Coexistence of defect morphologies in three dimensional active nematics

TL;DR

This paper investigates how activity influences the morphology of disclination lines in three-dimensional active nematic liquid crystals, revealing a crossover length scale and coexistence of different defect structures through numerical simulations.

Contribution

It introduces a defect detection algorithm and demonstrates the coexistence of regular and wrapping defect loops, establishing how activity determines defect morphology and scaling behaviors.

Findings

Activity sets a crossover length scale for defect morphology.

Regular defect lengths scale linearly with active length scale.

Wrapping defects scale inversely with the square of the active length.

Abstract

We establish how active stress globally affects the morphology of disclination lines of a three dimensional active nematic liquid crystal under chaotic flow. Thanks to a defect detection algorithm based on the local nematic orientation, we show that activity selects a crossover length scale in between the size of small defect loops and the one of long and tangled defect lines of fractal dimension $2$. This length scale crossover is consistent with the scaling of the average separation between defects as a function of activity. Moreover, on the basis of numerical simulation in a 3D periodic geometry, we show the presence of a network of regular defect loops, contractible onto the $3$-torus, always coexisting with wrapping defect lines. While the length of regular defects scales linearly with the emerging active length scale, it verifies an inverse quadratic dependence for wrapping defects. The shorter the active length scale, the more the defect lines wrap around the periodic boundaries, resulting in extremely long and buckled structures.