(338k) Minimum-Energy Shapes of Open Fluid Membranes with Boundaries

Solutions to membrane energy models, such as the Helfrich-Canham equation for elastic surfaces, have been famously and successfully applied to describe the shapes manifested by blood cells and vesicles among other systems. Relatively little attention, though, has been paid to open fluid membranes with boundaries, which are relevant to membrane opening processes, colloidal membranes, and 2D biological objects like kinetoplasts. To address this problem, we have developed a general feasibly projected sequential quadratic programming (SQP) / Riemannian Newton algorithm that was successfully used to optimize triangulated meshes. We present numerical (and some analytical) results on the shapes adopted by open membranes, axisymmetry breaking, and optimization challenges encountered along the way.