Extensive numerical study of the anomalous dynamic scaling of the Wolf–Villain model

In order to study the microscopic physical mechanisms of roughness surfaces exhibiting the anomalous scaling behavior, the Wolf–Villain model in 1+1 and 2+1 dimensions is investigated by the kinetic Monte-Carlo simulation on long time and large length scale (the growth time and the system size are respectively extended to t=229, L=400000 for 1+1 dimensions, and t=221, L×L=512×512 for 2+1 dimensions). In the 2+1-dimensional simulations, the noise reduction technique is employed so as to eliminate the crossover effects in the growth process. Our calculations show that the Wolf–Villain model in 1+1 dimensions very probably exhibits intrinsic anomalous scaling behavior in the time and length simulation range of this paper, and the 2+1-dimensional Wolf–Villain model leads to a pyramidal mounded morphology. Some properties of the mounded pattern in the 2+1-dimensional Wolf–Villain model are discussed in the final part of this presentation.