Scaling function for surface width for free boundary conditions.

Abstract

We study the restricted curvature model with both periodic and free boundary conditions and show that the scaling function of the surface width depends on the type of boundary conditions. When the free boundary condition is applied, the surface width shows a new dynamic scaling whose asymptotic behavior is different from the usual scaling behavior of the self-affine surfaces. We propose a generalized scaling function for the surface width for free boundary conditions and introduce a normalized surface width to clarify the origin of the superrough phenomena of the model.