The IceCube Neutrino Observatory (or simply IceCube) is a neutrino observatory constructed at the Amundsen–Scott South Pole Station in Antarctica. The project is a recognized CERN experiment (RE10).
Its thousands of sensors are located under the Antarctic ice, distributed over a cubic kilometre.
Similar to its predecessor, the Antarctic Muon And Neutrino Detector Array (AMANDA), IceCube consists of spherical optical sensors called Digital Optical Modules (DOMs), each with a photomultiplier tube (PMT) and a single-board data acquisition computer which sends digital data to the counting house on...
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Consider the surface of the Earth. It is a 2-sphere, i.e. a 2-dimensional manifold, named $M$. The collection of all longitude lines is a bunch of geodesics, each line is labeled by its longitude ($v$). Each point on a specific line is labeled by its latitude ($\tau$). So every point on the s...
In the theory of smooth manifolds, a congruence is the set of integral curves defined by a nonvanishing vector field defined on the manifold.
Congruences are an important concept in general relativity, and are also important in parts of Riemannian geometry.
== A motivational example ==
The idea of a congruence is probably better explained by giving an example than by a definition. Consider the smooth manifold R². Vector fields can be specified as first order linear partial differential operators, such as
X
→...
