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SUMMARY:Generic free surface singularities - Eggers\, J (University of Bri
 stol)
DTSTART:20121211T113000Z
DTEND:20121211T123000Z
UID:TALK41965@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Many important partial differential equations used in engineer
 ing or theoretical physics describe the motion of lines or surfaces. Locat
 ions of particular interest are those where the motion becomes (nearly) si
 ngular\, and the line or surface forms a cusp or a tip with a very large c
 urvature. Physical examples occur when viscous fluid is poured into a beak
 er\, or when caustics form at the bottom of a coffee cup.\n\nRecent work s
 uggests the structure of many such singularities can be understood using a
  local geometrical description. The local shape corresponds exactly to a s
 olution of the partial differential equation. Building on this insight\, w
 e propose a preliminary classification of such singular points\, including
  higher dimensions of both the surface and the space it lives in. We also 
 investigate how the observed singularity can be understood from the point 
 of view of the dynamical equation\, and how the geometrical description co
 uld be used in more complex situations.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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