  Structures involving solid particles of nanometric dimensions play an
increasingly important role in material sciences. These structures are often
characterized through the vibrational properties of their constituent
particles, which can be probed by spectroscopic methods. Interpretation of such
experimental data requires an extension of continuum elasticity theory down to
increasingly small scales. Using numerical simulation and exact diagonalization
for simple models, we show that continuum elasticity, applied to disordered
system, actually breaks down below a length scale of typically 30 to 50
molecular sizes. This length scale is likely related to the one which is
generally invoked to explain the peculiar vibrational properties of glassy
systems.
