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

In this work, we introduce a restricted ballistic deposition model with sym metric growth rules that favors the formation of local finite slopes. It is the simplest model which, even without including a diffusive relaxation mo de of the interface, leads to a macroscopic groove instability By employing a finite-size scaling of numerical simulation data, we determine the scali ng 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) proportional to L-alpha, with alpha = 1. The early-time dynamics is governed by the scalin g law w proportional to t(beta), with beta = 1/2. We further investigate th e sensitivity to initial conditions of the present model by applying damage spreading techniques. We find that the early-time distance between two ini tially close surface configurations grows in a ballistic fashion as D propo rtional to t, but a slower Brownian-like scaling (D proportional to t(1/2)) sets up for evolution times much larger than a characteristic time scale t (x) proportional to L-2.