Mathematical Methods in Elasticity Imaging
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A01=Abdul Wahab
A01=Elie Bretin
A01=Habib Ammari
A01=Hyeonbae Kang
A01=Hyundae Lee
A01=Josselin Garnier
Algorithm
Approximation
Approximation theory
Asymptotic analysis
Asymptotic expansion
Asymptotic formula
Author_Abdul Wahab
Author_Elie Bretin
Author_Habib Ammari
Author_Hyeonbae Kang
Author_Hyundae Lee
Author_Josselin Garnier
Bayesian information criterion
Bessel function
Boundary value problem
Category=PBWH
Category=TGMD
Central limit theorem
Coefficient
Continuous function (set theory)
Covariance function
Covariance matrix
Deformation (mechanics)
Dimension (vector space)
Dimensional analysis
Dirichlet boundary condition
Displacement (vector)
Displacement field (mechanics)
Distribution (mathematics)
Divergence theorem
Eigenvalue perturbation
Eigenvalues and eigenvectors
Elasticity (physics)
eq_bestseller
eq_isMigrated=1
eq_nobargain
eq_non-fiction
eq_tech-engineering
Equation
Estimator
Fourier inversion theorem
Fundamental solution
Gaussian process
Gradient descent
Helmholtz decomposition
Helmholtz equation
Hilbert transform
Identity (mathematics)
Inference
Integral equation
Invertible matrix
Lagrangian (field theory)
Linear elasticity
Linear map
Linearization
Mathematical analysis
Mathematical optimization
Measurement
Moment (mathematics)
Near-field (mathematics)
Neumann boundary condition
Newton's method
Optimization problem
Parameter
Parameter (computer programming)
Parametric model
Path dependence
Probability
Projection (linear algebra)
Proportionality (mathematics)
Random variable
Regularization (mathematics)
Result
Shape optimization
Shear modulus
Social science
Spline (mathematics)
Support (mathematics)
Theorem
Topological derivative
Variable (mathematics)
Viscoelasticity
Wave equation
Product details
- ISBN 9780691165318
- Weight: 539g
- Dimensions: 178 x 254mm
- Publication Date: 06 Apr 2015
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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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.
Habib Ammari is director of research at the French National Center for Scientific Research and professor of mathematics at the Ecole Normale Superieure. Elie Bretin is a postdoctoral researcher in mathematics at the Ecole Polytechnique. Josselin Garnier is professor of mathematics at Universite Paris VII. Hyeonbae Kang is the Jungseok Chair Professor of Mathematics at Inha University in South Korea. Hyundae Lee is assistant professor of mathematics at Inha University. Abdul Wahab is a postdoctoral researcher in mathematics at Universite Paris VII.
