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Award ID contains: 2308200

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  1. ; ; (, Inverse Problems)
    Abstract In previous work of the authors, we investigated the Born and inverse Born series for a scalar wave equation with linear and nonlinear terms, the nonlinearity being cubic of Kerr type (DeFilippiset al2023Inverse Problems39125015). We reported conditions which guarantee convergence of the inverse Born series, enabling recovery of the coefficients of the linear and nonlinear terms. In this work, we show that if the coefficient of the linear term is known, an arbitrarily strong Kerr nonlinearity can be reconstructed, for sufficiently small data. Additionally, we show that similar convergence results hold for general polynomial nonlinearities. Our results are illustrated with numerical examples. 
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    Free, publicly-accessible full text available November 26, 2025
  2. ; (, Journal of Mathematical Physics)
    We consider the asymptotic analysis of the resonances of the scalar Helmholtz equation corresponding to a bounded scatterer with a periodic index of refraction and small period size ϵ. When the homogenized resonance is simple, we derive an explicit formula for the first order corrections to the limiting resonances. For scatterers with boundary that has a flat part of rational normal, the first order corrections are not unique and depend on the interaction of the boundary of the scatterer with the microstructure. In this case the resonances converge only O(ϵ) in general. For smooth domains with no flat parts, the resonances converge o(ϵ), but the convergence is nonetheless sub-quadratic. 
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    Free, publicly-accessible full text available April 1, 2026
  3. ; ; ; ; (, Journal of Computational Physics)
    Free, publicly-accessible full text available January 17, 2026
  4. ; ; ; ; (, Springer Nature Switzerland)
    Free, publicly-accessible full text available January 1, 2026
  5. ; ; (, SIAM Journal on Imaging Sciences)
    Free, publicly-accessible full text available December 31, 2025