Scaling properties of self-expanding surfaces

Scaling properties of self-expanding surfaces are studied with a comparison to those of self-flattening surfaces [Phys. Rev. E 66, 040602(R) (2002)]. The evolution of self-expanding surfaces is described by a restricted solid-on-solid type monomer deposition-evaporation model in which both deposition at the globally lowest site and evaporation at the globally highest site are suppressed. We find numerically that equilibrium surface fluctuation has a scaling behavior with a roughness exponent alpha approximately 1 in one dimension (1D). In contrast, 2D equilibrium surfaces show the same dynamical scaling behavior with alpha=0 (log) and dynamic exponent z approximately 5/2 as 2D self-flattening surfaces. Stationary roughness can be understood analytically by relating the self-expanding growth model to self-repelling random walks. In the case of nonequilibrium growing/eroding surfaces, self-expanding dynamics cause the fluctuation of surfaces to be characterized by alpha approximately 1 in both 1D and 2D.