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SUMMARY:Topological Jumps in Fluid Mechanics  - Keith Moffatt (Damtp)
DTSTART:20130125T160000Z
DTEND:20130125T170000Z
UID:TALK42619@talks.cam.ac.uk
CONTACT:Dr Ed Brambley
DESCRIPTION:Dynamical systems have a natural tendency to relax through dis
 sipative processes to a minimum-energy state\, subject to any relevant con
 straints. An example is provided by the relaxation of a magnetic field in 
 a perfectly conducting but viscous fluid\, subject to the constraint that 
 the magnetic field lines are frozen in the fluid. One may infer the existe
 nce of magnetostatic equilibria (and analogous steady Euler flows) of arbi
 trary field-line topology. In general\, discontinuities (current sheets) a
 ppear during this relaxation process\, and this is where reconnection of f
 ield-lines (with associated change of topology) can occur. Slow change of 
 boundary conditions can lead to critical conditions in which such topologi
 cal jumps are inevitable.\n\nA simple example of this type of behaviour th
 at can be realised in the laboratory is provided by a soap-film bounded by
  a flexible wire (or wires) which can be continuously and slowly deformed.
  At each instant the soap-film is relaxed in quasi-static manner to a mini
 mum-area (i.e. minimum-energy) state compatible with the boundary configur
 ation. This can however pass through a critical configuration at which a t
 opological jump is inevitable. We have studied an interesting example of t
 his behaviour: the jump of a one-sided (Möbius strip) soap-film to a two-
 sided film as the boundary is unfolded and untwisted from the double cover
  of a circle. The nature of this jump will be demonstrated and explained.\
 n\n(Work in collaboration with Ray Goldstein and Adriana Pesci)\n\n
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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