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

ISBN-13: 9781441924490 / Angielski / Miękka / 2010 / 314 str.

Habib Ammari; Hyeonbae Kang

Opis

This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. 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. An extensive bibliography and open problems at the end of each chapter enhance the text.

Recenzje

From the reviews:

"The main purpose of the book is to assess the influence of small-volume buried inclusions on measurements performed at the boundary of a domain of interest. ... This self-contained book will serve as an excellent reference for any mathematician interested in the reconstruction of constitutive parameters in a differential equation from boundary measurements." (Guillaume Bal, Mathematical Reviews, Issue 2009 f)

"The present book deals with one of the most interesting topics in the theory of inverse problems ... . any chapter of the volume contains an interesting section devoted to 'Further results and open problems'. ... the volume is extremely well-written and organized, as well as (reasonably) self-contained, so that any reader with a good knowledge in elliptic PDE's and interest in inverse problems will enjoy it ... ." (Alfredo Lorenzi, Zentralblatt MATH, Vol. 1220, 2011)

Spis treści

Introduction.- 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 Expansion of the Displacement Field.- Imaging of Elastic Inclusions.- Effective Properties of Elastic Composites.- Appendices.- References.- Index.

Blurb

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.