Mean-field character of low-dimensional granular-packing dynamics

Determine whether the dynamics of low-dimensional granular packings should be regarded as mean-field.

Background

The paper investigates whether the discrepancy between granular-packing and p-spin shape parameters results from granular packings failing to exhibit mean-field behavior. Structural properties of granular packings have been shown to follow mean-field predictions even in two dimensions, but the authors note that dynamical properties are much less studied.

The evolution of the granular-packing Hessian eigenvalue distribution during minimization differs from the stationary-shape behavior expected for the p-spin model. This leaves unresolved whether the dynamics of low-dimensional granular packings can appropriately be treated within a mean-field framework.