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Mathematical Methods in Elasticity Imaging
Hyeonbae Kang, Abdul Wahab, Habib Ammari, et al.
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Bessel function, Linear map, Dirichlet boundary condition, Eigenvalue perturbation, Near-field (mathematics), Mathematical analysis, Path dependence, Divergence theorem, Elasticity (physics), Mathematical optimization, Proportionality (mathematics), Linear elasticity, Dimension (vector space), Inference, Approximation, Helmholtz decomposition, Optimization problem, Support (mathematics), Central limit theorem, Neumann boundary condition, Displacement (vector), Identity (mathematics), Continuous function (set theory), Spline (mathematics), Shape optimization, Invertible matrix, Measurement, Wave equation, Covariance function, Theorem, Topological derivative, Gradient descent, Linearization, Fourier inversion theorem, Boundary value problem, Random variable, Approximation theory, Helmholtz equation, Hilbert transform, Newton's method, Equation, Shear modulus, Covariance matrix, Variable (mathematics), Displacement field (mechanics), Parametric model, Result, Asymptotic expansion, Parameter, Estimator, Probability, Coefficient, Viscoelasticity, Asymptotic formula, Dimensional analysis, Integral equation, Lagrangian (field theory), Gaussian process, Distribution (mathematics), Deformation (mechanics), Regularization (mathematics), Algorithm, Bayesian information criterion, Asymptotic analysis, Fundamental solution, Eigenvalues and eigenvectors, Social science, Moment (mathematics), Parameter (computer programming), Projection (linear algebra)