Topological mechanics of knots and tangles
Topological mechanics of knots and tangles
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DOI：
10.1126/science.aaz0135
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发表时间：
2020-01-03
期刊：
影响因子：
56.9
通讯作者：
Dunkel, Jorn
中科院分区：
文献类型：
--
作者：
Patil, Vishal P.;Sandt, Joseph D.;Dunkel, Jorn
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，航行和手术中。尽管已经研究了几个世纪，但弹性结中拓扑学和力学之间的微妙相互作用仍然知之甚少。在这里，我们将光学机械实验与理论和模拟相结合，以分析在机械变形下改变颜色的打结纤维。利用与长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，与常用的攀登和航行弯曲的模拟和实验一致。我们的研究结果突出了扭曲和扭动在解开过程中的重要性，为复杂缠结系统的控制提供了指导。
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.