First passage times and distances along critical curves

Details First passage times and distances along critical curves First passage times and distances along critical curves

2007-05-10

arxiv.org/abs/0705.1474v2

EPL, 80 (2007) 40006

Physics

Condensed Matter

Statistical Mechanics

5 pages, 5 figures

Scientific paper

10.1209/0295-5075/80/40006

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 $d_f$. 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.

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