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Validity of the essential assumption in a projection operator method.
1Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan. okamura@rian.kyushu-u.ac.jp
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 13, 2006
Summary
The Mori projection operator method
Area of Science:
- Chaos theory
- Statistical mechanics
Background:
- The Mori projection operator method is crucial for analyzing chaotic systems.
- It relies on separating chaotic motion into coherent and fluctuating components.
Purpose of the Study:
- To validate the core assumption of the Mori projection operator method.
- To assess its applicability to chaotic systems using a specific model.
Main Methods:
- Utilized the Kuramoto-Sivashinsky equation as a model for chaotic dynamics.
- Analyzed the validity of motion separation for different wave modes.
Main Results:
- Confirmed the assumption's reasonableness for both long and short wave modes.
- Extracted the nonlinear term from the coherent motion.
- Quantified eddy viscosity as 9.0.
Conclusions:
- The Mori projection operator method's assumption is robust for the studied chaotic system.
- The calculated eddy viscosity aligns with previous estimations, supporting the method's efficacy.
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