# American Institute of Mathematical Sciences

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February  2005, 5(1): 125-136. doi: 10.3934/dcdsb.2005.5.125

## The Dirichlet quotient of point vortex interactions on the surface of the sphere examined by Monte Carlo experiments

 1 Department of Computational Science, National University of Singapore

Received  September 2003 Revised  December 2003 Published  November 2004

The point-vortex system on the surface of the sphere is examined by Monte Carlo methods. The statistical equilibria found in the system when it is constrained to keep circulation zero (but without other explicit constraints on site values) are found to be self-regulating in a sense. While site strengths will grow without bound as the number of sweeps increases, the Dirichlet quotient, the ratio of enstrophy to energy, is found to converge rapidly to a finite nonzero value. This unlimited growth in site values remains controlled. The dependences of this quotient on the temperature and on the mesh size are examined.
Citation: Joseph Nebus. The Dirichlet quotient of point vortex interactions on the surface of the sphere examined by Monte Carlo experiments. Discrete & Continuous Dynamical Systems - B, 2005, 5 (1) : 125-136. doi: 10.3934/dcdsb.2005.5.125
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