Normal Modes in Model Jammed Systems in Three Dimensions

TL;DR

This study investigates vibrational spectra and normal modes in three-dimensional jammed particle systems across various compressions, revealing localization at high frequencies and complex behaviors near the jamming transition.

Contribution

It provides a detailed analysis of normal modes in 3D jammed systems, highlighting how their nature varies with compression and near the jamming transition, which was less understood before.

Findings

High-frequency modes are localized at all compressions.

Low-frequency modes near the transition are neither plane-wave-like nor localized.

Normal mode behavior varies significantly with compression, especially near the jamming point.

Abstract

Vibrational spectra and normal modes of mechanically stable particle packings in three dimensions are analyzed over a range of compressions, from near the jamming transition, where the packings lose their rigidity, to far above it. At high frequency, the normal modes are localized at all compressions. At low frequency, the nature of the modes depends somewhat on compression. At large compressions, far from the transition, the lowest-frequency normal modes have some plane-wave character, though less than one would expect for a crystalline or isotropic solid. At low compressions near the jamming transition, the lowest-frequency modes are neither plane-wave-like nor localized. We characterize these differences, highlighting the unusual dispersion behavior that emerges for marginally jammed solids.