非局域Lai-Das Sarma-Villain方程动力学标度性质的研究

使用动力学重整化群和直接标度分析的方法研究了非局域Lai-Das Sarma-Villain方程的动力学标度性质.动力学重整化群分析表明非局域非线性项的存在能够导致新的固定点和连续变化的动力学标度指数的产生.使用直接标度分析方法则分别得到了在弱耦合和强耦合区内的标度指数值.在弱耦合区域内得到的标度指数与动力学重整化方法得到的标度指数值能很好地吻合. 关键词： 表面生长 动力学重整化群分析 标度分析     

含时空关联噪声的非局域及各向异性Kardar-Parisi -Zhang方程的直接标度分析

将直接标度分析方法推广应用到含时间空间关联噪声的非局域及各向异性KardarParisiZhang方程的动力学标度分析中,分别得到了方程在强耦合区和弱耦合区的标度指数值.在弱耦合区得到的标度指数能与使用动力学重整化方法得到的结果相吻合 关键词： 表面生长 标度分析 KPZ方程     

含有广义守恒律的生长方程标度奇异性的直接标度分析

利用直接标度分析方法研究一个含有广义守恒律生长方程的标度奇异性,得到强弱耦合区域的奇异标度指数.作为其特殊情况,这个方程包含Kardar-Parisi-Zhang（KPZ）方程、 Sun-Guo-Grant（SGG）方程以及分子束外延（MBE）生长方程,并能对其进行统一的研究.研究发现, KPZ方程和SGG方程,无论在弱耦合还是在强耦合区域内都遵从自仿射Family -Vicsek正常标度规律;而MBE 方程在弱耦合区域内服从正常标度,在强耦合区域内能呈现内禀奇异标度行为.这里所得到生长方程的奇异标度性质与利用重正化群理论、数值模拟以及实验相符很好. 关键词： 标度奇异性 强耦合 弱耦合     

点缺陷对表面生长动力学标度行为的影响

基于含噪声Kuramoto-Sivashinsky方程, 采用动力学重正化群技术, 研究生长表面存在点缺陷或杂质对表面生长动力学标度行为的影响, 得到了相应的粗糙度指数α 和动力学标度指数z. 所得结果表明, 点缺陷的存在使生长表面粗化, 并缩短达到稳定生长的弛豫时间.     

非局域Sun-Guo-Grant方程的自洽模耦合理论

通过选取具有正确渐近行为的标度函数形式，将自洽的模耦合理论推广应用到对非局域的Sun-Guo-Grant方程的动力学标度性质的研究中.通过分析得到，在强耦合区基底维数d=1,2的情况下，动力学指数z随非局域参数ρ的变化关系.将这一结果与动力学重正化群理论和直接标度分析得到的结果进行了对比. 关键词： 表面粗糙生长动力学 动力学标度 自洽模耦合理论     

含关联噪声的空间分数阶随机生长方程的动力学标度行为研究

为探讨含关联噪声的空间分数阶随机生长方程的动力学标度行为,本文利用Riesz分数阶导数和Grümwald-Letnikov分数阶导数定义方法研究了关联噪声驱动下的空间分数阶Edwards-Wilkinson (SFEW)方程在1+1维情况下的数值解,得到了不同噪声关联因子和分数阶数时的生长指数、粗糙度指数、动力学指数等,所求出的临界指数均与标度分析方法的结果相符合.研究表明噪声关联因子和分数阶数均影响到SFEW方程的动力学标度行为,且表现为连续变化的普适类.     

外场存在时界面生长的重整化群研究

用重整化群方法分析了有外场存在时的界面生长行为,得到了非平庸的稳定的固定点,固定点粗糙指数x和动力学标度指数z。结果表明,外场趋于使生长表面平滑并且不破坏伽利略不变性。 关键词：     

序参量守恒系统中空间相关的界面生长

用重整化群方法分析了序参量守恒系统在空间关联下的界面生长行为。得到了标度指数x和z作为空间维数d和相关指数ρ的函数。结果表明,序参量守恒条件使生长弛豫时间增长,空间相关使生长表面粗化。并与E.Medina等人和T.Sun等人的结果作了比较。 关键词：     

直接标度分析动力生长

用直接标度分析方法研究了分子束外延生长和在长程时间、空间关联条件下的动力生长过程。分别得到了在强、弱耦合区的粗糙指数和动力学指数,并对其结果进行了讨论,说明了其弱耦合的结果与动力重整化群的结果一致的原因。 关键词：     

随机稀释基底上刻蚀模型动力学标度行为的数值模拟研究

表面界面动力学粗化过程是凝聚态物理领域重要的研究内容,为研究基底不完整性对刻蚀模型动力学 标度行为的影响,本文采用Kinetic Monte Carlo(KMC)方法,分析研究了在随机稀释基底上刻蚀模型(Etching model)生长表面的动力学标度行为.研究发现:尽管随机稀释基底的不完整性会对刻蚀表面的动力学 行为产生显著的影响,导致刻蚀表面粗糙度指数和生长指数有明显的增加, 但其仍基本满足原有的动力学标度规律.此外,本文还对刻蚀表面动力学标度指数的有限尺寸效应进行了 分析讨论.     

