We show how the topological number of a static Hamiltonian can be measured from a
dynamical quench process. We focus on a two-band Chern insulator in two dimension, for …

We introduce new three-dimensional (3D) topological phases of two-band models using the
Pontryagin-Thom construction. In symmetry class A these are the infinitely many Hopf-Chern …

Inspired by experiments on topologically linked DNA networks, we consider the connectivity
of Borromean networks, in which no two rings share a pairwise-link, but groups of three rings …

Theoretical and Computational Fluid Mechanics: Existence, Blow-up, and Discrete Exterior
Calculus Algorithms centralizes the main and current topics in theoretical and applied fluid …

Abstract The Incompressible Navier-Stokes Equations (NSEs) are on the list of Millennium
Problems, to prove their existence and uniqueness of solutions. The NSEs can be …

We develop a minimal model to study the stochastic formation of Borromean links within
topologically entangled networks without requiring the use of knot invariants. Borromean …

To each three-component link in the 3-sphere we associate a generalized Gauss map from
the 3-torus to the 2-sphere, and show that the pairwise linking numbers and Milnor triple …

We introduce an alternative approach to the third order helicity of a volume preserving vector
field B, which leads us to a lower bound for the L 2-energy of B. The proposed approach …

Two new nonlocal asymptotic invariants of magnetic fields frozen into a finite domain filled
with an ideal liquid conducting medium are introduced. The velocity of variation of the …

To each three-component link in the 3-sphere, we associate a geometrically natural
characteristic map from the 3-torus to the 2-sphere, and show that the pairwise linking …