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- W2080615570 abstract "Previous calculations on the eigenvalue spectrum of the one-speed transport equation for two-region slabs and spheres are generalized. The criticality problem is investigated in c 1 ⊗ c 2 , where −∞ ≤ c 1 ≤ ∞ and −∞ ≤ c 2 ≤ ∞ are the criticality factors in the respective regions. The eigenvalue spectrum consists of non-intersecting, continuous lines on the ( c 1 , c 2 ) plane. The structure of the c -map (the aggregate of such eigenvalue curves) is investigated. It is shown that at some discrete, finite values of c 1 > 1, c 2 diverges to −∞, and Φ 2 vanishes (and vice versa for c 1 and Φ 1 at certain c 2 values). Oscillating properties and completeness of the eigenfunction sets along different lines c 2 = ξc 1 on the c-map are discussed, and some theorems about completeness are proven rigorously for different values of ξ. Finally, some time eigenvalues are calculated and compared with the c -eigenvalues." @default.
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- W2080615570 date "1992-01-01" @default.
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- W2080615570 title "Generalization of the eigenvalue problem of the one-speed neutron transport equation in two-region" @default.
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- W2080615570 doi "https://doi.org/10.1016/0149-1970(92)90009-r" @default.
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