This $575,244 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research into complex dynamics in higher dimensions at Indiana University from July 1, 2022 to June 30, 2025. The award will fund Ph.D. students' research into topics including holomorphic group actions on complex surfaces from Painlevé 6 differential equations, Migdal-Kadanoff renormalization mappings in statistical physics, and ergodic theory of rational maps...
The National Science Foundation Division of Mathematical Sciences awarded Indiana University a $178,120 Project Grant under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) to support research on "PARTIAL DIFFERENTIAL EQUATIONS WITH AND WITHOUT CONVEXITY CONSTRAINTS" from July 15, 2021 through June 30, 2024. The grant funding will allow Indiana University researchers to advance scientific understanding of major problems in mathematics through investigating...
The National Science Foundation awarded a $235,718 Project Grant to Indiana University under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) to study multi-dimensional and vorticity effects in inclined shallow water flow. Specifically, the Principal Investigator will use theoretical and computational methods to examine the impacts of rotational forces and multi-dimensional characteristics on the existence and stability of flow patterns. The research aims to incorporate...
The National Science Foundation Division of Mathematical Sciences awarded Indiana University a $246,244 Project Grant under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) for work on "COMPUTATIONAL AND COMBINATORIAL TECHNIQUES IN CONFORMAL DYNAMICS" from July 1, 2021 to June 30, 2024. The grant supports research using computational and combinatorial techniques to further understanding of major problems in conformal dynamics, consistent with the program's...
This Project Grant award for $300,000 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research on the stability and behavior of large-amplitude relaxation waves in shallow water flow and other physical systems. The principal investigator will study key open problems related to the nonlinear time-asymptotic stability of discontinuous periodic waves and multidimensional hydraulic shocks, with the goal of developing new...
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 $105,999 National Science Foundation Mathematical and Physical Sciences project grant funds collaborative research between U.S. and U.K. mathematicians to develop innovative methods for analyzing the stability of nonlinear partial differential equations across scales. The University of Wisconsin-Madison leads the research team in studying challenging problems in fluid dynamics, including shock wave interactions, vortex sheet stability, and vanishing viscosity limits. The project also...
The Trustees of Indiana University, doing business as Indiana University, was awarded a $269,390 project grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences (47.049) federal grant program. The grant will fund research from September 1, 2023 through August 31, 2026 mapping semigroups and classifying conformal dynamical systems. Dynamical systems model phenomena like neural networks, epidemics, and weather patterns. This project...
The National Science Foundation (NSF) awarded a $299,998 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to Georgia Tech Research Corporation to conduct fundamental research on the dynamics of nonlinear partial differential equation (PDE) systems that model fluid flow and nonlinear waves. The research will focus on analyzing the local dynamics near steady states in incompressible fluid PDEs with free surfaces, as well as a class of nonlinear...
This $186,811 Project Grant was awarded by the National Science Foundation's (NSF) Division of Mathematical Sciences to Georgetown University on September 1, 2024. The grant supports research on "Analytical Challenges Near Dynamical Thresholds for Nonlinear Wave and Fluid Equations" over a 3-year period through August 31, 2027. The research aims to develop a deeper understanding of the mathematical behavior of partial differential equations that model a variety of physical systems,...