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Path Integral Approach to Strongly Nonlinear Composite

Marc Barthelemy
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Abstract

We study strongly nonlinear disordered media using a functional method. We solve exactly the problem of a nonlinear impurity in a linear host and we obtain a Bruggeman-like formula for the effective nonlinear susceptibility. This formula reduces to the usual Bruggeman effective medium approximation in the linear case and has the following features: (i) It reproduces the weak contrast expansion to the second order and (ii) the effective medium exponent near the percolation threshold are $s=1$, $t=1+κ$, where $κ$ is the nonlinearity exponent. Finally, we give analytical expressions for previously numerically calculated quantities.

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Marc Barthelemy. 2000-05-29. Path Integral Approach to Strongly Nonlinear Composite. https://doi.org/10.1103/physrevb.62.8576

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