Construct · 2 fields · 2 citations

braid: one construct, many systems

One name. One construct. Different systems. One map.

● invariant · one construct, three systems Nearest construct by meaning·not indexed
same interlacing, in magnetic field linesbraid2 SYSTEMSBraid groupARTIN · BnMagnetic braidingPARKER · 1972

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1947Braid group1972Magnetic braiding
2026

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Braid groups

a group whose elements are crossing strands, equal when deformable into each other and composed by stacking.

The braid group turns the craftsman's braid into an exact mathematical object. Artin's 1947 Theory of braids takes n strands running downward and crossing one another, counts two braids as equal when one can be deformed into the other, and composes them by stacking, yielding a group whose generators are the elementary crossings. It is the same interlacing structure as a physical braid, now pinned down by its crossing relations, and it underlies knot theory and the magnetic tangles of the next field.[1]

Unit
An element of the braid group B_n (a word in crossing generators)
Recovery means
Not applicable
Measured by
By the group's generators and relations, braid-word length, and the braid index

Solar physics

the winding and crossing of the Sun's coronal magnetic field lines as surface motions shuffle their footpoints.

Astrophysicists use braiding for the same interlacing applied to magnetic field lines: as the footpoints of the Sun's coronal field are shuffled by motions at the surface, the field lines wind and cross one another. Parker's 1972 Topological dissipation and the small-scale fields in turbulent gases argued this braiding builds up thin current sheets whose reconnection helps explain the corona's extreme heat. It is the identical topological interlacing as a craft braid or a braid-group element, here realised in plasma and gauged by magnetic twist and energy release.[2]

Unit
The degree of magnetic braiding (field-line winding and stored energy)
Recovery means
Not applicable
Measured by
By field-line winding number, current-sheet formation, and the magnetic free energy released

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Nearby constructs

knot1 fields · 1 citationsanchor · a standalone constructbook1 fields · 1 citationsanchor · a standalone constructborrow1 fields · 1 citationsanchor · a standalone construct

References

  1. Artin, E. (1947). Theory of braids. Annals of Mathematics, 48(1), 101–126. https://doi.org/10.2307/1969218
  2. Parker, E. N. (1972). Topological dissipation and the small-scale fields in turbulent gases. The Astrophysical Journal, 174, 499–510. https://doi.org/10.1086/151512

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