On the numerical accuracy of the Fokker-Planck approximation to the hierarchy of master equations
This paper deals with the process of agglomeration of atomic clusters on clean surfaces during the early stages of the thin film formation. The evolution of the size distribution of the clusters is described by moments that are derived from both the hierarchical master equation and the equivalent Fokker-Planck approximation. The accuracy of the numerical moment solutions obtained with the two formulations in the following context is analyzed: only single atoms are mobile and the dissociation rate of clusters containing two or more atoms is negligible compared to the aggregation rate. The results show that a Fokker-Planck solution is a good approximation to the corresponding master equation.
scientific article; zbMATH DE number 168641