Lead clusters computational process

In order to characterize the interaction between different clusters, it is necessary to consider the mechanism of cluster identification during the process of the DA algorithm. As the temperature (Tk) is reduced after every iteration, the system undergoes a series of phase transitions (see (18) for details). In this annealing process, at high temperatures that are above a pre-computable critical value, all the lead compounds are located at the centroid of the entire descriptor space, thereby there is only one distinct location for the lead compounds. As the temperature is decreased, a critical temperature value is reached where a phase transition occurs, which results in a greater number of distinct locations for lead compounds and consequently finer clusters are formed. This provides us with a tool to control the number of clusters we want in our final selection. It is shown (18) for a square Euclidean distance d(xi,rj) = x, — rj that a cluster Rj splits at a critical temperature Tc when twice the maximum eigenvalue of the posterior covariance matrix, defined by Cx rj =... 

Excitation of the coupled A2, Bi states results in the decay rate designated X3 which appears to be nearly independent of cluster size. A small increase in the value of x3 appears to occur for (S02)m clusters from the monomer (0.6 ps) to the dimer (0.9 ps), but remains constant at about 1 ps for larger cluster sizes. A likely interpretation of the observed decay process can be found in a detailed computational study [6] which reports that following the initial vertical excitation of the 1 B state, the excited state wave packet travels from the Bi state into the double wells that result from the crossing of the 1A2 and Bi states. The transition of the excited state population into the double wells of the A2 and B states is believed to lead to the decay observed in the pump-probe experiment because the potential energy well minima of both of these states are outside of Franck-Condon region for the absorption of the probe laser pulse. Therefore, ion signal is not observed once the transition has occurred. The primary discrepancy between the computational results of Ref. [6] and the... 

Both analytic theory and computer simulations are included, and we note that the latter play an especially important role in understanding cluster reactions. Simulations not only provide quantitative results, but they provide insight into the dominant causes of observed behavior, and they can provide likelihood estimates for assessing qualitatively distinct mechanisms that can be used to explain the same experimental data. Simulations can also lead to a greater understanding of dynamical processes occurring in clusters by calculating details which cannot be observed experimentally. 

More recently, percolation theory and computer simulation of the dissolution process was applied. This latter approach resulted in 2D and 3D percolation thresholds (that is, composition thresholds at which infinite connected paths of the fast dissolving component were formed) as well as in images of the atomic scale disorder induced by dealloying. 3D site percolation thresholds 20 at.% in a fee lattice), leading to an infinite connected cluster of nearest neighbors of less noble atoms, were considered to correlate with the absolute parting limits of alloys with high such as... 

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