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Book
Rays, Waves, and Scattering : Topics in Classical Mathematical Physics
Author:
ISBN: 140088540X Year: 2017 Publisher: Princeton, NJ : Princeton University Press,

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Abstract

This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas.Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes.Provides a panoramic look at wave motion in many different contextsFeatures problems and exercises throughoutIncludes numerous appendixes, some on topics not often coveredAn ideal reference book for practitionersCan also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineeringAccessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable

Keywords

Mathematical physics. --- Physical mathematics --- Physics --- Mathematics --- Airy approximation. --- Airy functions. --- Airy integral. --- Airy theory. --- Airy wavefront. --- Alexander's dark band. --- Bessel functions. --- Earth. --- Fermat's principle. --- Fresnel integrals. --- Hamilton's principle. --- Hamilton-Jacobi equation. --- Hamilton-Jacobi theory. --- Hamiltonian. --- Hooke's law. --- Kepler's laws of planetary motion. --- Lagrangian. --- Liouville transformation. --- Love waves. --- Navier equations. --- Ptolemy's theorem. --- Rayleigh scattering. --- Schrödinger equation. --- Sir George Biddle Airy. --- Snell's laws. --- Taylor–Goldstein equation. --- WKB(J) approximation. --- Wiechert-Herglotz inverse problem. --- acoustic wave propagation. --- action. --- angle of minimum deviation. --- applied mathematics. --- atmospheric waves. --- billow clouds. --- boundary-value problem. --- buoyancy waves. --- caustics. --- classical mechanics. --- classical wave equation. --- colors. --- complex plane. --- constant phase lines. --- contours. --- corona. --- currents. --- cusp catastrophes. --- deep water waves. --- differential equations. --- diffraction catastrophes. --- diffraction. --- dispersion relations. --- dispersion. --- divergence problem. --- earthquakes. --- eikonal equation. --- elastic solid. --- elastic waves. --- elementary mathematics. --- equations of motion. --- fluid equations. --- fold catastrophes. --- free surface. --- geometric wavefronts. --- geometrical optics. --- glory. --- inhomogeneous medium. --- integrals. --- intensity law. --- internal gravity waves. --- inverse scattering problem. --- islands. --- leading waves. --- lee waves. --- light waves. --- long waves. --- mathematics. --- meteorological optics. --- mountain waves. --- ocean acoustic waveguides. --- ocean acoustics. --- ocean waves. --- one-dimensional waves. --- optics. --- path. --- plane wave incident. --- plane waves. --- polarization. --- potential well. --- rainbow. --- ray equations. --- ray optics. --- ray theory. --- rays. --- reflection. --- refraction. --- ridge. --- scattering. --- seafloor. --- seismic rays. --- seismic tomography. --- seismic waves. --- semicircle theorem. --- shallow water waves. --- ship waves. --- short waves. --- strain. --- stratified fluid. --- stress. --- surface gravity waves. --- surface waves. --- transient waves. --- tsunami propagation. --- tsunamis. --- wave energy. --- wave refraction. --- wave trapping. --- wavefront. --- wavepackets. --- waves. --- wind shear.


Book
Earthquake and volcano deformation
Author:
ISBN: 9780691133027 0691133026 1282608215 9786612608216 140083385X 9781400833856 9781282608214 Year: 2010 Publisher: Princeton, N.J. Princeton University Press

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Earthquake and Volcano Deformation is the first textbook to present the mechanical models of earthquake and volcanic processes, emphasizing earth-surface deformations that can be compared with observations from Global Positioning System (GPS) receivers, Interferometric Radar (InSAR), and borehole strain- and tiltmeters. Paul Segall provides the physical and mathematical fundamentals for the models used to interpret deformation measurements near active faults and volcanic centers.Segall highlights analytical methods of continuum mechanics applied to problems of active crustal deformation. Topics include elastic dislocation theory in homogeneous and layered half-spaces, crack models of faults and planar intrusions, elastic fields due to pressurized spherical and ellipsoidal magma chambers, time-dependent deformation resulting from faulting in an elastic layer overlying a viscoelastic half-space and related earthquake cycle models, poroelastic effects due to faulting and magma chamber inflation in a fluid-saturated crust, and the effects of gravity on deformation. He also explains changes in the gravitational field due to faulting and magmatic intrusion, effects of irregular surface topography and earth curvature, and modern concepts in rate- and state-dependent fault friction. This textbook presents sample calculations and compares model predictions against field data from seismic and volcanic settings from around the world.Earthquake and Volcano Deformation requires working knowledge of stress and strain, and advanced calculus. It is appropriate for advanced undergraduates and graduate students in geophysics, geology, and engineering. Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html

