Systematic Onset of Periodic Patterns in Random Disk Packings

We report startling evidence of a systematic onset of periodic structures in large piles of disks deposited between rigid walls, independently of the pile width, observed in numerically constructed monodisperse packings with up to 107 disks. Disordered transient phases preceding the periodicity onset are found to obey power-laws as a function of the channel height. Independently of the width, we invariably find packings to be asymptotically periodic after disordered transients which, however, may become very large as the channel width grows without bound. The probability density of finding periodic structures of a given period displays a series of discrete peaks which, however, are washed out when the channel width grows indefinitely.