Abstract
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=\ensuremath{\chi}\ensuremath{\Vert}E${\mathrm{\ensuremath{\Vert}}}^{2\mathrm{\ensuremath{\beta}}}$E (\ensuremath{\beta}>0) in a host medium, where \ensuremath{\chi} 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.
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