This three-year, $219,298 project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports collaborative research on the theoretical understanding and computational modeling of collapse phenomena and rogue waves. The University of Massachusetts Amherst will lead the research effort to reformulate underlying mathematical models of nonlinear differential equations and provide a unified analytical approach for studying self-similar solutions...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research aimed at advancing the mathematical analysis of nonlinear partial differential equations. The research has three main focus areas: (1) studying fluid dynamics problems with free boundaries, such as water waves, tsunamis, and hurricanes; (2) investigating the dynamics of gases and plasmas under physical kinetic boundary conditions,...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $160,000 Project Grant to The Regents of the University of Colorado (doing business as the University of Colorado) under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports fundamental research into nonlinear wave propagation, focused on enhancing scientific understanding of large amplitude waves and associated wave energy transfer dynamics. This work has potential applications for...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $219,997 Project Grant to the University of Delaware to conduct research in Hamiltonian formalism applied to wave turbulence problems. The research aims to develop new mathematical models to better understand nonlinear phenomena related to ocean waves, specifically wave-current interactions and wave-structure interactions. Key areas of focus include rogue wave generation, contaminant transport, sediment...
This Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $209,000 to the University of Pittsburgh to support research investigating nonlinear waves in lattices and metamaterials from August 1, 2022 to July 31, 2025. The award aims to advance fundamental understanding of energy transfer phenomena associated with wave propagation in spatially discrete systems, which is important for...
This three-year National Science Foundation Project Grant of $168,087 will support research into nonlinear wave models in bounded domains. The principal investigator and their team at the University of Kansas Center for Research will develop a methodology for analyzing the behavior of dispersive equations modeling optical and water wave phenomena in confined regions. They will provide tools to understand novel behaviors and design physical and numerical experiments. Three research components are...
The National Science Foundation Division of Mathematical Sciences awarded New York University a $435,000 Project Grant titled "GEOPHYSICAL WAVE-VORTEX INTERACTIONS AND TURBULENCE" under the Mathematical and Physical Sciences program (CFDA 47.049). The three-year award beginning September 1, 2021 will support research exploring geophysical wave-vortex interactions and turbulence. The Mathematical and Physical Sciences program aims to promote progress in mathematics and physical sciences...
This $176,355 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research on probabilistic aspects of dispersive and wave equations at the University of Chicago. The research aims to advance the mathematical theory of wave turbulence and the analysis of Gibbs measures for Hamiltonian systems, with applications to fields like plasma physics, nonlinear optics, and quantum field theory. Key focus areas...
This $100,011 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on stochastic growth models and mathematical structures called line ensembles, which have applications in fields ranging from magnetization to protein synthesis. The research aims to expand knowledge of line ensembles and related techniques, leading to solutions for previously intractable problems. The award includes organizing conferences...
This $145,000 Project Grant awarded by the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports collaborative research on the fundamental theory of wave turbulence. The research at Texas A&M University will tackle challenging problems at the intersection of physics and mathematical analysis, including the rigorous derivation of wave kinetic equations, analysis of the kinetic equation for the Fermi-Pasta-Ulam-Tsingou chain, and well-posedness...