This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $150,922 to Lehigh University to conduct research on asymptotic problems in kinetic theory. The project focuses on developing novel mathematical tools to characterize the multi-scale behaviors of particle systems in applications such as medical imaging, gas dynamics, and nuclear fusion. Key objectives include rigorous analysis to connect microscopic, mesoscopic, and macroscopic descriptions of particle dynamics, and quantifying the scope of their applicability. The research will leverage techniques like nonlinear energy methods, regularization, and remainder splitting to tackle non-classical boundary layer and "ghost" effects. In addition to the research, the project will provide mentoring for graduate and undergraduate students, develop new courses, and host a summer school. This award runs from August 1, 2024 through July 31, 2027.
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