This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) provides $300,000 to the University of California, Los Angeles (UCLA) to conduct research on dynamic free boundary problems. The project will analyze motions of physical interfaces, such as water freezing into ice, water droplets wetting surfaces, and tumor growth, in order to better understand the critical scales and singularities that arise in these processes. 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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program is supporting research by The Trustees of Columbia University in the City of New York to advance the theoretical understanding of partial differential equations, free boundary problems, and related mathematical concepts. The $273,927 award, with a performance period from July 1, 2024 to June 30, 2027, focuses on developing new methods and regularity theories for specific...
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 $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...
The National Science Foundation (NSF) awarded a $116,362 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to the University of California, Los Angeles (UCLA) to conduct research on scaling limits and phase transitions in spatial random processes. The funding, which runs from July 2024 through June 2027, will support UCLA's efforts to advance mathematical theories of critical phenomena and universality in areas such as branching Markov chains,...
This three-year National Science Foundation Project Grant of $197,999 supports research and education activities at Worcester Polytechnic Institute under the Mathematical and Physical Sciences program (CFDA 47.049). The award will fund the development of novel mathematical methods to analyze partial differential equations describing singularities in continuum mechanics and materials science systems. The principal investigator will extend differential inclusion theory on rigidity and flexibility,...
The University of California, Los Angeles was awarded a $360,000 project grant from the National Science Foundation under the Mathematical and Physical Sciences program (CFDA 47.049). The grant will support the "FREE PROBABILITY, TRANSPORT, AND APPLICATIONS" project from July 1, 2021 through June 30, 2024. The project aims to promote progress in the mathematical and physical sciences by increasing knowledge and understanding of major problems through activities focused on...
The National Science Foundation (NSF) awarded a $247,227 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Missouri System, doing business as the Curators of the University of Missouri, to conduct research related to boundary value problems and free boundary problems for elliptic and parabolic partial differential equations. The three-year project, starting on July 1, 2024 and ending on June 30, 2027, aims to: 1) characterize the space-time...
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...