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Emergence and melting of active vortex crystals.

ABSTRACT: Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Performing extensive hydrodynamic simulations, we find rich transition scenarios. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. The melting of this crystal proceeds through an intermediate hexatic phase. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.

SUBMITTER: James M

PROVIDER: S-EPMC8463610 | biostudies-literature | 2021 Sep

REPOSITORIES: biostudies-literature

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Emergence and melting of active vortex crystals.

James Martin M Suchla Dominik Anton DA Dunkel Jörn J Wilczek Michael M

Nature communications 20210924 1

Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of ...[more]

PMID: 34561437

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Project description:Vortex crystals are equilibrium states of point vortices whose relative configuration is unchanged throughout the evolution. They are examples of stationary point configurations subject to a logarithmic particle interaction energy, which give rise to phenomenological models of pattern formations in incompressible fluids, superconductors, superfluids and Bose–Einstein condensates. In this paper, we consider vortex crystals rotating at a constant speed in the latitudinal direction on the surface of a torus. The problem of finding vortex crystals is formulated as a linear null equation AΓ = 0 for a non-normal matrix A whose entities are derived from the locations of point vortices, and a vector Γ consisting of the strengths of point vortices and the latitudinal speed of rotation. Point configurations of vortex crystals are obtained numerically through the singular value decomposition by prescribing their locations and/or by moving them randomly so that the matrix A becomes rank deficient. Their strengths are taken from the null space corresponding to the zero singular values. The toroidal surface has a non-constant curvature and a handle structure, which are geometrically different from the plane and the spherical surface where vortex crystals have been constructed in the preceding studies. We find new vortex crystals that are associated with these toroidal geometry: (i) a polygonal arrangement of point vortices around the line of longitude; (ii) multiple latitudinal polygonal ring configurations of point vortices that are evenly arranged around the handle; and (iii) point configurations along helical curves corresponding to the fundamental group of the toroidal surface. We observe the strengths of point vortices and the behaviour of their distribution as the number of point vortices gets larger. Their linear stability is also examined. This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.

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Emergence and melting of active vortex crystals.

Publications

Emergence and melting of active vortex crystals.

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