Project Grant 2307357
- This $270,000 Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program, will support two research programs related to the mathematical theory of fluids, gases, and plasmas. The first program will examine non-uniqueness phenomena and instability in nonlinear partial differential equations, particularly those used in modeling incompressible fluid mechanics. The second program will investigate the structure of shock...
- This Project Grant award for $257,457 from the National Science Foundation (NSF) Division of Mathematical Sciences supports research by the University of Alabama at Birmingham (UAB) to investigate three key problems in fluid mechanics. The overarching objective is to utilize a novel mathematical framework developed by the Principal Investigator to study the spatial intermittency of turbulent flows, which is critical for understanding phenomena like vortex structures in turbulence. The three...
- 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...
- This $138,732 National Science Foundation Division of Mathematical Sciences Project Grant supports research into instability, chaos, and mixing in stochastic fluid mechanics and related models at Tulane University from August 1, 2022 to July 31, 2025. The research aims to develop mathematical tools to rigorously prove exponential sensitivity to initial conditions for various fluid mechanics models in the presence of small noise, gaining new insights into the unstable nature of fluid motion and...
- The National Science Foundation (NSF) awarded a $904,240 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to the University of Rochester to support an effort to understand the complexities of turbulence in high energy density plasmas. The 3-year project, running from August 1, 2024 to July 31, 2027, aims to characterize plasma turbulence across different scales using advanced interferometry and imaging diagnostics at the university's HADES pulsed power facility....
- This $112,000 Project Grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), will fund collaborative research between teams of U.S. and U.K. mathematicians. The research aims to develop innovative mathematical methods for analyzing the stability of nonlinear partial differential equations across scales, with a focus on four key objectives: stability of shock wave patterns including shock...
- This $124,914 project grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), will fund collaborative research between U.S. and U.K. mathematicians to develop innovative methods for studying stability questions in nonlinear partial differential equations across scales. The University of Texas at Austin will partner with other institutions to conduct research, workshops, and student involvement from August...
- The University of Texas at Austin received a three-year, $340,000 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program to develop mathematical tools for studying the stability theory of hyperbolic conservation laws. These laws model physical systems involving shocks or discontinuities in fluid and gas dynamics. The university will investigate the uniform stability of viscous approximations like the Navier-Stokes equation to mitigate shock...
- This Project Grant, awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program, supports collaborative research on microscale plasma processes in shock and turbulent environments. The $341,464 award to Columbia University, spanning August 2024 to July 2027, will focus on two key areas: 1) particle heating and acceleration in shocks, and 2) thermodynamics and transport driven by large-scale turbulence. The research aims to develop...
- This $125,000 three-year Project Grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), will support 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 research focuses on four objectives: stability analysis of shock wave patterns including gas dynamics problems; stability...
TURBULENCE, SHOCKS, AND STABILITY IN FLUIDS AND PLASMAS -THIS PROJECT WILL DEVELOP THE MATHEMATICAL THEORY OF LIQUIDS, GASES, AND PLASMAS, WHICH ARE UBIQUITOUS IN PROBLEMS FROM ENGINEERING, METEOROLOGY, AERODYNAMICS, AND MORE. THESE FUNDAMENTAL STATES OF MATTER EXHIBIT A WIDE RANGE OF BEHAVIORS, INCLUDING TURBULENT AND CHAOTIC BEHAVIOR, SHOCK WAVES, AND STABILITY. THE FIRST GOAL IS TO ADVANCE THE MATHEMATICAL THEORY OF TURBULENT FLUIDS, WHICH MAY BE OBSERVED EVERYWHERE FROM THE WAKES OF VEHICLES TO THE ATMOSPHERE. SECOND, THIS PROJECT WILL STUDY SHOCK WAVES, OR THE APPARENT DISCONTINUITIES IN PROPERTIES SUCH AS DENSITY AND FLOW VELOCITY, WHICH ARE OBSERVED IN ASTROPHYSICAL PLASMAS AND MORE. FINALLY, THE PROJECT WILL INVESTIGATE THE STABILIZING PROPERTIES OF FLUIDS AND PLASMAS NEAR BACKGROUND SHEARS, WHICH MAY BE USED IN A NUMBER OF IMPORTANT APPLICATIONS TO CONTROL THE BEHAVIOR OF THE FLUID OR PLASMA. THIS PROJECT ALSO INCLUDES TRAINING AND MENTORING OPPORTUNITIES FOR GRADUATE STUDENTS AND THE ORGANIZATION OF CONFERENCES AND SEMINARS. THE FIRST PORTION OF THIS PROJECT WILL CONSTRUCT DISSIPATIVE SOLUTIONS OF THE INCOMPRESSIBLE EULER AND NAVIER-STOKES EQUATIONS, AS WELL AS OTHER MODELS OF FLUID AND PLASMAS. INTERMITTENCY, WAVELET-BASED ITERATIONS, AND MORE WILL PLAY A KEY ROLE IN THE ANALYSIS. THE SECOND PORTION OF THIS PROJECT WILL BEGIN BY BUILDING SMALL-AMPLITUDE KINETIC SHOCK SOLUTIONS TO THE BOLTZMANN AND LANDAU EQUATIONS WHICH APPROXIMATE TRAVELING WAVE SOLUTIONS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS. TOOLS FROM THE STUDY OF COMPRESSIBLE FLUIDS, THE HYDRODYNAMIC LIMIT, AND KINETIC THEORY WILL BE DEVELOPED AND THEN USED TO INVESTIGATE MODELS OF DILUTE CHARGED PARTICLES, SUCH AS THE VLASOV-MAXWELL-BOLTZMANN SYSTEM. FINALLY, THIS PROJECT WILL STUDY HYDRODYNAMIC AND MAGNETOHYDRODYNAMIC STABILITY AND CONTROL. STABILIZING MECHANISMS, MIXING, AND ENHANCED DISSIPATION ARE OFTEN OBSERVED IN THE VICINITY OF SHEAR FLOWS AND WILL BE USED IN A NOVEL WAY TO SOLVE CONTROL PROBLEMS FOR FLUIDS AND PLASMAS. 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.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $84.2k | 7/1/25 | ||
| Not listed | $115.0k | 5/15/23 |