Browsing by All Authors "Tezcan, C."

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    The critical slab problem for linearly anisotropic scattering with the HN method
    (Azerbaijan National Academy of Sciences Institute of Radiation Problems ve Turkish Atomic Energy Authority, 2006) Tezcan, C.; Bölüm Yok
    Hn method, is used to calculate the critical slab problem for linearly anisotropic scattering. HN method is a combination of CN, FN and the method of elementary solutions. In CN method; the integral equations of the Fredholm type, that is; the third form of the transport equation has been used. The integral equations mentioned above have been related with the angular flux at the boundary of the given medium. They have been expressed in terms of the infinite medium Green function. Infinite medium Green function has been obtained by the Fourier transform technique. In FN method; the integro-differential form of the linear transport equation has been used, the values of eigenvalues have been selected. This selection has been based on an equal spacing scheme for choosing the first two eigenvalues as (v0,l) and the remaining eigenvalues have been spaced equally in interval (0,1). In Hn method, the integro-differential form of the transport equation has been used as in FN method, the eigenvalues have been calculated using the normalization condition of the eigenfunctions and a different numerical procedure has been considered. In this procedure the expansion of the angular flux ju) in terms of the eigenfunctions of the method of elementary solutions and their orthogonality relations have been used. In our work we have used HN method. We consider the angular flux Ψ(a, µ), -1 ≤ µ ≤ 1 at one of the boundaries of the slab together with the entering flux Ψ(a, -µ), 0 ≤ µ ≤ 1. Then, we multiply the angular flux Ψ(a, µ) with the singular eigenfunctions and integrate over µ Ɛ(-1, +1), to calculate the expansion coefficients in Ψ (x, µ) Here the orthogonality relation of the singular eigenfunctions of the method of elementary solutions are used. After obtaining these coefficients we consider the entering angular flux Ψ(a, -µ), 0 ≤ µ ≤ 1. We multiply this equation with µ m+1 and integrate over 0 ≤ µ ≤. Thus we get a system of linear algebraic equations. Therefore replacing the appropriate coefficients into the linear algebraic equations the final critically condition is obtained. It is shown that the method leads to concise equations and accurate numerical results even in the lowest order of approximations.
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    The critical slab problem for reflecting boundary conditions with the H(N) method
    (Institute of Nuclear Physics of Uzbekistan Academy of Science, Turkish Atomic Energy Authority, 2006) Tezcan, C.; 4130; Bölüm Yok
    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 coefficients) 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 are given in tables and compared with the data available in literature.
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    The critical slab problem for reflecting boundary conditions with the Hn method
    (Türkiye Atom Enerjisi Kurumu, TÜDNAEM, 2004) Tezcan, C.; Bölüm Yok
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    The singular eigenfunction method: the milne problem for isotropic and extremely anisotropic scattering
    (Turkish Atomic Energy Authority, 2000-10) Kaşkaş, A.; Güleçyüz, M. Ç.; Erdoğan, F.; Tezcan, C.; 4180; Bölüm Yok
    In the CN method of solving the third form of the transport equation, the medium as a result of Placzek lemma is extend to infinity. Infinite medium Green function which is obtained by the Fourier transform technique is used and the method is applied to one velocity problems in plane and cylindrical geometries. As the result of physical applications of the CN method in different geometries, it is seen that the only difficulty lies in writting the expression of the Green’s function in a form easy to handle. In the new method of solving of the third form of the transport equation (that we have generated recently), three methods, namely, CN, FN and the method of elementary solutions are considered, compared and the Green function in terms of the singular eigenfunctions is used. This method yields simple analytical expressions that can be solved numerically more efficiently than the CN method because the expression of the Green function is in the form easy to handle. Here this new method is applied to calculate the extrapolation length for the Milne problem which is classical problem in astrophysics concerned with the diffusion of radiation through a stellar atmosphere for both isotropic and extremely anisotropic scatterings. It is shown that the numerical results which are tabulated for selected cases are accurate even in the approximations of the lowest order and are in good agreement with the numerical results obtained by the other methods.