Theoretical Research Of Dynamic Scaling Behaviors Of The Discrete Growth Models On Several Substrates

The study of kinetic roughening process of growing surfaces and interfaces has been a very active research subject in none-equilibrium statistical physics and materials science in recent years. In this paper, the scaling analysis and Kinetic Monte-Carlo numerical simulation are used to study the dynamic scaling properties of the discrete growth models on several substrates, and the microphysical mechanisms for these scaling behaviors are discussed. The main work are as follows:Firstly, in order to study the anomalous scaling behavior and universality class of Das Sarma-Tamborenea (DT) model, the Kinetic Monte-Carlo method is used to simulate the growth process of DT model on large length and long time scale on the Euclidean substrate both in 1+1 and 2+1 dimensions. A noise reduction technique is utilized to get better scaling behavior. The simulation results show that DT model in 1+1 dimension exhibits normal scaling behavior and belongs to the Lai-Das Sarma-Villain (LDV) dynamic universality, which verify the correctness of the local slope theory from the point of view of numerical simulation. Further, we have found that the DT model in 2+1 dimension belongs to the Edwards-Wilkinson (EW)dynamic universality.Secondly, in order to study the effects of the microscopic details of fractal substrates on the scaling behavior of discrete model, a generalized linear fractal Langevin-type equation, (?)h/(?)t-(-1)n+1v?nzrwh, driven by nonconserved and conserved noise is proposed and investigated theoretically employing scaling analysis.The results show that under the condition of nonconserved noise, for n=1 and n=2, the results are the same as fractal EW equation and fractal Mullins-Herring(MH) equation, and can be tested by numerical results. Under the condition of conserved noise, for n?1,2, 3, the scaling relation 2??df?(n-1)zrw is satisfied.Finally, in order to make a deep understanding the interplay between the dynamic growth rules of discrete model and the structures of substrates,the dynamic scaling behaviors of the Restricted-solid-on-solid (RSOS) model on the honeycomb lattice and square-octagon lattice substrates are studied. The simulation results show that the Family-Vicsek scaling is still satisfied. The values of the roughness exponents fall between regular and fractal lattices. The surfaces of RSOS model on these two substrates are rougher than the model growth on regular lattices, and more smooth than fractal substrates. Deeper analysis show that the coordination number of the substrates play the crucial rule.The investigation of this thesis provide a deeper understanding about the physical mechanism for the different dynamic scaling behaviors of discrete model on several substrates, which is important for improving the material qualities.