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.…
Author details: | Denis S. GrebenkovORCiD, Ralf MetzlerORCiDGND, Gleb OshaninORCiDGND |
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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 |
Publication year: | 2020 |
Release date: | 2020/11/24 |
Tag: | diffusion; fastest first-passage time of N walkers; first-passage |
Volume: | 22 |
Number of pages: | 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): | CC-BY - Namensnennung 4.0 International |
External remark: | Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1018 |