First passages in bounded domains: When is the mean first passage time meaningful?

Mattos, Thiago and Mejia-Monasterio, Carlos and Metzler, Ralf and Oshanin, Gleb (2012). First passages in bounded domains: When is the mean first passage time meaningful?. "Physical Review E", v. 86 (n. 3); pp.. ISSN 1539-3755. https://doi.org/10.1103/PhysRevE.86.031143.

Description

Title: First passages in bounded domains: When is the mean first passage time meaningful?
Author/s:
  • Mattos, Thiago
  • Mejia-Monasterio, Carlos
  • Metzler, Ralf
  • Oshanin, Gleb
Item Type: Article
Título de Revista/Publicación: Physical Review E
Date: 27 September 2012
ISSN: 1539-3755
Volume: 86
Subjects:
Faculty: E.T.S.I. Agrónomos (UPM) [antigua denominación]
Department: Ingeniería Rural [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(ω) distribution of the random variable ω=τ1/(τ1+τ2), which is a measure for how similar the first passage times τ1 and τ2 are of two independent realizations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P(ω) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behavior. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behavior, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P(ω), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behavior even in bounded domains, in which all moments of the first passage distribution exist.

More information

Item ID: 15625
DC Identifier: http://oa.upm.es/15625/
OAI Identifier: oai:oa.upm.es:15625
DOI: 10.1103/PhysRevE.86.031143
Official URL: http://pre.aps.org/abstract/PRE/v86/i3/e031143
Deposited by: Memoria Investigacion
Deposited on: 20 Jun 2013 16:56
Last Modified: 17 Dec 2018 07:01
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