Princeton Series in Applied Mathematics
- 240 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Princeton Series in Applied Mathematics
About This Book
This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative–based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.
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Table of contents
- Cover Page
- Title Page
- Copyright Page
- Contents
- Introduction
- 1 Layer Potential Techniques
- 2 Elasticity Equations with High Contrast Parameters
- 3 Small-Volume Expansions of the Displacement Fields
- 4 Boundary Perturbations due to the Presence of Small Cracks
- 5 Backpropagation and Multiple Signal Classification Imaging of Small Inclusions
- 6 Topological Derivative Based Imaging of Small Inclusions in the Time-Harmonic Regime
- 7 Stability of Topological Derivative Based Imaging Functionals
- 8 Time-Reversal Imaging of Extended Source Terms
- 9 Optimal Control Imaging of Extended Inclusions
- 10 Imaging from Internal Data
- 11 Vibration Testing
- A Introduction to Random Processes
- B Asymptotics of the Attenuation Operator
- C The Generalized Argument Principle and Rouché’s Theorem
- References
- Index