A colloidal viewpoint on the sausage catastrophe and the finite sphere packing problem.
A colloidal viewpoint on the sausage catastrophe and the finite sphere packing problem.
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DOI：
10.1038/s41467-023-43722-0
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发表时间：
2023-11-30
影响因子：
16.6
通讯作者：
Dijkstra, Marjolein
中科院分区：
文献类型：
--
作者：
Marin-Aguilar, Susana;Camerin, Fabrizio;van der Ham, Stijn;Feasson, Andrea;Vutukuri, Hanumantha Rao;Dijkstra, Marjolein
人们普遍认为，将有限数量的大小相等的球体堆积起来的最有效方法是将它们紧密地排列在一个簇中。然而，数学家们已经证实，线性排列实际上可能导致密集堆积。在这里，我们的实验和模拟相结合的研究提供了一个物理实现的有限球包装问题，通过研究在一个松弛的脂质囊泡的胶体的安排。我们绘制了一个状态图显示线性，平面和集群构象的领域，以及由于膜波动的集群板和板线性构象之间的交替状态。最后，通过系统地分析截头多面体填充，我们确定了56 ≤ N ≤ 70个球的簇，不包括N = 57和63，比线性排列更有效地填充。在一个紧密簇中填充有限个球并不总是导致致密填充。在这里，作者提供了一个物理实现的有限球包装问题封闭胶体在一个松弛的脂质囊泡和映射出一个状态图，显示线性，平面和集群构象的球体，以及交替的集群板和板线性构象之间的双稳态。
It is commonly believed that the most efficient way to pack a finite number of equal-sized spheres is by arranging them tightly in a cluster. However, mathematicians have conjectured that a linear arrangement may actually result in the densest packing. Here, our combined experimental and simulation study provides a physical realization of the finite sphere packing problem by studying arrangements of colloids in a flaccid lipid vesicle. We map out a state diagram displaying linear, planar, and cluster conformations of spheres, as well as bistable states which alternate between cluster-plate and plate-linear conformations due to membrane fluctuations. Finally, by systematically analyzing truncated polyhedral packings, we identify clusters of 56 ≤ N ≤ 70 number of spheres, excluding N = 57 and 63, that pack more efficiently than linear arrangements. Packing a finite number of spheres in a compact cluster does not always result in the densest packing. Here, the authors provide a physical realization of the finite sphere packing problem by enclosing colloids in a flaccid lipid vesicle and mapping out a state diagram that displays linear, planar, and cluster conformations of spheres, as well as bistable states that alternate between cluster-plate and plate-linear conformations.
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