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TZID:Europe/Paris
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BEGIN:VEVENT
UID:1-339@lptms.universite-paris-saclay.fr
DTSTART:20150414T110000Z
DTEND:20150414T120000Z
DTSTAMP:20150303T100315Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
 s-alexey-sossinsky/
SUMMARY:Séminaire du LPTMS : Alexey Sossinsky - LPTMS\, salle 201\, 2ème 
 étage\, Bât 100\, Campus d'Orsay - 14 Avr 15 11:00
DESCRIPTION:Energetic reduction of elastic knots to normal form: Gradient d
 escent along the Euler functional\n\n Alexey Sossinsky\, Independent Univ
 ersity of Moscow\, Laboratoire Poncelet\n\nSimple physical experiments sho
 w that a deformed knotted resilient elastic wire always returns to its equ
 ilibrium shape (which we call the normal form of the wire knot). The aim o
 f this research (joint work with S.Avvakumov and O.Karpenkov) is to const
 ruct a mathematical model of such physical knots. This is done by supplyin
 g the space of knots with an energy functional and performing gradient des
 cent w.r.t. the functional. The energy functional that we use is the sum o
 f the Euler functional (the integral along the curve defining the knot of 
 the square of the curvature) and a simple repulsive functional (that forbi
 ds crossing changes). Using a discretized version of gradient descent alon
 g that functional\, we construct an algorithm that brings the knot to the 
 shape that minimizes its energy. The algorithm is implemented in a compute
 r animation that shows the isotopy bringing the knot to normal form.\n\nWe
  will show some of these animations and demonstrate a few of the physical 
 experiments with wire knots\, compare the results of physical and mathemat
 ical experiments\, and outline how our algorithm can be used in practice t
 o recognize knots and to unravel trivial knots.
LOCATION:LPTMS\, salle 201\, 2ème étage\, Bât 100\, Campus d'Orsay\, 15 
 Rue Georges Clemenceau\, Orsay\, 91405\, France
GEO:48.698185;2.181768
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=15 Rue Georges Clemenceau\,
  Orsay\, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=LPTMS\, salle 201\, 2è
 me étage\, Bât 100\, Campus d'Orsay:geo:48.698185,2.181768
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