SPECTRAL-FUNCTION FOR A CONDUCTING SHEET CONTAINING CIRCULAR INCLUSIONS

The conductivity (or dielectric behavior) of a binary composite system is conveniently expressed in terms of a spectral function, which is d etermined by the geometry of the composite. In this paper we examine t he case of circular inclusions in a conducting sheet and keep terms up to second order in the inclusion concentration f. The two-inclusion p roblem can be solved exactly using multiple images, and we use this so lution to construct the spectral function. We show that the spectral f unction is a truncated Lorentzian that can be calculated in a simple c losed form. Both the weight and the width of the spectral function are linear in f.