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SUMMARY:Boundary Singularities Produced by the Motion of Soap Films - Gold
 stein\, RE (University of Cambridge)
DTSTART:20140226T093000Z
DTEND:20140226T101500Z
UID:TALK51099@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: Adriana I. Pesci (University of Cambridge)\, Keith
  Moffatt (University of Cambridge)\, James McTavish (University of Cambrid
 ge)\, Renzo Ricca (University of Milano-Bicocca) \n\nRecent experiments ha
 ve shown that when a soap film with the topology of a Mobius strip\, is re
 ndered unstable by slow deformation of its frame past a threshold\, the fi
 lm changes its topology to that of a disc by means of a ``neck-pinching'' 
 singularity at its boundary. This behaviour is unlike the more familiar ca
 tenoid minimal surface supported on two parallel circular loops\, a two-si
 ded surface which\, when rendered unstable\, transitions to two disks thro
 ugh a neck-pinching singularity in the bulk. There is at present neither a
 n understanding of whether the type of singularity is in general a consequ
 ence of the topology of the surface\, nor of how this dependence could ari
 se from a surface equation of motion. We investigate experimentally\, comp
 utationally\, and theoretically the neck-pinching route to singularities o
 f soap films with several distinct topologies\, including a family of non-
 orientable surfaces that are sections of Klein bottles\, and provide evide
 nce that the location of singularities (bulk or boundary) may depend on th
 e path along which the boundary is deformed. Since in the unstable regime 
 the driving force for soap film motion is the surface's mean curvature\, t
 he narrowest part of the neck\, which can be associated with the shortest 
 nontrivial closed geodesic of the surface at each instant of time\, has th
 e highest curvature and is thus the fastest-moving. Just before the onset 
 of the instability there exists on the stable surface also a shortest clos
 ed geodesic\, which serves as an initial condition for the evolution of th
 e geodesics of the neck\, all of which have the same topological relations
 hip to the surface boundary. We find that if the initial geodesic is linke
 d to the boundary then the singularity will occur at the boundary\, wherea
 s if the two are unlinked initially then the singularity will occur in the
  bulk. Numerical study of mean curvature flows and experiments show consis
 tency with these conjectures.\n
LOCATION:Seminar Room 1\, Newton Institute
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