The Minimal Perimeter for N Confined Deformable Bubbles of Equal Area
The Minimal Perimeter for N Confined Deformable Bubbles of Equal Area
复制标题
N个等面积限域变形气泡的最小周长
DOI：
--
复制
发表时间：
2010
影响因子：
0.7
通讯作者：
E. Flikkema
中科院分区：
文献类型：
--
作者：
S. Cox;E. Flikkema
计算了各种多边形形状的最小周长划分为$N$平面连通等面积区域的候选区域，并与圆盘的划分进行了比较，并在二维单分散泡沫的能量基态的背景下进行了讨论。给出了总周长和外围区域的数量，并根据拓扑缺陷的数量和位置，即非六边形区域（气泡）进行了图案分类。发现等边三角形的最佳分区遵循基于不超过一个缺陷对的位置的模式，并且该模式在六边形的许多候选分区中重复。正方形和五边形的分割显示出更大的混乱。并计算了球面最小周长划分为$N$连通等面积区域的候选区域。对于小$N$，这些可能与简单的多面体有关，对于$N$ 14$，它们由12个五边形和$N-12$六边形组成。
Candidates to the least perimeter partition of various polygonal shapes into $N$ planar connected equal-area regions are calculated for $Nle 42$, compared to partitions of the disc, and discussed in the context of the energetic groundstate of a two-dimensional monodisperse foam. The total perimeter and the number of peripheral regions are presented, and the patterns classified according to the number and position of the topological defects, that is non-hexagonal regions (bubbles). The optimal partitions of an equilateral triangle are found to follow a pattern based on the position of no more than one defect pair, and this pattern is repeated for many of the candidate partitions of a hexagon. Partitions of a square and a pentagon show greater disorder. Candidates to the least perimeter partition of the surface of the sphere into $N$ connected equal-area regions are also calculated. For small $N$ these can be related to simple polyhedra and for $N ge 14$ they consist of 12 pentagons and $N-12$ hexagons.