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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 ]
An air-operated valve, also known as a pneumatic valve, is a type of power-operated pipe valve that uses air pressure to perform a function similar to a solenoid. As air pressure is increased, the compressed air starts to push against the piston or diaphragm walls which causes the valve to actuate. Whether the valve opens or closes depends on ...
The group velocity is positive (i.e., the envelope of the wave moves rightward), while the phase velocity is negative (i.e., the peaks and troughs move leftward). The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.
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 ...
Now we let this pulse propagate through a fibre with >, it will be affected by group velocity dispersion. For this sign of D, the dispersion is anomalous, so that the higher frequency components will propagate a little bit faster than the lower frequencies, thus arriving before at the end of the fiber. The overall signal we get is a wider ...
The solenoid can be useful for positioning, stopping mid-stroke, or for low velocity actuation; especially in a closed loop control system. A uni-directional solenoid would actuate against an opposing force or a dual solenoid system would be self cycling. The proportional concept is more fully described in SAE publication 860759 (1986).
Internal waves in a continuously stratified medium may propagate vertically as well as horizontally. The dispersion relation for such waves is curious: For a freely-propagating internal wave packet, the direction of propagation of energy (group velocity) is perpendicular to the direction of propagation of wave crests and troughs (phase velocity).
Dispersion of gravity–capillary waves on the surface of deep water. Phase and group velocity divided by 4 √ gσ / ρ as a function of inverse relative wavelength 1 / λ √ σ / ρg. Blue lines (A): phase velocity c p, Red lines (B): group velocity c g. Drawn lines: gravity–capillary waves. Dashed lines: gravity waves.