### 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) |
---|---|

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

**Numerical study of transport properties in continuum percolation.** / Zeng, Xiao C; J Bergman, J. B.; Stroud, D.

Research output: Contribution to journal › Letter

*Journal of Physics A: Mathematical and General*, vol. 21, no. 19, pp. L949-L953. https://doi.org/10.1088/0305-4470/21/19/005

}

TY - JOUR

T1 - Numerical study of transport properties in continuum percolation

AU - Zeng, Xiao C

AU - J Bergman, J. B.

AU - Stroud, D.

PY - 1988/10/7

Y1 - 1988/10/7

N2 - 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(geff)≃ω and the real part of conductance shows an anomalous frequency dependence Re(geff)≃ω2−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.

AB - 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(geff)≃ω and the real part of conductance shows an anomalous frequency dependence Re(geff)≃ω2−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.

UR - http://www.scopus.com/inward/record.url?scp=10644293607&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10644293607&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/21/19/005

DO - 10.1088/0305-4470/21/19/005

M3 - Letter

VL - 21

SP - L949-L953

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 19

ER -