Understanding the statistical behaviour of ensembles of point vortices is (almost!) a classical problem in physics. We have been particularly interested in the phenomenon of condensation, the spontaneous emergence of a mean circulation in a bounded domain, which occurs as the interaction energy of the vortices is increased.

Low energy simulations

High energy simulations

The above simulations illustrate uncondensed (low energy) and condensed (high energy) states. In the high energy case the vortices are at a formally negative temperature. Notice that the two domains have quite different condensed states!