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"Steiner trees" between cell walls of sisal
  • ISSN号:1001-6538
  • 期刊名称:科学通报(英文版)
  • 时间:0
  • 页码:3220-3224
  • 语言:中文
  • 分类:O241.82[理学—计算数学;理学—数学] TS102.22[轻工技术与工程—纺织工程;轻工技术与工程—纺织科学与工程]
  • 作者机构:[1]School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China, [2]School of Aerospace, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
  • 相关基金:Supported by the National Natural Science Foundation of China (Grant Nos. 10602040, 10872114)
  • 相关项目:生物纳米膜管网络的平衡与演化力学
中文摘要:

通过波罗麻纤维的剖面图上的小心的分析,在房间墙之间的中间的 lamellae 有清楚的几何特征,这被发现:在三个附近的房间的房间墙之间,中间的 lamellae 形式有 120 °对称的一个三路的连接。如果附近的三路的连接被连接,有尖对称和拓扑的不变的 Steiner 树的一个网络被形成。如果越来越多的 Steiner 树被连接, Steiner 戒指的一个网络被产生。在另一个词,理想化房间墙,中间的 lamellae 被 Steiner 几何学统治。这几何学不仅描绘几何对称,拓扑的不变和中间的 lamellae 的最小的性质,而且控制波罗麻纤维的力学。

英文摘要:

Through careful analysis on the cross-section of sisal fibers, it is found that the middle lamellae between the cell walls have clear geometric characteristics: between the cell walls of three neighboring cells, the middle lamellae form a three-way junction with 120° symmetry. If the neighboring three-way junctions are connected, a network of Steiner tree with angular symmetry and topological invariability is formed. If more and more Steiner trees are connected, a network of Steiner rings is generated. In another word, idealized cell walls and the middle lamellae are dominated by the Steiner geometry. This geometry not only depicts the geometric symmetry, the topological invariability and minimal property of the middle lamellae, but also controls the mechanics of sisal fibers.

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