Dynamics of Rough Surfaces Growing on Fractal Substrates

We report computer simulation results of the restricted solid-on-solid model as a prototype of rough surface growth on various fractal substrates with fractal dimensions 1 < d f < 2. The surface width was examined to show a power law behavior such as t β with time t . We find different values of β for two substrates with the same d f , which indicates explicitly that the universality class is not determined by only the substrate dimension d f . Some resulting values of β fit fairly well with the Kim-Kosterlitz (KK) conjecture, β= 1/( d f +2), while others do not agree with it. Using the effective dimension \(\tilde{d}\) derived through the averaged neighboring cell number, we also investigate the \(\tilde{d}\) dependence of β values, so that the latter class is found to approach the KK curve, although the former is distant from it.