Traveling time and traveling length in critical percolation clusters

Youngki Lee; José S. Andrade; Sergey V. Buldyrev; Nikolay V. Dokholyan; Shlomo Havlin; Peter R. King; Gerald Paul; H. Eugene Stanley

doi:10.1103/physreve.60.3425

Traveling time and traveling length in critical percolation clusters

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

Department of Physics - at Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

89 Scopus citations

Abstract

We study traveling time and traveling length for tracer dispersion in two-dimensional bond percolation, modeling flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance r. We find that the minimal traveling time [Formula Presented] scales as [Formula Presented] which is different from the scaling of the most probable traveling time, [Formula Presented] We also calculate the length of the path corresponding to the minimal traveling time and find [Formula Presented] and that the most probable traveling length scales as [Formula Presented] We present the relevant distribution functions and scaling relations.

Original language	English
Pages (from-to)	3425-3428
Number of pages	4
Journal	Physical Review E
Volume	60
Issue number	3
DOIs	https://doi.org/10.1103/physreve.60.3425
State	Published - Sep 1999

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title = "Traveling time and traveling length in critical percolation clusters",

abstract = "We study traveling time and traveling length for tracer dispersion in two-dimensional bond percolation, modeling flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance r. We find that the minimal traveling time [Formula Presented] scales as [Formula Presented] which is different from the scaling of the most probable traveling time, [Formula Presented] We also calculate the length of the path corresponding to the minimal traveling time and find [Formula Presented] and that the most probable traveling length scales as [Formula Presented] We present the relevant distribution functions and scaling relations.",

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AU - Andrade, José S.

AU - Buldyrev, Sergey V.

AU - Dokholyan, Nikolay V.

AU - Havlin, Shlomo

AU - King, Peter R.

AU - Paul, Gerald

AU - Stanley, H. Eugene

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AB - We study traveling time and traveling length for tracer dispersion in two-dimensional bond percolation, modeling flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance r. We find that the minimal traveling time [Formula Presented] scales as [Formula Presented] which is different from the scaling of the most probable traveling time, [Formula Presented] We also calculate the length of the path corresponding to the minimal traveling time and find [Formula Presented] and that the most probable traveling length scales as [Formula Presented] We present the relevant distribution functions and scaling relations.

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Traveling time and traveling length in critical percolation clusters

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