Bruna Maria, Chapman S Jonathan
Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford, OX1 3LB, UK,
Bull Math Biol. 2014 Apr;76(4):947-82. doi: 10.1007/s11538-013-9847-0. Epub 2013 May 10.
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear diffusion equation for the one-particle probability density function, with an overall collective diffusion that depends on both the excluded-volume and the narrow confinement. By including both these effects, the equation is able to interpolate between severe confinement (for example, single-file diffusion) and unconfined diffusion. Numerical solutions of both the effective nonlinear diffusion equation and the stochastic particle system are presented and compared. As an application, the case of diffusion under a ratchet potential is considered, and the change in transport properties due to excluded-volume and confinement effects is examined.
考虑有限尺寸硬核相互作用粒子在二维或三维受限域中的扩散，其中受限维度与粒子维度相当。结果得到了一个关于单粒子概率密度函数的非线性扩散方程，其整体集体扩散取决于排除体积和狭窄受限效应。通过同时包含这两种效应，该方程能够在强受限（例如，单文件扩散）和无受限扩散之间进行插值。给出并比较了有效非线性扩散方程和随机粒子系统的数值解。作为一个应用，考虑了棘轮势下的扩散情况，并研究了由于排除体积和受限效应导致的输运性质变化。
