Understanding of a mechanism of a structure formation in two-dimensional point vortex system at negative temperature

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A motivation of this work is to understand a dynamics of the two-dimensional point vortex system characterized by statistically-defined temperature. There are two topics to be focused: (1) to verify a validity of an equilibrium solution of the discrete point vortex system presented by Montgomery etal. that has been only checked for the continuous Euler system, (2) to determine parameters characterizing a structure formation that can be seen as vortex crystals, and decay processes. In topic (1), we have confirmed the validity of Montgomery's conjecture. In topic (2), we have found the conserved quantity does not conserve due to a diffusion effect arising from a discrete distribution of the vorticity. Now, we are trying to understand the effect quantitatively.