Published: Dec. 30, 2016

As the year comes to an end, the Dispersive Hydrodynamics LaboratoryDispHydroLabReflects reflects on a successful 2016. The lab was involved in Applied Mathematics’ first CU Wizards show, a 30+ year CU tradition. CU Wizards is a monthly, interactive show for children. The program brings the “magic of science” to kids and their families to further public science education and interest. The lab put on “Surfing with a Mathematician”, a demonstration on the ways nonlinear waves help us understand systems as diverse as the ocean, atmosphere, and lasers. The entire lab was involved with the event and can be seen doing the wave on the recording of their show.

In addition to papers published in Nature Communications and Physical Review Letters earlier this year, the lab published several more notable papers in 2016. Physical Review Letters accepted another paper from the lab members titled, Breaking of Galilean invariance in the hydrodynamic formulation of ferromagnetic thin films. In this article, Dr. Ezio Iacocca, Professor Mark Hoefer, and Dr. Thomas Silva (NIST) showed that the equations describing magnetization dynamics for a solid-state thin-film ferromagnet (i.e., a sheet of magnetic material about five nanometers thick) can be formulated as a dispersive hydrodynamic set of equations. In contrast to other dispersive fluids explored by the lab, magnets are peculiar in which Galilean invariance is broken. That means the physics are reference-frame dependent, an effect otherwise observed in relativity. This work opens up a new frontier for magnetics research, both from a fundamental physics and a dispersive fluid perspective.

SIAM Journal of Applied Mathematics has also accepted a paper from the lab.  The paper, Shock waves in dispersive hydrodynamics with non-convex dispersion, was co-authored by Patrick Sprenger and Professor Hoefer. They found new dispersive shock wave structures admitted by the Kawahara equation, a universal model for dispersive hydrodynamic systems with high order dispersion. Such phenomena occur in various physical systems including ultra-shallow water flow, nonlinear fiber optics and spin orbit coupled Bose-Einstein condensates. The shock waves that were observed in this work had been observed numerically but no theory existed to describe these non-classical structures. This work motivates a new shallow water experiment that is currently under development in the Dispersive Hydrodynamics Laboratory.

Additionally, Michelle Maiden and Professor Hoefer were published in Proceedings of the Royal Society A.  Their paper, Modulations of viscous fluid conduit periodic waves, theoretically identifies new coherent wave structures called envelope solitons. In their next project, they will attempt to observe these solitons in experiments with viscous fluid conduits.

This year also brought about two substantial review articles. Dispersive shock waves and modulation theory, authored by Dr. Gennady El (Loughborough University) and Professor Hoefer, appeared in a special issue of Physical D on dispersive hydrodynamics. The article surveys the mathematics behind much of the lab’s research. A second review article by Dr. El, Professor Hoefer, and Michael Shearer (NC State University), Dispersive and diffusive-dispersive shock waves for non-convex conservation laws, will appear in SIAM Review in early 2017. This article describes non-classical shock waves in dispersive fluids with and without dissipation.

The Dispersive Hydrodynamics Laboratory had an impressive year, full of diverse activities and research. The Applied Mathematics Department is excited for the lab’s future in 2017. For this upcoming year, the lab is seeking interested, enthusiastic undergraduate researchers. Contact Professor Mark Hoefer for details. If you are interested in learning more about the lab, please visit the lab’s new webpage.

Written by Danielle Hawley