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SUMMARY:Knot polynomial invariants in terms of helicity for tackling topol
 ogy of fluid knots - Liu\, X (School of Mathematics and Statistics\, Unive
 rsity of Sydney)
DTSTART:20121101T113000Z
DTEND:20121101T123000Z
UID:TALK41325@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:A new method based on the derivation of the Jones polynomial i
 nvariant of knot theory to tackle and quantify structural complexity of vo
 rtex filaments in ideal fluids is presented. First\, we show that the topo
 logy of a vortex tangle made by knots and links can be described by means 
 of the Jones polynomial expressed in terms of kinetic helicity. Then\, for
  the sake of illustration\, explicit calculations of the Jones polynomial 
 for the left-handed and right-handed trefoil knot and for the Whitehead li
 nk via the figure-of-eight knot are considered. The resulting polynomials 
 are thus function of the topology of the knot type and vortex circulation 
 and we provide several examples of those. While this approach extends the 
 use of helicity in terms of linking numbers to the much richer context of 
 knot polynomials\, it offers also new tools to investigate topological asp
 ects of mathematical fluid dynamics and\, by directly implementing them\, 
 to perform new real-time numerical diagnostics of complex flows.\n
LOCATION:Seminar Room 1\, Newton Institute
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