Collective ordering of bacterial vortices controlled by geometry and frustration

Controlling collective patterns has attracted interest due to their potential in exploiting their hidden ordered phase of active bacterial suspension. Here, by imposing a geometric boundary condition, we study controlled collective motion of Escherichia coli bacteria inside designed microwells. In a doublet circles, two vortices emerge but their spinning directions show two distinct phases of either parallel pattern (ferromagnetic vortices, FMV) or anti-parallel one (anti-ferromagnetic vortices, AFMV). The transition from FMV to AFMV occurs when the ratio of vortex size to vortex distance is sqrt2. Analytical solution with mean-field approximation accounts for this geometric rule [1]. By using this relation, we can control quadruplet pairing of bacterial vortices. Moreover, in a triplet circles, coexistence of FMV and AFMV pairings is emerged despite frustration, and the transition point from FMV pattern to coexisted phase is shifted because frustration stabilizes FMV pattern. Our result proposes simple design of boundary as promising mean in order to understand collective ordering of bacterial vortices.

Reference
[1] K. Beppu, et al., Soft Matter, 2017, 13, 5038