Computational Geometry Platform for Symmetry Breaking in Ellipsoids: Application to Shape Transitions and Curvature-Driven Self-Assembly Driving Force of Liquid and Soft Matter Drops and Capsules

This paper develops, implements, and uses integrated global and local geometric modelling of ellipsoids and transforms curvatures and shapes into energy metrics that predict potential curvature-driven self-assembly driving force pathways into fibers and films. Global parameterization is based on eccentricities and the local parameterization, based on mean and Gaussian curvatures, is mapped into shape and curvedness parameterizations that clearly distinguish critical shape effects from curvedness effects in contrast to mean and Gaussian curvatures. Finally, the geometric modelling is transformed, through a liquid membranology model, into bending energy densities that point the ways to fiber and film assembly pathways.