### Abstract

We present numerical simulations of AC conductance for a random resistorcapacitor network. The conductance obeys a probability density function p(g)∝g^{−α}(0<α<1). We use a highly efficient propagation algorithm to calculate the effective conductance of a long strip of a lattice. At low frequencies, we find that for the concentration p of conducting bonds less than the percolation threshold pc, the imaginary part of conductance is proportional to frequency Im(g_{eff})≃ω and the real part of conductance shows an anomalous frequency dependence Re(g_{eff})≃ω^{2−α}. The results of simulations in such a continuum system are in agreement with the predictions of the effective medium and the Maxwell-Garnett approximation. We also calculate the non-universal DC conductivity exponents in continuum percolation; the result are consistent with earlier theoretical predictions and numerical calculations.

Original language | English (US) |
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Pages (from-to) | L949-L953 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 21 |

Issue number | 19 |

DOIs | |

State | Published - Oct 7 1988 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and General*,

*21*(19), L949-L953. https://doi.org/10.1088/0305-4470/21/19/005