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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.