Overview
- Presents important developments in mathematical and computational methods used in impedance imaging and the theory of composite materials
- Theory is augmented by interesting practical examples and numerical illustrations
- Open problems at the end of each chapter
- Extensive bibliography enhances accessibility to specialized literature
Part of the book series: Applied Mathematical Sciences (AMS, volume 162)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
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)
Authors and Affiliations
Bibliographic Information
Book Title: Polarization and Moment Tensors
Book Subtitle: With Applications to Inverse Problems and Effective Medium Theory
Authors: Habib Ammari, Hyeonbae Kang
Series Title: Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-0-387-71566-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2007
Hardcover ISBN: 978-0-387-71565-0Published: 18 July 2007
Softcover ISBN: 978-1-4419-2449-0Published: 24 November 2010
eBook ISBN: 978-0-387-71566-7Published: 16 June 2007
Series ISSN: 0066-5452
Series E-ISSN: 2196-968X
Edition Number: 1
Number of Pages: X, 314
Topics: Applications of Mathematics, Biomedical Engineering and Bioengineering, Potential Theory, Partial Differential Equations, Imaging / Radiology