Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-04-11
Physics
Condensed Matter
Statistical Mechanics
28 pages, 13 figures, 3 tables
Scientific paper
10.1103/PhysRevB.66.174205
The approach of the elastic continuum limit in small amorphous bodies formed by weakly polydisperse Lennard-Jones beads is investigated in a systematic finite-size study. We show that classical continuum elasticity breaks down when the wavelength of the sollicitation is smaller than a characteristic length of approximately 30 molecular sizes. Due to this surprisingly large effect ensembles containing up to N=40,000 particles have been required in two dimensions to yield a convincing match with the classical continuum predictions for the eigenfrequency spectrum of disk-shaped aggregates and periodic bulk systems. The existence of an effective length scale \xi is confirmed by the analysis of the (non-gaussian) noisy part of the low frequency vibrational eigenmodes. Moreover, we relate it to the {\em non-affine} part of the displacement fields under imposed elongation and shear. Similar correlations (vortices) are indeed observed on distances up to \xi~30 particle sizes.
Barrat Jean Louis
Léonforte Fabien
Tanguy Anne
Wittmer Joachim P.
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