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Updated: Mar 13, 2026
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
671
Finite-size Lyapunov exponent for Levy processes.
1Department of Civil Engineering, Purdue University, West Lafayette, Indiana 47907, USA.
Summary
The finite-size Lyapunov exponent (FSLE) quantifies particle separation in chaotic systems. For Levy motion, FSLE relates to diffusion and particle distance, aiding superdiffusion analysis in environmental sciences.
Area of Science:
- Physics
- Environmental Science
- Mathematics
Background:
- The finite-size Lyapunov exponent (FSLE) measures dispersive mixing in chaotic systems by tracking particle separation rates.
- Understanding particle dispersion is crucial for modeling phenomena like atmospheric and oceanic transport.
Purpose of the Study:
- To analytically derive the relationship between FSLE and parameters of symmetric alpha-stable Levy motion.
- To establish a method for determining Levy process parameters using FSLE.
- To highlight the applicability of this method to superdiffusion in environmental sciences.
Main Methods:
- Analytical derivation of the FSLE for particle trajectories governed by symmetric alpha-stable Levy motion.
- Investigating the power-law relationship between FSLE, diffusion coefficient, and initial particle separation distance (r).
Main Results:
- The FSLE is shown to be proportional to the diffusion coefficient.
- The FSLE is demonstrated to be inversely proportional to r raised to the power of alpha (r^alpha).
- A power-law relationship was established for FSLE under Levy motion.
Conclusions:
- The derived power law offers a straightforward method for determining Levy process parameters.
- This finding has significant implications for studying superdiffusion in atmospheric, oceanic, and terrestrial systems.
- FSLE serves as a valuable tool for characterizing dispersive mixing in complex natural environments.
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