Kui Han

Dynamic scaling behaviors of the Etching model on fractal substrates

The dynamic scaling behaviors of the Etching model on fractal substrates are studied by means of Kinetic Monte Carlo simulations. Surface width and distributions of relative extremal height in the saturated surfaces are calculated respectively. Our results indicate that the structure of the substrates can affect the dynamic scaling properties of the surfaces and interfaces. Specially, the saturated properties of the surface, i.e. the roughness exponents α, are mainly determined by the dynamic exponents of random walk zRW on fractal lattices. In addition, it is shown that the relative extremal height of the saturated surfaces can be fitted by Asym2Sig (asymmetric double sigmoidal) distribution.

CONFORMAL INVARIANCE OF CONTOUR LINES ON THE (2 + 1)-DIMENSIONAL RESTRICTED SOLID-ON-SOLID SURFACE

The contour lines of the saturated surface of the (2 + 1)-dimensional restricted solid-on-solid (RSOS) growth model are investigated by numerical method. It is shown that the calculated contour lines are conformal invariant curves with fractal dimension df = 1.34, and they belong to the universality class at large-scale limit, called the Schramm–Loewner evolution with diffusivity κ = 4. This is identical to the value obtained from the inverse cascade of surface quasigeostrophic (SQG) turbulence [Phys. Rev. Lett.98 (2007) 024501]. We also found that the measured fractal dimensions of contours on the (2 + 1)-dimensional RSOS saturated surfaces do not coincide well with that of SLE4 df = 1 + κ/8.

SCALING APPROACH TO ANOMALOUS SURFACE ROUGHENING OF THE (d+1)-DIMENSIONAL MOLECULAR-BEAM EPITAXY GROWTH EQUATIONS

To determine anomalous dynamic scaling of continuum growth equations, Lopez12 proposed an analytical approach, which is based on the scaling analysis introduced by Hentschel and Family.15 In this work, we generalize this scaling analysis to the (d+1)-dimensional molecular-beam epitaxy equations to determine their anomalous dynamic scaling. The growth equations studied here include the linear molecular-beam epitaxy (LMBE) and Lai–Das Sarma–Villain (LDV). We find that both the LMBE and LDV equations, when the substrate dimension d>2, correspond to a standard Family–Vicsek scaling, however, when d<2, exhibit anomalous dynamic roughening of the local fluctuations of the growth height. When the growth equations exhibit anomalous dynamic scaling, we obtain the local roughness exponents by using scaling relation αloc=α-zκ, which are consistent with the corresponding numerical results.