THE ENHANCED NONLINEAR RESPONSE OF COMPOSITE WIRES - CROSSOVER FROM ONE-DIMENSIONAL TO 3-DIMENSIONAL BEHAVIOR

The effective response is calculated for nonlinear composite wires whi ch are modelled as random nonlinear conductance networks consisting of two different kinds of conductor, with lateral size L and square cros s section of width delta << L. The first kind is nonlinear and obeys a current-voltage (I-V) characteristic of the form I = sigma(1)V+chi(1) V(3), while the second one is linear with I = sigma(2)V. We invoke a r enormalization-group (RG) analysis to rescale the wire repeatedly by s mall-cell transformations to obtain a chain of nonlinear conductors, f or which exact formulas for the effective linear response sigma(e) and nonlinear response chi(e) are available. We calculate sigma(e) and ch i(e) as functions of the volume fraction and examine the dependence on delta. We observe a large enhancement in the nonlinear response as we ll as an interesting crossover from one- to three-dimensional behaviou r as delta increases. Numerical simulations are performed to validate the RG calculations.