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From single-particle stochastic kinetics to macroscopic reaction rates

  • We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives forWe consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.show moreshow less

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Metadaten
Author details:Denis S GrebenkovORCiD, Ralf MetzlerORCiDGND, Gleb OshaninORCiDGND
DOI:https://doi.org/10.1088/1367-2630/abb1de
ISSN:1367-2630
Title of parent work (English):New Journal of Physics
Subtitle (English):fastest first-passage time of N random walkers
Publisher:Dt. Physikalische Ges.
Place of publishing:Bad Honnef
Publication type:Article
Language:English
Date of first publication:2020/10/02
Completion year:2020
Release date:2020/11/24
Tag:diffusion; fastest first-passage time of N walkers; first-passage
Volume:22
Page number:28
Funding institution:Universität Potsdam
Funding number:PA 2020_095
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
DDC classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer review:Referiert
Grantor:Publikationsfonds der Universität Potsdam
Publishing method:Open Access / Gold Open-Access
License (German):License LogoCreative Commons - Namensnennung, 4.0 International
External remark:Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1018