48405
2020
2020
eng
29
1018
postprint
1
2020-11-24
2020-11-24
--
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 for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
fastest first-passage time of N random walkers
10.25932/publishup-48405
urn:nbn:de:kobv:517-opus4-484059
1866-8372
New Journal of Physics 22 (2020) Art. 103004 DOI: 10.1088/1367-2630/abb1de
103004
<a href="http://publishup.uni-potsdam.de/48404">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
false
true
CC-BY - Namensnennung 4.0 International
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
1018
eng
uncontrolled
diffusion
eng
uncontrolled
first-passage
eng
uncontrolled
fastest first-passage time of N walkers
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/48405/pmnr1018.pdf
48404
2020
2020
eng
28
22
article
Dt. Physikalische Ges.
Bad Honnef
1
2020-10-02
2020-10-02
--
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 for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.
New Journal of Physics
fastest first-passage time of N random walkers
10.1088/1367-2630/abb1de
1367-2630
Universität Potsdam
PA 2020_095
1418.10
103004
<a href="https://doi.org/10.25932/publishup-48405">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1018</a>
false
false
CC-BY - Namensnennung 4.0 International
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
diffusion
eng
uncontrolled
first-passage
eng
uncontrolled
fastest first-passage time of N walkers
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access