A model of random deposition with relaxation on fractal substrates

A model of random deposition with relaxation on both Sierpinski gasket and checkerboard fractal substrates is studied. The interface width W grows as tβ at early time t and it follows Lα for the saturated regime t>>Lz, where L is the system size. We obtain β≈0.158, α≈0.374 for the Sierpinski gasket and β≈0.203, α≈0.507 for the checkerboard fractal. The dynamic exponent z≈2.35 for the Sierpinski gasket and z≈2.50 for the checkerboard fractal were obtained by using the relation z = α/β. They satisfy the scaling relation 2α + df = z, where df is the fractal dimension of the substrate, and they are in good agreement with the predictions of a fractional Langevin equation