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Adaptive minimum action method for the study of rare events.
Xiang Zhou1, Weiqing Ren, Weinan E
1Program for Applied and Computational Mathematics, Princeton University, Princeton, NJ 08540, USA. xiangz@math.princeton.edu
The Journal of Chemical Physics
|March 19, 2008
Summary
This study introduces an adaptive minimum action method to find transition paths in complex systems. The novel approach efficiently computes the most probable pathways between stable states using a moving mesh strategy.
Area of Science:
- Computational physics
- Chemical dynamics
- Materials science
Background:
- Metastable systems exhibit complex dynamics.
- Identifying transition paths is crucial for understanding system evolution.
- Existing methods may struggle with systems lacking explicit energy functions.
Purpose of the Study:
- To propose an adaptive minimum action method for computing transition paths.
- To address systems without an underlying energy function.
- To enhance the efficiency of transition path computations.
Main Methods:
- Minimizing the action functional associated with transition paths.
- Employing a moving mesh strategy for adaptive grid point adjustment.
- Developing an algorithm for computing most probable transition paths.
Main Results:
- The proposed adaptive minimum action method effectively computes transition paths.
- Numerical examples demonstrate the algorithm's efficiency.
- The method is applicable to metastable systems without explicit energy functions.
Conclusions:
- The adaptive minimum action method offers an efficient approach for transition path computation.
- This method advances the study of dynamics in complex metastable systems.
- The moving mesh strategy enhances computational performance.
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