However these methods may face unaffordable computation loads when simulating

However these methods may face unaffordable

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However, these methods may face unaffordable computation loads when simulating complex systems with many competing events during the material evolution. The reason is that for a complex non-equilibrium process, each minimum energy state is connected to many other states, each new observed state is connected to more states, and so on. Therefore, such a breadth- first search algorithm can easily become very expensive com- putationally. For example, in a recent study on the annihilation of a dislocation-dipole [ 22 ], Wang et al showed that the ART could not drive the system to the final state due to the ‘very high computational load’, and had to employ the ABC method to observe the dipole dissociation processes. The ABC algorithm is also based on the activation-relax- ation procedure, and explores and reconstructs the system’s potential energy surface. It was developed by Kushima et al in computing the viscosity of supercooled liquids [ 14 ], and is inspired by Laio and Parrinello’s idea of escaping from the free- energy minima [ 23 ]. By adding a series of penalty functions into the given basin on the PES, the ABC algorithm evolves the system along the pathway that has the lowest energy bar- rier without prior assumption of the reaction coordinates. This feature enables the ABC method to capture the dominant path- ways of system evolution, where the states are connected in series over a 1D chain. Recently, Cao et al further optimized the ABC method by introducing a self-learning algorithm [ 24 ], which can significantly reduce the computational cost. The implementation of the ABC algorithm is technically straight- forward, and has been demonstrated to accurately capture the mechanism and kinetics of a series of unit processes, including the unfaulting of a self-interstitial atom (SIA) cluster in bcc Fe [ 25 ], the structure of a vacancy cluster in fcc Al [ 26 ], and the dislocation motion and structure [ 22 , 27 ] and interaction of dislocation with obstacles in both hcp Zr and bcc Fe [ 28 , 29 ]. However, when there are multiple competitive processes simultaneously, because of the 1D nature of the system evolu- tion, the original ABC method overestimates the system evolu- tion time [ 30 32 ]. This paper extends the ABC algorithm so that it can now capture multiple competing transition pathways from each minimum energy state explored on the PES. In this paper, we discuss the underlying reason for overesti- mating the evolution time by comparing the original ABC method with analytical transition state theory (TST) and kMC results. We describe the new algorithm that extends ABC (ABC-E) to capture multiple transition pathways from an individual basin on the PES. The ABC-E algorithm is benchmarked against the ana- lytical results on a hypothetical rough PES. We also demonstrate the prioritization of sampled paths by ABC-E and the relative computational efficiency by comparing the ABC-E method and ART in the simulation of vacancy migration in hcp Zr.
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  • Summer '19
  • Transition state, KMC

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