Particle pinning as a method to manipulate marginal stability

TL;DR

This paper investigates how pinning particles influences the vibrational properties and marginal stability of jammed packings, revealing effects on soft modes and deviations from mean-field predictions.

Contribution

It introduces a detailed analysis of particle pinning effects on marginal stability and vibrational modes near the jamming transition.

Findings

Soft modes form a plateau in the density of states.

Pinning affects the non-Debye scaling behavior.

Spatial structure of modes remains largely unaffected by pins.

Abstract

We study the critical behavior of low-frequency vibrations of packings with pinned particles near the jamming point. Soft modes form a plateau in the density of states and its frequency is controlled by the contact number as the ordinary jamming transition. The spatial structure of these modes is not largely affected by pins. Below the plateau, the non-Debye scaling predicted by mean-field theories and quasi-localized modes breaks down depending on the pinning procedures. We comprehensively explain these behaviors by the impact of pinning operations on the marginal stability of the packings.