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oai:oa.upm.es:9831
2018-12-17T06:57:05Z
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First passages for a search by a swarm of independent random searchers
Mejia-Monasterio, Carlos
Oshanin, Gleb
Schehr, Gregory
Physics
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.
E.T.S.I. Agrónomos (UPM)
http://creativecommons.org/licenses/by-nc/3.0/es/
2011
info:eu-repo/semantics/article
Article
Journal of Statistical Mechanics: Theory and Experiment, 2011, Vol. P06022
PeerReviewed
application/pdf
eng
http://iopscience.iop.org/1742-5468/2011/06/P06022/figures
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2011/06/P06022
http://oa.upm.es/9831/