Polarization and Moment Tensors

This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. The exposition brings simplicity to the advanced material by augmenting the theory with interesting practical examples and numerical illustrations. An introductory chapter covers the necessary basics. An extensive bibliography and open problems at the end of each chapter enhance the text. Graduate students and researchers in mathematics will benefit from this book. Researchers in engineering and physics might also find it helpful.

Contenu
Layer Potentials and Transmission Problems.- Uniqueness for Inverse Conductivity Problems.- Generalized Isotropic and Anisotropic Polarization Tensors.- Full Asymptotic Formula for the Potentials.- Near-Boundary Conductivity Inclusions.- Impedance Imaging of Conductivity Inclusions.- Effective Properties of Electrical Composites.- Transmission Problem for Elastostatics.- Elastic Moment Tensor.- Full Asymptotic Expansions of the Displacement Field.- Imaging of Elastic Inclusions.- Effective Properties of Elastic Composites.