First passages for a search by a swarm of independent random searchers

Carlos, Mejia-Monasterio; Gleb, Oshanin y Gregory, Schehr (2011). First passages for a search by a swarm of independent random searchers. "Journal of Statistical Mechanics: Theory and Experiment", v. P06022 ; pp.. https://doi.org/10.1088/1742-5468/2011/06/P06022.

Descripción

Título: First passages for a search by a swarm of independent random searchers
Autor/es:
  • Carlos, Mejia-Monasterio
  • Gleb, Oshanin
  • Gregory, Schehr
Tipo de Documento: Artículo
Título de Revista/Publicación: Journal of Statistical Mechanics: Theory and Experiment
Fecha: 2011
Volumen: P06022
Materias:
Escuela: E.T.S.I. Agrónomos (UPM) [antigua denominación]
Departamento: Ingeniería Rural [hasta 2014]
Grupo Investigación UPM: LPF-TAGRALIA
Licencias Creative Commons: Reconocimiento - No comercial

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Resumen

In this paper we study some aspects of search for an immobile target by a swarm of N non-communicating, randomly moving searchers (numbered by the index k, k = 1, 2, . . . ,N), which all start their random motion simultaneously at the same point in space. For each realization of the search process, we record the unordered set of time moments {τk}, where τk is the time of the first passage of the kth searcher to the location of the target. Clearly, τks are independent, identically distributed random variables with the same distribution function Ψ(τ ). We evaluate then the distribution P(ω) of the random variable ω ∼ τ1/¯τ , where ¯τ = N−1N k=1 τk is the ensemble-averaged realization-dependent first passage time. We show that P(ω) exhibits quite a non-trivial and sometimes a counterintuitive behavior. We demonstrate that in some well-studied cases (e.g. Brownian motion in finite d-dimensional domains) the mean first passage time is not a robust measure of the search efficiency, despite the fact that Ψ(τ ) has moments of arbitrary order. This implies, in particular, that even in this simplest case (not to mention complex systems and/or anomalous diffusion) first passage data extracted from a single-particle tracking should be regarded with appropriate caution because of the significant sample-to-sample fluctuations.

Más información

ID de Registro: 9831
Identificador DC: http://oa.upm.es/9831/
Identificador OAI: oai:oa.upm.es:9831
Identificador DOI: 10.1088/1742-5468/2011/06/P06022
URL Oficial: http://iopscience.iop.org/1742-5468/2011/06/P06022/figures
Depositado por: Dr. Carlos Mejia-Monasterio
Depositado el: 13 Dic 2011 12:40
Ultima Modificación: 20 Abr 2016 18:07
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