# Equilibrium configurations of hard spheres in a cylindrical harmonic potential

## TL;DR

This paper investigates the equilibrium structures of hard spheres in a cylindrical harmonic potential, combining experimental observations in a rotating liquid-filled tube with theoretical modeling to understand buckled configurations and bifurcations.

## Contribution

It provides a combined experimental and theoretical analysis of buckled structures of hard spheres in a cylindrical potential, highlighting bifurcation phenomena and stable configurations.

## Key findings

- Experimental observation of buckled structures in a rotating liquid-filled tube.
- Theoretical model predicts a wide range of bifurcating structures.
- Stable structures observed both experimentally and in theory.

## Abstract

A line of hard spheres confined by a transverse harmonic potential, with hard walls at its ends, exhibits a variety of buckled structures as it is compressed longitudinally. Here we show that these may be conveniently observed in a rotating liquid-filled tube (originally introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274 (2017)] to assemble ordered three dimensional structures at higher compressions). The corresponding theoretical model is transparent and easily investigated numerically, as well as by analytic approximations. Hence we explore a wide range of predicted structures occurring via bifurcation, of which the stable ones are also observed in our experiments. Qualitatively similar structures have previously been found in trapped ion systems.