Curvature-controlled defect dynamics in active systems

TL;DR

This paper investigates how the curvature of ellipsoidal surfaces influences the collective motion of active particles, revealing vortex formations at points of constant curvature and implications for cell migration.

Contribution

It introduces a study of defect dynamics in active systems constrained on curved surfaces, highlighting the role of geometry in collective behavior and vortex formation.

Findings

Vortices form around surface points of constant curvature (umbilics).

Four umbilics on ellipsoids tend to host vortices to minimize interaction energy.

Results suggest curved substrate geometry guides collective cell migration.

Abstract

We have studied the collective motion of polar active particles confined to ellipsoidal surfaces. The geometric constraints lead to the formation of vortices that encircle surface points of constant curvature (umbilics). We have found that collective motion patterns are particularly rich on ellipsoids, with four umbilics where vortices tend to be located near pairs of umbilical points to minimize their interaction energy. Our results provide a new perspective on the migration of living cells, which most likely use the information provided from the curved substrate geometry to guide their collective motion.