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柏拉图和阿基米德固体的密集包装
1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA. torquato@princeton.edu
Nature
|August 14, 2009
概括
研究人员探索了密集的多面体包装,发现了柏拉图固体的新密度配置. 这项研究表明对称多面体的最佳格子包装,类似于开普勒.
科学领域:
- 离散几何学的离散几何学.
- 数学理论是数的理论.
- 材料科学是一种材料科学.
- 计算物理学的计算物理.
背景情况:
- 密集的粒子包装模拟了物质和材料的各种状态.
- 研究主要集中在球形粒子上,对多面体包装的知识有限.
- 了解包装对称性在离散几何学和数论中至关重要.
研究的目的:
- 为了确定非的柏拉图固体 (四面体,八面体,十二面体,二面体) 已知的最密集的包装.
- 为了研究多面体包装密度和格子结构之间的关系.
- 提出关于对称的柏拉图和阿基米德固体最密集的包装的猜测.
主要方法:
- 制定了多面体包装生成作为一个优化问题.
- 使用具有周期边界条件的自适应基本细胞 ("自适应缩小细胞"方案).
- 在模拟中使用了多种多粒子初始配置.
主要成果:
- 实现了四面体 (0.782...),八面体 (0.947...),十二面体 (0.904...) 和二面体 (0.836...) 包装的记录密度.
- 发现八面体,十二面体和二面体的最密集包装与它们已知的最佳格子包装相对应.
- 最密集的四面体包装被证实不是Bravais.
结论:
- 已经确定了非地性柏拉图固体中最密集的包装.
- 提出了一个猜想:对称的柏拉图和阿基米德固体最密集的包装是它们最密集的格子包装.
- 这一发现将开普勒的球形猜想扩展到一个更广泛的多面体固体类别.
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