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

Mattos, Thiago; Mejia Monasterio, Carlos Roberto; Metzler, Ralf y 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.

Descripción

Título: First passages in bounded domains: When is the mean first passage time meaningful?
Autor/es:
  • Mattos, Thiago
  • Mejia Monasterio, Carlos Roberto
  • Metzler, Ralf
  • Oshanin, Gleb
Tipo de Documento: Artículo
Título de Revista/Publicación: Physical Review E
Fecha: 27 Septiembre 2012
Volumen: 86
Materias:
Escuela: E.T.S.I. Agrónomos (UPM) [antigua denominación]
Departamento: Ingeniería Rural [hasta 2014]
Licencias Creative Commons: Reconocimiento - Sin obra derivada - No comercial

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Resumen

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.

Más información

ID de Registro: 15625
Identificador DC: http://oa.upm.es/15625/
Identificador OAI: oai:oa.upm.es:15625
Identificador DOI: 10.1103/PhysRevE.86.031143
URL Oficial: http://pre.aps.org/abstract/PRE/v86/i3/e031143
Depositado por: Memoria Investigacion
Depositado el: 20 Jun 2013 16:56
Ultima Modificación: 21 Abr 2016 15:52
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