## Abstract

We study [Formula Presented] the average conductance of the backbone, defined by two points separated by Euclidean distance r, of mass [Formula Presented] on two-dimensional percolation clusters at the percolation threshold. We find that with increasing [Formula Presented] and for fixed [Formula Presented] asymptotically decreases to a constant, in contrast with the behavior of homogeneous systems and nonrandom fractals (such as the Sierpinski gasket) in which conductance increases with increasing [Formula Presented] We explain this behavior by studying the distribution of shortest paths between the two points on clusters with a given [Formula Presented] We also study the dependence of conductance on [Formula Presented] above the percolation threshold and find that (i) slightly above [Formula Presented] the conductance first decreases and then increases with increasing [Formula Presented] and (ii) further above [Formula Presented] the conductance increases monotonically for all values of [Formula Presented] as is the case for homogeneous systems.

Original language | English |
---|---|

Pages (from-to) | 3435-3440 |

Number of pages | 6 |

Journal | Physical Review E |

Volume | 61 |

Issue number | 4 |

DOIs | |

State | Published - 2000 |