How superfluid vortex knots untie
How superfluid vortex knots untie
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DOI：
10.1038/nphys3679
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发表时间：
2016-07-01
期刊：
影响因子：
19.6
通讯作者：
Irvine, William T. M.
中科院分区：
文献类型：
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作者：
Kleckner, Dustin;Kauffman, Louis H.;Irvine, William T. M.
结和链经常出现在物理系统中，包括摇晃的绳子（1）和DNA（参考文献2），以及更微妙的流体涡旋结构（3）和等离子体磁场（4）。没有耗散的流体流动理论预测，这些缠结的结构会持续存在（5），就像鞋带上的结一样约束着流动的演化。这种约束产生了一个被称为螺旋度（6，7）的守恒量，为控制复杂流动提供了基本的见解和诱人的可能性。然而，即使是少量的耗散也可以通过称为重连的“切割和拼接”操作来解开结（3，4，8 -11）。尽管这些重连在理解螺旋性和更普遍的打结场的稳定性方面具有潜在的基础作用，但它们的影响仅限于少数简单的结（12）。在这里，我们研究了超流体的Gross-Pitaevskii模型中322个基本结和链接的演化，发现它们普遍解开。我们观察到，中心线螺旋部分保存，即使结解开，理想化流体预测的完美的螺旋守恒的残余。此外，我们发现解结的拓扑路径具有最小二维结图的简单描述，并且倾向于集中在仅在一个方向上扭曲的状态。这些结果与先前对几个系统中简单结的研究有直接的类比，包括DNA重组（2）和经典流体（3，12）。这种几何和拓扑演化的相似性表明，耗散场中的结的行为具有普遍性。
Knots and links often occur in physical systems, including shaken strands of rope(1) and DNA (ref. 2), as well as the more subtle structure of vortices in fluids(3) and magnetic fields in plasmas(4). Theories of fluid flows without dissipation predict these tangled structures persist(5), constraining the evolution of the flow much like a knot tied in a shoelace. This constraint gives rise to a conserved quantity known as helicity(6,7), offering both fundamental insights and enticing possibilities for controlling complex flows. However, even small amounts of dissipation allow knots to untie by means of 'cut-and-splice' operations known as reconnections(3,4,8-11). Despite the potentially fundamental role of these reconnections in understanding helicity-and the stability of knotted fields more generally-their effect is known only for a handful of simple knots(12). Here we study the evolution of 322 elemental knots and links in the Gross-Pitaevskii model for a superfluid, and find that they universally untie. We observe that the centreline helicity is partially preserved even as the knots untie, a remnant of the perfect helicity conservation predicted for idealized fluids. Moreover, we find that the topological pathways of untying knots have simple descriptions in terms of minimal two-dimensional knot diagrams, and tend to concentrate in states which are twisted in only one direction. These results have direct analogies to previous studies of simple knots in several systems, including DNA recombination(2) and classical fluids(3,12). This similarity in the geometric and topological evolution suggests there are universal aspects in the behaviour of knots in dissipative fields.