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Book
Mathematical Methods for Geophysics and Space Physics
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ISBN: 152312458X 1400882826 Year: 2016 Publisher: Princeton, New Jersey : Princeton University Press,

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Abstract

Graduate students in the natural sciences-including not only geophysics and space physics but also atmospheric and planetary physics, ocean sciences, and astronomy-need a broad-based mathematical toolbox to facilitate their research. In addition, they need to survey a wider array of mathematical methods that, while outside their particular areas of expertise, are important in related ones. While it is unrealistic to expect them to develop an encyclopedic knowledge of all the methods that are out there, they need to know how and where to obtain reliable and effective insights into these broader areas. Here at last is a graduate textbook that provides these students with the mathematical skills they need to succeed in today's highly interdisciplinary research environment. This authoritative and accessible book covers everything from the elements of vector and tensor analysis to ordinary differential equations, special functions, and chaos and fractals. Other topics include integral transforms, complex analysis, and inverse theory; partial differential equations of mathematical geophysics; probability, statistics, and computational methods; and much more. Proven in the classroom, Mathematical Methods for Geophysics and Space Physics features numerous exercises throughout as well as suggestions for further reading. Provides an authoritative and accessible introduction to the subject Covers vector and tensor analysis, ordinary differential equations, integrals and approximations, Fourier transforms, diffusion and dispersion, sound waves and perturbation theory, randomness in data, and a host of other topics Features numerous exercises throughout Ideal for students and researchers alike an online illustration package is available to professors

Keywords

Geophysics --- Cosmic physics --- Physics --- Space sciences --- Mathematics. --- Analytical mechanics. --- Applied mathematics. --- Atmospheric physics. --- Bessel function. --- Bifurcation theory. --- Calculation. --- Calculus of variations. --- Cartesian coordinate system. --- Cauchy's theorem (geometry). --- Celestial mechanics. --- Central limit theorem. --- Chaos theory. --- Classical electromagnetism. --- Classical mechanics. --- Classical physics. --- Convolution theorem. --- Deformation (mechanics). --- Degeneracy (mathematics). --- Diagram (category theory). --- Differential equation. --- Drag (physics). --- Earth science. --- Eigenvalues and eigenvectors. --- Einstein notation. --- Elliptic integral. --- Elliptic orbit. --- Equation. --- Expectation value (quantum mechanics). --- Figure of the Earth. --- Forcing function (differential equations). --- Fourier series. --- Fourier transform. --- Fractal dimension. --- Function (mathematics). --- Gaussian function. --- Geochemistry. --- Geochronology. --- Geodesics in general relativity. --- Geometry. --- Geophysics. --- Gravitational acceleration. --- Gravitational constant. --- Gravitational potential. --- Gravitational two-body problem. --- Hamiltonian mechanics. --- Handbook of mathematical functions. --- Harmonic oscillator. --- Helmholtz equation. --- Hilbert transform. --- Hyperbolic partial differential equation. --- Integral equation. --- Isotope geochemistry. --- Lagrangian (field theory). --- Laplace transform. --- Laplace's equation. --- Laws of thermodynamics. --- Limit (mathematics). --- Line (geometry). --- Lorenz system. --- Mathematical analysis. --- Mathematical geophysics. --- Mathematical physics. --- Newton's law of universal gravitation. --- Newton's laws of motion. --- Newton's method. --- Newtonian dynamics. --- Numerical analysis. --- Numerical integration. --- Operator (physics). --- Orbit. --- Orbital resonance. --- Parseval's theorem. --- Partial differential equation. --- Perturbation theory (quantum mechanics). --- Perturbation theory. --- Planetary body. --- Planetary science. --- Poisson's equation. --- Pole (complex analysis). --- Proportionality (mathematics). --- Quantum mechanics. --- Rotation (mathematics). --- Satellite geodesy. --- Scalar (physics). --- Scientific notation. --- Separatrix (mathematics). --- Sign (mathematics). --- Space physics. --- Statistical mechanics. --- Stokes' theorem. --- Three-dimensional space (mathematics). --- Transformation geometry. --- Trapezoidal rule. --- Truncation error (numerical integration). --- Two-dimensional space. --- Van der Pol oscillator. --- Variable (mathematics). --- Vector space. --- Wave equation.


