This National Science Foundation (NSF) Division of Mathematical Sciences award provides $213,743 in Project Grant funding to the University of Tennessee, Knoxville for research conducted from August 1, 2023 to July 31, 2026. The project aims to develop highly efficient, positivity-preserving, and entropy-stable numerical schemes for variable-temperature phase field equations with singular energy potentials. This research will enhance understanding of two-phase flows and phase separation in...
This $219,782 Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences aims to develop innovative and robust numerical methods for simulating high-frequency electric charge transport phenomena. The research program under this 3-year award from September 2024 to August 2027 will advance space and time discretization techniques for hydrodynamic models of electric charge transport, such as the Euler-Maxwell and Euler-Poisson systems. The resulting numerical...
This Project Grant award of $254,498 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports three research projects at Princeton University focused on advancing the mathematical understanding of Gibbs measures and their dynamics. The principal investigator and collaborators are pursuing research at the interface of partial differential equations, probability theory, and differential geometry to address open problems in areas such as the...
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...
This $199,814 Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) supports the development of accurate, efficient, and stable numerical methods for solving reversible-irreversible thermodynamically consistent partial differential equations (RITC-PDEs). The key objectives of this 3-year project (8/1/2025 - 7/31/2028) are to: (a) Design innovative structure-preserving discretization methods to accurately simulate complex...
This $184,162 Project Grant awarded by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research on free boundary problems and phase interfaces in heterogeneous media. The project aims to advance the theory of phase interfaces by developing new techniques that connect partial differential equations, geometry, and statistical physics. The key outcomes will be: 1) a theory of large-scale regularity for free boundary and...
This Project Grant award of $302,028.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) supports fundamental research on nonlinear hyperbolic and dispersive partial differential equations (PDEs). The award aims to deepen the understanding of these PDEs, which are critical for describing natural phenomena across scales, by investigating long-term dynamics, singularity formation, and the stability of special solutions. Key...
This $170,913 project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) will support the development of efficient numerical tools to model incompressible multiphase flows applied to magnetohydrodynamics. The principal investigator at the University of Houston will use theoretical and computational mathematics to analyze and develop high-order numerical methods for solving nonlinear partial differential equations governing fluid dynamics with...
This $350,000 federal Project Grant was awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program. The goal of the research is to develop accurate mathematical models and computer simulations for studying non-equilibrium systems with memory effects, such as those found in biosystems, plasma evolution, and solid-state nanostructures. The Principal Investigator will focus on analytical and numerical approaches to statistical transport...
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,...