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- W4242309052 abstract "for the angular density is developed from the elementary solutions of the transport equation and then specialized to the desired geometry. For problems with plane symmetry, the resulting expression are used directly to determine the expansion coefficients, whereas in spherical and cylindrical geometries the specialization of the three-dimensional solutions yields a variety of representations for the respective angular densities. The second method consists of replacing the angular distributions by suitable density transforms and then determining the transforms completely with the aid of the integral equations for the neutron densities. In plane geometry this method leads to the conversion of the transport equation to a singular integral equation for the angular density. In spherical and cylindrical geometries the appropriate transforms are shown to satisfy separable equations whose solutions can be represented by unique expansions in terms of complete sets of singular expansion modes. The coefficients in the transform expansions are determined by resulting side conditions and the actual neutron distributions established by simple inversions. Although emphasis is on obtaining exact expressions for the neutron distributions and criticality conditions, the results are illustrated by approximate expressions and computations. (auth)" @default.
- W4242309052 created "2022-05-12" @default.
- W4242309052 creator A5072885830 @default.
- W4242309052 date "1967-01-01" @default.
- W4242309052 modified "2023-10-16" @default.
- W4242309052 title "A PROPOSED SOLUTION TO THE ''MATCH'' PROBLEM." @default.
- W4242309052 doi "https://doi.org/10.2172/4508148" @default.
- W4242309052 hasPublicationYear "1967" @default.
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