# Dynamical patterns in active nematics on a sphere

## TL;DR

This study uses agent-based simulations to explore the complex dynamical phases of active nematic particles on a spherical surface, revealing transitions from equilibrium states to turbulence influenced by curvature and activity.

## Contribution

The paper introduces a detailed phase diagram of active nematics on a sphere, connecting simulation results with experimental observations and highlighting the impact of nematic persistence on pattern formation.

## Key findings

- Reproduction of experimental phases with microtubules on vesicles
- Identification of a transition from nematic ground state to turbulent state
- Demonstration of the influence of curvature and nematic persistence on patterns

## Abstract

Using agent-based simulations of self-propelled particles subject to short-range repulsion and nematic alignment we explore the dynamical phases of a dense active material confined to the surface of a sphere. We map the dynamical phase diagram as a function of curvature, alignment strength and activity and reproduce phases seen in recent experiments on active microtubules moving on the surfaces of vesicles. At low driving, we recover the equilibrium nematic ground state with four +1/2 defects. As the driving is increased, geodesic forces drive the transition to a band of polar matter wrapping around an equator, with large bald spots corresponding to two +1 defects at the poles. Finally, bands fold onto themselves, followed by the system moving into a turbulent state marked by active proliferation of pairs of topological defects. We highlight the role of nematic persistence length and time for pattern formation in these confined systems with finite curvature.