Pair creation, motion, and annihilation of topological defects in 2D nematics

TL;DR

This paper introduces a new framework for analyzing the creation, motion, and annihilation of topological defects in 2D active nematic liquid crystals, combining order tensor formalism with dynamical systems.

Contribution

It develops a novel theoretical approach that models defect dynamics and production in active nematics using exact solutions and low-dimensional dynamical systems.

Findings

Derived exact multi-particle solutions for static defect configurations.

Modeled defect creation and annihilation consistent with experimental observations.

Estimated the critical density for defect production and annihilation balance.

Abstract

We present a novel framework for the study of disclinations in two-dimensional active nematic liquid crystals, and topological defects in general. The order tensor formalism is used to calculate exact multi-particle solutions of the linearized static equations inside a uniformly aligned state. Topological charge conservation requires a fixed difference between the number of half charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parameters of the static solutions, which describes the motion of a half-disclination pair, or of several pairs. Within this formalism, we model defect production and annihilation, as observed in experiments. Our dynamics also provide an estimate for the critical density at which production and annihilation rates are balanced.