Interrelationships between the relaxation-time distribution function and the spatial-density function of a metal–dielectric heterogeneous mixture

Abstract

The spatial-density function which characterizes how metal particles are embedded in a dielectric host medium, and which is used in calculating the effective permittivity of the mixture according to the theory of Bergman, can be simply related to the relaxation-time distribution function which describes the frequency dependence of the permittivity of the mixture. The direct and inverse formulae, for computing one from the other are given explicitly. New basic functions can consequently be proposed to expand spatial-density functions.