Material coherence from trajectories via Burau eigenanalysis of braids
Abstract
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.
- Authors:
-
[3]
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- UCA Inria, Sophia Antipolis (France)
- California Institute of Technology (CalTech), Pasadena, CA (United States); ShanghaiTech School of Information Science & Technology (China)
- Publication Date:
- Research Org.:
- Krell Institute, Ames, IA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1800894
- Alternate Identifier(s):
- OSTI ID: 1604239
- Grant/Contract Number:
- FG02-97ER25308
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Additional Journal Information:
- Journal Volume: 30; Journal Issue: 3; Journal ID: ISSN 1054-1500
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; Mathematics; Physics; Image processing; Dynamical systems; General topology; Geometric topology; Computational methods; Entropy; Fluid flows; Group theory
Citation Formats
Yeung, Melissa, Cohen-Steiner, David, and Desbrun, Mathieu. Material coherence from trajectories via Burau eigenanalysis of braids. United States: N. p., 2020.
Web. doi:10.1063/1.5128269.
Yeung, Melissa, Cohen-Steiner, David, & Desbrun, Mathieu. Material coherence from trajectories via Burau eigenanalysis of braids. United States. https://doi.org/10.1063/1.5128269
Yeung, Melissa, Cohen-Steiner, David, and Desbrun, Mathieu. Thu .
"Material coherence from trajectories via Burau eigenanalysis of braids". United States. https://doi.org/10.1063/1.5128269. https://www.osti.gov/servlets/purl/1800894.
@article{osti_1800894,
title = {Material coherence from trajectories via Burau eigenanalysis of braids},
author = {Yeung, Melissa and Cohen-Steiner, David and Desbrun, Mathieu},
abstractNote = {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.},
doi = {10.1063/1.5128269},
journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
number = 3,
volume = 30,
place = {United States},
year = {Thu Mar 12 00:00:00 EDT 2020},
month = {Thu Mar 12 00:00:00 EDT 2020}
}
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