  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.
