Brownian dynamics simulations on a hypersphere in 4-space
Brownian dynamics simulations on a hypersphere in 4-space
复制标题
4 空间超球面的布朗动力学模拟
DOI：
10.1063/1.1603729
复制
发表时间：
2003
影响因子：
4.4
通讯作者：
C. Elvingson
中科院分区：
文献类型：
--
作者：
Jarl Nissfolk;T. Ekholm;C. Elvingson
我们描述了一个算法执行布朗动力学模拟粒子扩散在S3上，一个四维的超球。选择该系统是因为最近人们对在封闭空间中进行计算机模拟感兴趣，在封闭空间中可以避免周期性边界条件。我们从相应的扩散方程的解出发，具体解决了如何在3球上生成随机漫步的问题，并讨论了基于控制近似的有效实现。由于S3是一个封闭的流形（空间），因此随机漫步期间的平均平方位移不再与经过的时间成正比，就像在R3中那样。相反，它的时间变化率不断减小，并随着时间变大而趋近于零。然而，我们证明了有效扩散系数仍然可以从平方位移的时间依赖性中得到。
We describe an algorithm for performing Brownian dynamics simulations of particles diffusing on S3, a hypersphere in four dimensions. The system is chosen due to recent interest in doing computer simulations in a closed space where periodic boundary conditions can be avoided. We specifically address the question how to generate a random walk on the 3-sphere, starting from the solution of the corresponding diffusion equation, and we also discuss an efficient implementation based on controlled approximations. Since S3 is a closed manifold (space), the average square displacement during a random walk is no longer proportional to the elapsed time, as in R3. Instead, its time rate of change is continuously decreasing, and approaches zero as time becomes large. We show, however, that the effective diffusion coefficient can still be obtained from the time dependence of the square displacement.