QGLAB: A MATLAB Package for Computations on Quantum Graphs
We describe QGLAB, a new MATLAB package for analyzing partial differential equations on quantum graphs. The supplementary material contains additional examples and a complete …
A new canonical reduction of three-vortex motion and its application to vortex-dipole scattering
We use Jacobi coordinates and Nambu brackets to derive a new representation of the motion of three vortices which, unlike all previous reductions, introduces no singularities into …
Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential
We use optimal control based on a Galerkin-truncated model to transfer a BEC from one well of a two-well potential to the other.
Apodizer Design to Efficiently Couple Light into a Fiber Bragg Grating
We use an optimal control framework to efficiently couple light into a fiber Bragg grating, improving a previously-reported 66 percent transmission to 88 percent.
Transition to instability of the leapfrogging vortex quartet
We show via analytical perturbation theory that the leapfrogging vortex quartet becomes unstable exactly at the critical ratio $\alpha= \phi^{-2}.$
An Optimal Control Approach to Gradient-Index Design for Beam Reshaping
We address the problem of reshaping light in the Schrödinger optics regime from the perspective of optimal control theory. In technological applications, Schrödinger optics is …
A Reduction-Based Strategy for Optimal Control of Bose-Einstein Condensates
Applications of Bose-Einstein Condensates (BEC) often require that the condensate be prepared in a specific complex state. Optimal control is a reliable framework to prepare such a …
Solitary Waves in Mass-in-Mass Lattices
We consider the existence of spatially localized traveling wave solutions of the mass-in-mass lattice. Under an anti-resonance condition first discovered by Kevrekidis, Stefanov …
Loss of Physical Reversibility in Reversible Systems
A dynamical system is said to be reversible if, given an output, the input can always be recovered in a well-posed manner. Nevertheless, we argue that reversible systems that have …
Stability of Leapfrogging Vortex Pairs: A Semi-analytic Approach
We investigate the stability of a one-parameter family of periodic solutions of the four-vortex problem known as _leapfrogging_ orbits. These solutions, which consists of two pairs …
