Filling of a Poisson trap by a population of random intermittent searchers

Handle URI:
http://hdl.handle.net/10754/598325
Title:
Filling of a Poisson trap by a population of random intermittent searchers
Authors:
Bressloff, Paul C.; Newby, Jay M.
Abstract:
We extend the continuum theory of random intermittent search processes to the case of N independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi-infinite track. Each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state. We assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process. The hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target; the particle is removed from the system after delivering its cargo. As a further generalization of previous models, we assume that up to n successive particles can find the target and deliver its cargo. Assuming that the rate of target detection scales as 1/N, we show that there exists a well-defined mean-field limit N→ in which the stochastic model reduces to a deterministic system of linear reaction-hyperbolic equations for the concentrations of particles in each of the internal states. These equations decouple from the stochastic process associated with filling the target with cargo. The latter can be modeled as a Poisson process in which the time-dependent rate of filling λ(t) depends on the concentration of stationary particles within the target domain. Hence, we refer to the target as a Poisson trap. We analyze the efficiency of filling the Poisson trap with n particles in terms of the waiting time density f n(t). The latter is determined by the integrated Poisson rate μ(t)=0tλ(s)ds, which in turn depends on the solution to the reaction-hyperbolic equations. We obtain an approximate solution for the particle concentrations by reducing the system of reaction-hyperbolic equations to a scalar advection-diffusion equation using a quasisteady-state analysis. We compare our analytical results for the mean-field model with Monte Carlo simulations for finite N. We thus determine how the mean first passage time (MFPT) for filling the target depends on N and n. © 2012 American Physical Society.
Citation:
Bressloff PC, Newby JM (2012) Filling of a Poisson trap by a population of random intermittent searchers. Phys Rev E 85. Available: http://dx.doi.org/10.1103/PhysRevE.85.031909.
Publisher:
American Physical Society (APS)
Journal:
Physical Review E
KAUST Grant Number:
KUK-C1-013-4
Issue Date:
Mar-2012
DOI:
10.1103/PhysRevE.85.031909
PubMed ID:
22587125
Type:
Article
ISSN:
1539-3755; 1550-2376
Sponsors:
This publication was based on work supported in part by the National Science Foundation (DMS-1120327) and by Award 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.accessioned2016-02-25T13:18:45Zen
dc.date.available2016-02-25T13:18:45Zen
dc.date.issued2012-03en
dc.identifier.citationBressloff PC, Newby JM (2012) Filling of a Poisson trap by a population of random intermittent searchers. Phys Rev E 85. Available: http://dx.doi.org/10.1103/PhysRevE.85.031909.en
dc.identifier.issn1539-3755en
dc.identifier.issn1550-2376en
dc.identifier.pmid22587125en
dc.identifier.doi10.1103/PhysRevE.85.031909en
dc.identifier.urihttp://hdl.handle.net/10754/598325en
dc.description.abstractWe extend the continuum theory of random intermittent search processes to the case of N independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi-infinite track. Each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state. We assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process. The hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target; the particle is removed from the system after delivering its cargo. As a further generalization of previous models, we assume that up to n successive particles can find the target and deliver its cargo. Assuming that the rate of target detection scales as 1/N, we show that there exists a well-defined mean-field limit N→ in which the stochastic model reduces to a deterministic system of linear reaction-hyperbolic equations for the concentrations of particles in each of the internal states. These equations decouple from the stochastic process associated with filling the target with cargo. The latter can be modeled as a Poisson process in which the time-dependent rate of filling λ(t) depends on the concentration of stationary particles within the target domain. Hence, we refer to the target as a Poisson trap. We analyze the efficiency of filling the Poisson trap with n particles in terms of the waiting time density f n(t). The latter is determined by the integrated Poisson rate μ(t)=0tλ(s)ds, which in turn depends on the solution to the reaction-hyperbolic equations. We obtain an approximate solution for the particle concentrations by reducing the system of reaction-hyperbolic equations to a scalar advection-diffusion equation using a quasisteady-state analysis. We compare our analytical results for the mean-field model with Monte Carlo simulations for finite N. We thus determine how the mean first passage time (MFPT) for filling the target depends on N and n. © 2012 American Physical Society.en
dc.description.sponsorshipThis publication was based on work supported in part by the National Science Foundation (DMS-1120327) and by Award No. KUK-C1-013-4 made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherAmerican Physical Society (APS)en
dc.titleFilling of a Poisson trap by a population of random intermittent searchersen
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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