Volume 80, Number 4, November 2007
|Number of page(s)||5|
|Published online||22 October 2007|
First-passage times and distances along critical curves
Department of Physics, Massachusetts Institute of Technology - Cambridge, MA 02139, USA
2 Department of Nuclear Engineering, Polytechnic of Milan - Milan 20133, Italy
3 School for Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University Tel Aviv 69978, Israel
Accepted: 24 September 2007
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.
PACS: 05.60.-k – Transport processes / 05.45.Df – Fractals / 02.50.Ey – Stochastic processes
© Europhysics Letters Association, 2007
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