The narrow capture problem with partially absorbing targets and stochastic resetting

2021/10/13 by Paul C. Bressloff, Bressloff, Paul C., Ryan D. Schumm +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Materials Science · #Diffusion and Search Dynamics #FOS: Mathematics #FOS: Physical sciences #Gold and Silver Nanoparticles Synthesis and Applications #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2110.06895

openalex publication_date 2021/10/13 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We consider a particle undergoing diffusion with stochastic resetting in a bounded domain \calU⊂ \R^d for d=2,3. The domain is perforated by a set of partially absorbing targets within which the particle may be absorbed at a rate κ. Each target is assumed to be much smaller than |\calU|, which allows us to use asymptotic and Green's function methods to solve the diffusion equation in Laplace space. In particular, we construct an inner solution within the interior and local exterior of each target, and match it with an outer solution in the bulk of \calU. This yields an asymptotic expansion of the Laplace transformed flux into each target in powers of ν=-1/ln ε (d=2) and ε (d=3), respectively, where ε is the non-dimensionalized target size. The fluxes determine how the mean first-passage time to absorption depends on the reaction rate κ and the resetting rate r. For a range of parameter values, the MFPT is a unimodal function of r, with a minimum at an optimal resetting rate r_{\rm opt} that depends on κ and the target configuration.

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• Fast integral methods for the Neumann Green's function: applications to capture and signaling problems in two dimensions
• The effect of target orientation on the mean first passage time of a Brownian particle to a small elliptical absorber

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