Theoretical Study Of Surface And Interface Growth Dynamics

A new approach to interface growth is introduced systemically in the article, which describe fractal growth using Langevin-type equation, such as Kardar Parisi and Zhang (KPZ), molecular-beam- epitaxy ( MBE) and Sun Guo Grant (SGG) equation, and become more advantage comparing with the numerical simulation and phenomelogical model.In this approach, a nonlinear, stochastic, square differential equationis used to describe the growth process, which contain the correlational interaction between the growing cells. The dynamical Renormalization group (DRG) method are developed from the static RG, which proposed by Forster, Nelson and Stephen ( FNS) and was very effective in soloving critical phenomena. Using DRG, we solved the KPZ equation satisfy conservation law and long-range spatial and long-time correlation, the roughen and dynamic exponent was found, the roughen transition was also discussed. Moveover, we solve the unstable growth, extend KPZ equation using DRG, find local interaction make the growth unstable, and the unstable effect are so strength that long range correlation and conservation law can not change it.Direct scaling analysis approach are introduced by Honda and Family (HF). Using this approach, we study the MBE, KPZ and SGG equation, find there are two different growth regions: strong- coupling and weak-coupling region. In different region the growth is rough and smooth, respectively. We solve the scaling exponent in each region, find the dynamic RG results are exact that in weak-coupling region.and illustrate the fact that many dynamic RG results are equal to the weak -coupling results.Next, we analyse the roughen transition, which challenge many people recently. We found there is phase transition as the space dimension increase. We propose a local correlation length, which not only define the coupling but also is very important in roughen transition.The scaling function and correlation function are also studied Using mode-coupling approach. we find the scaling function and correlation function of the KPZ, MBE and SGG equation. In color noise correlation, we give the asymptotic form of the functions.The article are arranged as following: Chapter 1 give the brief review of interface growth phenomena, the numerical simulation approach and phenological model, and give a introduction of the KPZ equation approach. In chapter 2 , we devote to study the conservational KPZ equation with long-range spatial and long-time correlation. Other RG result, such as SGG, KPZ, MHKZ and HF are also given. In chapter 3 we study the unstable growth. We analyse the extend KPZ eqution using...