Numerical evidence of persisting surface roughness when deposition stops

Do evolving surfaces become flat or not with time evolving when material deposition stops? As one qualitative exploration of this interesting issue, modified stochastic models for persisting roughness have been proposed by Schwartz and Edwards (2004 Phys. Rev. E 70 061602). In this work, we perform numerical simulations on the modified versions of Edwards–Wilkinson (EW) and Kardar–Parisi–Zhang (KPZ) systems when the angle of repose is introduced. Our results show that the evolving surface always presents persisting roughness during the flattening process, and sand dune-like morphology could gradually appear, even when the angle of repose is very small. Nontrivial scaling properties and differences of evolving surfaces between the modified EW and KPZ systems are also discussed.