The contact percolation transition

TL;DR

This study reveals a second-order-like contact percolation transition in athermal particle systems that occurs below the jamming point, indicating the onset of complex dynamics and heterogeneity before the system becomes rigid.

Contribution

It uncovers a novel contact percolation transition preceding jamming, linking cluster formation to the emergence of complex response in unjammed systems.

Findings

Contact percolation occurs at a packing fraction below jamming.

Heterogeneous particle motion begins before the jamming transition.

The transition signals the onset of complex spatiotemporal response.

Abstract

Typical quasistatic compression algorithms for generating jammed packings of athermal, purely repulsive particles begin with dilute configurations and then apply successive compressions with relaxation of the elastic energy allowed between each compression step. It is well-known that during isotropic compression athermal systems with purely repulsive interactions undergo a jamming transition at packing fraction $\phi_J$ from an unjammed state with zero pressure to a jammed, rigid state with nonzero pressure. Using extensive computer simulations, we show that a novel second-order-like transition, the contact percolation transition, which signals the formation of a system-spanning cluster of mutually contacting particles, occurs at $\phi_P < \phi_J$, preceding the jamming transition. By measuring the number of non-floppy modes of the dynamical matrix, and the displacement field and time-dependent pressure following compression, we find that the contact percolation transition also heralds the onset of complex spatiotemporal response to applied stress. Thus, highly heterogeneous, cooperative, and non-affine particle motion occurs in unjammed systems significantly below the jamming transition for $\phi_P < \phi < \phi_J$, not only for jammed systems with $\phi > \phi_J$.