论文标题
从单粒子随机动力学到宏观反应率：$ n $随机步行者的最快第一播放时间
From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of $N$ random walkers
论文作者
论文摘要
我们认为最初在有限域$ω$中均匀释放的$ n $相同独立粒子的第一票问题，然后向反应性区域$γ$扩散，这可能是$ω$的外边界的一部分，也可以是$ω$内部的反应中心的一部分。对于完美反应和部分反应的情况，我们在最快的第一学期时间（FFPT）的前两个时刻获得了明确的公式，即$ n $颗粒中的第一个反应$γ$的时间。此外，我们研究了FFPT的完全概率密度。我们讨论了初始条件在平均最快的第一学期时间的比例中的重要作用，即粒子数量$ n $，即，与在所有粒子上从所有粒子中都从同一固定点上释放出的众所周知的ivallemogarithmic行为相反，对部分和完美反应的目标的依赖性（分别为$ 1/n $和$ 1/n^2 $）分别为部分和完美地被动的目标。我们将分析解决方案与缩放参数和随机模拟相结合，以合理化我们的结果，这为研究分子反应的各种情况，尤其是在活细胞中的各种情况下研究了多个搜索者的相关性开辟了新的观点。
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 fastest first-passage time with the particle number $N$, namely, a much stronger dependence ($1/N$ and $1/N^2$ 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.
