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

Mathematical Methods in Elasticity Imaging (eBook)

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, Abdul Wahab (Autoren)

eBook Download: EPUB

2015
240 Seiten
Princeton University Press (Verlag)
978-1-4008-6662-5 (ISBN)

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 École Normale Superiéure. Elie Bretin is a postdoctoral researcher in mathematics at the École Polytechnique. Josselin Garnier is professor of mathematics at Université 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 Université Paris VII.

Erscheint lt. Verlag	5.4.2015
Reihe/Serie	Princeton Series in Applied Mathematics
Reihe/Serie	Princeton Series in Applied Mathematics
Zusatzinfo	22 halftones. 9 line illus. 1 table.
Verlagsort	Princeton
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Naturwissenschaften ► Physik / Astronomie
	Technik ► Maschinenbau
Schlagworte	Adjoint • algorithm • All rights reserved • Amplitude • Analysis • anisotropic elasticity • Applied mathematics • Approximation • Approximation Theory • Argument principle • asymptotic analysis • asymptotic expansion • asymptotic formula • asymptotic imaging • Asymptotic Theory • Asymptotic theory (statistics) • Attenuation Coefficient • backpropagation • Ball • Bayesian information criterion • Bessel function • Big O notation • boundary displacement • boundary perturbation • Boundary value problem • boundedness • British Library • causal inference • cellular structure • central limit theorem • Characteristic function (probability theory) • coefficient • compressional modulus • Computation • conditional expectation • Continuous function (set theory) • Copyright • Covariance function • Covariance matrix • crack • Deformation (mechanics) • Degeneracy (mathematics) • density parameter • Derivative • detection • Dimensional Analysis • Dimension (vector space) • Dirac equation • direct imaging • Dirichlet boundary condition • Dirichlet eigenvalue • Dirichlet function • Dirichlet problem • discrepancy function • Disk (mathematics) • Displacement • displacement field • Displacement field (mechanics) • Displacement (vector) • Distribution (mathematics) • Divergence Theorem • Eigenvalue perturbation • Eigenvalues and Eigenvectors • Einstein notation • elastic coefficient • elastic equation • elastic inclusion • Elasticity • elasticity equation • elasticity imaging • Elasticity (physics) • elastic moment tensor • elastic structure • elastic wave • elastic wave equation • Elastic Wave Propagation • Ellipse • energy functional • Equation • Error Correction Model • Estimator • Excitation (magnetic) • Explicit formulae (L-function) • exponential function • extended inclusion • extended source term • extended target • far-field measurement • filtered quadratic misfit • First-order partial differential equation • Fourier • Fourier inversion theorem • Fourier transform • frequency domain • Function (mathematics) • function space • fundamental solution • Gaussian process • Gradient descent • gradient scheme • Green's Function • hard inclusion • hard inclusions • Helmholtz decomposition • Helmholtz decomposition theorem • Helmholtz equation • HelmholtzЋirchhoff identities • Hermitian adjoint • heterogeneous shear distribution • high contrast coefficient • hilbert space • Hilbert transform • hole • Hooke's law • Hyperparameter • Identity (mathematics) • Illustration • Image Quality • Image Resolution • imaging functional • Inclusion • incompressible limit • inference • Integral • integral equation • internal displacement measurement • inverse problem • Invertible matrix • Iterative Method • Kelvin matrix • Kirchhoff migration • Lagrangian (field theory) • Lam system • layer potential • Leading-order term • Level set method • Linear combination • linear elasticity • Linearization • linearized reconstruction problem • Linear map • linear regression • linear transformation • Lipschitz domain • Magnetic Resonance Imaging • Mathematical Analysis • Mathematical Optimization • Mathematical problem • Maxima and minima • Measure (mathematics) • Measurement • Measurement Noise • medium noise • Moment (mathematics) • Multivariate normal distribution • MUSIC Algorithm • Nanoparticle • Near-field (mathematics) • Neumann boundary condition • Newton's method • nonlinear optimization problem • Nonlinear Problem • Normal (geometry) • Notation • operator-valued function • optimal control • optimization problem • Orthonormal basis • Parameter • Parameter (computer programming) • parametric model • path dependence • Poisson's ratio • Pole (complex analysis) • Polynomial Regression • potential energy functional • power law • Pressure • Probability • Projection (linear algebra) • Proportionality (mathematics) • Quantifier (logic) • Quantity • radiation condition • Random fluctuation • Random Variable • Regime • Regularization (mathematics) • Resolution • result • reverse-time migration • scalar wave equation • Search Algorithm • Set function • Shape • Shape Change • shape deformation • shape optimization • shear distribution • shear modulus • shear wave • Signal subspace • Singular value • small crack • small inclusion • small-volume expansion • small-volume inclusion • Social Science • soft inclusion • Special case • Spline (mathematics) • square root • stability • Stability Analysis • static regime • Statistic • Statistical stability • Stochastic Modeling • Subsurface (software) • Support (mathematics) • Symmetric matrix • Tensor • tensor product • Theorem • Three-dimensional space (mathematics) • time-harmonic regime • time-reversal imaging • Time reversibility • topological derivative • Trade-off • two-dimensional space • Unit disk • Variable (mathematics) • Variance • Vibration • Vibration testing • viscoelasticity • wave equation • Wavelength • wavenumber • wave propagation
ISBN-10	1-4008-6662-6 / 1400866626
ISBN-13	978-1-4008-6662-5 / 9781400866625

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