论文标题
在吸收柱子的纳米孔中生存
Survival in a nanoforest of absorbing pillars
论文作者
论文摘要
我们研究了两个平行反射平面向周期性吸收柱的平行反射平面之间扩散的生存概率。我们通过包含一个支柱的圆柱管近似该系统的周期性细胞。使用模式匹配方法，我们在该域中获得了修改后的Helmholtz方程的精确解，该解确定了生存概率的拉普拉斯变换和第一通道时间的相关分布。该解决方案揭示了几种几何参数的各自作用：支柱的高度和半径，柱间距离以及限制平面之间的距离。该模型使我们能够在第一学期时间的概率密度中探索不同的渐近状态。在限制平面之间距离很大距离的实际相关情况下，我们认为平均第一学期时间比典型的时间大得多，因此不信息。我们还说明了拉普拉斯操作员主要特征值的电容近似的故障。讨论了一些实际含义和未来观点。
We investigate the survival probability of a particle diffusing between two parallel reflecting planes toward a periodic array of absorbing pillars. We approximate the periodic cell of this system by a cylindrical tube containing a single pillar. Using a mode matching method, we obtain an exact solution of the modified Helmholtz equation in this domain that determines the Laplace transform of the survival probability and the associated distribution of first-passage times. This solution reveals the respective roles of several geometric parameters: the height and radius of the pillar, the inter-pillar distance, and the distance between confining planes. This model allows us to explore different asymptotic regimes in the probability density of the first-passage time. In the practically relevant case of a large distance between confining planes, we argue that the mean first-passage time is much larger than the typical time and thus uninformative. We also illustrate the failure of the capacitance approximation for the principal eigenvalue of the Laplace operator. Some practical implications and future perspectives are discussed.
