### 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 (US) |
---|---|

Pages (from-to) | 3435-3440 |

Number of pages | 6 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 61 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 2000 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*61*(4), 3435-3440. https://doi.org/10.1103/PhysRevE.61.3435

}

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 61, no. 4, pp. 3435-3440. https://doi.org/10.1103/PhysRevE.61.3435

**Dependence of conductance on percolation backbone mass.** / Paul, Gerald; Buldyrev, Sergey V.; Dokholyan, Nikolay V.; Havlin, Shlomo; King, Peter R.; Lee, Youngki; Eugene Stanley, H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Dependence of conductance on percolation backbone mass

AU - Paul, Gerald

AU - Buldyrev, Sergey V.

AU - Dokholyan, Nikolay V.

AU - Havlin, Shlomo

AU - King, Peter R.

AU - Lee, Youngki

AU - Eugene Stanley, H.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0042015113&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042015113&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.61.3435

DO - 10.1103/PhysRevE.61.3435

M3 - Article

AN - SCOPUS:0042015113

VL - 61

SP - 3435

EP - 3440

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

ER -