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 - Zweitveröffentlichungen 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 - 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 -