تصویربرداری، معادلات دیفرانسیل جزئی چند مقیاسی و با کنتراست بالا: کنفرانس ماهواره‌ای سئول ICM 2014

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. Cover 1 Title page 4 Contents 6 Preface 8 Wavelet methods for shape perception in electro-sensing 10 1. Introduction 10 2. Modelling of the electro-sensing problem 11 3. Polynomial basis and linear estimation 18 4. Wavelet basis and nonlinear estimation 19 5. Numerical experiments 23 6. Discussion 24 7. Conclusion 26 Appendix A. Proof of Lemma 2.2 27 Appendix B. Proof of Proposition 2.4 27 Appendix C. Proof of Proposition 4.1 28 References 28 Time-domain multiscale shape identification in electro-sensing 32 1. Introduction 32 2. Electro-sensing model 34 3. Representation of solution 36 4. Time-dependent GPTs and asymptotic expansions 40 5. Shape identification with pulse-type signals 44 6. Numerical Experiments 46 7. Discussion and conclusion 50 Appendix A. Numerical solution of the forward problem 51 References 51 Estimation of stress in the presence of closely located elastic inclusions: A numerical study 54 1. Introduction 54 2. The Lamé system 55 3. System of integral equations 57 4. Non-blow-up results 59 5. Numerical experiments 60 Conclusion 64 References 64 Array dependence of effective parameters of dilute periodic elastic composite 68 1. Introduction 68 2. Preliminaries 69 3. Evaluation of S2 72 4. Asymptotic expansion of the periodic Green function 75 5. Application to the effective elastic property of periodic media 78 References 79 A review on the enhancement of near-cloaking using the multilayer structure 82 1. Introduction 82 2. Small volume expansion 83 3. GPT vanishing structures 87 4. Small volume expansion and cloaking by mapping 89 References 94 On local non-zero constraints in PDE with analytic coefficients 98 1. Introduction 98 2. Proof of Theorem 4 102 3. Conclusions 105 References 105 Daylight imaging for virtual reflection seismology 108 1. Introduction 108 2. Wave propagation in a one-dimensional complex medium 109 3. Reflection seismology 113 4. Daylight imaging 114 5. Conclusion 118 Acknowledgements 118 Appendix A. The covariance of the empirical autocorrelation function 118 References 119 Mode-matching solution of a scattering problem in flexible waveguide with abrupt geometric changes 122 1. Introduction 122 2. Mathematical formulation 124 3. Mode-matching solution 126 4. Expressions for energy flux and power balance 129 5. Numerical results and discussion 131 References 136 Direct scattering by a sound hard small body 140 1. Introduction 140 2. Layer potential representation 142 References 145 Helmholtz equation in unbounded domains: Some convergence results for a constrained optimization problem 148 1. Introduction 148 2. Preliminaries 150 3. Convergence estimates 152 References 156 Back Cover 160 This volume contains the proceedings of the Seoul ICM 2014 Satellite Conference on Imaging, Multi-scale and High-Contrast PDEs, held in 2014. 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.