Elastic Surface Model For Beta-Barrels: Geometric, Computational, And Statistical Analysis

Over the past 2 decades, many different geometric models were created for beta barrels, including, but not limited to: cylinders, 1-sheeted hyperboloids, twisted hyperboloids, catenoids, and so forth. We are proponents of an elastic surface model for beta-barrels, which includes the minimal surface model as a particular case, but is a lot more comprehensive. Beta barrel models are obtained as numerical solutions of a boundary value problem, using the COMSOL Multiphysics Modeling Software. We have compared them against the best fitting statistical models, with positive results. The geometry of each individual beta barrel, as a rotational elastic surface, is determined by the ratio between the exterior diameter and the height. Through our COMSOL computational modeling, we created a rather large variety of generalized Willmore surfaces that may represent models for beta barrels. The catenoid is just a particular solution among all these shapes.