Conference: Emergent Phenomena in Nonlinear Dispersive Waves

University Of Colorado At Boulder, Boulder CO

Investigators

Abstract

A one-month research-intensive satellite program by the Isaac Newton Institute, Cambridge, UK titled "Emergent phenomena in nonlinear dispersive waves" (PDW) will be held at Northumbria University and the University of Newcastle in Newcastle Upon Tyne, UK from July 22–August 16, 2024 (see the program website https://www.newton.ac.uk/event/pdw/). The concept of emergence will be explored in the context of dynamic and stochastic, multiscale dispersive wave phenomena described by nonlinear partial differential equations. This program will host approximately 35 long-term, residential visitors at any given time and 60 or more participants in a one-week workshop. 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 workshop and the program. Traditionally underrepresented groups in applied mathematics will be encouraged to apply. This support enables sustained opportunities to interact with leading researchers from around 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. Emergence is a powerful concept that plays a fundamental role in many areas of theoretical and mathematical physics. In a system composed of a very large number of elementary constituents, e.g. classical or quantum particles, the observable macroscopic behavior can be highly nontrivial. This transition from short-to-large scales is at the heart of hydrodynamic theories for inhomogeneous, dynamic many-body states. A very different kind of hydrodynamics arises when the microscopic constituents are waves. The subject of dispersive hydrodynamics—the theory of multiscale phenomena in nonlinear dispersive waves—has attracted much attention recently and was the focus of the 2022 "Dispersive Hydrodynamics" (HYD2) program held at the Isaac Newton Institute, Cambridge, UK. The satellite PDW program aims to capitalize on the successful HYD2 program to explore new frontiers of dispersive hydrodynamics in relation to the overarching theme of emergent phenomena in nonlinear waves. In particular, PDW will focus on three highly synergistic themes: (i) emergent hydrodynamics in integrable and nonintegrable systems; (ii) stability of nonlinear dispersive waves and emergent phenomena in unstable wave systems; (iii) soliton gas, generalized hydrodynamics and statistical mechanics of integrable systems. 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.