Issue |
Europhys. Lett.
Volume 67, Number 5, September 2004
|
|
---|---|---|
Page(s) | 734 - 740 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i2004-10114-9 | |
Published online | 01 August 2004 |
Optimal random searches of revisitable targets: Crossover from superdiffusive to ballistic random walks
1
Departamento de Física, Universidade Federal do Paraná 81531-990, Curitiba-PR, Brazil
2
Laboratório de Física Teórica e Computacional, Departamento de Física Universidade Federal de Pernambuco - 50670-901, Recife-PE, Brazil
3
Departamento de Física, Universidade Federal de Alagoas 57072-970, Maceió-AL, Brazil
Received:
2
April
2004
Accepted:
16
June
2004
One of the most important aspects in the general search problem of
finding randomly located target sites concerns how to
characterize the role played by the non-revisitability delay time
τ during which a previously found target becomes unavailable
to the searcher. By using an appropriate parameterization of the
number of random walk steps undertaken between successive
targets, we show that for the case of sparse randomly distributed
sites the optimal search strategy shifts from a superdiffusive to
a ballistic strategy consisting of essentially rectilinear motion
between the targets, as τ increases from
to
, respectively. The crossover between
these limiting regimes occurs as a function of τ. These
conclusions are shown to hold even if dissipative phenomena are
considered in the searching dynamics. We discuss the results in
the context of their application to animal foraging.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EDP Sciences, 2004
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