Surface growth on diluted lattices using a restricted curvature model. (7th November 2016) - Lee, Sang Bub
Abstract: Surface growth using the equilibrium restricted curvature model was studied on diluted lattices, i.e. on percolation networks, embedded in a square lattice. The growth exponent β and the roughness exponent α were measured on infinite networks for the percolation probability p c ⩽ p ⩽ 1 and backbone networks at p c, where p c is the percolation threshold. For p   =   p c, both the infinite network and backbone network are known to be fractals with fractal dimensions different from each other, whereas for p   >   p c they are Euclidean. Therefore, our work for p   =   p c is regarded as the surface growth on random fractal substrates. The results were compared to the predicted results using power counting for the fractional Herring–Mullins equation with a noise restriction modified for the fractal substrates. For p   >   p c, the exponents appeared to be similar to those for the regular lattice, whereas for p   =   p c they were consistent with the predictions for both an infinite network and a backbone network. The scaling relation 2 α + d f = z was satisfied for both cases, where d f is the fractal dimension of the substrate and z is the dynamic exponent given as z = α / β .