In order to study statistical properties of surface fluctuation in a Wolf-Villain(WV) model。maximal-and minimal-heigIlt distributions(MAHD and MIHD) of saturated surfaces in a(1+1)-dimensional WV model are investigated with theory of extreme value statistics.It shows that both MAHD and MIHD csn be fitted well with universal functions of different system sizes.They are asymmetrical.MAHD takes on a generalized Fisher-Tippett-Gumbel(FTG) distribution,a typical extreme value distribution function.MIHD,however,displays a slightly different distribution,a modified FTG distribution.

Roughness distributions of 1+1 dimensional noisy Kuramoto-Sivashinsky(KS) equation at steady states are obtained and compared with Kardar-Parisi-Zhang(KPZ) equation's with numerical simulation.It is shown that the scaling functions of roughness distributions of the noise KS equation in 1+1 dimensions show small finite-size effects.They are in good agreement with the Kardar-Parisi-Zhang(KPZ) equation's.

Scaling of time-fractional Edwards-Wilkinson (TFEW) equation in 1+1 dimensions is investigated with numerical simulation and scaling analysis. It is found that the growth exponents obtained by numerical solution based on Caputo-type fractional derivative are consistent with scaling analysis.

1+1 dimensional Wolf-Villain model for molecular-beam epitaxy(MBE) growth is investigated with kinetic Monte-Carlo simulation in large scale and during long growth time so that crossover effects are eliminated.Global and local dynamic exponents are obtained.It is shown that Wolf-Villain model in 1+1 dimensions exhibits intrinsic anomalous scaling behavior in time and length simulated.The result is inconsistent with theoretical analysis by López.

A lattice kinetic Monte Carlo model for nano-crystal growth is presented and discussed in detail. As an example, we performed case studies of thin film growth. The result shows that an alteration of three-dimensional (3D) Ehrlich-Schwoebel (ES)barrier leads to shape transition of islands with multiple atomic layers in thin film growth.