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Random walks and first-passage properties: Trajectory analysis and search optimization

Abstract : First-passage properties in general, and the mean first-passage time (MFPT) in particular, are widely used in the context of diffusion-limited processes. Real processes are not always purely Brownian: in the last few years, non-Brownian behaviors have been observed in an increasing number of systems. Especially single particle experiments in living cells provide striking examples for systems in which non-Brownian behavior of subdiffusive kind has been repeatedly observed experimentally. Here we present a method based on first-passage properties to gain more detailed insight into the actual physical processes underlying the anomalous diffusion behavior, and to probe the environment in which this diffusion process evolves. This method allows us to discriminate between three prominent models of subdiffusion: continuous time random walks, diffusion on fractals, and fractional Brownian motion. We also investigate the search efficiency of random walks on discrete networks for a specific target. We show how to compute first-passage properties on those networks in order to optimize the search process, as well as general bounds on the global mean first-passage time (GMFPT). Using those results, we estimate the impact on the search efficiency of several parameters, namely the target connectivity, the target motion, or the network topology.
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https://tel.archives-ouvertes.fr/tel-00721294
Contributor : Vincent Tejedor Connect in order to contact the contributor
Submitted on : Friday, July 27, 2012 - 10:33:46 AM
Last modification on : Sunday, June 26, 2022 - 9:38:52 AM
Long-term archiving on: : Friday, December 16, 2016 - 3:45:28 AM

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  • HAL Id : tel-00721294, version 1

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Vincent Tejedor. Random walks and first-passage properties: Trajectory analysis and search optimization. Mécanique statistique [cond-mat.stat-mech]. Université Pierre et Marie Curie - Paris VI; Technische Universität München, 2012. Français. ⟨NNT : ⟩. ⟨tel-00721294⟩

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