The de Rham-Hodge theory is a landmark of the 20$^\text {th} $ Century's mathematics and
has had a great impact on mathematics, physics, computer science, and engineering. This …

This paper presents a differential geometry based model for the analysis and computation of
the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to …

This article presents a novel concept, the minimal molecular surface (MMS), for the
theoretical modeling of biomolecules. The MMS can be viewed as a result of the surface free …

Large chemical and biological systems such as fuel cells, ion channels, molecular motors,
and viruses are of great importance to the scientific community and public health. Typically …

In this article we discuss novel numerical schemes for the computation of the curve
shortening and mean curvature flows that are based on special reparametrizations. The …

This paper presents new geometrical flow equations for the theoretical modeling of
biomolecular surfaces in the context of multiscale implicit solvent models. To account for the …

Persistent homology provides a new approach for the topological simplification of big data
via measuring the life time of intrinsic topological features in a filtration process and has …

Over the last two decades, the field of geometric curve evolutions has attracted significant
attention from scientific computing. One of the most popular numerical methods for solving …

We propose a direct method for solving the evolution of plane curves satisfying the
geometric equation v= β (x, k, ν) where v is the normal velocity, k and ν are the curvature and …

Solvation is an elementary process in nature and is of paramount importance to more
sophisticated chemical, biological and biomolecular processes. The understanding of …