Magdalena Toda

Constructing isothermal curvature line coordinates on surfaces which admit them

Isothermic parameterizations are synonyms of isothermal curvature line parameterizations, for surfaces immersed in Euclidean spaces. We provide a method of constructing isothermic coordinate charts on surfaces which admit them, starting from an arbitrary chart. One of the primary applications of this work consists of numerical algorithms for surface visualization.

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.

Preface of the "Symposium on geometric methods for integrable systems and PDE with applications to engineering, biology and medicine"

The symposiums goal is to present recent advances in mathematical research of non-linear PDE and their immediate or long-term applications to the diverse engineering fields, as well as biology and medicine.