混沌流中柔性纤维的自发打结
Spontaneous knotting of a flexible fiber in chaotic flows
摘要：
我们考虑一个不可扩展的问题，但灵活的纤维平流由稳定的混沌流，并问一个简单的问题，纤维是否可以自发地结自己。使用1D Cosserat模型，一个简单的局部粘性阻力模型和离散的接触力，我们探讨了在任何给定的时间，当纤维是相互作用的ABC类的流量找到结的概率。的弯曲刚度示出具有边际效应相比，增加纤维长度。复杂的结形成多达11个交叉点，但有些结比其他结更有可能。流的有限时间李雅普诺夫指数对节点概率有积极的影响。最后，接触力似乎是至关重要的，因为打结的配置可以保持稳定的时间比流动的周转时间长得多，这是没有观察到当纤维可以自由交叉本身。
英文摘要：
We consider the problem of an inextensible but flexible fiber advected by a steady chaotic flow, and ask the simple question whether the fiber can spontaneously knot itself. Using a 1D Cosserat model, a simple local viscous drag model and discrete contact forces, we explore the probability of finding knots at any given time when the fiber is interacting with the ABC class of flows. The bending rigidity is shown to have a marginal effect compared to that of increasing the fiber length. Complex knots are formed up to 11 crossings, but some knots are more probable than others. The finite-time Lyapunov exponent of the flow is shown to have a positive effect on the knot probability. Finally, contact forces appear to be crucial since knotted configurations can remain stable for times much longer than the turnover time of the flow, something that is not observed when the fiber can freely cross itself.
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