Shape and symmetry of a fluid-supported elastic sheet

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.

8 pages

References in corpus (5)

• Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators
• Elasticity of an interfacial particle raft
• Symmetry Breaking and Order in the Age of Quasicrystals
• Microscopic Wrinkles on Supported Surfactant Monolayers
• Non-symmetric localized fold of a floating sheet

Cited by in corpus (10)

• Emergence of active nematics in bacterial biofilms
• Wrinkles and folds in a fluid-supported sheet of finite size
• Mechanics of large folds in thin interfacial films
• The compression of a heavy floating elastic film
• Pattern transitions in a compressible floating elastic sheet
• Nonlinear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate
• An Investigation of the Casimir Energy for a Fermion Coupled to the Sine-Gordon Soliton with Parity Decomposition
• Fluid-supported elastic sheet under compression: Multifold solutions
• Anomalously fast kinetics of lipid monolayer buckling
• Hidden Asymptotic Symmetry in Long Elastic Beams on Softening Foundations