Bounds on the index of rotationally symmetric self-shrinking tori

Geometriae Dedicata - A closed surface evolving under mean curvature flow becomes singular in finite time. Near the singularity, the surface resembles a self-shrinker, a surface that shrinks by...     

Duality in Finite Element Exterior Calculus and Hodge Duality on the Sphere

Foundations of Computational Mathematics - Finite element exterior calculus refers to the development of finite element methods for differential forms, generalizing several earlier finite element...     

Constraint-Preserving Hybrid Finite Element Methods for Maxwell’s Equations

Foundations of Computational Mathematics - Maxwell’s equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux...     

Hamel’s Formalism for Infinite-Dimensional Mechanical Systems

In this paper, we introduce Hamel’s formalism for infinite-dimensional mechanical systems and in particular consider its applications to the dynamics of nonholonomically constrained systems. This development is a nontrivial extension of its finite-dimensional counterpart. The analysis is applied to several continuum mechanical systems of interest, including coupled systems and systems with infinitely many constraints.