This $269,999 federal Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program supports research to develop novel inverse scattering techniques for complex materials with applications in areas such as renewable energy, medical diagnosis, underground exploration, infrastructure integrity, and advanced manufacturing.
The primary objectives are to investigate non-iterative approaches for solving inverse scattering problems in both linear and nonlinear inhomogeneous media, leveraging mathematical frameworks like the generalized linear sampling method and interior eigenvalues. The research aims to reduce reliance on a priori information about target physics and geometry, as well as computational complexities from complex background environments. The 3-year project at Rutgers University will also train graduate students in this research area. Key focus areas include imaging of inhomogeneous media, non-scattering phenomena, qualitative and spectral imaging of nonlinear media, and reconstructing local defects within almost-periodic layers.
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