@Article{CiCP-36-1411,
author = {Tsai , Yun Chen and Leung , Shingyu},
title = {Local Trajectory Variation Exponent (LTVE) for Visualizing Dynamical Systems},
journal = {Communications in Computational Physics},
year = {2024},
volume = {36},
number = {5},
pages = {1411--1439},
abstract = {<p style="text-align: justify;">The identification and visualization of Lagrangian structures in flows plays
a crucial role in the study of dynamic systems and fluid dynamics. The Finite Time
Lyapunov Exponent (FTLE) has been widely used for this purpose; however, it only
approximates the flow by considering the positions of particles at the initial and final
times, ignoring the actual trajectory of the particle. To overcome this limitation, we
propose a novel quantity that extends and generalizes the FTLE by incorporating trajectory metrics as a measure of similarity between trajectories. Our proposed method
utilizes trajectory metrics to quantify the distance between trajectories, providing a
more robust and accurate measure of the LCS. By incorporating trajectory metrics, we
can capture the actual path of the particle and account for its behavior over time, resulting in a more comprehensive analysis of the flow. Our approach extends the traditional
FTLE approach to include trajectory metrics as a means of capturing the complexity of
the flow.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0221},
url = {http://global-sci.org/intro/article_detail/cicp/23613.html}
}