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Mathematical Methods in Elasticity Imaging$
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Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

Print publication date: 2015

Print ISBN-13: 9780691165318

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691165318.001.0001

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(p.1) Introduction
Mathematical Methods in Elasticity Imaging

Habib Ammari

Elie Bretin

Josselin Garnier

Hyeonbae Kang

Hyundae Lee

Abdul Wahab

Princeton University Press

This book is about recent mathematical, numerical and statistical approaches for elasticity imaging of inclusions and cracks with waves at zero, single or multiple non-zero frequencies. It considers important developments in asymptotic imaging, stochastic modeling, and analysis of both deterministic and stochastic elastic wave propagation phenomena and puts them together in a coherent way. It gives emphasis on deriving the best possible imaging functionals for small inclusions and cracks in the sense of stability and resolution. For imaging extended elastic inclusions, the book develops accurate optimal control methodologies and examines the effect of uncertainties of the geometric or physical parameters on their stability and resolution properties. It also presents an asymptotic framework for vibration testing and a method for identifying, locating, and estimating inclusions and cracks in elastic structures by measuring their modal characteristics.

Keywords:   elasticity imaging, crack, asymptotic imaging, stochastic modeling, elastic wave propagation, small inclusion, optimal control, vibration testing, elastic structure, elastic inclusion

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