Stiff knots
Stiff knots
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DOI：
10.1103/physreve.75.031801
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发表时间：
2007-03-01
影响因子：
2.4
通讯作者：
Pierre-Louis, O.
中科院分区：
文献类型：
--
作者：
Gallotti, R.;Pierre-Louis, O.
我们报告了打结的刚性弦的几何和力学。我们同时讨论封闭结和开结。我们的两个主要结果是：(I)它们的平衡能量以及开结的平衡张力取决于桥数平方的结点类型；(Ii)辫子局部化是刚性弦纠缠的一般特征，而角度局部化和结点局部化是被禁止的。此外，我们还确定了一类平衡形状为圆形辫子的纽结。从蒙特卡罗模拟中还发现了另外两种平衡形状。这三种形状都得到了初步实验的证实。我们的方法也被推广到最小化具有最大允许曲率的结线的长度的问题。
We report on the geometry and mechanics of knotted stiff strings. We discuss both closed and open knots. Our two main results are that (i) their equilibrium energy as well as the equilibrium tension for open knots depends on the type of knot as the square of the bridge number and (ii) braid localization is found to be a general feature of stiff string entanglements, while angle and knot localizations are forbidden. Moreover, we identify a family of knots for which the equilibrium shape is a circular braid. Two other equilibrium shapes are found from Monte Carlo simulations. These three shapes are confirmed by rudimentary experiments. Our approach is also extended to the problem of the minimization of the length of a knotted string with a maximum allowed curvature.