Polarization and Moment Tensors: With Applications to Inverse Problems and Effective Medium Theory (Applied Mathematical Sciences, 162) - Softcover

Ammari, Habib

Softcover

ISBN 10: 1441924493 ISBN 13: 9781441924490

Publisher: Springer, 2010

Synopsis

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.

About this title

From the Back Cover:

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.

Review:

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)

About this edition

• Publisher: Springer
• Publication date: 2010
• ISBN 10: 1441924493
• ISBN 13: 9781441924490
• Binding: Paperback
• Number of pages: 324