Wave spectroscopy in a driven granular material

Abstract

Driven granular media constitute model systems in out-of-equilibrium statistical physics. By assimilating the motions of granular particles to those of atoms, by analogy, one can obtain macroscopic equivalent of phase transitions. Here, we study fluid-like and crystal-like two-dimensional states in a driven granular material. In our experimental device, a tunable magnetic field induces and controls remote interactions between the granular particles. We use high-speed video recordings to analyse the velocity fluctuations of individual particles in stationary regime. Using statistical averaging, we find that the particles self-organize into collective excitations characterized by dispersion relations in the frequency-wavenumber space. These findings thus reveal that mechanical waves analogous to condensed matter phonons propagate in driven granular media. When the magnetic coupling is weak, the waves are longitudinal, as expected for a fluid-like phase. When the coupling is stronger, both longitudinal and transverse waves propagate, which is typically seen in solid-like phases. We model the dispersion relations using the spatial distribution of particles and their interaction potential. Finally, we infer the elastic parameters of the granular assembly from equivalent sound velocities, thus realizing the spectroscopy of a granular material.

Damping-Driven Time Reversal for Waves

“…These disks are confined within a L ¼ 40 cm wide square arena delimited by repulsive magnetic walls to avoid contact with the edges. At rest, the magnetic disks selforganize into a hexagonal lattice resulting from the balance between repulsion and confinement [16]. Longitudinal-like phonon waves can be excited in this lattice by moving (in the plane) a 12 cm wide magnetically repulsive bar placed on one edge [see Fig.…”