Active Chiral & Nematic Membranes: Odd mechanics, spontaneous flows, shape instabilities & defect-driven protrusions

Date: Thursday 23 February 2023

Abstract

I will provide a brief introduction to the field of active hydrodynamics and its relevance for modern biological physics, particularly when considered in conjunction with the mechanics of flexable fluid membranes. I will pay particular attention to the role of chiral active stresses and nematic stresses and their role in developmental processes.

I will describe some recent work on formulating the mechanics of active fluid membranes in coordinate-free, geometric form, with particular focus on novel geometrically odd contributions to the stress. These generate tangential forces in response to gradients of mean curvature that are directed along contours of constant mean curvature and, as a result, necessarily induce tangential membrane flows. When the normal viscous force amplifies perturbations the membrane shape can become linearly unstable. I will then describe examples for membranes tubes and helicoids.

Following this, I will discuss the phenomonology of active nematic fluid surfaces , focussing in particular on instabilities in nematic tubes and the role topological defects in the nematic texture play in the generation of protrusions (this is particularly relevant for the development of the organism Hydra, small freshwater organisms whose limb locations have been shown to be controlled by nematic topological defects).

Finally I will discuss open challenges and current areas of research.