Critical scaling and aging in cooling systems near the jamming transition

TL;DR

This study uses simulations to reveal critical scaling, aging, and superdiffusive behavior near the jamming transition in soft sphere systems, highlighting a growing length scale governing relaxation.

Contribution

It demonstrates critical scaling of relaxation length and time, and links aging and superdiffusion phenomena to the jamming transition in soft spheres.

Findings

Identification of a growing length scale xi(t) near jamming

Scaling collapse of data onto master curves for different densities

Observation of aging and superdiffusion above jamming density

Abstract

We conduct athermal simulations of freely-cooling, viscous soft spheres around the jamming transition density \phi_{J}, and find evidence for a growing length \xi(t) that governs relaxation to mechanical equilibrium. \xi(t) is manifest in both the velocity correlation function, and the spatial correlations in a scalar measure of local force balance which we define. Data for different densities \phi can be collapsed onto two master curves by scaling \xi(t) and t by powers of |\phi-\phi_{J}|, indicative of critical scaling. Furthermore, particle transport for \phi>\phi_{J} exhibits aging and superdiffusion similar to a range of soft matter experiments, suggesting a common origin. Finally, we explain how \xi(t) at late times maps onto known behavior away from \phi_{J}.