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Full distribution of first exit times in the narrow escape problem

  • In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small 'escape window' in the otherwise impermeable boundary, once it arrives to this window and crosses an entropic barrier at the entrance to it. This generic problem is mathematically identical to that of a diffusion-mediated reaction with a partially-reactive site on the container's boundary. Considerable knowledge is available on the dependence of the mean first-reaction time (FRT) on the pertinent parameters. We here go a distinct step further and derive the full FRT distribution for the NEP. We demonstrate that typical FRTs may be orders of magnitude shorter than the mean one, thus resulting in a strong defocusing of characteristic temporal scales. We unveil the geometry-control of the typical times, emphasising the role of the initial distance to the target as a decisive parameter. A crucial finding is the further FRT defocusing due to the barrier, necessitating repeated escape or reaction attemptsIn the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small 'escape window' in the otherwise impermeable boundary, once it arrives to this window and crosses an entropic barrier at the entrance to it. This generic problem is mathematically identical to that of a diffusion-mediated reaction with a partially-reactive site on the container's boundary. Considerable knowledge is available on the dependence of the mean first-reaction time (FRT) on the pertinent parameters. We here go a distinct step further and derive the full FRT distribution for the NEP. We demonstrate that typical FRTs may be orders of magnitude shorter than the mean one, thus resulting in a strong defocusing of characteristic temporal scales. We unveil the geometry-control of the typical times, emphasising the role of the initial distance to the target as a decisive parameter. A crucial finding is the further FRT defocusing due to the barrier, necessitating repeated escape or reaction attempts interspersed with bulk excursions. These results add new perspectives and offer a broad comprehension of various features of the by-now classical NEP that are relevant for numerous biological and technological systems.show moreshow less

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Metadaten
Author:Denis S GrebenkovORCiD, Ralf MetzlerORCiDGND, Gleb OshaninORCiDGND
URN:urn:nbn:de:kobv:517-opus4-442883
DOI:https://doi.org/10.25932/publishup-44288
ISSN:1866-8372
Parent Title (German):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (810)
Document Type:Postprint
Language:English
Date of first Publication:2020/01/20
Year of Completion:2019
Publishing Institution:Universität Potsdam
Release Date:2020/01/20
Tag:first-passage time distribution; mean versus most probable reaction times; mixed boundary conditions; narrow escape problem
Issue:810
Pagenumber:24
Source:New Journal of Physics 21 (2019) DOI: 10.1088/1367-2630/ab5de4
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer Review:Referiert
Publication Way:Open Access
Licence (English):License LogoCreative Commons - Attribution 3.0 Unported
Notes extern:Bibliographieeintrag der Originalveröffentlichung/Quelle