Algorithm for generating a Brownian motion on a sphere

Carlsson, TobiasUppsala universitet,Institutionen för fysikalisk och analytisk kemi (author)

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.

Ekholm, Tobias,1970-Uppsala universitet,Matematiska institutionen,Geometry/Topology(Swepub:uu)tek26691 (author)
Elvingson, ChristerUppsala universitet,Institutionen för fysikalisk och analytisk kemi(Swepub:uu)chrielvi (author)
Uppsala universitetInstitutionen för fysikalisk och analytisk kemi (creator_code:org_t)

In:Journal of physics A: Mathematical and theoretical: IOP Publishing43:50, s. 505001-1751-81131751-8121

By the author/editor: Carlsson, Tobias; Ekholm, Tobias, ...; Elvingson, Chris ...

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