Strongly nonlinear response of fractal clusters

We have developed a differential effective medium approximation (DEMA) for the effective nonlinear response due to clustering of a strongly nonlinear conducting material of a current-field (J-E) response of the form J=χ‖E ${\mathrm{\Vert }}^{2\mathrm{\beta }}$ E (β>0) in a host medium, where χ is the nonlinear coefficient. The DEMA results are compared with numerical calculations in a deterministic fractal model. As a similar problem of a random medium, we further investigate the scaling behavior of the nonlinear response. It is shown that by choosing a relevant scaling variable properly, the nonlinear response function can be rescaled to collapse onto a universal curve.