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First-passage times in complex scale-invariant media | | S. Condamin
; O. Benichou
; V. Tejedor
; R. Voituriez
; J. Klafter
; | | Date: |
5 Nov 2007 | | Abstract: | How long does it take a random walker to reach a given target point? This
quantity, known as a first passage time (FPT), has led to a growing number of
theoretical investigations over the last decade1. The importance of FPTs
originates from the crucial role played by first encounter properties in
various real situations, including transport in disordered media, neuron firing
dynamics, spreading of diseases or target search processes. Most methods to
determine the FPT properties in confining domains have been limited to
effective 1D geometries, or for space dimensions larger than one only to
homogeneous media1. Here we propose a general theory which allows one to
accurately evaluate the mean FPT (MFPT) in complex media. Remarkably, this
analytical approach provides a universal scaling dependence of the MFPT on both
the volume of the confining domain and the source-target distance. This
analysis is applicable to a broad range of stochastic processes characterized
by length scale invariant properties. Our theoretical predictions are confirmed
by numerical simulations for several emblematic models of disordered media,
fractals, anomalous diffusion and scale free networks. | | Source: | arXiv, 0711.0682 | | Other source: | [GID 89510] pmid17972880 | | Services: | Forum | Review | PDF | Favorites | |
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