Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-02-02
Physics
Condensed Matter
Statistical Mechanics
35 pages, 33 figures, 2 tables. Supporting material available at http://cherrypit.princeton.edu/
Scientific paper
The densest local packings of N identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained using a nonlinear programming method operating in conjunction with a stochastic search of configuration space. Knowledge of Rmin(N) in d-dimensional Euclidean space allows for the construction both of a realizability condition for pair correlation functions of sphere packings and an upper bound on the maximal density of infinite sphere packings. In this paper, we focus on the two-dimensional circular disk problem. We find and present the putative densest packings and corresponding Rmin(N) for selected values of N up to N = 348 and use this knowledge to construct such a realizability condition and upper bound. We additionally analyze the properties and characteristics of the maximally dense packings, finding significant variability in their symmetries and contact networks, and that the vast majority differ substantially from the triangular lattice even for large N. Our work has implications for packaging problems, nucleation theory, and surface physics.
Hopkins Adam B.
Stillinger Frank H.
Torquato Salvatore
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