Recent developments in inverse problems, multi-scale analysis and effective medium theory reveal that these fields share several fundamental concepts. This book is the proceedings of the research conference, 'Workshop in Seoul: Inverse Problems, Multi-Scale Analysis and Homogenization,' held at Seoul National University, June 22-24, 2005. It highlights the benefits of sharing ideas among these areas, of merging the expertise of scientists working there, and of directing interest towards challenging issues such as imaging nanoscience and biological imaging. Contributions are written by prominent experts and are of interest to researchers and graduate students interested in partial differential equations and applications.
Generalized polarization tensors, inverse conductivity problems, and dilute composite materials: A review by H. Ammari and H. Kang Improved bounds on the polarization tensor for thick domains by Y. Capdeboscq and H. Kang On conjectures of Polya-Szego and Eshelby by H. Kang and G. W. Milton An FMM for periodic rigid-inclusion problems and its application to homogenisation by K. Houzaki, N. Nishimura, and Y. Otani Remarks on the implementation of the wideband FMM for the Helmholtz equation in two dimensions by H. Cheng, W. Crutchfield, Z. Gimbutas, L. Greengard, J. Huang, V. Rokhlin, N. Yarvin, and J. Zhao Multiscale computation of isotropic homogeneous turbulent flow by T. Hou, D. Yang, and H. Ran Optimality conditions on fields in microstructures and controllable differential schemes by N. Albin and A. Cherkaev Time-reversal acoustics by M. Fink What is recoverable in the inverse magnetoencephalography problem? by G. Dassios Convergence properties and stability issues in MREIT algorithm by J. J. Liu, H. C. Pyo, J. K. Seo, and E. J. Woo Oscillating-decaying solutions for elliptic systems by G. Nakamura, G. Uhlmann, and J.-N. Wang Stroh eigenvalues and identification of discontinuity in an anisotropic elastic material by M. Ikehata A comparative study between some non-iterative methods for the inverse scattering by G. Nakamura, R. Potthast, and M. Sini.