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