Deviations of High Frequency Conductivity of Disordered Granular Systems from Universality

The real part of high frequency phononless conductivity was calculated in the pair approximation for a disordered array of densely packed spherical nanogranules. The generalization of the theory of phononless conductivity for systems with hydrogenic impurities to the systems with finite size localization centers reveals that the high frequency conductivity depends on the distribution function [Formula: see text] of the distances between the surfaces of granules. This can lead to deviations from the linear frequency dependence of the real part of conductivity [Formula: see text]. In the vicinity of the frequency [Formula: see text] ([Formula: see text] is the pre-exponential factor of the resonance integral) for disordered granular systems, one should expect deviations of [Formula: see text] from universality ([Formula: see text]), associated with weakening of the frequency dependence of [Formula: see text], and its nonmonotonicity. With an increase in the size of the granules, nonmonotonicity of [Formula: see text] is expected at lower frequencies. This stems from a decrease in the pre-exponential factor [Formula: see text] of the resonance integral with an increase in the granule size.

Multi-Dimensional Heterogeneous Resonance Integral Tables Generated for Embedded Self-Shielding Method Towards Irregular Lattices

The concept of multi-dimensional heterogeneous resonance integral tables is proposed. The new type of resonance integral is designed for different fuel pins appearing in one lattice with two extra dimension of optical radius and number density ratio in the fuel. Numerical results show that this treatment improves the accuracy of embedded self-shielding method on irregular lattices.