Animations

Three animations are provided. Each reports,
from top to bottom, a plot of the angle  be-
tween successive particles versus the magnetic
index, a 3-D rendering, and (for two anima-
tions) the corresponding unwrapped Bravais lat-
tice. Animation-Fig5 presents dynamical simu-
lations of phenomena described in Figure 5 of
the Letter. Animation-Fig6 presents dynamical
simulations of phenomena described in Figure 6
of the Letter. Animation-Rotons demonstrates
the existence of rotons in the vibrational spec-
trum by showing showing the spatial localization
of energy and momentum in a wave-packet cen-
tered at a rotonic frequency.