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Topological mechanics of knots and tangles
Science ( IF 56.9 ) Pub Date : 2020-01-02 , DOI: 10.1126/science.aaz0135
Vishal P Patil 1 , Joseph D Sandt 2 , Mathias Kolle 2 , Jörn Dunkel 1
Affiliation  

It's knot what you know Why is it that some knots seem to hold tight while others readily slip apart? Patil et al. develop a theoretical analysis of the stability of knots and find links between topological parameters (twist charge, crossing numbers, handedness) and mechanical stability. The theory is confirmed using simulations and experiments on color-changing fibers that optically show localized stress differences in different parts of the knot as the two strands are pulled apart. The authors show why some common knots slip easily and untie, whereas others hold tight. Science, this issue p. 71 Simple counting rules predict the relative mechanical stability of knots and tangles. Knots play a fundamental role in the dynamics of biological and physical systems, from DNA to turbulent plasmas, as well as in climbing, weaving, sailing, and surgery. Despite having been studied for centuries, the subtle interplay between topology and mechanics in elastic knots remains poorly understood. Here, we combined optomechanical experiments with theory and simulations to analyze knotted fibers that change their color under mechanical deformations. Exploiting an analogy with long-range ferromagnetic spin systems, we identified simple topological counting rules to predict the relative mechanical stability of knots and tangles, in agreement with simulations and experiments for commonly used climbing and sailing bends. Our results highlight the importance of twist and writhe in unknotting processes, providing guidance for the control of systems with complex entanglements.

中文翻译:

结和缠结的拓扑力学

这是你所知道的打结 为什么有些打结看起来很紧,而另一些打结很容易散开?帕蒂尔等人。对结的稳定性进行理论分析,并找到拓扑参数(扭曲电荷、交叉数、旋向性)和机械稳定性之间的联系。该理论通过对变色纤维的模拟和实验得到证实,当两股线被拉开时,这些纤维在光学上显示了结不同部分的局部应力差异。作者展示了为什么一些常见的结很容易滑脱和解开,而另一些则紧紧抓住。科学,这个问题 p。71 简单的计数规则可以预测结和缠结的相对机械稳定性。结在生物和物理系统的动力学中发挥着重要作用,从 DNA 到湍流等离子体,以及在攀爬、编织、航行、和手术。尽管已经研究了几个世纪,但对弹性结中拓扑学和力学之间微妙的相互作用仍然知之甚少。在这里,我们将光机械实验与理论和模拟相结合,以分析在机械变形下会改变颜色的打结纤维。利用与远程铁磁自旋系统的类比,我们确定了简单的拓扑计数规则来预测结和缠结的相对机械稳定性,与常用的攀爬和航行弯道的模拟和实验一致。我们的结果强调了解开过程中扭曲和扭动的重要性,为控制具有复杂纠缠的系统提供了指导。弹性结中拓扑学和力学之间微妙的相互作用仍然知之甚少。在这里,我们将光机械实验与理论和模拟相结合,以分析在机械变形下会改变颜色的打结纤维。利用与远程铁磁自旋系统的类比,我们确定了简单的拓扑计数规则来预测结和缠结的相对机械稳定性,与常用的攀爬和航行弯道的模拟和实验一致。我们的结果强调了解开过程中扭曲和扭动的重要性,为控制具有复杂纠缠的系统提供了指导。弹性结中拓扑学和力学之间微妙的相互作用仍然知之甚少。在这里,我们将光机械实验与理论和模拟相结合,以分析在机械变形下会改变颜色的打结纤维。利用与远程铁磁自旋系统的类比,我们确定了简单的拓扑计数规则来预测结和缠结的相对机械稳定性,与常用的攀爬和航行弯道的模拟和实验一致。我们的结果强调了解开过程中扭曲和扭动的重要性,为控制具有复杂纠缠的系统提供了指导。利用与远程铁磁自旋系统的类比,我们确定了简单的拓扑计数规则来预测结和缠结的相对机械稳定性,与常用的攀爬和航行弯道的模拟和实验一致。我们的结果强调了解开过程中扭曲和扭动的重要性,为控制具有复杂纠缠的系统提供了指导。利用与远程铁磁自旋系统的类比,我们确定了简单的拓扑计数规则来预测结和缠结的相对机械稳定性,与常用的攀爬和航行弯道的模拟和实验一致。我们的结果强调了解开过程中扭曲和扭动的重要性,为控制具有复杂纠缠的系统提供了指导。
更新日期:2020-01-02
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