıldız, Il Nuova Cimento, 106, 999 (1993). [35] A. Sharma, SD Pranjape,... more ... [34] C. Tezcan and C. Yıldız, Il Nuova Cimento, 106, 999 (1993). [35] A. Sharma, SD Pranjape, A. Kumar and SR Dwivedi, Ann. Nucl. Energy, 21, 267 (1994). [36] GI Bell and S. Glasstone, Nuclear Reactor Theory, Van Nostrand-Reinhold, New York, NY (1972). ...
A synthetic model for the scattering phase function is used to develop simple algebraic equations... more A synthetic model for the scattering phase function is used to develop simple algebraic equations, valid for any water type, for evaluating the ratio of the backscattering to absorption coefficients of spatially uniform, very deep waters with data from upward and downward planar irradiances and the remotely sensed reflectance. The phase function is a variable combination of a forward-directed Dirac delta function plus isotropic scattering, which is an elementary model for strongly forward scattering such as that encountered in oceanic optics applications. The incident illumination at the surface is taken to be diffuse plus a collimated beam. The algorithms are compared with other analytic correlations that were previously derived from extensive numerical simulations, and they are also numerically tested with forward problem results computed with a modified FN method.
Kerntechnik, 2007
H N and singular eigenfunction methods[1,2,3] are used to determine the neutron distribution ever... more H N and singular eigenfunction methods[1,2,3] are used to determine the neutron distribution everywhere in a source-free half space with zero incident flux for a linearly anisotropic scattering kernel. The singular eigenfunction expansion of the method of elementary solutions is used. The orthogonality relations of the discrete and continuous eigenfunctions for linearly anisotropic scattering provides the determination of the expansion coefficients. Four different expansions of the exit distribution are used, these are; the expansion in powers of µ, the expansion in terms of Legendre polynomials and the expansion in powers of 1/(1+µ). Results are compared. In the second part of our work, third form of the transport equation and the infinite medium Green function are used.
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Papers by mustafa güleçyüz