The shapes of physical trefoil knots
The shapes of physical trefoil knots
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DOI：
10.1016/j.eml.2021.101172
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发表时间：
2021-01-23
影响因子：
4.7
通讯作者：
Reis, Pedro M.
中科院分区：
文献类型：
--
作者：
Johanns, Paul;Grandgeorge, Paul;Reis, Pedro M.
我们进行了比较和对比调查之间的平衡形状的物理和理想的三叶结，无论是在封闭和开放的配置。理想的结是纯粹的几何抽象的最紧密的配置绑在一个完美的灵活，自我避免管与不可扩展的中心线和不可变形的横截面。在这里，我们构建物理实现的紧三叶结绑在一个弹性体棒，并使用X射线断层扫描和三维有限元模拟的详细表征。具体而言，我们评估的作用，弹性在支配物理结？的整体形状，自接触区域，曲率轮廓，和横截面变形。我们比较我们的弹性结的形状，以前计算相应的理想配置。我们的结果紧物理结表现出许多相似之处，他们的纯几何对应，但也有一些惊人的不同之处，我们详细研究。这些观察结果提出了这样一个假设，即几何模型未捕获的局部弹性变形区域可以作为损害打结长丝强度的弱点的前体。(C)2021年，任作家。由爱思唯尔有限公司出版。这是一篇在CC BY-NC-ND许可证下的开放获取文章（http：//creativecommons.org/licenses/by-nc-nd/4.0/）。
We perform a compare-and-contrast investigation between the equilibrium shapes of physical and ideal trefoil knots, both in closed and open configurations. Ideal knots are purely geometric abstractions for the tightest configuration tied in a perfectly flexible, self-avoiding tube with an inextensible centerline and undeformable cross-sections. Here, we construct physical realizations of tight trefoil knots tied in an elastomeric rod, and use X-ray tomography and 3D finite element simulation for detailed characterization. Specifically, we evaluate the role of elasticity in dictating the physical knot?s overall shape, self-contact regions, curvature profile, and cross-section deformation. We compare the shape of our elastic knots to prior computations of the corresponding ideal configurations. Our results on tight physical knots exhibit many similarities to their purely geometric counterparts, but also some striking dissimilarities that we examine in detail. These observations raise the hypothesis that regions of localized elastic deformation, not captured by the geometric models, could act as precursors for the weak spots that compromise the strength of knotted filaments. (C) 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).