Kinetic simulations cluster approximation

Despite its severe limitations, the model shows interesting behavior, including kinetic phase transitions of two types continuous (second order) and discontinuous (first order). These phenomena are observed in many catalytic surface reactions. For this reason, the ZGB model has been widely studied and serves as a starting point for many more realistic models. This forms the first reason why we discuss the ZGB model in this section. The second reason is that MC simulations and mean-field (MF) solutions for this model give different results. Cluster approximations to the MF solutions offer a better agreement between the two methods, and then only small discrepancies remain. The ZGB model is therefore a nice example to illustrate the differences between the two approaches. 

Master equations have been used to describe relaxation and kinetics of clusters. The first approaches were extremely approximate, and served primarily as proof-of-principle. ° Master equations had been used to describe relaxation in models of proteins somewhat earlier and continue to be used in that context. " More elaborate master-equation descriptions of cluster behavior have now appeared. These have focused on how accurate the rate coefficients must be in order that the master equation s solutions reproduce the results of molecular dynamics simulations and then on what constitutes a robust statistical sample of a large master equation system, again based on both agreement with molecular dynamics simulations and on the results of a full master equation.These are only indications now of how master equations may be used in the future as a way to describe and even control the behavior of clusters and nanoscale systems of great complexity. ... 

Figure 8. Distributions of local K-entropy, vibrational mode-mode coupling, mean kinetic energy and negative curvature of the potential for the three-particle Lennard-Jones cluster simulating Ar3 at constant energy. The energy of the cluster corresponds to a temperature of approximately 30 K. [Reprinted with permission from R. J. Hinde and R. S. Berry, J. Chem. Phys. 99, 2942 (1993). Copyright 1993, American Institute of Physics.]...

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