Section on Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health , Bethesda, Maryland 20892, United States.
Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health , Bethesda, Maryland 20892, United States.
J Phys Chem B. 2017 Jun 1;121(21):5455-5460. doi: 10.1021/acs.jpcb.7b04037. Epub 2017 May 17.
Any trajectory of a diffusing particle making a transition between two end points of an interval can be divided into two segments, which we call direct-transit and looping parts. The former is the final segment of the trajectory, when the particle goes from one end point of the interval to the opposite end point, without retouching the starting point. The rest of the trajectory is the looping part. We study mean durations of the two parts in the presence of a symmetric linear cusp potential which, depending on the parameter values, forms either a barrier or a well between the end points. For the cusp barrier, we find that the mean direct-transit time decreases as the barrier height increases at a fixed interval length. This happens because the increase in the barrier height results in the increase of the magnitude of the force acting on the particle on both sides of the barrier. Interestingly, though the mean looping and direct-transit times are different in the case of the barrier and well potentials with equal height and depth, respectively, the mean first-passage times for the two cases are identical.
扩散粒子在区间的两个端点之间进行跃迁的任何轨迹都可以分为两段，我们称之为直接跃迁段和循环段。前者是轨迹的最后一段，此时粒子从区间的一端点移动到另一端点，而不触及起点。轨迹的其余部分是循环段。我们研究了在对称线性角点势存在的情况下这两段的平均持续时间，根据参数值，该角点势在端点之间形成势垒或势阱。对于角点势垒，我们发现，在固定的区间长度下，随着势垒高度的增加，平均直接跃迁时间会减少。这是因为势垒高度的增加导致作用在势垒两侧的粒子上的力的大小增加。有趣的是，尽管在势垒和阱势的情况下，平均循环和直接跃迁时间分别与相等高度和深度的情况不同，但两种情况下的平均首次通过时间是相同的。
