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.…
Author details: | Denis S. GrebenkovORCiD, Ralf MetzlerORCiDGND, Gleb OshaninORCiDGND |
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URN: | urn:nbn:de:kobv:517-opus4-442883 |
DOI: | https://doi.org/10.25932/publishup-44288 |
ISSN: | 1866-8372 |
Title of parent work (German): | Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (810) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2020/01/20 |
Publication year: | 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 |
Number of pages: | 24 |
Source: | New Journal of Physics 21 (2019) DOI: 10.1088/1367-2630/ab5de4 |
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 |
License (English): | Creative Commons - Namensnennung 3.0 Unported |
External remark: | Bibliographieeintrag der Originalveröffentlichung/Quelle |