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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
URN:urn:nbn:de:kobv:517-opus4-484059
DOI:https://doi.org/10.25932/publishup-48405
ISSN:1866-8372
Title of parent work (German):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
Subtitle (English):fastest first-passage time of N random walkers
Publication series (Volume number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (1018)
Publication type:Postprint
Language:English
Date of first publication:2020/11/24
Completion year:2020
Publishing institution:Universität Potsdam
Release date:2020/11/24
Tag:diffusion; fastest first-passage time of N walkers; first-passage
Issue:1018
Page number:29
Source:New Journal of Physics 22 (2020) Art. 103004 DOI: 10.1088/1367-2630/abb1de
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
DDC classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer review:Referiert
Publishing method:Open Access / Green Open-Access
License (German):License LogoCreative Commons - Namensnennung, 4.0 International
External remark:Bibliographieeintrag der Originalveröffentlichung/Quelle