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Periodic Disc Packings Generated by Random Deposition in Narrow Channels

Periodic structures have been found to be characteristic of two-dimensional Visscher-Bolsterli disc packings in narrow channels. The effective period d is related to the disc diameter, d0, and the channel width, w, by d ≃ ma'dd0 and ⟨d⟩ ≃ adw, where ad ≃ 2⟨tg (θ)⟩ (θ is the angle of inclination of bonds between contacting discs in large w → ∞ packings and m is an integer) and a'd ≃ 2.75. Similar results were obtained for disc packing simulations in narrow strips with periodic boundary conditions in the lateral direction.