Multi-Scale and High-Contrast PDE : From Modelling, to Mathematical Analysis, to Inversion.

Intro -- Preface -- Enhancement of near-cloaking. Part III: Numerical simulations, statistical stability, and related questions -- 1. Introduction -- 2. Enhancement of near cloaking in the quasi-static limit -- 3. Enhancement of near cloaking for the Helmholtz equation -- 4. Concluding remarks -- Appendix A. Statistical sensitivity analysis -- References -- Looking at the world through liquid crystal glasses -- 1. Introduction -- 2. Polarizing microscopy -- 3. LC-PolScope: Variable and universal compensators -- 4. Fluorescence Confocal Polarizing Microscopy -- 5. Coherent Anti-Stokes Raman Scattering Microscopy -- 6. Fermat Principle and Extraordinary Mode in Liquid Crystals with Gradient Properties -- 7. Conclusion -- Acknowledgement -- References -- A remark on the observability of conservative linear systems -- 1. Introduction -- 2. Proof of the main result -- 3. Applications -- 4. Time-discrete conservative systems -- 5. Ingham type inequalities -- 6. Further comments an open problems -- References -- On the scattered field generated by a ball inhomogeneity of constant index in dimension three -- 1. Introduction -- 2. Main results -- 3. Proofs of the main results -- Acknowledgements -- References -- Pointwise bounds on the gradient and the spectrum of the Neumann-Poincaré operator: The case of 2 discs -- 1. Introduction -- 2. The system of integral equations -- 3. The spectrum of the Neumann-Poincaré operator for a pair of close-to-touching discs -- 4. Asymptotics of the layer potential -- References -- A high-contrast fourth-order PDE from imaging: numerical solution by ADI splitting -- 1. Introduction -- 2. Self-similar solutions of the equation -- 3. Numerical solution with ADI splitting -- Acknowledgements -- References -- Imaging with noise blending -- 1. Introduction -- 2. Multi-offset sources -- 3. Stationary random sources.

4. Incoherence by blending -- 5. Applications -- 6. Numerical illustrations -- 7. Conclusion -- Appendix A. Statistical stability for a continuum of point sources -- Appendix B. Resolution analysis -- References -- Correlations of heterogeneous wave fields propagating in homogeneous media -- 1. Introduction -- 2. Main result -- 3. Radiative transfer models for correlations -- 4. Correlation filtering and derivation of Result 1 -- 5. Application to the imaging of sources -- 6. Numerical simulations -- 7. Conclusion -- Acknowledgment -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.