Numerical Simulation Of The Dynamic Scaling Of Equilibrium Restricted Curvature Model And Etching Model On Some Fractal Substrates

The kinetic growth phenomena are related to a wide variety of practical growth process. Based on various continuum growth equations and discrete growth models, there were great progresses for non-equilibrium growth on the Euclidean substrates. With the development of fractal theory, people began to investigate the dynamic behaviors of kinetic growth phenomena on fractal substrates. The dynamic behaviors of the interfaces of Equilibrium restricted curvature(ERC) model and Etching model on the non-complete substrates are investigated by numerical simulation. The main results are as follows:1) The Equilibrium restricted curvature(ERC) model on fractal substrates exhibit excellent dynamic scaling behavior and the Family-Viseck scaling law is still satisfied. The exponents of ERC model on fractal substrates are consistent with the results of the fractional MH equation, implying that the ERC model for growth on a fractal substrate can be described by the fractional MH equation.2) For the Etching model on fractal substrates, the Kardar-Parisi-Zhang(KPZ) equation valid in Euclidean substrates cannot be used to describe the growth process on fractal substrates. The roughness exponent increases with the random walk exponent on fractal substrates, meanwhile the growth exponent exhibits more complex behavior.3) We also analysis the distributions of relative extreme height in the saturated surfaces and the results show that the maximal height of the saturated width can be fitted by Asym2 Sig distribution, not by three kinds of usual extreme statistical distributions, which are Weibull,Gumbel, and Frechet distribution.From the investigation of this thesis, we have a further understanding about the dynamic scaling behavior of discrete growth models on various fractal substrates, which is of importance for establishing more perfect theoretical function and discrete growth models.