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SUMMARY:Equilibrium states of vortex points and vortex sheets - Takashi Sa
 kajo (Kyoto University)
DTSTART:20230727T150000Z
DTEND:20230727T160000Z
UID:TALK202819@talks.cam.ac.uk
DESCRIPTION:Vortex dynamics is a model of interacting particles in a poten
 tial field with logarithmic singularities. It is not only an intrinsic the
 oretical extension in the field of classical fluid mechanics\, but it woul
 d also be applicable to modern physics such as quantum mechanics and flows
  of superfluid films. We consider the equilibrium states of these vortex s
 tructures. The method of complex analysis plays a significant role in cons
 tructing vortex equilibria. After my stay on the occasion of the CAT progr
 am at Isaac Newton Institute in 2019\, many international collaborations w
 ere initiated\, and we have thus obtained more new results on vortex equil
 ibria. In this talk\, I will provide these recent results: First\, we cons
 ider point vortex equilibria on the surface of a curved torus and a flat t
 orus (i.e.\, a doubly periodic plane). They are embedded in the background
  smooth vorticity distributions such as a constant vorticity distribution 
 and a Liouville-type vorticity distribution\, where the vorticity is repre
 sented by an exponential function of the stream function. Second\, we show
  the existence of a family of equilibrium states involving different membe
 rs of straight vortex sheets rotating about a center of rotation and with 
 endpoints at the vortices of a regular polygon.
LOCATION:Seminar Room 1\, Newton Institute
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