First-passage times and distances along critical curves

A. Zoia*, Y. Kantor, M. Kardar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a model for anomalous transport in inhomogeneous environments, such as fractured rocks, in which particles move only along pre-existing self-similar curves (cracks). The stochastic Loewner equation is used to efficiently generate such curves with tunable fractal dimension df. We numerically compute the probability of first passage (in length or time) from one point on the edge of the semi-infinite plane to any point on the semi-circle of radius R. The scaled probability distributions have a variance which increases with df, a non-monotonic skewness, and tails that decay faster than a simple exponential. The latter is in sharp contrast to predictions based on fractional dynamics and provides an experimental signature for our model.

Original languageEnglish
Article number40006
JournalJournal de Physique (Paris), Lettres
Volume80
Issue number4
DOIs
StatePublished - 1 Nov 2007

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