Roughness scaling and sensitivity to initial conditions in a symmetric restricted ballistic deposition model
Departamento de Física, Universidade Federal de Alagoas,
Maceió-AL, 57072-970, Brazil
Published online: 15 October 2000
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 .
PACS: 05.70.Np – Interface and surface thermodynamics / 68.35.Ct – Interface structure and roughness / 81.15.Aa – Theory and models of film growth
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000