Algorithm for generating a Brownian motion on a sphere
Algorithm for generating a Brownian motion on a sphere
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在球体上生成布朗运动的算法
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
C. Elvingson
中科院分区：
文献类型：
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作者：
T. Carlsson;T. Ekholm;C. Elvingson
提出了一种新的算法，用于生成二维球面上的随机游动。该算法是通过将2-球看作是3-球中的赤道，3-球被一个无限薄的带所包围，带的边界反映布朗粒子，然后应用已知的有效方法在3-球上生成布朗运动。为了测试该方法，在计算机模拟中使用新算法计算扩散系数，并且为了进行比较，还使用常用的方法，其中颗粒在2球的切平面中采取布朗步骤，然后投影回球面。这两种方法是在短时间步长很好的协议，而本文提出的方法继续给出良好的结果，也为较大的时间步长，当替代方法变得不稳定。
We present a new algorithm for generation of a random walk on a two-dimensional sphere. The algorithm is obtained by viewing the 2-sphere as the equator in the 3-sphere surrounded by an infinitesimally thin band with boundary which reflects Brownian particles and then applying known effective methods for generating Brownian motion on the 3-sphere. To test the method, the diffusion coefficient was calculated in computer simulations using the new algorithm and, for comparison, also using a commonly used method in which the particle takes a Brownian step in the tangent plane to the 2-sphere and is then projected back to the spherical surface. The two methods are in good agreement for short time steps, while the method presented in this paper continues to give good results also for larger time steps, when the alternative method becomes unstable.