Dynamics and scaling of one-dimensional surface structures

We study several one-dimensional step flow models. Numerical simulations sh ow that the slope of the profile exhibits scaling in all cases. We apply a scaling ansatz to the various step flow models and investigate their long t ime evolution. This evolution is described in terms of a continuous step de nsity function, which scales in time according to D(x,t)=F(xt(-1/gamma)). T he value of the scaling exponent gamma depends on the mass transport mechan ism. When steps exchange atoms with a global reservoir the value of gamma i s 2. On the other hand, when the steps can only exchange atoms with neighbo ring terraces, gamma=4. We compute the step density scaling function for th ree different profiles for both global and local exchange mechanisms. The c omputed density functions coincide with simulations of the discrete systems . These results are compared to those given by the continuum approach of Mu llins.