Enumerating Finite Sphere Packings
نویسندگان
چکیده
We consider packings of n identical spherical particles that bind to one another without deformation or overlap, and without any long range interactions. Combining graph theoretic enumeration with basic geometry, we analytically solve for packings of n ≤ 10 particles satisfying minimal rigidity constraints (≥ 3 contacts per particle and ≥ 3n− 6 total contacts). We find that the onset of packings that have different numbers of contacts occurs at n = 10, and that the number of packings that can not be constructed iteratively from < n particle packings proliferates at n ≥ 9 particles.
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