Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106 Warsaw, Poland.
Institute of Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
Phys Rev Lett. 2018 Sep 21;121(12):127801. doi: 10.1103/PhysRevLett.121.127801.
We study the dynamics of knotted deformable closed chains sedimenting in a viscous fluid. We show experimentally that trefoil and other torus knots often attain a remarkably regular horizontal toroidal structure while sedimenting, with a number of intertwined loops, oscillating periodically around each other. We then recover this motion numerically and find out that it is accompanied by a very slow rotation around the vertical symmetry axis. We analyze the dependence of the characteristic timescales on the chain flexibility and aspect ratio. It is observed in the experiments that this oscillating mode of the dynamics can spontaneously form even when starting from a qualitatively different initial configuration. In numerical simulations, the oscillating modes are usually present as transients or final stages of the evolution, depending on chain aspect ratio and flexibility, and the number of loops.
我们研究了在粘性流体中沉降的扭结可变形封闭链的动力学。我们通过实验表明，三叶结和其他环纽结在沉降时经常呈现出一种非常规则的水平环形结构，多个相互交织的环围绕着彼此周期性地振荡。然后，我们通过数值模拟再现了这种运动，并发现它伴随着绕垂直对称轴的非常缓慢的旋转。我们分析了特征时间尺度对链的柔韧性和纵横比的依赖性。实验中观察到，即使从定性上不同的初始构型开始，这种动态的振荡模式也可以自发形成。在数值模拟中，取决于链的纵横比和柔韧性以及环的数量，振荡模式通常作为瞬态或演化的最终阶段出现。
