Dynamics of orientational ordering in fluid membranes

TL;DR

This paper investigates the slow evolution of orientational order in fluid membranes, revealing subdiffusive curvature effects that limit coarsening and influence defect structures and correlations.

Contribution

It introduces a numerical study of slow coarsening dynamics in fluid membranes, highlighting the role of curvature-mediated long-range interactions.

Findings

Coarsening is unusually slow, with growth exponent less than 1/4.

Membrane curvature mediates long-range interactions affecting defect profiles.

Correlation patterns are influenced by curvature elasticity.

Abstract

We study the dynamics of orientational phase ordering in fluid membranes. Through numerical simulation we find an unusually slow coarsening of topological texture, which is limited by subdiffusive propagation of membrane curvature. The growth of the orientational correlation length $\xi$ obeys a power law $\xi \propto t^w$ with $w < 1/4$ in the late stage. We also discuss defect profiles and correlation patterns in terms of long-range interaction mediated by curvature elasticity.