Parallelization of kinetic Monte Carlo algorithm to simulate AL3Sc precipitation

The present paper reports the precipitation process of Al3Sc structures in an aluminum scandium alloy, which has been simulated with a synchronous parallel kinetic Monte Carlo (spkMC) algorithm. The spkMC implementation is based on the vacancy diffusion mechanism. To filter the raw data generated by the spkMC simulations, the density-based clustering with noise (DBSCAN) method has been employed. spkMC and DBSCAN algorithms were implemented in the C language and using MPI library. The simulations were conducted in the SeARCH cluster located at the University of Minho. The Al3Sc precipitation was successfully simulated at the atomistic scale with the spkMC. DBSCAN proved to be a valuable aid to identify the precipitates by performing a cluster analysis of the simulation results. The achieved simulations results are in good agreement with those reported in the literature under sequential kinetic Monte Carlo simulations (kMC). The parallel implementation of kMC has provided a 4x speedup over the sequential version.

On the Hill estimator: a comparison of methods

Extreme value theory (EVT) deals with the occurrence of extreme phenomena. The tail index is a very important parameter appearing in the estimation of the probability of rare events. Under a semiparametric framework, inference requires the choice of a number k of upper order statistics to be considered. This is the crux of the matter and there is no definite formula to do it, since a small k leads to high variance and large values of k tend to increase the bias. Several methodologies have emerged in literature, specially concerning the most popular Hill estimator (Hill, 1975). In this work we compare through simulation well-known procedures presented in Drees and Kaufmann (1998), Matthys and Beirlant (2000), Beirlant et al. (2002) and de Sousa and Michailidis (2004), with a heuristic scheme considered in Frahm et al. (2005) within the estimation of a different tail measure but with a similar context. We will see that the new method may be an interesting alternative.