Book
The Little Book of Black Holes
Authors: ---
ISBN: 1400888298 Year: 2017 Publisher: Princeton, NJ : Princeton University Press,

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Dive into a mind-bending exploration of the physics of black holesBlack holes, predicted by Albert Einstein's general theory of relativity more than a century ago, have long intrigued scientists and the public with their bizarre and fantastical properties. Although Einstein understood that black holes were mathematical solutions to his equations, he never accepted their physical reality-a viewpoint many shared. This all changed in the 1960s and 1970s, when a deeper conceptual understanding of black holes developed just as new observations revealed the existence of quasars and X-ray binary star systems, whose mysterious properties could be explained by the presence of black holes. Black holes have since been the subject of intense research-and the physics governing how they behave and affect their surroundings is stranger and more mind-bending than any fiction.After introducing the basics of the special and general theories of relativity, this book describes black holes both as astrophysical objects and theoretical "laboratories" in which physicists can test their understanding of gravitational, quantum, and thermal physics. From Schwarzschild black holes to rotating and colliding black holes, and from gravitational radiation to Hawking radiation and information loss, Steven Gubser and Frans Pretorius use creative thought experiments and analogies to explain their subject accessibly. They also describe the decades-long quest to observe the universe in gravitational waves, which recently resulted in the LIGO observatories' detection of the distinctive gravitational wave "chirp" of two colliding black holes-the first direct observation of black holes' existence.The Little Book of Black Holes takes readers deep into the mysterious heart of the subject, offering rare clarity of insight into the physics that makes black holes simple yet destructive manifestations of geometric destiny.

Keywords

Black holes (Astronomy) --- Frozen stars --- Compact objects (Astronomy) --- Gravitational collapse --- Stars --- A-frame. --- Acceleration. --- Accretion disk. --- Alice and Bob. --- Angular momentum. --- Astronomer. --- Atomic nucleus. --- Binary black hole. --- Binary star. --- Black hole information paradox. --- Black hole thermodynamics. --- Black hole. --- Calculation. --- Circular orbit. --- Classical mechanics. --- Closed timelike curve. --- Cosmological constant. --- Curvature. --- Cygnus X-1. --- Degenerate matter. --- Differential equation. --- Differential geometry. --- Doppler effect. --- Earth. --- Einstein field equations. --- Electric charge. --- Electric field. --- Electromagnetism. --- Ergosphere. --- Escape velocity. --- Event horizon. --- Excitation (magnetic). --- Frame-dragging. --- Galactic Center. --- General relativity. --- Gravitational acceleration. --- Gravitational collapse. --- Gravitational constant. --- Gravitational energy. --- Gravitational field. --- Gravitational redshift. --- Gravitational wave. --- Gravitational-wave observatory. --- Gravity. --- Hawking radiation. --- Inner core. --- Kerr metric. --- Kinetic energy. --- LIGO. --- Length contraction. --- Lorentz transformation. --- Magnetic field. --- Mass–energy equivalence. --- Maxwell's equations. --- Metric expansion of space. --- Metric tensor. --- Milky Way. --- Minkowski space. --- Negative energy. --- Neutrino. --- Neutron star. --- Neutron. --- Newton's law of universal gravitation. --- No-hair theorem. --- Nuclear fusion. --- Nuclear reaction. --- Orbit. --- Orbital mechanics. --- Orbital period. --- Penrose process. --- Photon. --- Physicist. --- Primordial black hole. --- Projectile. --- Quantum entanglement. --- Quantum gravity. --- Quantum mechanics. --- Quantum state. --- Quasar. --- Ray (optics). --- Rotational energy. --- Roy Kerr. --- Schwarzschild metric. --- Schwarzschild radius. --- Solar mass. --- Special relativity. --- Star. --- Stellar mass. --- Stephen Hawking. --- Stress–energy tensor. --- String theory. --- Supermassive black hole. --- Temperature. --- Theory of relativity. --- Thought experiment. --- Tidal force. --- Time dilation. --- Wavelength. --- White hole. --- Wormhole.


