FIG. 1: Time-dependence of the quantities x ( t ), y ( t ) and c$_{N}$ ( t ) as results from a numerical solution of the full model, Eqs.(1), with the parameters given in the text. FIG. 2: The dimensionless growth velocity, dNc$_{N}$ dk 0 t , as a function of time for the same parameters as used in Fig. 1. The supersaturation in this case is log ( x/x $^{∗}$) ≈ − 0 . 84. In order to study both the possibility of multiple growth regimes without vanishing nucle- ation barrier and the roughening transition, we have performed Kinetic Monte Carlo simu- lations of the growth of a simple, one-dimensional surface in the spirit of the Solid-On-Solid III. ONE-DIMENSIONAL KINETIC MONTE CARLO MODEL 8