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- W2150001453 abstract "Abstract A method has been developed to solve the neutron transport equation in multi-dimensional convex and homogenous assemblies with linearly anisotropic scattering. The method consists of solving the Fourier transformed integral transport equations for flux and partial currents and is a generalization of the method developed by Sahni (1972) to treat the one group criticality problem for multi-dimensional geometries. The kernels of the transformed integral equations get factorized into components depending on only one of the dimensions of the assembly. These factorized kernels in each of the dimensions are then decomposed into their respective degenerate forms involving suitable spherical Bessel functions. The transformed flux and partial currents are expanded in a series of products of suitable spherical Bessel functions commensurate with the symmetry and dimensionality of the problem, which can be truncated after very few terms. The one group criticality problem is then converted into the eigenvalue problem of a matrix equation of finite order. The order of this matrix depends upon the truncation order of the transformed flux and partial currents; on the other hand the matrix elements themselves do not depend upon the order of truncation. A striking similarity between one group criticality problem of an infinite rectangular prism of dimensions 2 a and 2 b along x and y directions and a finite cylinder of diameter 2 R and height 2 H is brought out, as far as the structure of their matrix equations and calculational procedure of their general matrix elements is concerned. Some results of the criticality problems of the infinite rectangular prism and the finite cylinder are tabulated." @default.
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- W2150001453 date "1981-01-01" @default.
- W2150001453 modified "2023-09-27" @default.
- W2150001453 title "Integral transform method for solving multi-dimensional neutron transport problems with linearly anisotropic scattering" @default.
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- W2150001453 doi "https://doi.org/10.1016/0306-4549(81)90079-7" @default.
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