Packing Squares in a Torus
Statistical Mechanics
2012-03-20 v2
Abstract
The densest packings of N unit squares in a torus are studied using analytical methods as well as simulated annealing. A rich array of dense packing solutions are found: density-one packings when N is the sum of two square integers; a family of "gapped bricklayer" Bravais lattice solutions with density N/(N+1); and some surprising non-Bravais lattice configurations, including lattices of holes as well as a configuration for N=23 in which not all squares share the same orientation. The entropy of some of these configurations and the frequency and orientation of density-one solutions as N goes to infinity are discussed.
Cite
@article{arxiv.1110.5348,
title = {Packing Squares in a Torus},
author = {Don Blair and Christian D. Santangelo and Jon Machta},
journal= {arXiv preprint arXiv:1110.5348},
year = {2012}
}
Comments
14 pages, 9 figures; v2 reflects minor changes in published version