Density fluctuations in 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 is explored in detail using extensive molecular dynamics simulations. We measure the density and density fluctuations of the ensemble of mechanically stable configurations reached after the energy induced by the perturbation has dissipated. We show that the peak in density fluctuations concurs with the density undergoing the transition. We find that different horizontal sub-regions (”layers”) along the height of the pile traverse the transition in a similar manner but at distinct tap intensities, demonstrating that at a given intensity certain regions of the same pile may respond glassy while others remain equilibrated. To address this phenomenon, we supplement the conventional approach based purely on properties of the static configurations with investigations of the grain-scale dynamics, induced by a tap, by which the energy is transmitted throughout the pile. We find that the effective energy that particles dissipate is a function of the particles location in the pile and, moreover, that its value plays a distinctive role in the transformation between configurations. This internal energy provides a “temperature-like” parameter that allows us to align the transition into the glassy state for all layers as well as different annealing schedules at a critical value.