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

Research output: Contribution to journalArticlepeer-review

85 Scopus citations


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 languageEnglish
Pages (from-to)3425-3428
Number of pages4
JournalPhysical Review E
Issue number3
StatePublished - Sep 1999


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