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SUMMARY:A Soap-Film Mobius Strip Changes Topology with a Twist Singularity
  - Goldstein\, RE\, Moffatt\, HK\, Pesci\, AI (University of Cambridge)
DTSTART:20120725T111000Z
DTEND:20120725T113000Z
UID:TALK39059@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:It is well-known that a soap film spanning a looped wire can h
 ave the topology of a Mbius strip and that deformations of the wire can in
 duce a transformation to a two-sided film\, but the process by which this 
 transformation is achieved has remained unknown. In this talk I will disuc
 ss recent experimental and theoretical work [Goldstein\, Moffatt\, Pesci\,
  and Ricca\, PNAS 107\, 21979 (2010)] that has uncovered the dynamics of t
 his transition. We find that this process consists of a collapse of the fi
 lm toward the boundary that produces a previously unrecognized finite-time
  twist singularity that changes the linking number of the film's Plateau b
 order and the centerline of the wire. We conjecture that it is a general f
 eature of this type of transition that the singularity always occurs at th
 e surface boundary. The change in linking number is shown to be a conseque
 nce of a viscous reconnection of the Plateau border at the moment of the s
 ingularity. High-speed imaging of the collapse dynamics of the film's thro
 at\, similar to that of the central opening of a catenoid\, reveals a cros
 sover between two power laws. Far from the singularity\, it is suggested t
 hat the collapse is controlled by dissipation within the fluid film surrou
 nding the wire\, whereas closer to the transition the power law has the cl
 assical form arising from a balance between air inertia and surface tensio
 n. Analytical and numerical studies of minimal surfaces and ruled surfaces
  are used to gain insight into the energetics underlying the transition an
 d the twisted geometry in the neighborhood of the singularity. \nA number 
 of challenging mathematical questions arising from these observations are 
 posed.\n
LOCATION:Seminar Room 1\, Newton Institute
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