This three-year, $237,648 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) will support the development of structure-preserving hybrid finite element methods. The principal investigator will investigate techniques for capturing fundamental physical laws like conservation and dissipation within simulations performed using finite element methods. Specifically, the research will focus on circumventing barriers to local structure...
This National Science Foundation (NSF) Project Grant, funded under the Mathematical and Physical Sciences program (CFDA 47.049), provides $125,000 in funding to Wichita State University from August 2023 to July 2025. The research objectives are to investigate the classification of four and higher-dimensional spaces, including compact Riemannian manifolds, Einstein manifolds, and shrinking gradient Ricci solitons, whose curvature satisfies a positivity condition. Key strategies involve...
This Project Grant award, valued at $270,195, was provided by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049). The award supports collaborative research to develop highly efficient, positivity-preserving, and entropy-stable numerical schemes for variable-temperature phase field equations with singular energy potentials. The goal is to enhance the understanding of two-phase flows and phase separation in...
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 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 Missouri at Kansas City received a three-year, $146,326 Project Grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports collaborative research to develop computational models of complex interface dynamics between reactive fluids driven out of equilibrium. Researchers will establish a framework to model non-equilibrium phenomena and design algorithms and experiments...
The National Science Foundation Division of Mathematical Sciences awarded $152,848 under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to develop efficient hybridizable discontinuous Galerkin methods for phase field fluid models. The Research Foundation for the State University of New York will receive funding on behalf of researchers at the University at Buffalo from December 1, 2022 to July 31, 2025. Under this Project Grant, the awardees will develop high-order...
This $119,799 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research by Wichita State University (WSU) into higher-order curvature quantities in differential geometry. The key objectives are to study the Q-curvature Yamabe problem for manifolds with corners or boundaries in four or more dimensions, and investigate geometric properties and inequalities for a class of scalar invariants related to...
Kansas State University was awarded a $241,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) to support research titled "NOVEL DECOMPOSITIONS AND FAST NUMERICAL METHODS FOR PERIDYNAMICS" from August 1, 2021 to July 31, 2024. Under this award, Kansas State University researchers will develop novel mathematical decompositions and fast numerical methods to simulate peridynamic models, a non-local reformulation of...
This $359,790 Project Grant awarded by the National Science Foundation (NSF) Division of Materials Research supports theoretical and computational research at the University of Central Florida (UCF) aimed at advancing the fundamental understanding of solid-solid phase transitions. The research seeks to identify the physical principles and structural motifs controlling the kinetics of these phase transitions, and to develop a machine learning method for rapid and accurate prediction of transition...