PERCOLATION EFFECTS IN 2-COMPONENT STRONGLY NONLINEAR COMPOSITES - UNIVERSAL SCALING BEHAVIOR

We have studied the effective nonlinear response of a class of strongly nonlinear conducting composite media which obey a current field (J-E) relation of the form J = chi\E\(2 beta)E, where chi is the nonlinear coefficient and beta > 0. We consider a d-dimensional, two-component strongly nonlinear composite in which a volume fraction p of nonlinear material of coefficient chi(i) is randomly embedded in a host medium of volume fraction q of chi(m) (p+q = 1). We examine the normal conductor-insulator (N/I) composite (chi(m) = 0) and the superconductor-normal conductor (S/N) composite (chi(m) = infinity). Near the percolation threshold (p(c) or q(c)), the effective nonlinear response behaves as chi(e) approximate to (p-p(c))(t) for the N/I limit while chi(e) approximate to (q, - q)(-s) for the S/N limit. We summarize various estimates of the critical exponents t(beta) and s(beta) and discuss a more general duality relation in two dimensions. For a finite chi(m)/chi(i), we propose various scaling relations for chi(e). The effective nonlinear response is calculated in the effective-medium approximation and numerical simulations. The scaling functions are extracted and the exponents are determined and compared to proposed scaling forms; excellent agreement is found.