Department of Physics Papers

Document Type

Journal Article

Date of this Version



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.


Suggested Citation:
Silbert, L.E., A.J. Liu and S.R. Nagel. (2009). "Normal modes in model jammed systems in three dimensions." Physical Review E. 79, 021308.

© 2009 The American Physical Society

Included in

Physics Commons



Date Posted: 06 January 2011

This document has been peer reviewed.