含时空关联噪声生长方程的标度奇异性分析

基于动力学重整化群理论研究表面界面生长动力学标度奇异性问题, 得到含时空关联噪声的表面生长方程标度奇异指数的一般结果,并将此方法应用于几种典型的局域生长方程——Kardar-Parisi-Zhang（KPZ）方程、线性生长方程、Lai-Das Sarma-Villain（LDV）方程.结果表明,在长波长极限下局域生长方程的动力学标度奇异性与最相关项、基底维数以及噪声有关,并且若出现标度奇异性,只会是超粗化（super rough）奇异标度行为,而不是内禀（intrinsically）奇异标度行为. 关键词： 标度奇异性 动力学重整化群理论 时空关联噪声     

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     

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     

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：     

Kuramoto-Sivashinsky与Karda-Parisi-Zhang模型中生长界面分形特性研究

在（2＋1）维情况下，利用数值模拟研究了Kuramoto-Sivashinsky (K-S)与Karda-Parisi-Z hang (KPZ)模型所决定的非平衡态界面生长演化过程.结果表明，KPZ与K-S模型都表现出明 显的时间和空间标度特性.相对于KPZ模型而言，K-S模型所对应的表面具有更明显的颗粒特 征，当生长时间较长时，生长界面呈现蜂窝状结构.通过数值相关分析得到了生长界面的粗 糙度指数、生长指数和动态标度指数等参数.从两种模型对应的表面形貌特征和表面参数来 看，在(2+1)维情况下，KPZ与K-S模型所决定的表面具有完全不同的动态标度行为，属于不 同的两类物理模型. 关键词： Kuramoto-Sivashinsky (K-S)模型 Karda-Parisi-Zhang(KPZ)模型 分形 数值模拟     

1+1维Wolf-Villain模型奇异标度行为的数值模拟

采用Kinetic Monte Carlo(KMC)方法对描述分子束外延生长(MBE)的1+1维Wolf-Villain模型进行大尺寸和长生长时间的数值模拟研究,以消除渡越行为的影响.计算得到整体和局域标度指数.结果显示,在所模拟的空间和时间尺度范围内,1+1维Wolf-Villain模型仍呈现出固有奇异标度行为.这一结论与López等人最近的理论分析结果不一致.     

1+1维含噪声Kuramoto-Sivashinsky方程表面宽度分布率的数值计算

通过对1+1维含噪声Kuramoto-Sivashinsky(KS)方程进行数值计算,得到其在饱和状态下的表面宽度分布率并与Kardar-Parisi-Zhang(KPZ)方程进行比较.结果表明,1+1维含噪声KS方程的表面宽度分布率标度函数受有限尺寸效应影响较小,并与KPZ方程具有相近的表面宽度分布率标度函数.     

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     

时间分数阶Edwards-Wilkinson方程的标度行为研究

分别采用数值模拟和标度分析方法对1+1维时间分数阶Edwards-Wilkinson方程的标度行为进行研究.利用Caputo分数阶导数数值解求得的生长指数与采用直接标度分析方法得到的结果一致.     

多标度分形上的输运方程

 利用质量守恒定律,得到在三维情况下多标度无序分形介质中的一般输运方程,并在讨论布朗运动和分数布朗运动以及在分形介质上的标准扩散方程的基础上,得到多标度无序分形介质中的分数阶输运方程。     

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.     

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.     

Scaling of crack surfaces and implications for fracture mechanics

The scaling laws describing the roughness development of crack surfaces are incorporated into the Griffith criterion. We show that, in the case of a Family-Vicsek scaling, the energy balance leads to a purely elastic brittle behavior. On the contrary, it appears that an anomalous scaling reflects an R-curve behavior associated with a size effect of the critical resistance to crack growth in agreement with the fracture process of heterogeneous brittle materials exhibiting a microcracking damage.     

The Most Effective Model for Describing the Universal Behavior of a Noisy Kuramoto–Sivashinsky Equation as a Paradigmatic Model

We study a noisy Kuramoto–Sivashinsky (KS) equation which describes unstable surface growth and chemical turbulence. It has been conjectured that the universal long-wavelength behavior of the equation, which is characterized by scale-dependent parameters, is described by a Kardar–Parisi–Zhang (KPZ) equation. We consider this conjecture by analyzing a renormalization-group equation for a class of generalized KPZ equations. We then uniquely determine the parameter values of the KPZ equation that most effectively describes the universal long-wavelength behavior of the noisy KS equation.     

Coupled Kardar-Parisi-Zhang Equations in One Dimension

Over the past years our understanding of the scaling properties of the solutions to the one-dimensional KPZ equation has advanced considerably, both theoretically and experimentally. In our contribution we export these insights to the case of coupled KPZ equations in one dimension. We establish equivalence with nonlinear fluctuating hydrodynamics for multi-component driven stochastic lattice gases. To check the predictions of the theory, we perform Monte Carlo simulations of the two-component AHR model. Its steady state is computed using the matrix product ansatz. Thereby all coefficients appearing in the coupled KPZ equations are deduced from the microscopic model. Time correlations in the steady state are simulated and we confirm not only the scaling exponent, but also the scaling function and the non-universal coefficients.     

On the renormalization of the Kardar-Parisi-Zhang equation

The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally subtracted perturbation expansion about d = 2. For the KPZ roughening transition in dimensions d > 2, this renormalization group yields the dynamic exponent z = 2 and the roughness exponent χ = 0, which are exact to all orders in ε ≡ (2 − d)/2. The expansion becomes singular in d = 4. If this singularity persists in the strong-coupling phase, it indicates that d = 4 is the upper critical dimension of the KPZ equation. Further implications of this perturbation theory for the strong-coupling phase are discussed. In particular, it is shown that the correlation functions and the coupling constant defined in minimal subtraction develop an essential singularity at the strong-coupling fixed point.     

Dynamics of rough interfaces in chemical vapor deposition: experiments and a model for silica films

We study the surface dynamics of silica films grown by low pressure chemical vapor deposition. Atomic force microscopy measurements show that the surface reaches a scale invariant stationary state compatible with the Kardar-Parisi-Zhang (KPZ) equation in three dimensions. At intermediate times the surface undergoes an unstable transient due to shadowing effects. By varying growth conditions and using spectroscopic techniques, we determine the physical origin of KPZ scaling to be a low value of the surface sticking probability, related to the surface concentration of reactive groups. We propose a stochastic equation that describes the qualitative behavior of our experimental system.     

Interplay between carrier and impurity concentrations in annealed Ga1-xMnxAs: intrinsic anomalous hall effect

Investigating the scaling behavior of annealed Ga1-xMnxAs anomalous Hall coefficients, we note a universal crossover regime where the scaling behavior changes from quadratic to linear. Furthermore, measured anomalous Hall conductivities in the quadratic regime when properly scaled by carrier concentration remain constant, spanning nearly a decade in conductivity as well as over 100 K in T_[C] and comparing favorably to theoretically predicated values for the intrinsic origins of the anomalous Hall effect. Both qualitative and quantitative agreements strongly point to the validity of new equations of motion including the Berry phase contributions as well as the tunability of the anomalous Hall effect.     

Exact Scaling Functions for One-Dimensional Stationary KPZ Growth

We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann–Hilbert problem related to the Painlevé II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore⁽¹⁾ obtained from the mode coupling approximation.