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Two Types of Dispsersion There are two ways to think about dispersion, spatial and temporal. … The longer the memory of these previous currents, the stronger the temporal dispersion. …

Definitions deep water limit : when the wavelength of the mode/wave is much less than the depth of the water shallow water limit : when the wavelength of the mode/wave is much larger than the wate …

Thus, the dispersion relation goes to: $$ D\left( \omega \right) = 1 - \left( \frac{ \omega_{pi} }{ \omega } \right)^{2} - \left( \frac{ \omega_{pe} }{ \left( \omega - \mathbf{k} \cdot \mathbf{V}_{o} \ …

First, keep the derivative in terms of the wavenumber, $k$, and the thermal speed, $v_{th}$ to see that the group speed is given by: $$ \frac{ \partial \omega }{ \partial k } = \frac{ 3 \ k \ v_{th}^{ …

Let us assume that a dispersion relation, $\omega$ $=$ $\mathcal{W}\left( \boldsymbol{\kappa}, \textbf{x}, t \right)$, exists and may be solved for positive real roots. … In general, there will be multiple solutions to the dispersion relation, where each solution is referred to as different modes. …

The top panel shows the real part of the frequency, $\omega_{r}$, and the bottom the imaginary part, $\gamma$, versus the projection of the wave vector orthogonal to the quasi-static magnetic field, $ …

In the above, there is one propagation mode (in blue) which extends out to infinite radius in k-space, which seems to physically makes no sense, since $\omega$ is fixed, so you'd expect the dispersion … So this is probably a simple question, but is there any type of material which can have this sort of dispersion relation, or is there some reason why real materials can never behave in this manner (ie, …

The following is taken from the intro to this question: https://physics.stackexchange.com/a/381974/59023 Background Let us define some relevant parameters: Wave Number $\equiv$ $\mathbf{k} = \mathbf{ …

I tried to derive the dispersion relation by linearising the electron momentum and continuity equations and Gauss' law, but very quickly ran into something that could not be converted into a dispersion … If you are specifically curious about a Langmuir wave running into a density gradient, look at the Krafft et al. [2014] paper for a proper dispersion relation. …

For instance, a whistler mode wave can have a cubic dispersion relation at low frequencies. In this limit, the higher(smaller) frequencies(wavelengths) propagate faster than the converse. …

Dispersion effects, on the other hand, do not affect reversibility and increase the order of the derivatives in the equations by an even number. … Interestingly, dispersion is not an irreversible term because it increases the order of the derivatives in the equations by an even number. …