Morphodynamics of active nematic fluid surfaces

Morphodynamic equations governing the behaviour of active nematic fluids on deformable curved surfaces are constructed in large deformation limit. Emphasis is placed formulation objective rates that account for normal deformations whilst ensuring tangential flows Eulerian, and use surface derivative (rather than covariant derivative) free energy, which elastically couples local order to out-of-plane bending surface. Focusing geometry its dynamical interplay with hydrodynamics, several illustrative instabilities then characterised. These include cases where role Scriven-Love number analogue non-negligible, forcing can be characterised by an F\"{o}ppl-von-K\'{a}rm\'{a}n number. For former, changes texture coupled viscous dissipation. This shown result non-trivial relaxation dynamics a tube. latter, terms resulting extensile (active ruffling) contractile pearling) tube shape, as well bend texture. In comparison flat case, such now have threshold set extrinsic curvature Finally, we examine topological defect located almost show there exists steady state combination elasticity, activity non-negligible spin-connection drive shape change