Jamming on curved surfaces

TL;DR

This study investigates the jamming transition of particles on curved ellipsoidal surfaces through simulations, revealing unique structural properties and differences from flat space jamming, including fewer contacts needed for stability.

Contribution

It introduces a simulation-based analysis of jamming on curved surfaces, highlighting how curvature influences contact number and structural order compared to flat geometries.

Findings

Fewer contacts per particle are needed in curved geometries.

Jammed structures can be unjammed and reformed through surface evolution.

Ordered packings exhibit signatures similar to disordered packings.

Abstract

Colloidal and other granular media experience a transition to rigidity known as jamming if the fill fraction is increased beyond a critical value. The resulting jammed structures are locally disordered, bear applied loads inhomogenously, possess the minimal number of contacts required for stability and elastic properties that scale differently with volume fraction to crystalline media. Here the jamming transition is studied on a curved ellipsoidal surface by computer simulation, where shape evolution leads to a reduction in area, crowding the particles and preventing further evolution of the surface. The arrested structures can be unjammed and the surface further evolved iteratively, eventually leading to a rigid metric-jammed state that is stable with respect to motion of the particles and some specified space of deformations of the manifold. The structures obtained are compared with those obtained in flat space; it is found that jammed states in curved geometries require fewer contacts per particle due to the nonlinearity of the surface constraints. In addition, structures composed of soft particles are compressed above the jamming point. It is observed that relatively well-ordered but geometrically frustrated monodisperse packings share many signatures of disordered bidisperse packings.