Granular piles traversing the glass transition: A grain-scale characterization via the internal energy*

The transition into a glassy state of a tapped granular pile [1,2] is revisited using extensive molecular dynamics simulations. We supplement the conventional approach -- based purely on the properties of the ensemble of mechanically stable, static configurations -- with the investigation of the grain-scale dynamics of the energy, injected through a tap, as it is transmitted and dissipated throughout the pile [3]. We propose an effective measure of this internal energy to play the role  of the long-sought "temperature-like" parameter, allowing us to predict the macroscopic state of the static configurations. We show that different horizontal sub-regions ("layers") along the height of the pile experience different "temperatures" under a same perturbation, resulting in certain regions of the same pile responding glassy while others remain equilibrated at a given tap intensity. Plotting the macroscopic properties (specifically, density and density fluctuations) of each layers as a function of this local effective energy allows us to quantitatively align the results measured in the different layers. We will show that for this collapse with the effective energy, the peak exhibited for the density fluctuations concurs with the point where the different parts of the pile undergo their respective glass transition.

[1] Nowak, E. R., et al. "Reversibility and irreversibility in the packing of vibrated granular material." Powder Technology. 94.1 (1997): 79.

[2] Gago, Paula A., and Boettcher, Stefan. "Universal features of annealing and aging in compaction of granular piles." PNAS 117.52 (2020): 33072. (https://doi.org/10.1073/pnas.2012757117)

[3] Gago, Paula A., and Boettcher, Stefan. "Density fluctuations in granular piles traversing the glass transition: A grain-scale characterization of the transition via the internal energy."  (https://arxiv.org/abs/2107.07764)