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Periodic travelling waves play a fundamental role in many mathematical equations, including self-oscillatory systems, [1] [2] excitable systems [3] and reaction–diffusion–advection systems. [4] Equations of these types are widely used as mathematical models of biology, chemistry and physics, and many examples in phenomena resembling ...
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Due to mode conversion, a P-wave can reflect upwards as an S-wave (also known as a secondary, shear or transverse wave) when it hits an interface (e.g., solid-liquid). Other P-wave to S-wave (P-S) conversions can occur, but the down-up conversion is the primary focus. Unlike P-waves, converted shear waves are largely unaffected by fluids. [1]
It is a purely mathematical fact that the characteristic polynomial of the Einstein tensor of any pp-wave spacetime vanishes identically. Equivalently, we can find a Newman–Penrose complex null tetrad such that the Ricci-NP scalars (describing any matter or nongravitational fields which may be present in a spacetime) and the Weyl-NP scalars (describing any gravitational field which may be ...
Finally only in this case the superposition principle fully apply, i.e. the wave function in a point P can be expanded as a superposition of waves on a border surface enclosing P. Wave functions can be interpreted in the usual quantum mechanical sense as probability densities where the formalism of Green's functions and propagators apply. What ...
The R wave and the L wave are right-hand and left-hand circularly polarized, respectively. The R wave has a cut-off at ω R (hence the designation of this frequency) and a resonance at ω c. The L wave has a cut-off at ω L and no resonance. R waves at frequencies below ω c /2 are also known as whistler modes. [6]
/ = / (+), which indicates that these long equatorial Rossby waves move in the opposite direction (westward) of Kelvin waves (which move eastward) with speeds reduced by factors of 3, 5, 7, etc. To illustrate, suppose c = 2.8 m/s for the first baroclinic mode in the Pacific; then the Rossby wave speed would correspond to ~0.9 m/s, requiring a 6 ...
Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability in the dielectric function of a free electron gas. The frequency depends only weakly on the ...
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