Spatially correlated ballistic deposition on one- and two-dimensional surfaces

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Abstract
Simulations of spatially correlated ballistic deposition have been carried out using simple two- and three-dimensional lattice models. In these models particles are deposited, one at a time, from the ends of the steps in a Levy flight taking place in a line or plane above the surface of the deposit. For deposition on a line, the exponent α that describes the dependence of ξ (the surface width) on the lateral system size (L) is given by α=(1/2 for f≤1/2 and α=(1/2+(f- 1) / 2 )/3 for (1/2≤f≤2. Here f is the fractal dimensionality of the Levy flight. For deposition with transfer of the deposited particle (site) to the nearest local minimum (deposition with restructuring), α=(1/2(1+f) for 0≤f≤1 and α=1 for f>1. For deposition onto a plane the uncertainties are much larger, but our results suggest that α≃0.36 for f≤1 and that α grows linearly to a value of about (1/2 for f in the range 1≤f≤2. For deposition onto a plane with restructuring, α≃f/2. All of our simulation results are consistent with the scaling relationships α+α/β=2 for deposition without restructuring and α/β=2 for deposition with restructuring. Overall, our results are in good agreement with the theoretical predictions of Medina et al. [Phys. Rev. A 39, 3053 (1989)].