A variational method for homogenizing a heterogeneous medium
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 , However, since in this article the results are obtained by using the kinetic theory (Spinrad  used elementary neutron diffusion theory), we may assert that they are more nearly correct.
KeywordsAnisotropy Flux Density Variational Method Diffusion Equation Neutron Flux
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