Scaling of rough surfaces with nonlinear diffusion

Surface properties of a random-deposition model that includes the effects of surface diffusion with nonlinear diffusivity are studied in 1+1 dimensions. The nonlinear diffusivity D(h) obeys a power law ${\mathit{h}}^{\mathit{k}}$. For a sufficiently large deposit, the variation of the surface thickness with the height of deposit shows anomalous behavior for the power k. It is found that the exponent β, describing how the surface thickness grows with the height, is given by β=(1-k)/4<0 (for k>1), β=0 (for k=1), β=(1-k)/4>0 (for 1>k>0), β=1/4 (for k=0; linear diffusion), and β=1/2 (for k<0). The case of k=1 is a marginal state, and the surface thickness approaches a constant value with increasing height.