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Spherical Ornstein-Uhlenbeck processes

Wilkinson, Michael and Pumir, Alain (2011). Spherical Ornstein-Uhlenbeck processes. Journal of Statistical Physics, 145(1) pp. 113–142.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1007/s10955-011-0332-6
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Abstract

The paper considers random motion of a point on the surface of a sphere, in the case where the angular velocity is determined by an Ornstein-Uhlenbeck process. The solution is fully characterised by only one dimensionless number, the persistence angle, which is the typical angle of rotation during the correlation time of the angular velocity. We first show that the two-dimensional case is exactly solvable. When the persistence angle is large, a series for the correlation function has the surprising property that its sum varies much more slowly than any of its individual terms. In three dimensions we obtain asymptotic forms for the correlation function, in the limits where the persistence angle is very small and very large. The latter case exhibits a complicated transient, followed by a much slower exponential decay. The decay rate is determined by the solution of a radial Schrödinger equation in which the angular momentum quantum number takes an irrational value, namely j=½ (√17-1). Possible applications of the model to objects tumbling in a turbulent environment are discussed.

Item Type: Journal Article
Copyright Holders: 2011 Springer Science+Business Media
ISSN: 0022-4715
Keywords: diffusion, Ornstein-Uhlenbeck process
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 30917
Depositing User: Michael Wilkinson
Date Deposited: 06 Jan 2012 16:14
Last Modified: 30 Oct 2013 13:10
URI: http://oro.open.ac.uk/id/eprint/30917
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