This $350,000 Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program supports the development of robust and efficient numerical algorithms for solving nonlinear second-order wave equations. The research aims to create computational tools that can accurately simulate a wide range of wave phenomena in areas such as geophysics, plasma physics, and quantum science. The project focuses on constructing fully discrete,...
This Project Grant award of $300,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports research on the stability and behavior of large amplitude relaxation waves. The Principal Investigator will study key open problems related to the stability and behavior of shallow water waves, including phenomena like destructive rogue waves and herringbone flow patterns, using a blend of finite- and infinite-dimensional dynamical systems tools...
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 dispersive and wave equations at the University of Chicago. The project aims to advance the mathematical theory of wave turbulence and the analysis of Gibbs measures for Hamiltonian systems, with applications to fields such as plasma physics, nonlinear optics, and quantum field theory. Key research activities include extending...
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...
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,...
This $224,621 Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program supports research on nonlinear waves and solitons in integrable and non-integrable systems. The principal investigator and their team at The Research Foundation for the State University of New York (RF SUNY), Sponsored Projects Services, will conduct an in-depth investigation into the mathematical properties and physical applications of nonlinear...
This Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) provides $299,863 to the Regents of the University of Michigan to conduct research on integrable nonlinear waves and related topics. The project aims to uncover new solutions of integrable equations, study their properties, and impact applications in areas such as marine engineering and condensed matter physics. Key activities include establishing long-time asymptotics for the...
This three-year, $295,778 Project Grant from the National Science Foundation's Division of Mathematical Sciences will support research addressing long-standing problems in the nonlinear propagation of waves. The principal investigator and collaborators at the University of Chicago will conduct mathematical studies of soliton resolution for energy critical nonlinear wave equations and related models, both with and without symmetries. Quantitative unique continuation properties with connections to...
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 $100,972 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports fundamental research on nonlinear partial differential equations and their applications in fields such as crystal growth, combustion, and game theory. The primary investigator (PI) will study the regularity, large-time behavior, and qualitative properties of solutions to these equations, which have connections to areas like the calculus of...