Polarization and Moment Tensors: With Applications to Inverse Problems and Effective Medium Theory

Habib Ammari, Hyeonbae Kang (auth.)0387715657, 9780387715667, 9780387715650

This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. The methods involved come from various areas of pure and applied mathematics, such as potential theory, PDEs, complex analysis, and numerical methods. The unifying thread in this book is the use of generalized polarization and moment tensors.

The main approach is based on modern layer potential techniques. By augmenting the theory with interesting practical examples and numerical illustrations, the exposition brings simplicity to the advanced material. An introductory chapter covers the necessary basics.

With its extensive list of references and open problems, the book should enhance accessibility to specialized literature and stimulate progress in the fields of impedance imaging and composite materials. Graduate students and researchers in applied mathematics will benefit from this book. Researchers in engineering and physics might also find this book helpful.

Table of contents :
Front Matter….Pages I-X
Introduction….Pages 1-6
Layer Potentials and Transmission Problems….Pages 7-66
Uniqueness for Inverse Conductivity Problems….Pages 67-74
Generalized Isotropic and Anisotropic Polarization Tensors….Pages 75-127
Full Asymptotic Formula for the Potentials….Pages 129-144
Near-Boundary Conductivity Inclusions….Pages 145-160
Impedance Imaging of Conductivity Inclusions….Pages 161-194
Effective Properties of Electrical Composites….Pages 195-210
Transmission Problem for Elastostatics….Pages 211-235
Elastic Moment Tensor….Pages 237-259
Full Asymptotic Expansions of the Displacement Field….Pages 261-268
Imaging of Elastic Inclusions….Pages 269-284
Effective Properties of Elastic Composites….Pages 285-289
Back Matter….Pages 291-312