Effective nonlinear response of fractal clusters

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Abstract
The enhancement in the effective response due to clustering of a nonlinear material in a host medium is demonstrated in an exactly solvable fractal model. We calculate the effective nonlinear response of a fractal cluster embedded in a hierarchical lattice. The results show that a large enhancement in the nonlinear response is found for the case of a nonlinear fractal embedded in a linear host and when the linear host is the better conductor.