障碍物存在时晶格上的随机行走：短时瞬态区、反常扩散和拥挤
Random walk on a lattice in the presence of obstacles: The short-time transient regime, anomalous diffusion and crowding
摘要：
在拥挤的环境中，粒子的扩散通常通过三种方式进行：在很短的时间内，粒子自由扩散，直到它第一次与障碍物碰撞，而在很长的时间内，扩散运动是Fickian的，扩散系数$D$取决于系统中存在的障碍物的浓度和类型。对于中间时间，粒子的均方位移通常近似增加为$~t^α$，其中$α<1$是通常称为异常扩散的典型。然而，如何识别或选择能够给出$α$的可靠估计的时间或位移间隔尚不清楚。在本文中，我们使用两种精确的数值方法来获得一个简单的格子蒙特卡罗模型在两个时间限制的扩散数据。这使我们能够提出一个客观的定义的瞬态制度和一个独特的价值$α$。此外，我们的方法直接给了我们的长度尺度，在过渡状态切换到稳态政权。我们测试我们提出的方法使用几种类型的障碍系统，我们引入了新的概念，过量扩散长度。最后，我们表明，描述异常瞬态制度的参数的值取决于用于描述粒子的动态的Monte Carlo移动，我们提出了一个新的算法，正确地模拟短时间扩散的粒子在晶格上。
英文摘要：
The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the motion is Fickian with a diffusion coefficient $D$ that depends on the concentration and type of obstacles present in the system. For intermediate times, the mean-square displacement of the particle often increases approximately as $~t^α$, with $α<1$, typical of what is generally called anomalous diffusion. However, it is not clear how one can identify or choose a time or displacement interval that would give a reliable estimate of $α$. In this paper, we use two exact numerical approaches to obtain diffusion data for a simple Lattice Monte Carlo model in both time limits. This allows us to propose an objective definition of the transient regime and a unique value for $α$. Furthermore, our methodology directly gives us the length scale over which the transient regime switches to the steady-state regime. We test our proposed approach using several types of obstacle systems, and we introduce the novel concept of excess diffusion lengths. Finally, we show that the values of the parameters describing the anomalous transient regime depend on the Monte Carlo moves used to describe the dynamics of the particle, and we propose a new algorithm that correctly models the short time diffusion of a particle on a lattice.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
