Shaking a Box of Sand

– We present a simple model of a vibrated box of sand, and discuss its dynamics in terms of two parameters reflecting static and dynamic disorder respectively. The fluidised, intermediate and frozen (‘glassy’) dynamical regimes are extensively probed by analysing the response of the packing fraction to steady, as well as cyclic, shaking, and indicators of the onset of glassy behaviour are analysed. In the ‘glassy’ regime, our model is exactly solvable, and allows for the qualitative description of ageing phenomena in terms of two characteristic lengths; predictions are also made about the influence of grain shape anisotropy on ageing behaviour. Vibrating sand results in very varied dynamics, ranging from glassy [1, 2] to fluidised [3, 4]. Recent experiments, e.g. [5], have gone some way in validating the notion [6] that its essential features are captured by models which incorporate the fast relaxation of individual particles together with the cooperative rearrangements of clusters. In this Letter we present a simple model of a vibrated sand-box, which interpolates between the glassy and fluidised regimes, and is based on the generalisation of an earlier cellular automaton (CA) model [7] of an avalanching sandpile. Our model shows both fast and slow dynamics in the appropriate regimes: in particular, it reduces to an exactly solvable model in the frozen (‘glassy’) regime, and provides one with a toy model for ageing in vibrated sand [8, 9]. We consider a rectangular lattice of height H and width W with N ≤ HW grains located at its lattice points, shaken with vibration intensity Γ. Each ‘grain’ is a rectangle with sides 1 and a ≤ 1, respectively. Consider a grain (i, j) in row i, column j whose height at any given time is given by hij = nij− + anij+, with nij− the number of vertical grains and nij+ the number of horizontal grains below (i, j): (∗) E-mail: [email protected] (∗∗) E-mail: [email protected] (∗∗∗) E-mail: [email protected] (∗∗∗) URA 2306 of CNRS