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Introduction

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

in Mathematical Methods in Elasticity Imaging

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691165318
eISBN:
9781400866625
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691165318.003.0001
Subject:
Mathematics, Applied Mathematics

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 ... More


Vibration Testing

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

in Mathematical Methods in Elasticity Imaging

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691165318
eISBN:
9781400866625
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691165318.003.0012
Subject:
Mathematics, Applied Mathematics

This chapter deals with vibration testing, which aims to identify inclusions, cracks, or shape changes in a structure by measuring its modal characteristics. The measured eigenparameters are related ... More


Backpropagation and Multiple Signal Classification Imaging of Small Inclusions

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

in Mathematical Methods in Elasticity Imaging

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691165318
eISBN:
9781400866625
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691165318.003.0006
Subject:
Mathematics, Applied Mathematics

This chapter deals with direct imaging of small inclusions and cracks in the static regime, focusing on MUSIC- and migration-type algorithms for detecting the small defects. MUSIC, reverse-time ... More


Small-Volume Expansions of the Displacement Fields

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

in Mathematical Methods in Elasticity Imaging

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691165318
eISBN:
9781400866625
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691165318.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter deals with small-volume expansions of the displacement fields. It first introduces the notion of elastic moment tensor, a geometric quantity associated with a small-volume inclusion, ... More


Topological Derivative Based Imaging of Small Inclusions in the Time-Harmonic Regime

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

in Mathematical Methods in Elasticity Imaging

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691165318
eISBN:
9781400866625
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691165318.003.0007
Subject:
Mathematics, Applied Mathematics

This chapter introduces a topological derivative (TD) based imaging framework for detecting small inclusions in the time-harmonic regime. Based on a weighted Helmholtz decomposition of the TD based ... More


Optimal Control Imaging of Extended Inclusions

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

in Mathematical Methods in Elasticity Imaging

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691165318
eISBN:
9781400866625
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691165318.003.0010
Subject:
Mathematics, Applied Mathematics

This chapter describes the use of time-reversal imaging techniques for optimal control of extended inclusions. It first considers the problem of reconstructing shape deformations of an extended ... More


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