First passage times and distances along critical curves

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dc.creatorZoia, A.
dc.creatorKantor, Y.
dc.creatorKardar, M.
dc.date2007-05-10
dc.date2007-11-13
dc.date.accessioned2026-07-07T08:42:09Z
dc.date.available2026-07-07T08:42:09Z
dc.descriptionWe 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 $d_f$. 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 $d_f$, 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.
dc.description5 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/0705.1474
dc.identifierhttp://arxiv.org/abs/0705.1474
dc.identifierEPL, 80 (2007) 40006
dc.identifierdoi:10.1209/0295-5075/80/40006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141868
dc.subjectStatistical Mechanics
dc.titleFirst passage times and distances along critical curves
dc.typetext

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