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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Boundary Singularities Produced by the Motion of S
oap Films - Goldstein\, RE (University of Cambridg
e)
DTSTART;TZID=Europe/London:20140226T093000
DTEND;TZID=Europe/London:20140226T101500
UID:TALK51099AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/51099
DESCRIPTION:Co-authors: Adriana I. Pesci (University of Cambri
dge)\, Keith Moffatt (University of Cambridge)\, J
ames McTavish (University of Cambridge)\, Renzo Ri
cca (University of Milano-Bicocca) \n\nRecent expe
riments have shown that when a soap film with the
topology of a Mobius strip\, is rendered unstable
by slow deformation of its frame past a threshold\
, the film changes its topology to that of a disc
by means of a ``neck-pinching'' singularity at its
boundary. This behaviour is unlike the more famil
iar catenoid minimal surface supported on two para
llel circular loops\, a two-sided surface which\,
when rendered unstable\, transitions to two disks
through a neck-pinching singularity in the bulk. T
here is at present neither an understanding of whe
ther the type of singularity is in general a conse
quence of the topology of the surface\, nor of how
this dependence could arise from a surface equati
on of motion. We investigate experimentally\, comp
utationally\, and theoretically the neck-pinching
route to singularities of soap films with several
distinct topologies\, including a family of non-or
ientable surfaces that are sections of Klein bottl
es\, and provide evidence that the location of sin
gularities (bulk or boundary) may depend on the pa
th along which the boundary is deformed. Since in
the unstable regime the driving force for soap fil
m motion is the surface's mean curvature\, the nar
rowest part of the neck\, which can be associated
with the shortest nontrivial closed geodesic of th
e surface at each instant of time\, has the highes
t curvature and is thus the fastest-moving. Just b
efore the onset of the instability there exists on
the stable surface also a shortest closed geodesi
c\, which serves as an initial condition for the e
volution of the geodesics of the neck\, all of whi
ch have the same topological relationship to the s
urface boundary. We find that if the initial geode
sic is linked to the boundary then the singularity
will occur at the boundary\, whereas if the two a
re unlinked initially then the singularity will oc
cur in the bulk. Numerical study of mean curvature
flows and experiments show consistency with these
conjectures.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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