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Self-organization of microswimmers in arrays of obstacles
Bacterial suspensions, a paradigmatic example of an active fluid, are known to exhibit a state denoted as mesoscale turbulence which is characterized by chaotic dynamics of vortices of a characteristic size. In a recent experiment, these vortices have been stabilized into a square lattice with antiferromagnetic order by geometrically constraining the bacterial suspension using periodic arrays of obstacles with a spacing in the range of the unconstrained vortex size . Interestingly, the vortices are consistently located in the gaps between the obstacles rather than forming around them .
We aim to reproduce the patterns observed in the experiment using a recently derived fourth-order field theory for a vectorial order parameter representing an effective microswimmer velocity . In this continuum-theoretical framework, we propose a set of boundary conditions that implicitly favors negatively charged topological defects located in the centers of the pillars. By tuning the pillar size we can influence the topological charge already for a single pillar in otherwise unconstrained mesoscale turbulence and, in particular, stabilize an antiferromagnetic vortex lattice in a large configuration of pillars.
 D. Nishiguchi, I. S. Aranson, A. Snezhko and A. Sokolov, Nat. Comm. 9, 4486 (2018).
 H. Reinken, S. H. L. Klapp, M. Bär, and S. Heidenreich, Phys. Rev. E 97, 022613 (2018).