A mean field description of jamming in non-cohesive frictionless particulate systems

TL;DR

This paper develops a mean field theory for the jamming transition in frictionless particulate systems, predicting critical exponents and linking static and dynamic arrest to elastic buckling, supported by simulations.

Contribution

It introduces a simplified one-particle mean field model that captures the critical behavior of jamming and predicts exponents consistent with simulations.

Findings

Predicted critical exponents for macroscopic quantities near jamming.

Identified the arrested states as near elastic buckling transition.

Provided numerical evidence supporting the scaling laws.

Abstract

A theory for kinetic arrest in isotropic systems of repulsive, radially-interacting particles is presented that predicts exponents for the scaling of various macroscopic quantities near the rigidity transition that are in agreement with simulations, including the non-trivial shear exponent. Both statics and dynamics are treated in a simplified, one-particle level description, and coupled via the assumption that kinetic arrest occurs on the boundary between mechanically stable and unstable regions of the static parameter diagram. This suggests the arrested states observed in simulations are at (or near) an elastic buckling transition. Some additional numerical evidence to confirm the scaling of microscopic quantities is also provided.