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Instability of a Möbius strip minimal surface and a link with systolic geometry
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Pesci, Adriana I., Goldstein, Raymond E., Alexander, Gareth P. and Moffatt, H. K. (2015) Instability of a Möbius strip minimal surface and a link with systolic geometry. Physical Review Letters, 114 . pp. 1-5. 127801.
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Official URL: http://dx.doi.org/10.1103/PhysRevLett.114.127801
Abstract
We describe the first analytically tractable example of an instability of a nonorientable minimal surface under parametric variation of its boundary. A one-parameter family of incomplete Meeks Möbius surfaces is defined and shown to exhibit an instability threshold as the bounding curve is opened up from a double-covering of the circle. Numerical and analytical methods are used to determine the instability threshold by solution of the Jacobi equation on the double covering of the surface. The unstable eigenmode shows excellent qualitative agreement with that found experimentally for a closely related surface. A connection is proposed between systolic geometry and the instability by showing that the shortest noncontractable closed geodesic on the surface (the systolic curve) passes near the maximum of the unstable eigenmode.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Research Centres > Centre for Complexity Science Faculty of Science, Engineering and Medicine > Science > Physics |
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| Library of Congress Subject Headings (LCSH): | Möbius function | ||||||
| Journal or Publication Title: | Physical Review Letters | ||||||
| Publisher: | American Physical Society | ||||||
| ISSN: | 0031-9007 | ||||||
| Official Date: | 24 March 2015 | ||||||
| Dates: |
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| Volume: | 114 | ||||||
| Number of Pages: | 5 | ||||||
| Page Range: | pp. 1-5 | ||||||
| Article Number: | 127801 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), University of Cambridge | ||||||
| Grant number: | EP/IO36060/1 (EPSRC) |
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