Nonequilibrium hard-disk packings with controlled orientational order

This paper addresses one of the fundamental questions in the theory of hard-disk packings—how order within a system relates to packing density. The algorithm presented is a seed-based, growth protocol in which new disks are added sequentially to the surface of a growing cluster. The angular position of the new disk is chosen based on the minimization of an objective function designed to control order, as measured by the global bond-orientational order parameter $ψ6,$ which varies between 0 and 1 (with 1 indicating perfect hexagonal close-packed order). Modifying the objective function allows the final packing fraction to be biased while maintaining tight control over $ψ6.$ Inside of the range $0⩽ψ6⩽0.70,$ the targeted order parameter $ψ6$ is achieved to within two decimal places of accuracy. Furthermore, it is found that random structures $(ψ6∼0.01)$ can be generated with packing fractions in the range $0.40⩽η⩽0.77.$ Interestingly, the algorithm can produce nonequilibrium hard-disk configurations that are considerably more disordered than those typical of the equilibrium fluid.