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Creators/Authors contains: "Schotland, John C"

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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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  2. ; (, Journal of Mathematical Physics)
    We consider the propagation of light in a random medium of two-level atoms. We investigate the dynamics of the field and atomic probability amplitudes for a two-photon state and show that at long times and large distances, the corresponding average probability densities can be determined from the solutions to a system of kinetic equations. 
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  3. ; ; (, Inverse Problems)
    Abstract We consider the Born and inverse Born series for scalar waves with a cubic nonlinearity of Kerr type. We find a recursive formula for the operators in the Born series and prove their boundedness. This result gives conditions which guarantee convergence of the Born series, and subsequently yields conditions which guarantee convergence of the inverse Born series. We also use fixed point theory to give alternate explicit conditions for convergence of the Born series. We illustrate our results with numerical experiments. 
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  4. ; ; ; ; (, SIAM Journal on Applied Mathematics)
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  5. ; ; ; (, SIAM Journal on Applied Mathematics)
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  6. ; ; ; (, Journal of Computational Physics)
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  7. ; (, Inverse Problems)
    Abstract We analyze the convergence and approximation error of the inverse Born series, obtaining results that hold under qualitatively weaker conditions than previously known. Our approach makes use of tools from geometric function theory in Banach spaces. An application to the inverse scattering problem with diffuse waves is described. 
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  8. ; ; ; (, SIAM Journal on Imaging Sciences)
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  9. ; (, Journal of Mathematical Physics)
    We consider the theory of spontaneous emission for a random medium of stationary two-level atoms. We investigate the dynamics of the field and atomic probability amplitudes for a one-photon state of the system. At long times and large distances, we show that the corresponding average probability densities can be determined from the solutions to a pair of kinetic equations. 
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  10. ; ; (, Inverse Problems)
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