Interparticle interaction and structure of deposits for competitive model in (2+1)- dimensions

A competitive (2+1)-dimensional model of deposit formation, based on the combination of random sequential absorption deposition (RSAD), ballistic deposition (BD) and random deposition (RD) models, is proposed. This model was named as RSAD$_{1-s}$(RD$_f$BD$_{1-f}$)$_s$. It allows to consider different cases of interparticle interactions from complete repulsion between near-neighbors in the RSAD model ($s=0$) to sticking interactions in the BD model ($s=1, f=0$) or absence of interactions in the RD model ($s=1$, $f=0$). The ideal checkerboard ordered structure was observed for the pure RSAD model ($s=0$) in the limit of $h \to \infty$. Defects in the ordered structure were observed at small $h$. The density of deposit $p$ versus system size $L$ dependencies were investigated and the scaling parameters and values of $p_\infty=p(L=\infty)$ were determined. Dependencies of $p$ versus parameters of the competitive model $s$ and $f$ were studied. We observed the anomalous behaviour of the eposit density $p_\infty$ with change of the inter-particle repulsion, which goes through minimum on change of the parameter $s$. For pure RSAD model, the concentration of defects decreases with $h$ increase in accordance with the critical law $\rho\propto h^{-\chi_{RSAD}}$, where $\chi_{RSAD} \approx 0.119 \pm 0.04$.Comment: 10 pages,4 figures, Latex, uses iopart.cl

Percolation in deposits for competitive models in (1+1)-dimensions

The percolation behaviour during the deposit formation, when the spanning cluster was formed in the substrate plane, was studied. Two competitive or mixed models of surface layer formation were considered in (1+1)-dimensional geometry. These models are based on the combination of ballistic deposition (BD) and random deposition (RD) models or BD and Family deposition (FD) models. Numerically we find, that for pure RD, FD or BD models the mean height of the percolation deposit $\bar h$ grows with the substrate length $L$ according to the generalized logarithmic law $\bar h\propto (\ln (L))^\gamma$, where $\gamma=1.0$ (RD), $\gamma=0.88\pm 0.020$ (FD) and $\gamma=1.52\pm 0.020$ (BD). For BD model, the scaling law between deposit density $p$ and its mean height $\bar h$ at the point of percolation of type $p-p_\infty \propto \bar h^{-1/\nu_h}$ are observed, where $\nu_h =1.74\pm0.02$ is a scaling coefficient. For competitive models the crossover, %in $h$ versus $L$ corresponding to the RD or FD -like behaviour at small $L$ and the BD-like behaviour at large $L$ are observed.Comment: 8 pages,4 figures, Latex, uses iopart.cl