Polarization and Moment Tensors: With Applications to Inverse Problems and Effective Medium TheoryThis 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
| 7 | |
Uniqueness for Inverse Conductivity Problems | 67 |
Generalized Isotropic and Anisotropic Polarization Tensors | 75 |
Full Asymptotic Formula for the Potentials 129 | 128 |
NearBoundary Conductivity Inclusions | 145 |
Impedance Imaging of Conductivity Inclusions | 161 |
Effective Properties of Electrical Composites | 195 |
Transmission Problem for Elastostatics | 211 |
Other editions - View all
Polarization and Moment Tensors: With Applications to Inverse Problems and ... Habib Ammari,Hyeonbae Kang No preview available - 2007 |
Polarization and Moment Tensors: With Applications to Inverse Problems and ... Habib Ammari,Hyeonbae Kang No preview available - 2010 |
Common terms and phrases
algorithm Ammari anisotropic Appl asymptotic expansion asymptotic formula boundary measurements bounded Lipschitz domain chapter compact compute conductivity inclusions constant C exists defined denote derive det(A Dirichlet disk domain in Rd eigenvalues elastic moment tensors elasticity tensor electrical impedance tomography ellipse EMTs estimate first-order following theorem given GPTs Green's formula Green's function harmonic function harmonic polynomial hence integral equation inverse conductivity problem Inverse Problems isotropic Kang L(OD L˛(ƏD L˛(OD Lamé Lamé constants Lamé parameters layer potentials Lemma linear Lipschitz character Math Mathematical matrix method Neumann numerical obtain operator perturbations polarization tensor Pólya-Szegö prove radius reconstruction satisfies SIAM small inclusions Suppose symmetric Theory transmission problem Vogelius voltage potential volume fraction zero ΘΩ ὃν ΣΣ ән дв ди ди
Popular passages
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].