@Article{CiCP-33-3,
author = {Wai, Ming, Chau and Shingyu, Leung},
title = {Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems},
journal = {Communications in Computational Physics},
year = {2023},
volume = {33},
number = {3},
pages = {824--848},
abstract = {<p style="text-align: justify;">We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite
time interval as a high-dimensional data point and then cluster these data from different initial locations into groups. The method then uses the normalized standard
deviation or mean absolute deviation to quantify the deformation. Unlike the usual
finite-time Lyapunov exponent (FTLE), the proposed algorithm considers the complete
traveling history of the particles. We also suggest two extensions of the method. To improve the computational efficiency, we develop an adaptive approach that constructs
different subsamples of the whole particle trajectory based on a finite time interval. To
start the computation in parallel to the flow trajectory data collection, we also develop
an on-the-fly approach to improve the solution as we continue to provide more measurements for the algorithm. The method can efficiently compute the WCVE over a
different time interval by modifying the available data points.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0177},
url = {https://global-sci.com/article/90819/within-cluster-variability-exponent-for-identifying-coherent-structures-in-dynamical-systems}
}