Kinetic Monte Carlo Simulations at Spatiotemporal Scales of Experiments

In comparison with MD, the kinetic Monte Carlo (kMC) method allows the treatment of much larger systems for much longer time periods on the atomistic level. Implementing the kMC method as a stochastic probabilistic cellular automaton according to the definition of Steven Wolfram, the simulations can be performed with many-body potentials projected onto a lattice, and a bit-coding makes the calculations extremely fast. Additionally, by Massively Parallel Programming (MPP) using NVIDIA graphic cards with CUDA programming, we accelerated kMC simulations by almost two orders of magnitude. Other than for finite element and MD codes, MPP cannot be straightforward implemented for the stochastic probabilistic Markov chain of kMC. We have extended the recently by Tobias Preis developed MPP method (Ising model with spin-flip kinetics) to much more complex conservative cellular automata with Kawasaki exchanges. Based on these methodological developments, we present large-scale simulations on the self-organization of surface nanopatterns under ion irradiation and on the scaling behavior of nanosponge formation.