Dispersion Relation / and Worldview: South Georgia & the South Sandwich Islands, West tip of South America & north of Antarctica, Nicaragua & Costa Rica, Mexico

 

dscn0172Above photo taken from my house on the Olympic Peninsula WA

Dispersion Relation

In physical sciences and electrical engineering, dispersion relations describe the effect of dispersion in a medium on the properties of a wave traveling within that medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. From this relation the phase velocity and group velocity of the wave have convenient expressions which then determine the refractive index of the medium. More general than the geometry-dependent and material-dependent dispersion relations, there are the overarching Kramers–Kronig relations that describe the frequency dependence of wave propagation and attenuation.

Dispersion may be caused either by geometric boundary conditions (waveguides, shallow water) or by interaction of the waves with the transmitting medium. Elementary particles, considered as matter waves, have a nontrivial dispersion relation even in the absence of geometric constraints and other media.

In the presence of dispersion, wave velocity is no longer uniquely defined, giving rise to the distinction of phase velocity and group velocity.

Waves and optics
Further information: Dispersion (optics)
The name “dispersion relation” originally comes from optics. It is possible to make the effective speed of light dependent on wavelength by making light pass through a material which has a non-constant index of refraction, or by using light in a non-uniform medium such as a waveguide. In this case, the waveform will spread over time, such that a narrow pulse will become an extended pulse, i.e., be dispersed. In these materials, is known as the group velocity and corresponds to the speed at which the peak of the pulse propagates, a value different from the phase velocity.

Phonons
Phonons are to sound waves in a solid what photons are to light: they are the quanta that carry it. The dispersion relation of phonons is also important and non-trivial. Most systems will show two separate bands on which phonons live. Phonons on the band that cross the origin are known as acoustic phonons, the others as optical phonons.

Electron optics
With high energy (e.g., 200 keV) electrons in a transmission electron microscope, the energy dependence of higher order Laue zone (HOLZ) lines in convergent beam electron diffraction (CBED) patterns allows one, in effect, to directly image cross-sections of a crystal’s three-dimensional dispersion surface. This dynamical effect has found application in the precise measurement of lattice parameters, beam energy, and more recently for the electronics industry: lattice strain.

https://en.wikipedia.org/wiki/Dispersion_relation

 

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http://go.nasa.gov/2g8CeBC       http://go.nasa.gov/2gxahAh

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South Georgia (two above) and the South Sandwich Islands (SGSSI) is a British overseas territory in the southern Atlantic Ocean. It is a remote and inhospitable collection of islands, consisting of South Georgia and a chain of smaller islands known as the South Sandwich Islands. South Georgia is 165 kilometres (103 mi) long and 1 to 35 km (1 to 22 miles) wide[3] and is by far the largest island in the territory. The South Sandwich Islands lie about 700 kilometres (430 mi) southeast of South Georgia. The total land area of the territory is 3,903 square kilometres (1,507 sq mi).

There is no permanent population on the islands. The present inhabitants are the British Government Officer, Deputy Postmaster, scientists, and support staff from the British Antarctic Survey who maintain scientific bases at Bird Island and at the capital, King Edward Point, as well as museum staff at nearby Grytviken.

The United Kingdom claimed sovereignty over South Georgia in 1775 and the South Sandwich Islands in 1908. The territory of “South Georgia and the South Sandwich Islands” was formed in 1985; previously it had been governed as part of the Falkland Islands Dependencies. Argentina claimed South Georgia in 1927 and claimed the South Sandwich Islands in 1938.

Argentina maintained a naval station, Corbeta Uruguay, on Thule Island in the South Sandwich Islands from 1976 until 1982 when it was closed by the Royal Navy. The Argentine claim over South Georgia contributed to the 1982 Falklands War, during which Argentine forces briefly occupied the island. Argentina continues to claim sovereignty over South Georgia and the South Sandwich Islands.

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http://go.nasa.gov/2gx5Khq

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http://go.nasa.gov/2gxd4JO

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West tip of South America & north of Antarctica (three above)

http://go.nasa.gov/2g8x4Wf

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http://go.nasa.gov/2g8xH1W

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Nicaragua & Costa Rica (two above)     http://go.nasa.gov/2gx67Zu

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Mexico (above and below)  http://go.nasa.gov/2gx3Sp1   http://go.nasa.gov/2g8yHTY

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