Cages and anomalous diffusion in vibrated dense granular media

TL;DR

This study investigates the complex dynamics of a vibrated dense granular medium using a rotating blade as a probe, revealing caging effects, resonant frequencies, and super-diffusive behavior through a diffusing harmonic cage model.

Contribution

It introduces a mesorheological approach with a rotating blade to analyze dense granular media and models the observed dynamics with a diffusing harmonic cage, revealing new insights into their micro- and macro-scale behavior.

Findings

Identification of caging effects and transient sub-diffusion in dense granular media.

Detection of a resonant frequency around 10 Hz in the velocity power density spectrum.

Observation of super-diffusive behavior and power-law velocity inversion times at long times.

Abstract

A vertically shaken granular medium hosts a blade rotating around a fixed vertical axis, which acts as a mesorheological probe. At high densities, independently from the shaking intensity, the blade's dynamics show strong caging effects, marked by transient sub-diffusion and a maximum in the velocity power density spectrum (vpds), at a resonant frequency $\sim 10$ Hz. Interpreting the data through a diffusing harmonic cage model allows us to retrieve the elastic constant of the granular medium and its collective diffusion coefficient. For high frequencies $f$, a tail $\sim 1/f$ in the vpds reveals non-trivial correlations in the intra-cage micro-dynamics. At very long times (larger than $10$ s), a super-diffusive behavior emerges, ballistic in the most extreme cases. Consistently, the distribution of slow velocity inversion times $\tau$ displays a power-law decay, likely due to persistent collective fluctuations of the host medium.