Time-Dependent Particle Densities in Finite Particle Deposition Systems

Abstract: This paper contains calculations of the time-dependent particle densities in multi-layer particle deposition systems without screening. Several calculation methods are used. These methods can be used to calculate densities in all layers and are demonstrated with a number of examples. The densities in deposition systems of size 3 and 5 are calculated up to the third layer. It is also proven that border sites tend to have a higher density than sites in the middle. This partly explains why finite-sized systems tend to reach higher packing densities in higher layers than in low layers.