Study On The Multi-scaling And Anomalous Dynamical Properties Of Villian-Lai-Das Sarma Equation

Stochastic process of surface interface growth always shows a nontrivial scaling property.In addition,the surface interface can be transformed into a stationary state which is consistent with the scale invariance in the growth dynamics.With these two characteristics,we can study the interface growth process of the material surface.On the basis of the scale invariance of the growth surface,we have the most basic theory and standard to study the growth process of the material surface,and can be widely used in the theoretical model and experimental research of the growth process.The most important framework to study the scaling behavior of surface growth dynamics is composed of self-affine fractal,scaling and universality classes,which is also the basic support of dynamic scaling theory.In this thesis,based on the scaling theory of surface roughening growth dynamics,the continuous stochastic equation of surface interface growth is studied by numerical simulation.The main research focuses on the linear MBE equation and the nonlinear VLDS equation.In the non-equilibrium system,when different critical exponents are used to scale the growth process at different times,multiple exponents phenomenon will appear,that is multiple scaling.This multiple exponents scaling behavior is nontrivial,and is related to the fractal properties of different scales.The Family-Vicsek scaling relationship has made a clear explanation for the physical mechanism of the dynamic growth process of the surface roughness of materials,and it has also been widely used in theoretical research and experimental observation.However,in recent years,a large number of theoretical and experimental studies have shown that the Family-Vicsek dynamic scaling relationship can not be sure of the local surface width.When the scaling behavior of the whole surface is different from that of the local surface,it means that the anomalous scaling behavior appears in the dynamic process of surface growth.In this thesis,the linear MBE equation and nonlinear VLDS equation are studied with multiple scaling and anomalous scaling respectively.For the linear MBE and nonlinear VLDS equations,both of them show the scaling properties of anomalous dynamics in(1+1)-dimensions.On this foundation,our attention most focus on whether the existence of infinite nonlinear term in VLDS equation affects the scaling behavior of MBE growth.In the course of our research,the continuous stochastic growth equation is discretized,and then the scaling behavior of this kind of dynamic equation is studied by numerical simulation.In the simulation of nonlinear growth equations,numerical diffusion often occurs due to the instability of nonlinear.So when we study the scaling properties of nonlinear VLDS equation,in addition to the conventional discretization of the nonlinear terms,we also introduce the exponential decay technique to control the growth instability of the VLDS system.The results show that the modified VLDS equation still belongs to the VLDS universality class.Based on the theoretical research in this thesis,it is not difficult to come to the conclusion that in the VLDS growth system,the existence of high-order nonlinear terms has little effect on the growth exponent and roughness exponent.However,with the addition of weak correlation nonlinear terms,the new nonlinear coefficient?_nneeds to be reduced appropriately,and?_n?0 when n??.Our study shows that the scaling behavior of anomalous dynamics exists in both linear MBE equation and nonlinear VLDS equation.Our results show that in the(1+1)dimension,super roughening anomalous scaling appears in the surface growth process of linear MBE equation,while the intrinsic anomalous scaling appears in the VLDS growth system.