Abstract

Firstly, I will review some concepts in the mechanics of fluid membranes (such as lipid membrane making up cell bilayers). I will then discuss how hydrodynamical equations governing the membrane dynamics can be derived before focussing on a specific example of a lipid membrane tube under azimuthal shear. Hear we find that shear forces drive helical instabilities in the tube shape which are eventually stabilised by the underlying advection, these dynamics do however lead to a novel non-equilibrium steady-state in the shape fluctuations of the membrane tube. We discuss the possible role of this shear driven fluctuation amplification in the process of dynamin mediated tube scission.

Secondly, I will discuss some theoretical work I have done extending the notions of active hydrodynamics to deformable surfaces with nematic ordering. We derive fully covariant hydrodynamical equations in the large deformation limit for active liquid crystal surfaces and characterise such equations in terms of typical dimensionless numbers. I will present some simple examples of instabilities and morphology generation from the coupling between ordering, flows and shape and their relevance to morphogenetic processes, such as Hydra morphogenesis.