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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Knot polynomial invariants in terms of helicity fo
r tackling topology of fluid knots - Liu\, X (Scho
ol of Mathematics and Statistics\, University of S
ydney)
DTSTART;TZID=Europe/London:20121101T113000
DTEND;TZID=Europe/London:20121101T123000
UID:TALK41325AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/41325
DESCRIPTION:A new method based on the derivation of the Jones
polynomial invariant of knot theory to tackle and
quantify structural complexity of vortex filaments
in ideal fluids is presented. First\, we show tha
t the topology of a vortex tangle made by knots an
d links can be described by means of the Jones pol
ynomial expressed in terms of kinetic helicity. Th
en\, for the sake of illustration\, explicit calcu
lations of the Jones polynomial for the left-hande
d and right-handed trefoil knot and for the Whiteh
ead link via the figure-of-eight knot are consider
ed. The resulting polynomials are thus function of
the topology of the knot type and vortex circulat
ion and we provide several examples of those. Whil
e this approach extends the use of helicity in ter
ms of linking numbers to the much richer context o
f knot polynomials\, it offers also new tools to i
nvestigate topological aspects of mathematical flu
id dynamics and\, by directly implementing them\,
to perform new real-time numerical diagnostics of
complex flows.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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