In this paper, we provide a numerical tool to study a material’s coherence from a set of 2D Lagrangian trajectories sampling a dynamical system, i.e., from the motion of passive tracers. We show that eigenvectors of the Burau representation of a topological braid derived from the trajectories have levelsets corresponding to components of the Nielsen–Thurston decomposition of the dynamical system. One can thus detect and identify clusters of space–time trajectories corresponding to coherent regions of the dynamical system by solving an eigenvalue problem. Unlike previous methods, the scalable computational complexity of our braid-based approach allows the analysis of large amounts of trajectories.

中文翻译：

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通过Burau编织物本征分析从轨迹获得材料相干性

在本文中，我们提供了一种数值工具，用于从一组二维的拉格朗日轨迹中研究材料的相干性，该轨迹采样了一个动力系统，即从无源示踪剂的运动中获取。我们表明，从轨迹得出的拓扑辫子的Burau表示的特征向量具有与动力系统的Nielsen-Thurston分解分量相对应的能级集。因此，通过解决一个特征值问题，就可以检测和识别出与动力系统相干区域相对应的时空轨迹簇。与以前的方法不同，基于辫子的方法具有可扩展的计算复杂性，可以分析大量轨迹。