Bressloff, P. C. and Newby, J. M. (2011) Quasisteady state analysis of twodimensional random intermittent search processes. Physical Review E . (Submitted)

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Abstract
We use perturbation methods to analyze a twodimensional 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 quasisteady state (QSS) analysis is applied to the corresponding ChapmanKolmogorov (CK) equation. This generates a reduced FokkerPlanck (FP) 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 radiallysymmetric 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.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1264 
Deposited By:  Peter Hudston 
Deposited On:  26 May 2011 06:44 
Last Modified:  29 May 2015 18:57 
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