Decay of one-dimensional surface modulations

The relaxation process of one-dimensional surface modulations is re-examine d. Surface evolution is described in terms of a standard step flow model. N umerical evidence that the surface slope D(x,t) obeys the scaling ansatz D (x, t) = alpha (t)F(x) is provided. We use the scaling ansatz to transform the discrete step model into a continuum model for surface dynamics. The mo del consists of differential equations for the functions alpha (t) and F(x) . The solutions of these equations agree with simulation results of the dis crete step model. We identify two types of possible scaling solutions. Solu tions of the first type have facets at the extremum points, while in soluti ons of the second type the facets are replaced by cusps. Interactions betwe en steps of opposite signs determine whether a system is of the first or se cond type. Finally, we relate our model to an actual experiment and find go od agreement between a measured atomic force microscope snapshot and a solu tion of our continuum model.