Roughness scaling and sensitivity to initial conditions in a symmetric restricted ballistic deposition model

摘要

In this work, we introduce a restricted ballistic deposition model with symmetric growth rules that favors the formation of local finite slopes. It is the simplest model which, even without including a diffusive relaxation mode of the interface, leads to a macroscopic groove instability. By employing a finitesize scaling of numerical simulation data, we determine the scaling behavior of the surface structure grown over a one-dimensional substrate of linear size L. We found that the surface profile develops a macroscopic groove with the asymptotic surface width scaling as w_(sat) ∝ L~α, with α = 1. The early-time dynamics is governed by the scaling law w ∝ t~β, with β = 1/2. We further investigate the sensitivity to initial conditions of the present model by applying damage spreading techniques. We find that the early-time distance between two initially close surface configurations grows in a ballistic fashion as D ∝ t, but a slower Brownian-like scaling (D ∝ T~(1/2)) sets up for evolution times much larger than a characteristic time scale t_x ∝ L~2.