# Curvature controlled defect dynamics in topological active nematics

## TL;DR

This paper investigates how topological constraints and geometry influence defect dynamics in active nematic films, revealing tunable oscillatory and rotating states linked to curvature and shape.

## Contribution

It introduces a detailed analysis of defect behavior in topologically constrained active nematics on ellipsoids, highlighting the role of geometry in defect dynamics.

## Key findings

- Defects exhibit two main dynamic modes: oscillatory and rotating.
- Defect locations correlate with high Gaussian curvature and umbilical points.
- Limits are identified for modeling defects as self-propelled particles.

## Abstract

We study the spatiotemporal patterns that emerge when an active nematic film is topologically constraint. These topological constraints allow to control the non-equilibrium dynamics of the active system. We consider ellipsoidal shapes for which the resulting defects are 1/2 disclinations and analyze the relation between their location and dynamics and local geometric properties of the ellipsoid. We highlight two dynamic modes: a tunable periodic state that oscillates between two defect configurations on a spherical shape and a tunable rotating state for oblate spheroids. We further demonstrate the relation between defects and high Gaussian curvature and umbilical points and point out limits for a coarse-grained description of defects as self-propelled particles.