This federal Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) provides $337,407 to The Pennsylvania State University (Penn State) for research on transport phenomena in quantum systems. The project aims to extend recent advances in synthetic dimensions and lattices to the study of transport in strongly interacting Rydberg atom arrays, with a focus on understanding the interplay of topology and interactions. An...
This National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences program (CFDA 47.049) will fund research at Carnegie Mellon University (CMU) on mean-field and singular limits of deterministic and stochastic interacting particle systems. The $187,382 award, with a performance period from July 1, 2023 to May 31, 2025, aims to achieve a substantial reduction in computational complexity for modeling the behavior of large numbers of interacting particles,...
This $293,784 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental and applied research on fluctuating systems, random environments, and stochastic algorithms. The research aims to improve understanding and exploitation of randomness across diverse settings, including materials science, fluid dynamics, and machine learning. Key areas of focus include stochastic homogenization, stochastic partial...
This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $748,840 to The Pennsylvania State University under the Mathematical and Physical Sciences program (CFDA 47.049) from September 1, 2022 to August 31, 2025. The funding supports research into partial differential equations modeling incompressible fluids and elastic solids, with a focus on fluid-structure interaction problems, transport of vectors by fluid flow, and seismic fault monitoring. The...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on efficient sampling algorithms for target probability distributions. The key objectives are to: Develop a theoretical framework to analyze the long-term convergence properties of sampling dynamics characterized by kinetic equations. Use techniques from optimization, optimal transport, and applied analysis to study sampling dynamics structured as...
This Project Grant from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) provides $210,272 to Penn State University for collaborative research on adaptive mixed-dimensional modeling and simulation of porous media from August 1, 2022 to July 31, 2025. The research aims to develop stable numerical methods for simulating flow in fractured porous media based on mixed-dimensional modeling approaches. Key products include advanced...
This $300,000 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) will support the development of new frameworks for studying large multi-agent and many-particle systems at Penn State University from August 2022 through July 2025. The grantee aims to reduce complexity in systems with very large numbers of non-identical, non-exchangeable agents or particles by replacing exact interactions with a mean field approximation. Novel methods will...
This $300,000 Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), will support the development of next-generation mathematical and algorithmic tools to address two key issues in applying machine learning to statistical modeling of time-evolving complex systems: a shortage of informative training data and the high computational costs of high-dimensional problems. Specifically, the...
This five-year $154,264 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research and educational activities at Drexel University related to uncertainty quantification, long-time statistics, and singularity formation in fluid flow models. The Principal Investigator will address topics including parameter recovery from sparse noisy observations using Bayesian inverse problems and Markov chain Monte Carlo algorithms applied to...
This $100,011 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on stochastic growth models and mathematical structures called line ensembles, which have applications in fields ranging from magnetization to protein synthesis. The research aims to expand knowledge of line ensembles and related techniques, leading to solutions for previously intractable problems. The award includes organizing conferences...