Vibrational similarities in jamming-unjamming of polycrystalline and disordered granular packings

Abstract: We investigate the vibrational properties of polycrystalline monodisperse and disordered bidisperse granular packings during jamming and unjamming using discrete element method simulations. Both systems deviate from Debye scaling at low frequencies $(\omega)$, but only bidisperse packings exhibit a low-$\omega$ plateau. The low $\omega$ exponent ($\alpha$) in bidisperse packings evolves smoothly from zero (plateau) to near one (Debye scaling) with increasing packing fraction, whereas in polycrystalline packings, it changes discontinuously near jamming/unjamming, due to the nature of the contact network rearrangements. Despite structural modifications during the compression-decompression cycle, the exponent remains unchanged at the same distance from jamming density, regardless of the history. Nonaffine displacements and contact orientational order further confirm that structural features that impact low-$\omega$ vibrational states and, hence, mechanical properties are largely restored upon decompression, reinforcing vibrational similarities between jamming and unjamming states.