VI.—On Vortex Motion

Abstract

1. The mathematical work of the present paper has been performed to illustrate the hypothesis, that space is continuously occupied by an incompressible frictionless liquid acted on by no force, and that material phenomena of every kind depend solely on motions created in this liquid. But I take, in the first place, as subject of investigation, a finite mass of incompressible frictionless fluid completely enclosed in a rigid fixed boundary.

Vortex knots in a Bose-Einstein condensate

“…In 1867, following the works of Helmholtz on vortices and of Riemann on abelian functions, Lord Kelvin modelled atoms as knotted vortex tubes in the ether [1], effectively giving birth to knot theory [2]. This discipline has fascinated mathematicians and physicists since.…”

Slowing down of vortex rings in Bose-Einstein condensates

“…Thin-cored vortex rings have fascinated physicists since the times of Helmholtz and Kelvin [1,2]. Vortex ring dynamics is still a very active area of research [3][4][5][6].…”

Preon Model, Knot Algebra and Gravity

“…Early work on knots in physics goes back in time to 19th and 18th century [7] [8]. More recently Finkelstein has proposed a model based on the group SLq(2) …”