“…Sometimes it will be instructive to introduce "excess densities" δρ = ρ -ρeq or equivalently δn(i,j) = n(i,j) -neq. In this mapping between discrete and continuous models, the deposition rate per unit area in the continuum model is given by F = a -2 F, or Fti = a -2 Fti, and the terrace diffusion rate satisfies D = a 2 h. Below, we shall see that there is some ambiguity or flexibility in mapping discrete onto continuous models which result in slightly different expressions for K ± and P. Also, in the discrete model, there is potentially a significant contribution to step propagation velocity from adatoms depositing directly at the step edge (i.e., at the row of sites directly adjacent to the step edge) [21]. The precise form of this contribution is tied to the definition of K ± .…”