Three-Dimensional Active Defect Loops

TL;DR

This paper investigates the dynamics and morphology of topological defect loops in three-dimensional active nematics, revealing how local orientational profiles influence material flow, shape changes, and defect formation through bend instability.

Contribution

It provides a comprehensive analysis of defect loop behaviors in 3D active nematics, linking geometry, topology, and flow dynamics through theory and numerical modeling.

Findings

Defect loops can drive material flow along or perpendicular to the loop.

Local curvature correlates with the orientational profile, indicating dynamic coupling.

Defect loops form via bend instability from various initial distortions.

Abstract

We describe the flows and morphological dynamics of topological defect lines and loops in three-dimensional active nematics and show, using theory and numerical modelling, that they are governed by the local profile of the orientational order surrounding the defects. Analysing a continuous span of defect loop profiles, ranging from radial and tangential twist to wedge $\pm 1/2$ profiles, we show that the distinct geometries can drive material flow perpendicular or along the local defect loop segment, whose variation around a closed loop can lead to net loop motion, elongation or compression of shape, or buckling of the loops. We demonstrate a correlation between local curvature and the local orientational profile of the defect loop, indicating dynamic coupling between geometry and topology. To address the general formation of defect loops in three dimensions, we show their creation via bend instability from different initial elastic distortions.