Effective medium approximation for hopping conductivity and Josephson junctions

In the framework of self-consistency effective medium approximation, we derive an expression for the effective resistivity of the Miller-Abrahams resistor networks with hopping conductivities, and we compare it with results of numerical simulations of such networks. In our approach we modify the effective medium approximation to include the presence of the Josephson junctions in granular (low- and high- Tc) superconductors.