Vibrations and diverging length scales near the unjamming transition |
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Authors: | Silbert Leonardo E Liu Andrea J Nagel Sidney R |
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Institution: | James Franck Institute, University of Chicago, Chicago, IL 60637, USA. |
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Abstract: | We numerically study the vibrations of jammed packings of particles interacting with finite-range, repulsive potentials at zero temperature. As the packing fraction phi is lowered towards the onset of unjamming at phi(c), the density of vibrational states approaches a nonzero value in the limit of zero frequency. For phi >phi(c), there is a crossover frequency, omega* below which the density of states drops towards zero. This crossover frequency obeys power-law scaling with phi-phi(c). Characteristic length scales, determined from the dominant wave vector contributing to the eigenmode at omega*, diverge as power laws at the unjamming transition. |
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