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A central velocity dispersion refers to the σ of the interior regions of an extended object, such as a galaxy or cluster. The relationship between velocity dispersion and matter (or the observed electromagnetic radiation emitted by this matter) takes several forms – specific correlations – in astronomy based on the object(s) being observed.
Group-velocity dispersion is quantified as the derivative of the reciprocal of the group velocity with respect to angular frequency, which results in group-velocity dispersion = d 2 k/dω 2. If a light pulse is propagated through a material with positive group-velocity dispersion, then the shorter-wavelength components travel slower than the ...
Given the dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig relations describe the frequency ...
In optics, group-velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium affects the duration of an optical pulse traveling through it. Formally, GVD is defined as the derivative of the inverse of group velocity of light in a material with respect to angular frequency , [ 1 ] [ 2 ]
Dispersion of gravity waves on a fluid surface. Phase and group velocity divided by shallow-water phase velocity √ gh as a function of relative depth h / λ. Blue lines (A): phase velocity; Red lines (B): group velocity; Black dashed line (C): phase and group velocity √ gh valid in shallow water.
Frequency dispersion in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the green circles propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red square overtakes two green circles when moving from the left to the right of the figure.
Phase and group velocity divided by √ gh as a function of h / λ . A: phase velocity, B: group velocity, C: phase and group velocity √ gh valid in shallow water. Drawn lines: based on dispersion relation valid in arbitrary depth. Dashed lines: based on dispersion relation valid in deep water.
Shear velocity also helps in thinking about the rate of shear and dispersion in a flow. Shear velocity scales well to rates of dispersion and bedload sediment transport. A general rule is that the shear velocity is between 5% and 10% of the mean flow velocity. For river base case, the shear velocity can be calculated by Manning's equation.