Activity patterning induced order and turbulence in active nematics

In large, unbound systems, active nematics exhibit active turbulence, a state characterized by chaotic flows and spontaneous topological defect nucleation. Recently, it has been shown that activity patterning is an experimentally viable route to controlling the flow behavior of active nematics. Here we numerically study two-dimensional active nematics with several simple, periodic activity patterned motifs. We find that a system of active circles arranged in a triangular lattice may transition from a state of localized vortices to full-system active turbulence as activity density is increased. Interestingly, the critical activity density increases as activity strength increases, a result counterintuitive to the understanding that higher activity promotes more turbulent behavior. We find a similar transition in a system with periodic stripes, with the addition of an intermediate one-dimensional active turbulence state localized within the stripes at moderate activity density and activity strength. Finally, we show that the localized vortex state in the stripe system orders antiferromagnetically along the stripe direction, while the system tends to order ferromagnetically transverse to the stripe direction.