Collisional Statistics and Dynamics of 2D Hard-Disk Systems: From Fluid to Solid

TL;DR

This study uses extensive MD simulations to analyze collision statistics and dynamics in 2D hard-disk systems across fluid and solid phases, revealing phase-dependent behaviors and similarities to glassy and jammed materials.

Contribution

It provides detailed analysis of collision and dynamical properties in 2D hard-disk systems, highlighting phase-dependent changes and analogies with glassy and granular media.

Findings

Mean free flight time and path length change drastically in coexistence phase.

Single particle dynamics show crossovers between fluid and solid phases.

Dynamical behaviors resemble those in granular media, colloids, and supercooled liquids.

Abstract

We perform extensive MD simulations of two-dimensional systems of hard disks, focusing on the \emph{on}-collision statistical properties. We analyze the distribution functions of velocity, free flight time and free path length for packing fractions ranging from the fluid to the solid phase. The behaviors of the mean free flight time and path length between subsequent collisions are found to drastically change in the coexistence phase. We show that single particle dynamical properties behave analogously in collisional and continuous time representations, exhibiting apparent crossovers between the fluid and the solid phase. We find that, both in collisional and continuous time representation, the mean square displacement, velocity autocorrelation functions, intermediate scattering functions and self part of the van Hove function (propagator), closely reproduce the same behavior exhibited by the corresponding quantities in granular media, colloids and supercooled liquids close to the glass or jamming transition.