论文标题
部分可观测时空混沌系统的无模型预测
Circle packing in regular polygons
论文作者
论文摘要
我们研究了常规多边形内大量一致和非重叠圆的包装。 We have devised efficient algorithms that allow one to generate configurations of $N$ densely packed circles inside a regular polygon and we have carried out intensive numerical experiments spanning several polygons (the largest number of sides considered here being $16$) and up to $200$ circles ($400$ circles in the special cases of the equilateral triangle and the regular hexagon) .我们发现的某些配置可能不是包装分数的全局最大值，尤其是对于$ n \ gg 1 $，由于问题的计算复杂性很高，但尽管如此，它们仍应在给定的$ n $下为包装分数提供良好的下限。这是常规多边形中填充物的首次系统数值研究，以前仅针对等边三角形，正方形和圆圈进行。
We study the packing of a large number of congruent and non--overlapping circles inside a regular polygon. We have devised efficient algorithms that allow one to generate configurations of $N$ densely packed circles inside a regular polygon and we have carried out intensive numerical experiments spanning several polygons (the largest number of sides considered here being $16$) and up to $200$ circles ($400$ circles in the special cases of the equilateral triangle and the regular hexagon) . Some of the configurations that we have found possibly are not global maxima of the packing fraction, particularly for $N \gg 1$, due to the great computational complexity of the problem, but nonetheless they should provide good lower bounds for the packing fraction at a given $N$. This is the first systematic numerical study of packing in regular polygons, which previously had only been carried out for the equilateral triangle, the square and the circle.
