Long wavelength structural anomalies in jammed systems

TL;DR

This study uses large-scale simulations to link low-wavenumber anomalies in the structure factor of jammed spheres to collective vibrational modes, revealing how friction influences these properties near the jamming transition.

Contribution

It introduces a dispersion relation connecting structural anomalies to vibrational modes and highlights the impact of friction on jamming behavior.

Findings

Anomalous $S(k) o 0$ at the transition for frictionless spheres.

Suppression of anomalies in frictional systems.

Structural features relate to low-frequency vibrational modes.

Abstract

The structural properties of static, jammed packings of monodisperse spheres in the vicinity of the jamming transition are investigated using large-scale computer simulations. At small wavenumber $k$, we argue that the anomalous behavior in the static structure factor, $S(k) \sim k$, is consequential of an excess of low-frequency, collective excitations seen in the vibrational spectrum. This anomalous feature becomes more pronounced closest to the jamming transition, such that $S(0) \to 0$ at the transition point. We introduce an appropriate dispersion relation that accounts for these phenomena that leads us to relate these structural features to characteristic length scales associated with the low-frequency vibrational modes of these systems. When the particles are frictional, this anomalous behavior is suppressed providing yet more evidence that jamming transitions of frictional spheres lie at lower packing fractions that that for frictionless spheres. These results suggest that the mechanical properties of jammed and glassy media may therefore be inferred from measurements of both the static and dynamical structure factors.