Volume 7, Issue 3
Simulation of a Soap Film Möbius Strip Transformation

Yongsam Kim, Ming-Chih Lai & Yunchang Seol

East Asian J. Appl. Math., 7 (2017), pp. 615-628.

Published online: 2018-02

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  • Abstract

If the closed wire frame of a soap film having the shape of a Möbius strip is pulled apart and gradually deformed into a planar circle, the soap film transforms into a two-sided orientable surface. In the presence of a finite-time twist singularity, which changes the linking number of the film’s Plateau border and the centreline of the wire, the topological transformation involves the collapse of the film toward the wire. In contrast to experimental studies of this process reported elsewhere, we use a numerical approach based on the immersed boundary method, which treats the soap film as a massless membrane in a Navier-Stokes fluid. In addition to known effects, we discover vibrating motions of the film arising after the topological change is completed, similar to the vibration of a circular membrane.

  • Keywords

Möbius strip, minimal surface, twist singularity, topological change, Navier-Stokes equation, immersed boundary method.

  • AMS Subject Headings

68U20, 74K35, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-615, author = {}, title = {Simulation of a Soap Film Möbius Strip Transformation}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {3}, pages = {615--628}, abstract = {

If the closed wire frame of a soap film having the shape of a Möbius strip is pulled apart and gradually deformed into a planar circle, the soap film transforms into a two-sided orientable surface. In the presence of a finite-time twist singularity, which changes the linking number of the film’s Plateau border and the centreline of the wire, the topological transformation involves the collapse of the film toward the wire. In contrast to experimental studies of this process reported elsewhere, we use a numerical approach based on the immersed boundary method, which treats the soap film as a massless membrane in a Navier-Stokes fluid. In addition to known effects, we discover vibrating motions of the film arising after the topological change is completed, similar to the vibration of a circular membrane.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.070217.120617a}, url = {http://global-sci.org/intro/article_detail/eajam/10768.html} }
TY - JOUR T1 - Simulation of a Soap Film Möbius Strip Transformation JO - East Asian Journal on Applied Mathematics VL - 3 SP - 615 EP - 628 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.070217.120617a UR - https://global-sci.org/intro/article_detail/eajam/10768.html KW - Möbius strip, minimal surface, twist singularity, topological change, Navier-Stokes equation, immersed boundary method. AB -

If the closed wire frame of a soap film having the shape of a Möbius strip is pulled apart and gradually deformed into a planar circle, the soap film transforms into a two-sided orientable surface. In the presence of a finite-time twist singularity, which changes the linking number of the film’s Plateau border and the centreline of the wire, the topological transformation involves the collapse of the film toward the wire. In contrast to experimental studies of this process reported elsewhere, we use a numerical approach based on the immersed boundary method, which treats the soap film as a massless membrane in a Navier-Stokes fluid. In addition to known effects, we discover vibrating motions of the film arising after the topological change is completed, similar to the vibration of a circular membrane.

Yongsam Kim, Ming-Chih Lai & Yunchang Seol. (2020). Simulation of a Soap Film Möbius Strip Transformation. East Asian Journal on Applied Mathematics. 7 (3). 615-628. doi:10.4208/eajam.070217.120617a
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