球面上Smoluchowski方程的几何方法
A Geometrical Method for the Smoluchowski Equation on the Sphere
摘要：
研究了一个被动的布朗粒子在球表面上的扩散，并受到外部势的影响，线性耦合到粒子的位置的概率密度，提出了通过设计来模拟布朗粒子的合奏轨迹的数值算法。该算法以初等几何为基础，实际上只使用代数运算，这使得算法高效、简单，并且在\textit{weak sense}中收敛于球面上Smoluchowski方程的解.我们的研究结果表明，曲率的整体影响都考虑到了时间相关的和平稳的过程。
英文摘要：
A study of the diffusion of a passive Brownian particle on the surface of a sphere and subject to the effects of an external potential, coupled linearly to the probability density of the particle's position, is presented through a numerical algorithm devised to simulate the trajectories of an ensemble of Brownian particles. The algorithm is based on elementary geometry and practically only algebraic operations are used, which makes the algorithm efficient and simple, and converges, in the \textit{weak sense}, to the solutions of the Smoluchowski equation on the sphere. Our findings show that the global effects of curvature are taken into account in both the time dependent and stationary processes.
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