Enhanced collective vibrations in granular materials

Abstract

Granular materials are defined as collections of macroscopic dissipative particles. Although these systems are ubiquitous in our lives, the nature and the causes of their non-trivial collective dynamics still remain elusive and have attracted significant interest in non-equilibrium physics. Here, we focus on the vibrational dynamics of granular materials. While the vibrational dynamics of random packings have been examined concerning the jamming transition, previous research has overlooked the role of contact dissipations. We conducted numerical and analytical investigations into the vibrational dynamics of random packings influenced by the normal dissipative force, which is the simplest model for contact dissipations. Our findings reveal that the kinetic energy per mode diverges in the low-frequency range, following the scaling law $\mathcal{K}_l \propto \omega^{-2}_l$ with the frequency $\omega_l$, indicating that low-frequency modes experience strong excitation and that the equipartition of energy is violated. Additionally, the spatial structure factor of the velocity field displays the scaling law $S_v(q) \propto q^{-2}$ with the wavenumber $q$, which signifies that the velocity field has an infinitely long range. We demonstrate that these phenomena arise from the effects of weaker damping on softer modes, where the particle displacements parallel to the contacts are minimal in the low-frequency modes, rendering normal dissipation ineffective at dampening these modes.