School of Mathematics


The theoretical analysis of neutron wave experiments in the polycrystalline moderators, beryllium oxide and graphite, began historically with the calculation of a fundamental eigenvalue of the system. Following upon the discovery of non-asymptotic modes of wave propagation, theory progressed tm-zards a full determination of the neutron space and energy dependent flux resulting from a sinusoidal source incident upon a semiinfinite spatially homogeneous medium. This development is surveyed in terms of an operator formalism that compactly presents transport and diffusion theory transfer operator solutions and eigenfunction summation solutions for such an idealization of the typical experimental configuration. New material is presented in a demonstration that the transfer operator and eigenexpansion methods can give solutions for a more realistic finite and spatially heterogeneous assembly. It has been found more expedient, however, to include such added experimental detail in a multigroup, finite difference diffusion computer code, MYOPIC. Quantitative conditions on source frequency are established for asymptotic wave propagation in BeO and graphite. Diffusion and thermalization parameters are obtained from asymptotic MYOPIC calculations below the critical frequency and the non-asymptotic propagation systematics above for a homogeneous assembly are compared with other theoretical studies.