几种基底上离散生长模型动力学标度行为的理论研究

发布时间：2018-07-10 11:23

本文选题：动力学标度行为 + Das　；参考：《中国矿业大学》2017年硕士论文

【摘要】：近年来,对非平衡条件下材料表面界面动力学粗化过程的研究引起了研究人员的广泛关注。本文运用直接标度分析和Kinetic Monte-Carlo数值模拟的方法对几种基底上离散生长模型的动力学标度行为进行了研究,并在微观上对引起这些动力学标度行为的物理机制进行了讨论。主要工作分为以下三部分:首先,为了探讨Das Sarma-Tamborenea (DT)模型的奇异动力学标度行为以及不同维数所属的普适类,采用Kinetic Monte-Carlo数值模拟的方法对1+1维和2+1维DT模型在欧几里得基底上的生长过程进行了大尺寸及长时间的数值模拟。并且引入了噪声衰减技术来减小渡越行为对生长过程的影响。模拟结果显示:1+1维DT模型表现出正常的动力学标度性质,属于Lai-Das Sarma-Villain (LDV)方程所描述的普适类。该结果澄清了以往工作对1+1维DT模型所属普适类的争论,并且从数值模拟的角度验证了局域坡度理论的正确性。而2+1维DT模型则属于Edwards-Wilkinson (EW)方程所描述的普适类。其次,为了探究分形基底的微观结构对离散模型动力学标度行为的影响,提出了非守恒噪声和守恒噪声驱动下广义的线性分数阶Langevin方程,(?)h/(?)t=(-1)n+1v%絥zrwh,并利用直接标度分析方法对方程的动力学标度行为进行了理论解析。研究结果表明:在非守恒噪声条件下,当n=1和2时,结果分别与分形的EW方程和分形的Mullins-Herring (MH)方程相同,并且可以被相应的数值模拟结果所验证。在守恒噪声条件下,n = 1,2,3时,满足标度关系2α +df=(n-1)zrw 。最后,为了进一步深入了解离散模型的动力学生长规则和基底结构之间的关系,对受限固-固模型在蜂巢晶格和正方-八边形晶格基底上的动力学标度行为进行了数值模拟。模拟结果显示:受限固-固模型的生长过程仍然遵循Family-Vicsek的标度规律。通过计算表面宽度得到的动力学标度指数表明,模型在两种新型晶格基底上的生长表面比欧几里得基底更加粗糙,但比分形基底更加光滑。深入分析发现,受限固-固模型在蜂巢晶格基底和正方-八边形晶格基底上饱和表面的标度行为主要由配位数决定。本文的研究,使我们对引起几种基底上离散模型动力学标度行为的物理机制有了更加深入的认知,这对改善材料的性质有着非常重要的意义。
[Abstract]:In recent years, the research on the coarsening process of interfacial dynamics of materials under non-equilibrium conditions has attracted extensive attention of researchers. In this paper, the dynamic scaling behavior of several discrete growth models on substrates is studied by means of direct scale analysis and Kinetic Monte-Carlo numerical simulation, and the physical mechanisms that cause these dynamic scaling behaviors are discussed microscopically. The main work is divided into the following three parts: firstly, in order to study the singular dynamic scaling behavior of Das Sarma-Tamborenea (DT) model and the universal classes of different dimensions, Kinetic Monte-Carlo method is used to simulate the growth process of 11 and 21 D DT models on Euclidean substrates. The noise attenuation technique is introduced to reduce the influence of the transition behavior on the growth process. The simulation results show that the 1: 11 dimensional DT model shows normal dynamic scaling properties and belongs to the universal class described by the Lai-Das Sarma-Villain (LDV) equation. This result clarifies the argument that the 11-dimensional DT model belongs to the universal class in the past, and verifies the correctness of the local slope theory from the point of view of numerical simulation. The 21-dimensional DT model belongs to the general class described by the Edwards-Wilkinson (EW) equation. Secondly, in order to explore the influence of the microstructure of the fractal substrate on the dynamic scaling behavior of the discrete model, In this paper, a generalized linear fractional Langevin equation driven by nonconserved noise and conserved noise, (?) h / t = (-1) n 1v% zrwh. the dynamic scaling behavior of the equation is theoretically analyzed by means of direct scaling analysis. The results show that the results are the same as the fractal EW equation and the fractal Mullins-Herring (MH) equation under the condition of non-conserved noise, and can be verified by the corresponding numerical simulation results. Under the condition of conserved noise, n = 1g 2,3, the scaling relation 2 伪 DF = (n-1) zrw.) is satisfied. Finally, in order to further understand the relationship between the dynamic growth rules of the discrete model and the substrate structure, the dynamic scaling behavior of the confined solid-solid model on the honeycomb lattice and the square-octagonal lattice is numerically simulated. The simulation results show that the growth process of the confined solid-solid model still follows the scaling law of Family-Vicsek. The kinetic scaling index obtained by calculating the surface width shows that the growth surface of the model on the two new lattice substrates is rougher than the Euclidean substrate but smoother than the fractal substrate. It is found that the scaling behavior of the saturated surface of the confined solid-solid model on the honeycomb lattice substrate and the square-octagonal lattice substrate is mainly determined by the coordination number. The research in this paper makes us have a deeper understanding of the physical mechanism that causes the dynamic scaling behavior of several discrete models on the substrate, which is of great significance to improve the properties of materials.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB30

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