TY - JOUR
A1 - Grebenkov, Denis S
A1 - Metzler, Ralf
A1 - Oshanin, Gleb
T1 - From single-particle stochastic kinetics to macroscopic reaction rates
BT - fastest first-passage time of N random walkers
JF - New Journal of Physics
N2 - 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.
KW - diffusion
KW - first-passage
KW - fastest first-passage time of N walkers
Y1 - 2020
U6 - https://doi.org/10.1088/1367-2630/abb1de
SN - 1367-2630
VL - 22
PB - Dt. Physikalische Ges.
CY - Bad Honnef
ER -
TY - GEN
A1 - Grebenkov, Denis S
A1 - Metzler, Ralf
A1 - Oshanin, Gleb
T1 - From single-particle stochastic kinetics to macroscopic reaction rates
BT - fastest first-passage time of N random walkers
T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2 - 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.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1018
KW - diffusion
KW - first-passage
KW - fastest first-passage time of N walkers
Y1 - 2020
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-484059
SN - 1866-8372
IS - 1018
ER -