are directly connected to the original state and if r c is too large the

Are directly connected to the original state and if r

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are directly connected to the original state, and if r c is too large, the simulation might include unphysical transitions. Regardless of the precise accuracy of the kMC method, the comparison in figure  3 ( b ) demonstrates that the time overesti- mation in the original ABC algorithm is due to the 1D nature of the identified transitions, rather than an inherent limitation of finding the dominant pathway. In particular for non-equilibrium processes, the ABC method has been shown to be able to find the governing evo- lution pathways. For instance, in our recent work [ 29 ] in simu- lating dislocation-defect interactions in metals as a function of strain rate and temperature, it is demonstrated that ABC gives exactly the same mechanism and kinetics as MD simula- tions in the fast strain-rate regime, and in the slow strain-rate regime, it gives results that are credible and consistent with experiments. Another recent study by Wang, et al [ 22 ] on the annihilation of dislocation dipoles also shows that ABC could well explain the observations from experiments. In another example simulating the vacancy-clustering process, both ABC [ 31 ] and k-ART [ 30 ] give the void nucleation and growth behavior similarly, and the key difference is the time scales predicted by the two methods. (ABC as the one overes- timating the timescale.) 2.3. Extension of the ABC (ABC-E) method to sample multiple transition pathways To address the concern over the time overestimation explained above, the ABC method is modified by the following algo- rithm to sample multiple transition pathways in the system evolution: 1. For a given initial state, apply the original ABC algorithm steps until the first neighboring state is observed. Each original ABC step consists of two stages—activation and relaxation. During the activation stage, a penalty function in Gaussian form [ 14 ] is added into the given basin on PES. The activation is then followed by a relaxation stage to minimize the energy of the system. In the examples studied in this work, each relaxation stage consists of 500 force evaluations through the steepest descent method. 2. Record the new state, and put the system back to the previous state. 3. Add a blocking penalty function (also in Gaussian form) on the previously observed saddle point. The detailed parameters of the blocking penalty function are shown in the beginning of section  3 for the studied system in this paper. 4. Implement regular ABC steps until the next new minimum energy state is observed. 5. Judge whether a new state or a previously visited state is found: (a) if it is a previously visited state, then put the system back to the previous state, and add an additional blocking function on the saddle point; restart step 4. (b) if it’s a new state, go to step 2.
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  • Summer '19
  • Transition state, KMC

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