  Vibrational spectra and normal modes of mechanically stable particle packings
in three dimensions are analyzed over a range of compressions, from near the
jamming transition, where the packings lose their rigidity, to far above it. At
high frequency, the normal modes are localized at all compressions. At low
frequency, the nature of the modes depends somewhat on compression. At large
compressions, far from the transition, the lowest-frequency normal modes have
some plane-wave character, though less than one would expect for a crystalline
or isotropic solid. At low compressions near the jamming transition, the
lowest-frequency modes are neither plane-wave-like nor localized. We
characterize these differences, highlighting the unusual dispersion behavior
that emerges for marginally jammed solids.
