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

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Springer Science & Business Media, Jun 16, 2007 - Mathematics - 314 pages

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.

 

Contents

Contents
1
Layer Potentials and Transmission Problems
7
3
32
Uniqueness for Inverse Conductivity Problems
67
4
75
Full Asymptotic Formula for the Potentials 129
128
NearBoundary Conductivity Inclusions
145
Impedance Imaging of Conductivity Inclusions
161
Transmission Problem for Elastostatics
211
Elastic Moment Tensor
237
Full Asymptotic Expansions of the Displacement Field 261
260
Imaging of Elastic Inclusions
269
Effective Properties of Elastic Composites
285
References
295
Index
311
Copyright

Effective Properties of Electrical Composites
195

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Page 1 - ... 1. Introduction Impedance imaging uses measurements of boundary voltage potentials and associated boundary currents to infer information about the internal conductivity profile of an object. Complete information about all voltages and currents is known to uniquely characterize an isotropic internal conductivity profile [8, 27, 33, 34].

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