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, 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.