# Hydrodynamics of Active Defects: from order to chaos to defect ordering

## TL;DR

This paper develops a hydrodynamic theory for 2D active nematics with many defects, revealing transitions from active turbulence to defect-ordered phases and showing how activity gradients can control defect dynamics.

## Contribution

It introduces a comprehensive hydrodynamic model capturing defect-driven flows, chaos, and ordered phases in active nematics, and explores defect manipulation via activity gradients.

## Key findings

- Characterization of defect chaos and turbulence in active nematics.
- Discovery of a defect-ordered polar liquid phase at high activity.
- Demonstration of activity gradients controlling defect charge sorting.

## Abstract

Topological defects play a prominent role in the physics of two-dimensional materials. When driven out of equilibrium in active nematics, disclinations can acquire spontaneous self-propulsion and drive self-sustained flows upon proliferation. Here we construct a general hydrodynamic theory for a two-dimensional active nematic interrupted by a large number of such defects. Our equations describe the flows and spatio-temporal defect chaos characterizing active turbulence, even close to the defect unbinding transition. At high activity, nonequilibrium torques combined with many-body screening cause the active disclinations to spontaneously break rotational symmetry forming a collectively moving defect ordered polar liquid. By recognizing defects as the relevant quasiparticle excitations, we construct a comprehensive phase diagram for two-dimensional active nematics. Using our hydrodynamic approach, we additionally show that activity gradients can act like "electric fields", driving the sorting of topological charge. This demonstrates the versatility of our continuum model and its relevance for quantifying the use of spatially inhomogeneous activity for controlling active flows and for the fabrication of active devices with targeted transport capabilities.