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- W4379388634 abstract "We study axis-symmetric Onsager clustered states of a neutral point vortex system confined to a two-dimensional disc. Our analysis is based on the mean field of bounded point vortices in the microcanonical ensemble. The clustered vortex states are specified by the inverse temperature $beta$ and the rotation frequency $omega$, which are the conjugate variables of energy $E$ and angular momentum $L$, respectively. The formation of the axis-symmetric clustered vortex states (azimuthal angle independent) involves the separating of vortices with opposite circulation and the clustering of vortices with same circulation around origin and edge. The state preserves $rm SO(2)$ symmetry while breaks $mathbb Z_2$ symmetry. We find that, near the uniform state ($E=0$), the rotation free state ($omega=0$) emerges at particular values of $L^2/E$ and $beta$. At large energies, we obtain asymptotically exact vortex density distributions, whose validity condition gives rise the lower bound of $beta$ for the rotation free states. Noticeably, the obtained vortex density distribution near the edge at large energies provides a novel exact vortex density distribution for the corresponding chiral vortex system." @default.
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- W4379388634 date "2023-08-10" @default.
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- W4379388634 title "Axis-symmetric Onsager clustered states of point vortices in a bounded domain" @default.
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- W4379388634 doi "https://doi.org/10.1088/1572-9494/acdb57" @default.
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