Emergent Dynamics of Active Systems on Curved Environments

TL;DR

This paper investigates how curvature influences the collective behavior of active matter on curved surfaces, revealing effects like trapping and altered flocking driven by geometric forces.

Contribution

It introduces a geometric framework showing how curvature affects active particle motion, highlighting effects like trapping and geodesic-driven trajectories.

Findings

Curvature causes non-trivial effects on active particle motion.

Geometric torque influences flocking and trapping behaviors.

Particles tend to move along geodesics in the absence of noise and interactions.

Abstract

Curvature plays a central role in the proper function of many biological processes. With active matter being a standard framework for understanding many aspects of the physics of life, it is natural to ask what effect curvature has on the collective behaviour of active matter. In this paper, we use the classical theory of surfaces to explore the active motion of self-propelled agents confined to move on a smooth curved two-dimensional surface embedded in Euclidean space. Even without interactions and alignment, the motion is non-trivially affected by the presence of curvature, leading to effects akin, e.g.\ to gravitational lensing and tidal forces. Such effects can lead to intermittent trapping of particles and profoundly affect their flocking behaviour. We show that these effects are governed by a geometric torque that, in the absence of noise and interactions, compels particles to move along geodesics.