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Earthquakes, a plucked string, ocean waves crashing on the beach, the sound waves that allow us to recognize known voices. Waves are everywhere, and the propagation and classical properties of these apparently disparate phenomena can be described by the same mathematical methods: variational calculus, characteristics theory, and caustics. Taking a medium-by-medium approach, Julian Davis explains the mathematics needed to understand wave propagation in inviscid and viscous fluids, elastic solids, viscoelastic solids, and thermoelastic media, including hyperbolic partial differential equations and characteristics theory, which makes possible geometric solutions to nonlinear wave problems. The result is a clear and unified treatment of wave propagation that makes a diverse body of mathematics accessible to engineers, physicists, and applied mathematicians engaged in research on elasticity, aerodynamics, and fluid mechanics. This book will particularly appeal to those working across specializations and those who seek the truly interdisciplinary understanding necessary to fully grasp waves and their behavior. By proceeding from concrete phenomena (e.g., the Doppler effect, the motion of sinusoidal waves, energy dissipation in viscous fluids, thermal stress) rather than abstract mathematical principles, Davis also creates a one-stop reference that will be prized by students of continuum mechanics and by mathematicians needing information on the physics of waves.
Wave-motion, Theory of. --- Acoustic impedance. --- Adiabatic condition. --- Adjoint operators. --- Bessel's equation. --- Boundary layer. --- Brachistochrome problem. --- Bulk modulus. --- Canonical transformations. --- Caustic or focal curves. --- Characteristic coordinates. --- Characteristic line element. --- Characteristics, method of. --- Critical sound speed. --- Cyclic coordinates. --- Deformation. --- Direction field. --- Doppler effect. --- Eigenfunctions. --- Eigenvalues. --- Epicycloid. --- Fermat's principle. --- Finite bar. --- Friction, internal. --- Generalized force. --- Generalized velocity. --- Hamilton-Jacoby theory. --- Hamiltonian. --- Ideal or perfect gas. --- Integral surfaces. --- Isothermal condition. --- Jacobian. --- Kinetic energy. --- Lagrangian function. --- Lame constants. --- Laminar flow. --- Memory function. --- Minimizing curve. --- Monge axis. --- Monge cone. --- Navier equations. --- Oseen approximation. --- Physics of propagating waves. --- Plane elastic waves. --- Poiseuille flow. --- Progressing wave. --- Quantum mechanics. --- Radially symmetric waves. --- Regressing wave. --- Reynold's law. --- Self-adjoint operator. --- Sinusoidal waves. --- Undulatory theory --- Mechanics
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This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to mathematical modelling. The contributions have been carefully selected so that they cover interesting theoretical and practical analysis performed in the deterministic and the stochastic settings. The reader will find a complete overview of recent advances in ordinary and partial delay differential equations with applications in other multidisciplinary areas such as Finance, Epidemiology or Engineering
Research & information: general --- Mathematics & science --- delay systems --- nonstandard numerical methods --- dynamic consistency --- semilinear problems with delay --- hyperbolic equations --- difference scheme --- stability --- Hilbert space --- SEIRS model --- age structure --- time delay --- traveling wave solution --- local asymptotic stability --- Hopf bifurcation --- spot freight rates --- freight options --- stochastic diffusion process --- stochastic delay differential equation --- risk-neutral measure --- arbitration arguments --- partial differential equations --- second-order dual phase lag equation --- laser heating --- thin metal films --- melting and resolidification --- finite difference method --- random linear delay differential equation --- stochastic forcing term --- random Lp-calculus --- uncertainty quantification --- delay random differential equation --- non-standard finite difference method --- mean square convergence --- size-structured population --- consumer-resource model --- delay differential equation --- numerical methods --- characteristics method --- convergence analysis --- implementation delay --- information delay --- stability switching curve --- Cournot oligopoly --- growth rate dynamics --- fractional convection diffusion-wave equations --- compact difference scheme --- nonlinear delay --- spatial variable coefficients --- convergence and stability --- Gerasimov–Caputo fractional derivative --- differential equation with delay --- degenerate evolution equation --- fixed point theorem --- relaxation mode --- large parameter --- asymptotics --- HIV infection --- mathematical delay model --- eclipse phase --- NSFD --- numerical simulation --- delay systems --- nonstandard numerical methods --- dynamic consistency --- semilinear problems with delay --- hyperbolic equations --- difference scheme --- stability --- Hilbert space --- SEIRS model --- age structure --- time delay --- traveling wave solution --- local asymptotic stability --- Hopf bifurcation --- spot freight rates --- freight options --- stochastic diffusion process --- stochastic delay differential equation --- risk-neutral measure --- arbitration arguments --- partial differential equations --- second-order dual phase lag equation --- laser heating --- thin metal films --- melting and resolidification --- finite difference method --- random linear delay differential equation --- stochastic forcing term --- random Lp-calculus --- uncertainty quantification --- delay random differential equation --- non-standard finite difference method --- mean square convergence --- size-structured population --- consumer-resource model --- delay differential equation --- numerical methods --- characteristics method --- convergence analysis --- implementation delay --- information delay --- stability switching curve --- Cournot oligopoly --- growth rate dynamics --- fractional convection diffusion-wave equations --- compact difference scheme --- nonlinear delay --- spatial variable coefficients --- convergence and stability --- Gerasimov–Caputo fractional derivative --- differential equation with delay --- degenerate evolution equation --- fixed point theorem --- relaxation mode --- large parameter --- asymptotics --- HIV infection --- mathematical delay model --- eclipse phase --- NSFD --- numerical simulation
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This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to mathematical modelling. The contributions have been carefully selected so that they cover interesting theoretical and practical analysis performed in the deterministic and the stochastic settings. The reader will find a complete overview of recent advances in ordinary and partial delay differential equations with applications in other multidisciplinary areas such as Finance, Epidemiology or Engineering
delay systems --- nonstandard numerical methods --- dynamic consistency --- semilinear problems with delay --- hyperbolic equations --- difference scheme --- stability --- Hilbert space --- SEIRS model --- age structure --- time delay --- traveling wave solution --- local asymptotic stability --- Hopf bifurcation --- spot freight rates --- freight options --- stochastic diffusion process --- stochastic delay differential equation --- risk-neutral measure --- arbitration arguments --- partial differential equations --- second-order dual phase lag equation --- laser heating --- thin metal films --- melting and resolidification --- finite difference method --- random linear delay differential equation --- stochastic forcing term --- random Lp-calculus --- uncertainty quantification --- delay random differential equation --- non-standard finite difference method --- mean square convergence --- size-structured population --- consumer-resource model --- delay differential equation --- numerical methods --- characteristics method --- convergence analysis --- implementation delay --- information delay --- stability switching curve --- Cournot oligopoly --- growth rate dynamics --- fractional convection diffusion-wave equations --- compact difference scheme --- nonlinear delay --- spatial variable coefficients --- convergence and stability --- Gerasimov–Caputo fractional derivative --- differential equation with delay --- degenerate evolution equation --- fixed point theorem --- relaxation mode --- large parameter --- asymptotics --- HIV infection --- mathematical delay model --- eclipse phase --- NSFD --- numerical simulation
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