Mon K K
Department of Physics and Astronomy and Nanoscale Science and Engineering Center, University of Georgia, Athens, Georgia 30602, USA.
J Chem Phys. 2009 May 14;130(18):184701. doi: 10.1063/1.3127764.
We use Brownian dynamics simulations of two hard disks in a channel to study the mean first passage time to pass each other. The disks have a diameter sigma and are confined in a channel with hard reflective walls. The mean first passage time diverges with an exponent eta as the channel width (2R(p)) approaches that of the nonpassing limit (2sigma). There are two different theoretical predictions for the exponent eta of the two disk hopping time divergences. Transition state theory and a Fick-Jacobs type of dimensional reduction approach predict exponents of 2 and 32, respectively. Previous Brownian dynamics simulations results have a range of effective exponents and are inconclusive. Here, we present extensive Brownian dynamics simulations results which are consistent with the predictions of transition state theory. The new data show that one must be close to the nonpassing limit to observe the asymptotic scaling exponent. The scaling dependence crosses over from the bulk limit to the nonpassing limit as the width of the channel narrows, corresponding to a range of effective exponents between 0 and 2. This crossover provides an explanation of the inconclusive results reported in previous Brownian dynamics simulations.
我们使用通道中两个硬磁盘的布朗动力学模拟来研究相互通过的平均首次通过时间。磁盘直径为σ，被限制在具有硬反射壁的通道中。当通道宽度（2R(p)）接近非通过极限（2σ）时，平均首次通过时间以指数η发散。对于两个磁盘跳跃时间发散的指数η，有两种不同的理论预测。过渡态理论和菲克 - 雅各布斯类型的降维方法分别预测指数为2和32。先前的布朗动力学模拟结果有一系列有效的指数，尚无定论。在此，我们展示了与过渡态理论预测一致的广泛布朗动力学模拟结果。新数据表明，必须接近非通过极限才能观察到渐近标度指数。随着通道宽度变窄，标度依赖性从体极限转变为非通过极限，对应于0到2之间的一系列有效指数。这种转变解释了先前布朗动力学模拟中报告的不确定结果。
