Dynamics of active nematic defects on the surface of a sphere

Abstract

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 regular tetrahedron inscribed within the sphere, since this minimizes the Frank elastic energy. If additionally the individual nematogens exhibit self-driven directional motion, the resulting active system creates large-scale flow that drives it out of equilibrium. In particular, the defects now follow complex dynamic trajectories which, depending on the strength of the active forcing, can be periodic (for weak forcing) or chaotic (for strong forcing). In this paper we derive an effective particle theory for this system, in which the topological defects are the degrees of freedom, whose exact equations of motion we subsequently determine. Numerical solutions of these equations confirm previously observed characteristics of their dynamics and clarify the role played by the time dependence of their global rotation. We also show that Onsager's variational principle offers an exceptionally transparent way to derive these dynamical equations, and we explain the defect mobility at the hydrodynamics level.

16 pages, 7 figures

References in corpus (13)

• Spontaneous Skyrmion Ground States in Magnetic Metals
• Topology and Dynamics of Active Nematic Vesicles
• Active matter
• Steady-state hydrodynamic instabilities of active liquid crystals: Hybrid lattice Boltzmann simulations
• Defect dynamics in active nematics
• Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi
• Nematic textures in spherical shells
• Topological Defects in Spherical Nematics
• Interplay of Structure, Elasticity and Dynamics in Actin-Based Nematic Materials
• Orientation of topological defects in 2D nematic liquid crystals
• Topology and morphology of self-deforming active shells
• Hydrodynamic theory for nematic shells: the interplay among curvature, flow and alignment
• Dynamics of active nematic defects on the surface of a sphere

Cited by in corpus (14)

• Topological active matter
• Onsager's variational principle in active soft matter
• Design of nematic liquid crystals to control microscale dynamics
• Dynamics of active nematic defects on the surface of a sphere
• Active nematodynamics on curved surfaces -- the influence of geometric forces on motion patterns of topological defects
• Flow around topological defects in active nematic films
• Tuneable defect-curvature coupling and topological transitions in active shells
• Many-defect solutions in planar nematics: interactions, spiral textures and boundary conditions
• Cooling a spherical nematic shell
• Multi-defect Dynamics in Active Nematics
• Locomotion without force, and impulse via dissipation: Robotic swimming in curved space via geometric phase
• Active topological defect absorption by a curvature singularity
• Analytical model for the motion and interaction of two-dimensional active nematic defects
• Statistical formulation of Onsager-Machlup variational principle