Results 41 to 50 of about 2,698,771 (284)
Acoustics, 2022 The second-order partial differential wave Equation (Cauchy’s first equation of motion), derived from Newton’s force equilibrium, describes a standing wave field consisting of two waves propagating in opposite directions, and is, therefore, a “two-way ...
Hans-Joachim Raida
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From the Newton Equation to the Wave Equation: The Case of Shock Waves [PDF]
Applied Mathematics Research eXpress, 2017 We study the macroscopic limit of a chain of atoms governed by the Newton equation. It is known from the work of Blanc, Le Bris, Lions, that this limit is the solution of a nonlinear wave equation, as long as this solution remains smooth. We show, numerically and mathematically that, if the distances between particles remain bounded, it is not the case
Blanc, Xavier, Josien, Marc
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Finite element heterogeneous multiscale methods for the wave equation [PDF]
, 2013 Wave phenomena appear in a wide range of applications such as full-waveform seismic inversion, medical imaging, or composite materials. Often, they are modeled by the acoustic wave equation.
Stohrer, Christian
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One-Way Wave Equation Derived from Impedance Theorem
Acoustics, 2020 The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions with
Oskar Bschorr, Hans-Joachim Raida
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Wave-equation Qs Inversion of Skeletonized Surface Waves [PDF]
, 2017 We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data ...
Dutta, Gaurav +2 more
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The Wave Equation for a Moving Source and a Moving Receiver
MathematicsThe ordinary 3D wave equation for nondissipative, homogeneous, isotropic media admits solutions where the point sources are permitted to move, but as shown in this paper, it does not admit solutions where the receiver is allowed to move. To overcome this
Hrvoje Dodig
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Boundary Value Problems, 2021 Under the acoustic boundary conditions, the initial boundary value problem of a wave equation with multiple nonlinear source terms is considered. This paper gives the energy functional of regular solutions for the wave equation and proves the decreasing ...
Shoubo Jin, Jian Li
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Eigenwavelets of the Wave Equation [PDF]
, 2008 We study a class of localized solutions of the wave equation, called eigenwavelets, obtained by extending its fundamental solutions to complex spacetime in the sense of hyperfunctions. The imaginary spacetime variables y, which form a timelike vector, act as scale parameters generalizing the scale variable of wavelets in one dimension.
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On the generalized Jacobi equation. [PDF]
, 2008 The standard text-book Jacobi equation (equation of geodesic deviation) arises by linearizing the geodesic equation around some chosen geodesic, where the linearization is done with respect to the coordinates and the velocities.
Perlick, Volker
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Numerical study on the generation and evolution of the super-rogue waves
Journal of Ocean Engineering and Science, 2016 The super-rogue wave solutions of the nonlinear Schrödinger equation (NLS) are numerically studied based on the weakly nonlinear hydrodynamic equation. The super-rogue wave solutions up to the 5th order, also known as the so-called super-rogue waves, are
Jianmin Yang, Wenyue Lu
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