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Structures involving solid particles of nanometric dimensions play anincreasingly important role in material sciences. These structures are oftencharacterized through the vibrational properties of their constituentparticles, which can be probed by spectroscopic methods. Interpretation of suchexperimental data requires an extension of continuum elasticity theory down toincreasingly small scales. Using numerical simulation and exact diagonalizationfor simple models, we show that continuum elasticity, applied to disorderedsystem, actually breaks down below a length scale of typically 30 to 50molecular sizes. This length scale is likely related to the one which isgenerally invoked to explain the peculiar vibrational properties of glassysystems.Comment: 4 pages, 5 figures, LATEX, Europhysics Letters accepte

Vibrations of amorphous, nanometric structures: When does continuum theory apply?