Quasi-steady-state analysis of two-dimensional random intermittent search processes

Handle URI:
http://hdl.handle.net/10754/599434
Title:
Quasi-steady-state analysis of two-dimensional random intermittent search processes
Authors:
Bressloff, Paul C.; Newby, Jay M.
Abstract:
We use perturbation methods to analyze a two-dimensional random intermittent search process, in which a searcher alternates between a diffusive search phase and a ballistic movement phase whose velocity direction is random. A hidden target is introduced within a rectangular domain with reflecting boundaries. If the searcher moves within range of the target and is in the search phase, it has a chance of detecting the target. A quasi-steady-state analysis is applied to the corresponding Chapman-Kolmogorov equation. This generates a reduced Fokker-Planck description of the search process involving a nonzero drift term and an anisotropic diffusion tensor. In the case of a uniform direction distribution, for which there is zero drift, and isotropic diffusion, we use the method of matched asymptotics to compute the mean first passage time (MFPT) to the target, under the assumption that the detection range of the target is much smaller than the size of the domain. We show that an optimal search strategy exists, consistent with previous studies of intermittent search in a radially symmetric domain that were based on a decoupling or moment closure approximation. We also show how the decoupling approximation can break down in the case of biased search processes. Finally, we analyze the MFPT in the case of anisotropic diffusion and find that anisotropy can be useful when the searcher starts from a fixed location. © 2011 American Physical Society.
Citation:
Bressloff PC, Newby JM (2011) Quasi-steady-state analysis of two-dimensional random intermittent search processes. Phys Rev E 83. Available: http://dx.doi.org/10.1103/PhysRevE.83.061139.
Publisher:
American Physical Society (APS)
Journal:
Physical Review E
KAUST Grant Number:
KUK-C1-013-4
Issue Date:
Jun-2011
DOI:
10.1103/PhysRevE.83.061139
PubMed ID:
21797334
Type:
Article
ISSN:
1539-3755; 1550-2376
Sponsors:
This publication was based on work supported in part by the National Science Foundation (DMS-0813677) and by Grant No. KUK-C1-013-4 made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorBressloff, Paul C.en
dc.contributor.authorNewby, Jay M.en
dc.date.accessioned2016-02-28T05:51:03Zen
dc.date.available2016-02-28T05:51:03Zen
dc.date.issued2011-06en
dc.identifier.citationBressloff PC, Newby JM (2011) Quasi-steady-state analysis of two-dimensional random intermittent search processes. Phys Rev E 83. Available: http://dx.doi.org/10.1103/PhysRevE.83.061139.en
dc.identifier.issn1539-3755en
dc.identifier.issn1550-2376en
dc.identifier.pmid21797334en
dc.identifier.doi10.1103/PhysRevE.83.061139en
dc.identifier.urihttp://hdl.handle.net/10754/599434en
dc.description.abstractWe use perturbation methods to analyze a two-dimensional random intermittent search process, in which a searcher alternates between a diffusive search phase and a ballistic movement phase whose velocity direction is random. A hidden target is introduced within a rectangular domain with reflecting boundaries. If the searcher moves within range of the target and is in the search phase, it has a chance of detecting the target. A quasi-steady-state analysis is applied to the corresponding Chapman-Kolmogorov equation. This generates a reduced Fokker-Planck description of the search process involving a nonzero drift term and an anisotropic diffusion tensor. In the case of a uniform direction distribution, for which there is zero drift, and isotropic diffusion, we use the method of matched asymptotics to compute the mean first passage time (MFPT) to the target, under the assumption that the detection range of the target is much smaller than the size of the domain. We show that an optimal search strategy exists, consistent with previous studies of intermittent search in a radially symmetric domain that were based on a decoupling or moment closure approximation. We also show how the decoupling approximation can break down in the case of biased search processes. Finally, we analyze the MFPT in the case of anisotropic diffusion and find that anisotropy can be useful when the searcher starts from a fixed location. © 2011 American Physical Society.en
dc.description.sponsorshipThis publication was based on work supported in part by the National Science Foundation (DMS-0813677) and by Grant No. KUK-C1-013-4 made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherAmerican Physical Society (APS)en
dc.titleQuasi-steady-state analysis of two-dimensional random intermittent search processesen
dc.typeArticleen
dc.identifier.journalPhysical Review Een
dc.contributor.institutionUniversity of Utah, Salt Lake City, United Statesen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-4en

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