Fig. 1.

(A) Schematic of the setup used to vibrate the assembly of monodisperse balls. The global coordinate system aligned with the box edges is also indicated. Gravity acts in the negative $z-$ direction, and the box is vibrated along the $x-$ direction. (B) X-ray Computed Tomography (XCT) reconstruction of the initial random assembly of the balls. The dimensions of the box and the initial random assembly are indicated on the image. The crystallized assembly after vibrating for $N=3,000$ cycles with an amplitude $a=2.0\text{mm}$ and frequency $f=20\text{Hz}$ is also included. The crystallized assembly is colored to indicate the crystal structures and thereby also the polycrystalline nature of the crystallized assembly. (C) Measurements and discrete-element predictions of the steady-state crystallinity fraction ${\phi }_{\mathit{ss}}$ as a function of the nondimensional vibration intensity $\mathrm{\Gamma }\equiv a{\omega }^2/g$ for two amplitudes $a$ . (D) Sketch illustrating the mechanisms for balls to rearrange within the assembly resulting in crystallization of the assembly. The balls need to ride-up on each other with balls in the lower layers displacing balls that lie in layers further-up in the assembly.