Department of Computer Science, University of Verona, Cà Vignal 2, Strada Le Grazie 15, 37134 Verona, Italy.
Department of Mathematics and Applications, University of Milano-Bicocca, Via Cozzi 55, 20125 Milano, Italy and BDIC, Beijing University of Technology, 100 Pingleyuan, Beijing 100124, People's Republic of China.
Phys Rev E. 2019 Jul;100(1-1):011101. doi: 10.1103/PhysRevE.100.011101.
Here we show how to apply a recently introduced method based on the geometric interpretation of linear momentum of vortex lines to determine dynamical properties of a network of knots and links. To show how the method works and to prove its feasibility, we consider the evolution of quantum vortices governed by the Gross-Pitaevskii equation. Accurate estimates of the momentum of interacting and reconnecting vortex rings, links, and knots are determined. The method is of general validity and it proves particularly useful in practical situations where no analytical information is available. It can be easily adapted to situations where morphological information can be extracted from experimental or computational data, thus providing a powerful tool for real-time diagnostics of vortex filaments or other networks of filamentary structures.
在这里，我们展示如何应用一种最近提出的基于涡旋线线性动量的几何解释的方法来确定结和链路网络的动力学特性。为了展示该方法的工作原理并证明其可行性，我们考虑了由 Gross-Pitaevskii 方程控制的量子涡旋的演化。准确确定了相互作用和重新连接的涡旋环、结和链路的动量。该方法具有普遍的有效性，在没有分析信息可用的实际情况下特别有用。它可以很容易地适应可以从实验或计算数据中提取形态信息的情况，从而为涡旋丝或其他丝状结构网络的实时诊断提供强大的工具。
