本文選題：動力學(xué)標(biāo)度行為 + Das　； 參考：《中國礦業(yè)大學(xué)》2017年碩士論文

【摘要】：近年來,對非平衡條件下材料表面界面動力學(xué)粗化過程的研究引起了研究人員的廣泛關(guān)注。本文運用直接標(biāo)度分析和Kinetic Monte-Carlo數(shù)值模擬的方法對幾種基底上離散生長模型的動力學(xué)標(biāo)度行為進(jìn)行了研究,并在微觀上對引起這些動力學(xué)標(biāo)度行為的物理機(jī)制進(jìn)行了討論。主要工作分為以下三部分:首先,為了探討Das Sarma-Tamborenea (DT)模型的奇異動力學(xué)標(biāo)度行為以及不同維數(shù)所屬的普適類,采用Kinetic Monte-Carlo數(shù)值模擬的方法對1+1維和2+1維DT模型在歐幾里得基底上的生長過程進(jìn)行了大尺寸及長時間的數(shù)值模擬。并且引入了噪聲衰減技術(shù)來減小渡越行為對生長過程的影響。模擬結(jié)果顯示:1+1維DT模型表現(xiàn)出正常的動力學(xué)標(biāo)度性質(zhì),屬于Lai-Das Sarma-Villain (LDV)方程所描述的普適類。該結(jié)果澄清了以往工作對1+1維DT模型所屬普適類的爭論,并且從數(shù)值模擬的角度驗證了局域坡度理論的正確性。而2+1維DT模型則屬于Edwards-Wilkinson (EW)方程所描述的普適類。其次,為了探究分形基底的微觀結(jié)構(gòu)對離散模型動力學(xué)標(biāo)度行為的影響,提出了非守恒噪聲和守恒噪聲驅(qū)動下廣義的線性分?jǐn)?shù)階Langevin方程,(?)h/(?)t=(-1)n+1v%絥zrwh,并利用直接標(biāo)度分析方法對方程的動力學(xué)標(biāo)度行為進(jìn)行了理論解析。研究結(jié)果表明:在非守恒噪聲條件下,當(dāng)n=1和2時,結(jié)果分別與分形的EW方程和分形的Mullins-Herring (MH)方程相同,并且可以被相應(yīng)的數(shù)值模擬結(jié)果所驗證。在守恒噪聲條件下,n = 1,2,3時,滿足標(biāo)度關(guān)系2α +df=(n-1)zrw 。最后,為了進(jìn)一步深入了解離散模型的動力學(xué)生長規(guī)則和基底結(jié)構(gòu)之間的關(guān)系,對受限固-固模型在蜂巢晶格和正方-八邊形晶格基底上的動力學(xué)標(biāo)度行為進(jìn)行了數(shù)值模擬。模擬結(jié)果顯示:受限固-固模型的生長過程仍然遵循Family-Vicsek的標(biāo)度規(guī)律。通過計算表面寬度得到的動力學(xué)標(biāo)度指數(shù)表明,模型在兩種新型晶格基底上的生長表面比歐幾里得基底更加粗糙,但比分形基底更加光滑。深入分析發(fā)現(xiàn),受限固-固模型在蜂巢晶格基底和正方-八邊形晶格基底上飽和表面的標(biāo)度行為主要由配位數(shù)決定。本文的研究,使我們對引起幾種基底上離散模型動力學(xué)標(biāo)度行為的物理機(jī)制有了更加深入的認(rèn)知,這對改善材料的性質(zhì)有著非常重要的意義。
[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 偽 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.
【學(xué)位授予單位】：中國礦業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TB30

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相關(guān)期刊論文 前3條

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本文編號：2113239