Stable elastic knots with no self-contact
Stable elastic knots with no self-contact
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DOI：
10.1016/j.jmps.2018.03.019
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发表时间：
2018-07-01
影响因子：
5.3
通讯作者：
Neukirch, Sebastien
中科院分区：
文献类型：
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作者：
Moulton, Derek E.;Grandgeorge, Paul;Neukirch, Sebastien
我们研究了一根弹性杆弯曲成一个开放的三叶结，并在两端夹住。我们考虑的问题是是否存在不存在自接触点的稳定构型。这个想法可以很容易地复制在一张薄纸上，但更困难的是，甚至不可能用柔性电线。在一个简单的实验中，我们在三个与自由度相关的调谐参数的空间中寻找这样的构型。在数学上，我们证明，在标准Kirchhoff理论和弹性条理论中，可以找到稳定和无接触的结构型，并对相应的参数区域进行分类。数值结果与渐近分析相辅相成，证明了双覆盖环附近存在结。在带状模型的情况下，还提供了良好结区域的定量实验来验证理论。(C) 2018 Elsevier Ltd.版权所有。
We study an elastic rod bent into an open trefoil knot and clamped at both ends. The question we consider is whether there are stable configurations for which there are no points of self-contact. This idea can be fairly easily replicated with a thin strip of paper, but is more difficult or even impossible with a flexible wire. We search for such configurations within the space of three tuning parameters related to the degrees of freedom in a simple experiment. Mathematically, we show, both within standard Kirchhoff theory as well within an elastic strip theory, that stable and contact-free knotted configurations can be found, and we classify the corresponding parametric regions. Numerical results are complemented with an asymptotic analysis that demonstrates the presence of knots near the doubly-covered ring. In the case of the strip model, quantitative experiments of the region of good knots are also provided to validate the theory. (C) 2018 Elsevier Ltd. All rights reserved.