论文标题
二进制碟片的密度：使用化学计量计
Density of Binary Disc Packings: Playing with Stoichiometry
论文作者
论文摘要
我们考虑在比率$ \ sqrt {2} -1 $之内的圆盘大小的硬盘混合物，也就是说，小光盘恰好适合四个大圆盘之间的孔。对于每个大型和小圆盘的规定化学计量学，最密集的包装都是通过计算机辅助证明来严格确定的。 1：1化学计量学的密度最大：然后在每个间隙位点形成一个平方网格，一个小圆盘筑巢。当大量圆盘过量时，最浓的包装是由单相制成的，该相位将两种类型的盘以混乱的方式混合在一起（可以通过方形砖块来描述）。相反，当过量的小光盘中过量时，出现相位分离的现象：大圆盘涉及最密集的1：1化学计量阶段，而过量的小盘则形成紧凑的六边形相。
We consider hard-disc mixtures with disc sizes within ratio $\sqrt{2}-1$, that is, the small disc exactly fits in the hole between four large discs. For each prescribed stoichiometry of large and small discs, the densest packings are rigorously determined via a computer-assisted proof. The density is maximal for the 1:1 stoichiometry: the large discs then form a square grid in each interstitial site of which a small disc nests. When there is an excess of large discs, the densest packings are made of a single phase which mixes the two types of discs in a chaotic way (it can be described by square-triangle tilings). When there is an excess of small discs, on the contrary, a phenomenon of phase separation appears: the large discs are involved in the densest 1:1 stoichiometry phases while the excess of small discs form compact hexagonal phases.
