The model is based on a kinetic mean field (KMF) approach but we made it stochastic by introducing dynamic Langevin noise. The result is a stochastic kinetic mean field model (SKMF) which gives similar results as lattice kinetic Monte Carlo (KMC). SKMF is, however, far more cost-effective and easier to realize the algorithm (open source program code is provided). The result of one SKMF run may be corresponded to the average of several KMC runs. The number of KMC runs is inversely proportional to the amplitude square of the noise in SKMF. This makes SKMF an ideal tool also for statistical purposes.
The model can be generalized to e.g. vacancy mechanism, ternary (etc.) systems, where SKMF will be even more efficient compared to KMC. We intend to keep developing the model and publish also the codes of the new algorithms as open source.
Introduction of the model
This article introduces the main concept of the model. To check and illustrate the effectiveness of SKMF, we applied it to the two examples (hover/click on the images to start movies):
Erdélyi Z, Pasichnyy M, Bezpalchuk V, Tomán J, B. Gajdics, Gusak A, Stochastic Kinetic Mean Field Model, Computer Physics Communications 204: pp. 31-37. (2016) (available online: http://dx.doi.org/10.1016/j.cpc.2016.03.003)