First-passage times and distances along critical curvesA. Zoia1, 2, Y. Kantor3 and M. Kardar1
1 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
received 9 August 2007; accepted in final form 24 September 2007; published November 2007
published online 22 October 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.
05.60.-k - Transport processes.
05.45.Df - Fractals.
02.50.Ey - Stochastic processes.
© Europhysics Letters Association 2007