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 innnitely high contrast, the eeective impedance and the magnetic eld 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 eeective impedance of the media and we assess the accuracy of the asymptotic approximation by numerical computations.