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This book presents the theory of waves propagation in a fluid-saturated porous medium (a Biot medium) and its application in Applied Geophysics. In particular, a derivation of absorbing boundary conditions in viscoelastic and poroelastic media is presented, which later is employed in the applications. The partial differential equations describing the propagation of waves in Biot media are solved using the Finite Element Method (FEM). Waves propagating in a Biot medium suffer attenuation and dispersion effects. In particular the fast compressional and shear waves are converted to slow diffusion-type waves at mesoscopic-scale heterogeneities (on the order of centimeters), effect usually occurring in the seismic range of frequencies. In some cases, a Biot medium presents a dense set of fractures oriented in preference directions. When the average distance between fractures is much smaller than the wavelengths of the travelling fast compressional and shear waves, the medium behaves as an effective viscoelastic and anisotropic medium at the macroscale. The book presents a procedure determine the coefficients of the effective medium employing a collection of time-harmonic compressibility and shear experiments, in the context of Numerical Rock Physics. Each experiment is associated with a boundary value problem, that is solved using the FEM. This approach offers an alternative to laboratory observations with the advantages that they are inexpensive, repeatable and essentially free from experimental errors. The different topics are followed by illustrative examples of application in Geophysical Exploration. In particular, the effects caused by mesoscopic-scale heterogeneities or the presence of aligned fractures are taking into account in the seismic wave propagation models at the macroscale. The numerical simulations of wave propagation are presented with sufficient detail as to be easily implemented assuming the knowledge of scientific programming techniques.

Mathematics. --- Geophysics. --- Partial differential equations. --- Mathematical physics. --- Mathematical models. --- Mathematical Modeling and Industrial Mathematics. --- Geophysics/Geodesy. --- Partial Differential Equations. --- Geophysics and Environmental Physics. --- Mathematical Applications in the Physical Sciences. --- Physical geography. --- Differential equations, partial. --- Geography --- Partial differential equations --- Geophysics --- Seismic waves --- Waves, Seismic --- Elastic waves --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics --- Physical mathematics --- Models, Mathematical --- Simulation methods --- Mathematics

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This monograph investigates the stability and vibrations of conductive, perfectly conductive and superconductive thin bodies in electromagnetic fields. It introduces the main principles and obtains basic equations and relations describing interconnected mechanical and electromagnetic processes in deformable electroconductive bodies placed in an external inhomogeneous magnetic field and under the influence of various types of force interactions. Basic equations and relations are addressed in the nonlinear formulation. A special emphasis is put on the mechanical interaction of superconducting thin bodies plates with magnetic field.

Materials Science --- Applied Mathematics --- Chemical & Materials Engineering --- Engineering & Applied Sciences --- Magnetostriction. --- Elastic plates and shells. --- Elastic shells --- Plates, Elastic --- Shells, Elastic --- Magnetoelasticity --- Magnetostriction constant --- Magnetostriction saturations --- Negative magnetostriction --- Positive magnetostriction --- Elastic waves --- Elasticity --- Plasticity --- Magnetism --- Mechanics. --- Mechanics, Applied. --- Computer science --- Surfaces (Physics). --- Solid Mechanics. --- Classical Mechanics. --- Computational Mathematics and Numerical Analysis. --- Characterization and Evaluation of Materials. --- Mathematics. --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Surface chemistry --- Surfaces (Technology) --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Mathematics --- Computer mathematics. --- Materials science. --- Material science --- Physical sciences