Turbulence to order transitions in activity patterned active nematics

We numerically study two-dimensional active nematics with periodic activity patterning. For stripes of activity, we observe a transition from two-dimensional to one-dimensional active turbulence as the maximum active force and distance between activity stripes increases, followed by a transition to stable vortices ordered antiferromagnetically along the stripes and ferromagnetically transverse to the stripes. By comparing to a triangular lattice of activity circles, we find that transitions to two-dimensional active turbulence emerge from interplays between the active length scale and activity density, independent of the patterning geometry. The vortex ordering, on the other hand, is highly sensitive to patterning geometry, which we show by comparing the activity stripes to columns of activity circles, where the vortex ordering is lost. Our results provide a mechanism for inducing non-equilibrium phase transitions in active nematics using activity inhomogeneity, which can be further exploited to create activity patterned ordered phases.