Abstract:
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 finite-size 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 , with . The early-time dynamics is governed by the scaling law , with . 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 , but a slower Brownian-like scaling () sets up for evolution times much larger than a characteristic time scale .
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Received 26 May 2000
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da Silva, R., Lyra, M., da Silva, C. et al. Roughness scaling and sensitivity to initial conditions in a symmetric restricted ballistic deposition model. Eur. Phys. J. B 17, 693–697 (2000). https://doi.org/10.1007/s100510070110
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DOI: https://doi.org/10.1007/s100510070110