Dependence of conductance on percolation backbone mass

Gerald Paul, Sergey V. Buldyrev, Nikolay V. Dokholyan, Shlomo Havlin, Peter R. King, Youngki Lee, H. Eugene Stanley

Research output: Contribution to journalArticle

14 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)3435-3440
Number of pages6
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume61
Issue number4
DOIs
StatePublished - Jan 1 2000

Fingerprint

Conductance
Backbone
Percolation Threshold
Sierpinski Gasket
Decrease
thresholds
Euclidean Distance
Shortest path
Fractal
fractals

All Science Journal Classification (ASJC) codes

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

Cite this

Paul, Gerald ; Buldyrev, Sergey V. ; Dokholyan, Nikolay V. ; Havlin, Shlomo ; King, Peter R. ; Lee, Youngki ; Eugene Stanley, H. / Dependence of conductance on percolation backbone mass. In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 2000 ; Vol. 61, No. 4. pp. 3435-3440.
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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.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 61, No. 4, 01.01.2000, p. 3435-3440.

Research output: Contribution to journalArticle

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