Coherent structures in active flows on curved deformable surfaces

Flows on curved deformable surfaces are ubiquitous in living and synthetic active matter. Recent computational and imaging advances enabled the measurements of these flows, which are pivotal to understanding their generating forces and biological functions. Lagrangian coherent structures (LCS) is a mathematical framework to understand and characterize the key features of complex spatio-temporal flow. Here, we extend the LCS framework to analyze flows on curved dynamic surfaces and apply it to nematic active flows on synthetic deformable nematic vesicles and in-vivo developing organs. We find that the dynamics of LCSs (attractors and repellers) are mediated by defect motion, which, in turn, is influenced by the underlying dynamic surface geometry. We show results using data from pancreatic spheroids and the beating heart of a zebrafish embryo, uncovering previously undocumented flow structures with implications for mechanosensitive mechanisms and material transport control.