Dispersive Hydrodynamics Program at the Isaac Newton Institute

University Of Colorado At Boulder, Boulder CO

Investigators

Abstract

A 6-month research-intensive program titled "Dispersive hydrodynamics: mathematics, simulations and experiments, with applications in nonlinear waves" will be held at the Isaac Newton Institute, University of Cambridge, UK from July 6–December 18, 2020. Dispersive hydrodynamics is an emergent mathematical field of research focusing on dynamic and stochastic, multiscale wave phenomena described by nonlinear partial differential equations that physically encompass the complex interplay between long-scale, hydrodynamic, and short-scale, dispersive, effects. Building upon at least six dedicated workshops and numerous conference minisymposia on the subject since 2012, this will be the first extended program on dispersive hydrodynamics. It will attract at least 25 long-term, residential visitors at any given time and 40 or more participants in each of 5 week-long workshops. The diverse, international roster of participants includes leading researchers in the applied mathematical sciences. This National Science Foundation award provides travel support for early career applied mathematicians from the United States to participate in the workshops and the long-term program. Traditionally underrepresented groups in applied mathematics will be encouraged to apply. This support enables sustained opportunities to interact with leading researchers from across the world. Such interactions and contacts are invaluable to beginning researchers, both to inspire research, and for professional development, thereby helping to cultivate the very best young researchers. These researchers will be the next generation of applied mathematicians who advance this and other applied mathematical fields of research. Dispersive hydrodynamics has emerged as a unified mathematical framework for the description of multiscale nonlinear wave phenomena in dispersive media, encompassing both dynamic and stochastic aspects of wave propagation. Theoretical and experimental developments have spawned new areas of applied mathematical research. The mathematical program weaves together research topics on integrable and nonintegrable dispersive PDEs, convex and nonconvex dispersive hydrodynamic systems, multidimensional waves, asymptotic analysis, numerical analysis, randomness and turbulence in nonlinear dispersive waves. Applications include fluid mechanics and go well beyond, to nonlinear optics, superfluids (Bose-Einstein condensates), condensed matter, and granular crystals. The program website can be found at http://www.newton.ac.uk/event/hyd, with links to the workshops and other activities. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.