Analytical predictions of topological defect interactions in active nematics.

In active nematics, topological defects may be motile and are sources for flow generation. Predicting and controlling the behavior of defects has practical applications for collective motion, colloidal assembly, and material transport. Here, we build off of a recently developed analytical method for predicting defect motion in passive nematics and extend it to defects in active nematics. By using appropriate approximations for the nematic order parameter and velocity fields, we find analytical expressions for the velocity of +1/2 and -1/2 winding number topological defects as a function of their distance and orientation. We test our predictions with numerical simulations of the full nonlinear equations governing the nematic order parameter.