Anomalous roughening of Hele-Shaw flows with quenched disorder

The kinetic roughening of a stable oil-air interface moving in a Hele-Shaw cell that contains a quenched columnar disorder (tracks) has been studied. A capillary effect is responsible for the dynamic evolution of the resulting rough interface, which exhibits anomalous scaling. The three independent exponents needed to characterize the anomalous scaling are determined experimentally. The anomalous scaling is explained in terms of the initial acceleration and subsequent deceleration of the interface tips in the tracks coupled by mass conservation. A phenomenological model that reproduces the measured global and local exponents is introduced.     

Scaling of the interface roughness in Fe-Cr superlattices: self-affine versus non-self-affine

We have analyzed kinetic roughening in Fe-Cr superlattices by energy-filtered transmission electron microscopy. The direct access to individual interfaces provides both static and dynamic roughness exponents. We find an anomalous non-self-affine scaling of the interface roughness with a time dependent local roughness at short length scales. While the deposition conditions affect strongly the long-range dynamics, the anomalous short-range exponent remains unchanged. The different short- and long-range dynamics outline the importance of long-range interactions in kinetic roughening.     

Evidence for the anomalous scaling behaviour of the molecular-beam epitaxy growth equation

According to the scaling idea of local slope, we investigate numerically and analytically anomalous dynamic scaling behaviour of (1+1)-dimensional growth equation for molecular-beam epitaxy. The growth model includes the linear molecular-beam epitaxy (LMBE) and the nonlinear Lai--Das Sarma--Villain (LDV) equations. The anomalous scaling exponents in both the LMBE and the LDV equations are obtained, respectively. Numerical results are consistent with the corresponding analytical predictions.     

Anomalous Scaling of Surface Growth Equations with Spatially and Temporally Correlated Noise

Based on the scaling idea of local slopes by López et al. [Phys. Rev. Lett. 94 (2005) 166103], we investigate anomalous dynamic scaling of (d+1)-dimensional surface growth equations with spatially and temporally correlated noise. The growth equations studied include the Kardar-Parisi-Zhang (KPZ), Sun-Guo-Grant (SGG), and Lai-Das Sarma-Villain (LDV) equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively.     

Dynamical scaling and kinetic roughening of single valued fronts propagating in fractal media

We consider the dynamical scaling and kinetic roughening of single-valued interfaces propagating in 2D fractal media. Assuming that the nearest-neighbor height difference distribution function of the fronts obeys Lévy statistics with a well-defined algebraic decay exponent, we consider the generalized scaling forms and derive analytic expressions for the local scaling exponents. We show that the kinetic roughening of the interfaces displays intrinsic anomalous scaling and multiscaling in the relevant correlation functions. We test the predictions of the scaling theory with a variety of well-known models which produce fractal growth structures. Results are in excellent agreement with theory. For some models, we find interesting crossover behavior related to large-scale structural instabilities of the growing aggregates. Received 22 May 2002 Published online 19 November 2002     

Anomalous scaling of the surface width during Cu electrodeposition

Kinetic roughening during thin film growth is a widely studied phenomenon, with many systems found to follow simple scaling laws. We show that for Cu electrodeposition from additive-free acid sulphate electrolyte, an extra scaling exponent is required to characterize the time evolution of the local roughness. The surface width w(l,t) scales as t(beta(loc))lH, when the deposition time t is large or the size l of the region over which w is measured is small, and as t(beta+beta(loc)) when l is large or t is small. This is the first report of such anomalous scaling for an experimental ( 2+1)-dimensional system. When the deposition current density or Cu concentration is varied, only beta(loc) changes, while the other power law exponents H and beta remain constant.     

Exact results for the Kardar-Parisi-Zhang equation with spatially correlated noise

We investigate the Kardar-Parisi-Zhang (KPZ) equation in d spatial dimensions with Gaussian spatially long-range correlated noise -- characterized by its second moment -- by means of dynamic field theory and the renormalization group. Using a stochastic Cole-Hopf transformation we derive exact exponents and scaling functions for the roughening transition and the smooth phase above the lower critical dimension . Below the lower critical dimension, there is a line marking the stability boundary between the short-range and long-range noise fixed points. For , the general structure of the renormalization-group equations fixes the values of the dynamic and roughness exponents exactly, whereas above , one has to rely on some perturbational techniques. We discuss the location of this stability boundary in light of the exact results derived in this paper, and from results known in the literature. In particular, we conjecture that there might be two qualitatively different strong-coupling phases above and below the lower critical dimension, respectively. Received 5 August 1998     

Anomalous dynamic scaling of the non-local growth equations

The anomalous dynamic scaling behavior of the d+1 dimensional non-local growth equations is investigated based on the scaling approach. The growth equations studied include the non-local Kardar-Parisi-Zhang (NKPZ), non-local Sun-Guo-Grant (NSGG), and non-local Lai-Das Sarma-Villain (NLDV) equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively. Our results show that non-local interactions can affect anomalous scaling properties of surface fluctuations.