PMID: 22587125May 17, 2012Paper

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Paul C Bressloff, Jay Newby

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...Continue Reading

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Citations

Jun 13, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Aljaž Godec, Ralf Metzler
Nov 15, 2016·Physical Review. E·Karsten SchwarzHeiko Rieger
Oct 4, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Thiago G MattosGleb Oshanin

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