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Vibrations and diverging length scales near the unjamming transition

L. E. Silbert·A. J. Liu·S. R. Nagel
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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 $ϕ$ is lowered towards the onset of unjamming at $ϕ_{c}$, the density of vibrational states approaches a non-zero value in the limit of zero frequency. For $ϕ>ϕ_{c}$, there is a crossover frequency, $ω^{*}$ below which the density of states drops towards zero. This crossover frequency obeys power-law scaling with $ϕ-ϕ_{c}$. Characteristic length scales, determined from the dominant wavevector contributing to the eigenmode at $ω^{*}$, diverge as power-laws at the unjamming transition.

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L. E. Silbert, A. J. Liu, S. R. Nagel. 2005-01-26. Vibrations and diverging length scales near the unjamming transition. https://doi.org/10.1103/physrevlett.95.098301

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