Cuncheng Zhu

Abstract Coherent structures---flow features that organize material transport and deformation---are central to analyzing complex flows in fluids, plasmas, and active matter. Yet, identifying such structures on dynamic surfaces remains an open challenge, limiting their application to many living and synthetic systems. Here, we introduce a geometric framework to extract Lagrangian and Eulerian coherent structures from velocity data on arbitrarily shaped, time-evolving surfaces.

We note that the notation for the discrete curvature, (∫C)i is used only in this illustrative example; in the remainder of the text, we will omit the parenthesis and use the simplified notation, ∫Ci. To make sense of the integral over a discrete object, additional care must be taken to represent the curvature from a distributional sense ( ).

Abstract Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations.