Curvature-controlled defect dynamics in active systems.

We have studied the collective motion of polar active particles confined to ellipsoidal surfaces. The geometric constraints lead to the formation of vortices that encircle surface points of constant curvature (umbilics). We have found that collective motion patterns are particularly rich on ellipsoids with four umbilics where vortices tend to be located near pairs of umbilical points to minimize their interaction energy. Our results provide a perspective on the migration of living cells, which most likely use the information provided from the curved substrate geometry to guide their collective motion.