MRSEC scientists and
collaborators have shown [1] that the localized buckling of a compressed thin
sheet, important for molecular interfaces, [2] has the same mathematical origin
as the localization of kinetic energy in a line of swinging pendulums. It is a form of soliton.
The relationship of a pendulum
soliton to a buckled sheet: connected
pendulums at left are swinging in a "breather" mode, a form of
soliton. It remains localized in space because of its high swings. Height of
the surface under the pendulums shows their swing angles. Surface extends to
the right to show the time-dependence of the swinging pattern. The diagonal
edge is accentuated. Red curve is drawn to have its slope-angle at each point
equal to the swing angle along the edge. This curve has the shape of a film
floating on a liquid compressed so that it buckles and folds [1]. Black
tie-lines indicate corresponding points on the two curves. Below the red line is a photo of a thin plastic film 6 cm long floating on a trough of water, viewed edge-on, from [2].
