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通过使用圆形来提高塞无序包装的密度
Aleksandar Donev1, Ibrahim Cisse, David Sachs
1Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA.
概括
体可以比球体更密集地包装,达到高达0.71.1的包装分数. 这种提高的包装密度与更多的颗粒接触有关,影响了颗粒介质和材料科学.
科学领域:
- 物理 物理学 物理
- 材料科学 材料科学 材料科学
- 几何几何学 几何几何学
背景情况:
- 包装问题,确定最大物体密度,是科学中的基本问题.
- 均等的球体达到大约0.74.4的最大包装分数.
- 随机球包通常达到较低的密度,大约为0.64.
研究的目的:
- 为了研究圆体是否可以达到比球体更高的随机包装密度.
- 探索粒子形状,自由度和包装密度之间的关系.
- 分析稳定包装所需的颗粒接触次数.
主要方法:
- 圆体的实验包装.
- 开发一个新的模拟算法,用于包装研究.
- 每个粒子 (Z) 的粒子接触的测量.
主要成果:
- 体随机地比球体更密集,达到0.68到0.71.7的分数.
- 包装密度接近0.74对于特定的圆形面积比.
- 球形包装显示每个粒子约有10次接触,而球形包装则只有6次接触.
结论:
- 圆形状允许比球形状更密集的随机包装.
- 增加的粒子接触,由于更高的自由度,稳定更密集的包装.
- 这些发现对颗粒材料,陶,玻璃形成和离散几何学有影响.
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