Defect dynamics in dry active nematics by residue calculus for holomorphic functions of nematic director field

This paper proposes a theory for modeling the dynamics of topological defects in dry active nematics. We introduce a holomorphic function for integral curves of the director field and show the density of the integral curves corresponds to that of active nematic liquid crystals such as confined spindle-shaped cells. Then, we derive equations of motion for defects by considering active stress defined from the integral curves. A mathematical analysis of the equations reveals that the dynamics of the defects can be explicitly expressed with the residues of holomorphic functions derived from the director field. We verify the proposed theory using existing work on the motion of a defect pair and demonstrate estimation of parameters for active stress by cell culture experiments.