Title Multi-scale and high-contrast PDE : from modelling, to mathematical analysis, to inversion. Conference on Multi-scale and High-contrast PDE: from Modelling, to Mathematical Analysis, to Inversion, June 28-July 1, 2011, University of Oxford, United Kingdom / Habib Ammari, Yves Capdeboscq, Hyeonbae Kang, editors

Published Providence, RI : American Mathematical Society, ©2010

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Description 1 online resource Series Contemporary Mathematics, ; v. 577 Contemporary mathematics (American Mathematical Society) ; 577. Contents 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 Microscopy6. 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 splittingAcknowledgements -- 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 15. Application to the imaging of sources -- 6. Numerical simulations -- 7. Conclusion -- Acknowledgment -- References Bibliography Includes bibliographical references and index Notes Print version record Subject Image processing -- Mathematics -- Congresses Multiscale modeling -- Congresses Differential equations, Partial -- Congresses Differential equations, Partial Image processing -- Mathematics Multiscale modeling Partial differential equations -- Qualitative properties of solutions -- Dependence of solutions on initial and boundary data, parameters. Partial differential equations -- Elliptic equations and systems -- Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation. Partial differential equations -- Elliptic equations and systems -- Boundary value problems for second-order elliptic equations. Partial differential equations -- Parabolic equations and systems -- Initial-boundary value problems for higher-order parabolic equations. Partial differential equations -- Miscellaneous topics -- Inverse problems. Numerical analysis -- Partial differential equations, initial value and time-dependent initial-boundary value problems -- Finite difference methods. Fluid mechanics -- Foundations, constitutive equations, rheology -- Liquid crystals. Partial differential equations -- Hyperbolic equations and systems -- Wave equation. Systems theory; control -- Controllability, observability, and system structure -- Controllability. Genre/Form Conference papers and proceedings Form Electronic book Author Ammari, Habib Capdeboscq, Yves, 1971- Kang, Hyeonbae American Mathematical Society ISBN 9780821891001 0821891006

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