Thin cylindrical conductivity inclusions in a three-dimensional domain: A polarization tensor and unique determination from boundary data

We consider a three-dimensional conductor containing an inclusion that can be represented as a cylinder with a fixed axis and a small basis. As the size of the basis of the cylinder approaches zero, the voltage perturbation can be described by means of a polarization tensor. We give an explicit characterization of the polarization tensor of cylindrical inclusions in terms of the polarization tensor of its base, and we use this result to show that the axis of the inclusion can be uniquely determined by boundary values of the voltage perturbation. We also present a reconstruction algorithm and some numerical simulations.