Numerical evidence for anomalous dynamic scaling in conserved surface growth

Abstract

According to the scaling idea of local slope, we investigate the anomalous dynamic scaling of a class of nonequilibrium conserved growth equations in (1+1)- and (2+1)-dimensions using numerical integration. The conserved growth models include the linear Molecular-Beam Epitaxy (LMBE), the nonlinear Villain–Lai–Das Sarma (VLDS) and Sun–Guo–Grant (SGG) equations. To suppress the instability in the VLDS and SGG equations, the nonlinear terms are replaced by exponentially decreasing functions. The critical exponents in different growth regions are obtained. Our results are consistent with the corresponding analytical predictions. The anomalous scaling properties are proved in (1+1)-dimensional LMBE and VLDS equations for Molecular-Beam Epitaxy (MBE) growth. However, anomalous roughening in the LMBE and VLDS surfaces is very weak in the physically relevant case of (2+1)-dimensions. Furthermore, we find that, in both (1+1)- and (2+1)-dimensions, anomalous scaling behavior does not appear in the SGG surface based on scaling approach and numerical evidence.