  We calculate the vibrational density-of-states in an insulating nanoparticle
that is in weak mechanical contact with a semi-infinite substrate. The work is
motivated by a recent experiment by Yang et al., where the low-energy phonon
density-of-states of Y2O3 nanoparticles doped with Eu was measured. Preliminary
results presented here, based on the conventional quasiparticle-pole
approximation for the phonon propagator, are in reasonable agreement with
experiment.
