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M. A. Tavel, B. E. Clancy, and G. C. Pomraningt
Nuclear Science and Engineering | Volume 29 | Number 1 | July 1967 | Pages 58-66
Technical Paper | doi.org/10.13182/NSE67-A17810
Articles are hosted by Taylor and Francis Online.
A use of the variational method which has been neglected in reactor theory is discussed. This is the invariance theorem of E. Noether which has been widely utilized in other areas of mathematical physics. Following a derivation of the theorem, its use to obtain solutions of the time-independent diffusion equation is demonstrated. The theorem is used to construct a complete analogy between the time-dependent diffusion process and classical mechanics. Certain “conservation laws” arise in the construction of this analogy and their possible application is discussed. An analogy between the neutron diffusion equation and the time-dependent Schroedinger equation is also given. Several suggestions for generalizations of Noether's theorem for use in reactor theory are made.
