Polarization and Moment Tensors [electronic resource] : With Applications to Inverse Problems and Effective Medium Theory / by Habib Ammari, Hyeonbae Kang.
Contributor(s): Kang, Hyeonbae [author.] | SpringerLink (Online service)Material type: TextSeries: Applied Mathematical Sciences: 162Publisher: New York, NY : Springer New York, 2007Description: X, 314 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387715667Subject(s): Mathematics | Radiology | Partial differential equations | Potential theory (Mathematics) | Applied mathematics | Engineering mathematics | Biomedical engineering | Mathematics | Applications of Mathematics | Biomedical Engineering | Potential Theory | Partial Differential Equations | Imaging / RadiologyAdditional physical formats: Printed edition:: No titleDDC classification: 519 LOC classification: T57-57.97Online resources: Click here to access online
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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 Expansions of the Displacement Field -- Imaging of Elastic Inclusions -- Effective Properties of Elastic Composites.
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.