Asymptotic analysis of extended two-dimensional narrow capture problems

被引:17
作者
Bressloff, P. C. [1 ]
机构
[1] Univ Utah, Dept Math, 155 South 1400 East, Salt Lake City, UT 84112 USA
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2021年 / 477卷 / 2246期
关键词
search processes; matched asymptotic; first passage times; stochastic resetting; 1ST PASSAGE TIME; DIFFUSION;
D O I
10.1098/rspa.2020.0771
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
In this paper, we extend our recent work on two-dimensional diffusive search-and-capture processes with multiple small targets (narrow capture problems) by considering an asymptotic expansion of the Laplace transformed probability flux into each target. The latter determines the distribution of arrival or capture times into an individual target, conditioned on the set of events that result in capture by that target. A characteristic feature of strongly localized perturbations in two dimensions is that matched asymptotics generates a series expansion in v = -1/ln epsilon rather than epsilon, 0 < epsilon << 1, where epsilon specifies the size of each target relative to the size of the search domain. Moreover, it is possible to sum over all logarithmic terms non-perturbatively. We exploit this fact to show how a Taylor expansion in the Laplace variable s for fixed. provides an efficient method for obtaining corresponding asymptotic expansions of the splitting probabilities and moments of the conditional first-passage-time densities. We then use our asymptotic analysis to derive new results for two major extensions of the classical narrow capture problem: optimal search strategies under stochastic resetting and the accumulation of target resources under multiple rounds of search-and-capture.
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页数:17
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