Shape and symmetry of a fluid-supported elastic sheet.
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.
Raymond & Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel. hdiamant@tau.ac.il
Haim
H
Diamant
Thomas A
TA
Witten