Orientation of topological defects in 2D nematic liquid crystals

Abstract

Topological defects are an essential part of the structure and dynamics of all liquid crystals, and they are particularly important in experiments and simulations on active liquid crystals. In a recent paper, Vromans and Giomi [Soft Matter, 2016, 12, 6490] pointed out that topological defects are not point-like objects but actually have orientational properties, which strongly affect the energetics and motion of the defects. That paper developed a mathematical formalism which describes the orientational properties as vectors. Here, we agree with the basic concept of defect orientation, but we suggest an alternative mathematical formalism. We represent the defect orientation by a tensor, with a rank that depends on the topological charge: rank 1 for a charge of +1/2, rank 3 for a charge of -1/2. Using this tensor formalism, we calculate the orientation-dependent interaction between defects, and we present numerical simulations of defect motion.

Cited by in corpus (7)

• Interplay of Structure, Elasticity and Dynamics in Actin-Based Nematic Materials
• Dynamics of active nematic defects on the surface of a sphere
• Singularity identification for the characterization of topology, geometry, and motion of nematic disclination lines
• Multi-defect Dynamics in Active Nematics
• Annihilation trajectory of defects in smectic-C films
• Active Nematic Multipoles: Flow Responses and the Dynamics of Defects and Colloids
• The symmetries of octupolar tensors