Periodic Planar Disk Packings

Details Periodic Planar Disk Packings Periodic Planar Disk Packings

2012-01-28

arxiv.org/abs/1201.5965v1

Mathematics

Metric Geometry

26 pages, 13 figures

Scientific paper

Several conditions are given when a packing of equal disks in a torus is locally maximally dense, where the torus is defined as the quotient of the plane by a two-dimensional lattice. Conjectures are presented that claim that the density of any strictly jammed packings, whose graph does not consist of all triangles and the torus lattice is the standard triangular lattice, is at most $\frac{n}{n+1}\frac{\pi}{\sqrt{12}}$, where $n$ is the number of packing disks. Several classes of collectively jammed packings are presented where the conjecture holds.

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