Periodic orbits, pair nucleation, and unbinding of active nematic defects on cones

TL;DR

This study explores how geometric confinement and curvature influence defect dynamics in active nematics on cones, revealing complex behaviors like periodic orbits, defect unbinding, and pair nucleation through combined analytical and numerical methods.

Contribution

It introduces a comprehensive analysis of active nematic defect dynamics on conical surfaces, highlighting the effects of curvature and confinement with a novel phase diagram and defect behavior characterization.

Findings

Identification of exotic periodic defect orbits depending on activity and cone apex charge.

Observation of defect unbinding and pair nucleation at the cone apex.

Confirmation of theoretical predictions through numerical simulations.

Abstract

Geometric confinement and topological constraints present promising means of controlling active materials. By combining analytical arguments derived from the Born-Oppenheimer approximation with numerical simulations, we investigate the simultaneous impact of confinement together with curvature singularity by characterizing the dynamics of an active nematic on a cone. Here, the Born-Oppenheimer approximation means that textures can follow defect positions rapidly on the time scales of interest. Upon imposing strong anchoring boundary conditions at the base of a cone, we find a a rich phase diagram of multi-defect dynamics including exotic periodic orbits of one or two $+1/2$ flank defects, depending on activity and non-quantized geometric charge at the cone apex. By characterizing the transitions between these ordered dynamical states, we can understand (i) defect unbinding, (ii) defect absorption and (iii) defect pair nucleation at the apex. Numerical simulations confirm theoretical predictions of not only the nature of the circular orbits but also defect unbinding from the apex.