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The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology.

Differentiable dynamical systems. --- Chaotic behavior in systems. --- Stochastic systems. --- Systems, Stochastic --- Stochastic processes --- System analysis --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Affine transformation. --- Amplitude. --- Arbitrarily large. --- Attractor. --- Autocovariance. --- Big O notation. --- Central limit theorem. --- Change of variables. --- Chaos theory. --- Coefficient of variation. --- Compound Probability. --- Computational problem. --- Control theory. --- Convolution. --- Coriolis force. --- Correlation coefficient. --- Covariance function. --- Cross-covariance. --- Cumulative distribution function. --- Cutoff frequency. --- Deformation (mechanics). --- Derivative. --- Deterministic system. --- Diagram (category theory). --- Diffeomorphism. --- Differential equation. --- Dirac delta function. --- Discriminant. --- Dissipation. --- Dissipative system. --- Dynamical system. --- Eigenvalues and eigenvectors. --- Equations of motion. --- Even and odd functions. --- Excitation (magnetic). --- Exponential decay. --- Extreme value theory. --- Flow velocity. --- Fluid dynamics. --- Forcing (recursion theory). --- Fourier series. --- Fourier transform. --- Fractal dimension. --- Frequency domain. --- Gaussian noise. --- Gaussian process. --- Harmonic analysis. --- Harmonic function. --- Heteroclinic orbit. --- Homeomorphism. --- Homoclinic orbit. --- Hyperbolic point. --- Inference. --- Initial condition. --- Instability. --- Integrable system. --- Invariant manifold. --- Iteration. --- Joint probability distribution. --- LTI system theory. --- Limit cycle. --- Linear differential equation. --- Logistic map. --- Marginal distribution. --- Moduli (physics). --- Multiplicative noise. --- Noise (electronics). --- Nonlinear control. --- Nonlinear system. --- Ornstein–Uhlenbeck process. --- Oscillation. --- Parameter space. --- Parameter. --- Partial differential equation. --- Perturbation function. --- Phase plane. --- Phase space. --- Poisson distribution. --- Probability density function. --- Probability distribution. --- Probability theory. --- Probability. --- Production–possibility frontier. --- Relative velocity. --- Scale factor. --- Shear stress. --- Spectral density. --- Spectral gap. --- Standard deviation. --- Stochastic process. --- Stochastic resonance. --- Stochastic. --- Stream function. --- Surface stress. --- Symbolic dynamics. --- The Signal and the Noise. --- Topological conjugacy. --- Transfer function. --- Variance. --- Vorticity.

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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

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).