We review our recent contributions to anisotropic soft matter models for liquid crystal
interfaces, drops and membranes, emphasizing validations with experimental and biological …

Abstract The Young-Laplace, Kelvin, and Gibbs-Thomson equations form a cornerstone of
colloidal and surface sciences and have found successful applications in many subfields of …

Oscillating shape motion of a freely falling and bouncing water droplet has long fascinated
and inspired scientists. We propose dynamic non-linear equations for closed, two …

Capillary condensation, which takes place in confined geometries, is the first-order vapor-to-
liquid phase transition and is explained by the Kelvin equation, but the equation's …

We revise general relativity (GR) from the perspective of calculus for moving surfaces (CMS).
While GR is intrinsically constructed in pseudo-Riemannian geometry, a complete …

A new approach to solve the compressible Navier-Stokes equations in cylindrical co-
ordinates using Geometric Algebra is proposed. This work was recently initiated by …

We present dynamic equations for two dimensional closed surfaces and analytically solve it
for some simplified cases. We derive final equations for surface normal motions by two …

We have developed dynamic manifold solutions for the Navier-Stokes equations using an
extension of differential geometry called the calculus for moving surfaces. Specifically, we …

In 2010, a book published on the work of Jaques Hadamard, entitled" Introduction to Tensor
Analysis and the Calculus of Moving Surfaces" by Dr. Pavel Grinfeld, proposed an extension …

This paper presents an extension for principles of Differential Geometry on Surfaces (re-
hashed through the budding field of CMS, the Calculus of Moving Surfaces). It analyzes …