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Updated: May 9, 2026
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Distributional ergodicity in stored-energy-driven Lévy flights
Takuma Akimoto1, Tomoshige Miyaguchi
1Department of Mechanical Engineering, Keio University, Yokohama, 223-8522, Japan. akimoto@z8.keio.jp
Summary
Stored-energy-driven Lévy flights (SEDLF) exhibit anomalous diffusion, showing subdiffusion or superdiffusion based on coupling parameters. Their diffusion coefficients are random, demonstrating aging or growth with time.
Area of Science:
- Physics
- Statistical Mechanics
- Complex Systems
Background:
- Random walks are fundamental models in statistical physics.
- Anomalous diffusion describes non-standard transport phenomena.
- Lévy flights are characterized by heavy-tailed jump distributions.
Purpose of the Study:
- To introduce and analyze the stored-energy-driven Lévy flight (SEDLF) model.
- To investigate the subdiffusion and superdiffusion behaviors of SEDLF.
- To explore the statistical properties of diffusion coefficients in SEDLF.
Main Methods:
- Analytical treatment of continuous-time random walks.
- Coupling analysis of jump lengths and trapping times.
- Examination of ensemble-averaged and time-averaged mean-square displacements.
Main Results:
- SEDLF exhibits both subdiffusive and superdiffusive regimes, controlled by a coupling parameter.
- Time-averaged mean-square displacements show linear growth, indicating distributional ergodicity.
- Diffusion coefficients are intrinsically random, exhibiting aging in subdiffusion and growth in superdiffusion.
Conclusions:
- SEDLF provides a novel framework for anomalous diffusion.
- The interplay between stored energy and trapping dynamics governs diffusion behavior.
- The model offers insights into systems with memory effects and random transport properties.
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