Low frequency vibrations of deformable particles

Disk packings at jamming onset exhibit an excess of low-frequency vibrational modes compared to the number predicted by Debye scaling. The excess number of modes, which controls the mechanical response of packings, decreases as the packings are compressed above jamming onset. In this work, we calculate the spectrum of vibrational modes from the eigenvalues of the dynamical matrix for truly deformable particles at jamming onset as a function of the shape parameter A = p²/(4πa), where p is the perimeter and a is the area of the particle. We show that there is an excess number of low frequency, collective modes in the density of vibrational modes for jammed packings of deformable particles over a wide range of particle shape both above and below the characteristic value A ≈ 1.15 at which the system is confluent.