Imaging, Multi-scale and High Contrast Partial Differential Equations.

Cover -- Title page -- Contents -- Preface -- Wavelet methods for shape perception in electro-sensing -- 1. Introduction -- 2. Modelling of the electro-sensing problem -- 3. Polynomial basis and linear estimation -- 4. Wavelet basis and nonlinear estimation -- 5. Numerical experiments -- 6. Discussion -- 7. Conclusion -- Appendix A. Proof of Lemma 2.2 -- Appendix B. Proof of Proposition 2.4 -- Appendix C. Proof of Proposition 4.1 -- References -- Time-domain multiscale shape identification in electro-sensing -- 1. Introduction -- 2. Electro-sensing model -- 3. Representation of solution -- 4. Time-dependent GPTs and asymptotic expansions -- 5. Shape identification with pulse-type signals -- 6. Numerical Experiments -- 7. Discussion and conclusion -- Appendix A. Numerical solution of the forward problem -- References -- Estimation of stress in the presence of closely located elastic inclusions: A numerical study -- 1. Introduction -- 2. The Lamé system -- 3. System of integral equations -- 4. Non-blow-up results -- 5. Numerical experiments -- Conclusion -- References -- Array dependence of effective parameters of dilute periodic elastic composite -- 1. Introduction -- 2. Preliminaries -- 3. Evaluation of ₂ -- 4. Asymptotic expansion of the periodic Green function -- 5. Application to the effective elastic property of periodic media -- References -- A review on the enhancement of near-cloaking using the multilayer structure -- 1. Introduction -- 2. Small volume expansion -- 3. GPT vanishing structures -- 4. Small volume expansion and cloaking by mapping -- References -- On local non-zero constraints in PDE with analytic coefficients -- 1. Introduction -- 2. Proof of Theorem 4 -- 3. Conclusions -- References -- Daylight imaging for virtual reflection seismology -- 1. Introduction -- 2. Wave propagation in a one-dimensional complex medium.

3. Reflection seismology -- 4. Daylight imaging -- 5. Conclusion -- Acknowledgements -- Appendix A. The covariance of the empirical autocorrelation function -- References -- Mode-matching solution of a scattering problem in flexible waveguide with abrupt geometric changes -- 1. Introduction -- 2. Mathematical formulation -- 3. Mode-matching solution -- 4. Expressions for energy flux and power balance -- 5. Numerical results and discussion -- References -- Direct scattering by a sound hard small body -- 1. Introduction -- 2. Layer potential representation -- References -- Helmholtz equation in unbounded domains: Some convergence results for a constrained optimization problem -- 1. Introduction -- 2. Preliminaries -- 3. Convergence estimates -- References -- Back Cover.

This volume contains the proceedings of the Seoul ICM 2014 Satellite Conference on Imaging, Multi-scale and High-Contrast PDEs, held from August 7-9, 2014, in Daejeon, Korea. The mathematical analysis of partial differential equations modelling materials, or tissues, presenting multiple scales has been a very active area of research. The study of the corresponding imaging or reconstruction problem is a more recent area. If the material parameters of the partial differential equation present high contrast ratio, then the solution to the PDE becomes particularly challenging to analyze and compute. On the other hand, imaging in highly heterogeneous media poses significant challenges to the mathematical community. The focus of this volume is on recent progress towards complete understanding of the direct problem with high contrast or high frequencies, and unified approaches to the inverse and imaging problems for both small and large contrast or frequencies. Of particular importance in imaging are shape representation techniques and regularization approaches. Special attention is devoted to new models and problems coming from physics leading to innovative imaging and signal processing methods.

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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.