Shape and symmetry of a fluid-supported elastic sheet

Haim Diamant*, Thomas A. Witten

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A connection between the dynamics of a sine-Gordon chain and a certain static membrane folding problem was recently found. The one-dimensional membrane profile is a cross section of the position-time sine-Gordon amplitude profile. Here we show that when one system is embedded in a higher-dimensional system in this way, obvious symmetries in the larger system can lead to nontrivial symmetries in the embedded system. In particular, a thin buckled membrane on a fluid substrate has a continuous degeneracy that interpolates between a symmetric and an antisymmetric fold. We find the Hamiltonian generator of this symmetry and the corresponding conserved momentum by interpreting the simple translational symmetries of the sine-Gordon chain in terms of the embedded coordinates. We discuss possible extensions to other embedded dynamical systems.

Original languageEnglish
Article number012401
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume88
Issue number1
DOIs
StatePublished - 11 Jul 2013

Funding

FundersFunder number
National Science Foundation
Directorate for Mathematical and Physical Sciences0820054

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