Critical currents and voltages in weakly nonlinear inhomogeneous media

A random mixture of two components is considered. It is assumed that both t hese components have current-voltage characteristics which contain weak non linear terms of a power-law type. General results for the effective nonline ar susceptibility as well as for critical current and voltage, defined as t he crossovers from linear to nonlinear behaviour are obtained, both above a nd below the percolation threshold. They agree with the results obtained pr eviously for some less general composites. New results for the mixture of ' nonlinear insulator' + 'linear metal' are found. All these results are vali d in the low-field limit. For larger fields it is shown that the exponent x describing the scaling of critical current as a function of conductance ob eys the relation: x less than or equal to (d - 1)nu/t for a random metal-in sulator composite and x greater than or equal to 1 - nu/q for a superconduc tor-normal conductor composite (d is dimensionality, nu is the percolation correlation length exponent and t and q are conductivity critical exponents for metal-insulator and superconductor-normal conductor percolation, respe ctively).