Asymptotic analysis of quasi-static transport in high contrast conductive media

We show that transport in high contrast conductive media has a discrete behavior. In the asymptotic limit of infinitely high contrast, the effective impedance and the magnetic field in such media are given by discrete min-max variational principles. Furthermore, we show that the transport problem has an asymptotic, resistor-inductor-capacitor network approximation. We use new variational formulations of the effective impedance of the media, and we assess the accuracy of the asymptotic approximation by numerical computations.