The Soviet Journal of Atomic Energy

, Volume 2, Issue 3, pp 277–290 | Cite as

A variational method for homogenizing a heterogeneous medium

  • L. Trlifal


A heterogeneous medium Is homogenized by solving the varlational problem corresponding to the kinetic diffusion equation for monocnergetic neutrons. It is established that the homogenized constants of a heterogeneous medium depend in general on the mutual orientation of the neutron flux density and anisotropy of the heterogeneous medium. As the thickness of the layers which make up the heterogeneous medium approaches zero, the values of the homogenized constants begin not to depend-on the above mutual orientation and become equal to the constants of the corresponding homogeneous mixture. This last conclusion is in contradiction to that of Spinrad [3], However, since in this article the results are obtained by using the kinetic theory (Spinrad [3] used elementary neutron diffusion theory), we may assert that they are more nearly correct.


Anisotropy Flux Density Variational Method Diffusion Equation Neutron Flux 
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Literature cited

  1. [1]
    G. A. Bat and D. F. Zaretsky, Reactor Construction and Theory, Reports of the Soviet Delegation to die International Conference on the Peaceful Uses of Atomic Energy (Acad. Sci. USSR Press, 1955), p. 294.Google Scholar
  2. [2]
    I. M. Ryzhik and I. S. Gradshtein, Tables of lntegrals, Sums, Series, and Derivatives (State Tech. Press. Moscow-Leningrad, 1951). pp. 350, 263, 99.Google Scholar
  3. [3]
    B. I. Spinrad, J. Appl. Phys. 26, 548 (1955).Google Scholar

Copyright information

© Consultants Bureau 1957

Authors and Affiliations

  • L. Trlifal
    • 1
  1. 1.Nuclear Physics InstitutePrague

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