Active nematodynamics on curved surfaces -- the influence of geometric forces on motion patterns of topological defects

TL;DR

This paper develops a numerical model for active nematodynamics on curved surfaces, analyzing how geometric forces and curvature influence defect motion and flow patterns, with potential for surface property tuning.

Contribution

It introduces a surface active nematodynamics model that incorporates both intrinsic and extrinsic curvature effects, advancing understanding of defect dynamics on curved surfaces.

Findings

Extrinsic curvature significantly affects defect motion.

Geometric properties can be used to tune flow patterns.

Numerical validation on spherical and ellipsoidal surfaces.

Abstract

We derive and numerically solve a surface active nematodynamics model. We validate the numerical approach on a sphere and analyse the influence of hydrodynamics on the oscillatory motion of topological defects. For ellipsoidal surfaces the influence of geometric forces on these motion patterns is addressed by taking into account the effects of intrinsic as well as extrinsic curvature contributions. The numerical experiments demonstrate the stronger coupling with geometric properties if extrinsic curvature contributions are present and provide a possibility to tune flow and defect motion by surface properties.