Book
The whole truth : a cosmologist's reflections on the search for objective reality
Author:
ISBN: 0691231362 Year: 2022 Publisher: Princeton, N. J. : Princeton University Press,

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From the Nobel Prize–winning physicist, a personal meditation on the quest for objective reality in natural scienceA century ago, thoughtful people questioned how reality could agree with physical theories that keep changing, from a mechanical model of the ether to electric and magnetic fields, and from homogeneous matter to electrons and atoms. Today, concepts like dark matter and dark energy further complicate and enrich the search for objective reality. The Whole Truth is a personal reflection on this ongoing quest by one of the world’s most esteemed cosmologists.What lies at the heart of physical science? What are the foundational ideas that inform and guide the enterprise? Is the concept of objective reality meaningful? If so, do our established physical theories usefully approximate it? P. J. E. Peebles takes on these and other big questions about the nature of science, drawing on a lifetime of experience as a leading physicist and using cosmology as an example. He traces the history of thought about the nature of physical science since Einstein, and succinctly lays out the fundamental working assumptions. Through a careful examination of the general theory of relativity, Einstein’s cosmological principle, and the theory of an expanding universe, Peebles shows the evidence that we are discovering the nature of reality in successive approximations through increasingly demanding scrutiny.A landmark work, The Whole Truth is essential reading for anyone interested in the practice of science.

Keywords

Cosmology. --- Physics. --- Reality. --- Science --- SCIENCE / Cosmology. --- Philosophy. --- Absolute magnitude. --- Acceleration. --- Angular momentum. --- Approximation. --- Astronomer. --- Astronomy. --- Asymptotically flat spacetime. --- Atomic nucleus. --- Atomic number. --- Baryon. --- Big Bang. --- Calculation. --- Chronology of the universe. --- Classical limit. --- Classical physics. --- Comprehension (logic). --- Conservation law. --- Cosmic Evolution (book). --- Cosmological constant. --- Cosmological principle. --- Density. --- Empirical research. --- Equivalence principle. --- Existence. --- Extrapolation. --- Fred Hoyle. --- Galaxy cluster. --- Galaxy rotation curve. --- General relativity. --- George Gamow. --- Goodness of fit. --- Gravitational acceleration. --- Gravitational redshift. --- Gravity. --- Hubble's law. --- Inverse-square law. --- Jupiter. --- Kinetic energy. --- Kuiper belt. --- Length scale. --- Linear scale. --- Mach's principle. --- Mass distribution. --- Measurement. --- Metric expansion of space. --- Minkowski space. --- Modified Newtonian dynamics. --- Multiple discovery. --- NGC 2403. --- Natural science. --- Neutrino. --- Neutron. --- Newton's law of universal gravitation. --- Number density. --- Observation. --- Order of magnitude. --- Paradigm shift. --- Partial derivative. --- Particle physics in cosmology. --- Peirce (crater). --- Photon. --- Physical cosmology. --- Physical law. --- Physicist. --- Planetary nebula. --- Planetary system. --- Power law. --- Prediction. --- Predictive power. --- Present value. --- Quantum electrodynamics. --- Quantum mechanics. --- Redshift. --- Repeatability. --- Richard Feynman. --- Satellite. --- Scattering. --- Schwarzschild metric. --- Science wars. --- Scientist. --- Sirius. --- Social constructionism. --- Special relativity. --- Spiral galaxy. --- Steady State theory. --- Stellar classification. --- Supersymmetry. --- Temperature. --- Tests of general relativity. --- The Unreasonable Effectiveness of Mathematics in the Natural Sciences. --- Theoretical physics. --- Theory of relativity. --- Theory. --- Thermal radiation. --- Thomas Kuhn. --- Thought. --- Verificationism. --- Wavelength. --- White dwarf. --- Zero-point energy. --- Normal science --- Philosophy of science --- Philosophy --- Truth --- Nominalism --- Pluralism --- Pragmatism --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Astronomy --- Deism --- Metaphysics --- SCIENCE / Space Science / Cosmology --- SCIENCE / History


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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