何时需要对 Fick-Jacobs 方程进行下一步的扩展？

When is the next extending of Fick-Jacobs equation necessary?

机构信息

Institute of Physics, Slovak Academy of Sciences, Dúbravska cesta 9, 84511 Bratislava, Slovakia.

出版信息

J Chem Phys. 2013 Aug 7;139(5):054116. doi: 10.1063/1.4817198.

Abstract

Applicability of the effective one-dimensional equations, such as Fick-Jacobs equation and its extensions, describing diffusion of particles in 2D or 3D channels with varying cross section A(x) along the longitudinal coordinate x, is studied. The leading nonstationary correction to Zwanzig-Reguera-Rubí equation [R. Zwanzig, J. Phys. Chem. 96, 3926 (1992); D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001)] is derived and tested on the exactly solvable model, diffusion in a 2D linear cone. The effects of such correction are demonstrated and discussed on elementary nonstationary processes, a time dependent perturbation of the stationary flow and calculation of the mean first passage time.

摘要

研究了有效一维方程（如菲克-雅可比方程及其扩展）在描述具有沿纵向坐标 x 变化的横截面 A(x)的 2D 或 3D 通道中粒子扩散的适用性。推导出了对 Zwanzig-Reguera-Rubí 方程（R. Zwanzig，J. Phys. Chem. 96, 3926 (1992); D. Reguera 和 J. M. Rubí，Phys. Rev. E 64, 061106 (2001)）的主要非稳态修正，并在可精确求解的模型（2D 线性锥体中的扩散）上进行了测试。展示并讨论了这种修正对基本非稳态过程、对稳态流的时变扰动以及平均首次通过时间的计算的影响。