The Dynamics of Active Nematic Defects on The Sphere Surface

A nematic liquid crystal confined to the surface of a sphere exhibits topological defects of total charge +2 due to the topological constraint. In equilibrium, the nematic field forms four +1/2 defects, located at the corners of a tetrahedron inscribed within the sphere, since this minimizes the Frank elastic energy. Here we study the active counterpart of such a system, in which a self-driven directional motion of the individual nematogens creates a large-scale flow that drives the system out of equilibrium. In this new state, defects exhibit complex dynamics which, depending on the strength of the active forcing, can be simple and periodic (for weak forcing) or chaotic (for strong forcing). We show that Onsager’s variational principle offers an exceptionally transparent way to derive the exact dynamical equations of the defects in such an active spherical nematic, and we explain its mobility at the hydrodynamics level.