Defect binding-unbinding transition in active nematic membranes

TL;DR

This study models active nematic membranes to understand how active stress and curvature influence defect dynamics and membrane shape, revealing a transition from defect trapping to active turbulence with a critical activity threshold.

Contribution

The paper introduces a minimal coupled model for active nematic membranes, identifying a continuous transition influenced by activity and membrane properties, supported by scaling analysis and numerical simulations.

Findings

Critical activity threshold scales as α²/κ, confirmed numerically.

Defects are trapped by local deformation in curvature-dominated regime.

Active turbulence features persistent correlations between nematic order and membrane shape.

Abstract

We investigate the dynamics of active nematic liquid crystals on deformable membranes, focusing on the interplay between active stress and anisotropic curvature coupling. Using a minimal model, we simulate the coupled evolution of the nematic order parameter and membrane height. We demonstrate a continuous transition from a curvature-dominated regime, where topological defects are trapped by local deformation, to an activity-dominated regime exhibiting active turbulence. A scaling analysis reveals that the critical activity threshold $\zeta_c$ scales as $\alpha^2/\kappa$, where $\alpha$ and $\kappa$ are the coupling constant and bending stiffness, respectively; this relationship is confirmed by our numerical results. Furthermore, we find that significant correlations between the orientational pattern and membrane geometry persist even in the turbulent regime. Specifically, we identify that "walls" in the director field induce characteristic wave-like curvature profiles, providing a mechanism for dynamic coupling between order and shape. These results offer a physical framework for understanding defect-mediated deformation in nonequilibrium biological membranes.