Keywords

Rock deformation --- Strains and stresses --- Volcanism. --- Earthquakes. --- Deformations (Mechanics) --- Mathematical models. --- Volcanism --- Earthquakes --- Volcanisme --- Tremblements de terre --- Déformations (Mécanique) --- Mathematical models --- Deformations (Mechanics). --- Rock deformation - Mathematical models. --- Rock deformation -- Mathematical models. --- Strains and stresses - Mathematical models. --- Strains and stresses -- Mathematical models. --- Volcanicity --- Vulcanism --- Stresses and strains --- Elastic solids --- Mechanics --- Rheology --- Structural failures --- Quakes (Earthquakes) --- Earth movements --- Natural disasters --- Seismology --- Geodynamics --- Volcanology --- Architectural engineering --- Engineering, Architectural --- Architecture --- Flexure --- Statics --- Structural analysis (Engineering) --- Elasticity --- Engineering design --- Graphic statics --- Strength of materials --- Stress waves --- Structural design --- Deformation, Rock --- Geology, Structural --- Rock deformation - Mathematical models --- Strains and stresses - Mathematical models --- 1906 San Francisco earthquake. --- 1980 eruption of Mount St. Helens. --- 1989 Loma Prieta earthquake. --- 1992 Landers earthquake. --- 1999 Hector Mine earthquake. --- Active fault. --- Atmospheric refraction. --- Cauchy stress tensor. --- Compressive stress. --- Continental collision. --- Continuum mechanics. --- Crust (geology). --- Deformation (engineering). --- Deformation (mechanics). --- Deformation monitoring. --- Dike (geology). --- Dislocation. --- Displacement field (mechanics). --- Earthquake prediction. --- Earthquake rupture. --- Earthquake swarm. --- Elasticity (physics). --- Explosive eruption. --- Fault (geology). --- Fault friction. --- Figure of the Earth. --- Fracture mechanics. --- Fracture toughness. --- Fracture zone. --- Fracture. --- Friction. --- Geodetic datum. --- Geologic time scale. --- Geothermal gradient. --- Gravitational acceleration. --- Gravitational potential. --- Gravity Recovery and Climate Experiment. --- Hawaiian Volcano Observatory. --- Infinitesimal strain theory. --- Intraplate earthquake. --- Lava dome. --- Lava lake. --- Lava. --- Long Valley Caldera. --- Magma chamber. --- Magnetic anomaly. --- Melting point. --- Mount St. Helens. --- Nucleation. --- Orogeny. --- Oscillation. --- Parkfield earthquake. --- Plane stress. --- Plate tectonics. --- Porosity. --- Pressure gradient. --- Radiation stress. --- Resurgent dome. --- Rift zone. --- Rock (geology). --- Rock mechanics. --- San Andreas Fault. --- Seafloor spreading. --- Seismic gap. --- Seismic hazard. --- Seismic moment. --- Seismic risk. --- Seismic tomography. --- Seismic wave. --- Seismology. --- Shear modulus. --- Shear stress. --- Shear zone. --- Shearing (physics). --- Shield volcano. --- Strain energy. --- Strain rate. --- Stratovolcano. --- Stress concentration. --- Stress functions. --- Stress intensity factor. --- Subduction. --- Subsidence. --- Surface energy. --- Surface gravity. --- Surface stress. --- Tectonophysics. --- Tension (physics). --- Thermal expansion. --- Thrust fault. --- Traction (engineering). --- Transform fault. --- Types of volcanic eruptions. --- Vibration. --- Viscoelasticity. --- Volcanic hazards. --- Volcanic pipe. --- Volcano. --- Wavenumber. --- Yield (engineering).

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