On array models theoretical predictions versus measurements for the growth of cells and dendrites in the transient solidification of binary alloys

Most of the theoretical studies of the growth of cells/dendrites in the literature are based on the assumption that it is a steady-state phenomenon. The analysis of cells/dendritic structures in the unsteady-state regime is very important, since it encompasses the majority of industrial solidification processes. The aim of the present investigation was to validate the predictions furnished by the cellular and primary dendritic growth models in the literature for unsteady-state conditions against a large spectrum of experimental data, which includes those for a variety of Al alloys (Al–Cu, Al–Si, Al–Fe, Al–Bi, Al–Ni, Al–Sn) and low thermal diffusivity alloys, such as Sn–Pb and Pb–Sb. The predictions furnished by the Hunt–Lu model do not match the cellular experimental scatter for any examined alloy system. However, this model matches well with the primary dendritic growth of Al alloys, with the exception of Al–Sn alloys, for which the Hunt–Thomas approach has to be applied. The primary dendritic predictions of Bouchard–Kirkaldy's model, performed with the originally suggested a ₁ calibration factors are, in most cases, located above the experimental points. Experimental growth laws relating cellular and dendritic spacings with the tip growth rate and the cooling rate, respectively, are established.     

液相对流对定向凝固胞/枝晶间距的影响

采用类金属透明模型合金丁二腈-1.8 wt%丙酮(SCN-1.8 wt%Ace)合金, 研究了平行于生长界面前沿的液相对流对定向凝固胞/枝晶生长行为及胞/枝晶间距的影响. 对于胞晶生长, 在液相对流作用下, 其尖端将会出现分岔, 使得胞晶间距减小, 并且液相对流流速越大, 胞晶尖端分岔越明显, 胞晶组织越细小, 胞晶间距越小. 至于枝晶生长, 其生长行为与胞晶不同. 当抽拉速度较小时, 液相对流作用下枝晶两侧三次臂的生长速度将会超过枝晶尖端生长速度, 形成新的枝晶列, 使得枝晶一次间距减小, 并且液相对流流速越大枝晶一次间距越小; 当抽拉速度较大时, 液相对流作用下迎流侧二次臂生长发达,且会抑制上游枝晶生长, 使得枝晶一次间距增大, 并且液相对流越强枝晶一次间距越大. 关键词： 定向凝固 胞晶间距 枝晶间距 液相对流     

宏微观耦合模拟熔池不同区域中枝晶竞争生长过程

针对熔化焊过程建立了宏微观耦合模型,模拟了熔池内不同区域凝固过程中随机取向枝晶的竞争生长过程. 通过宏观三维有限元模型计算熔池中瞬态的传热传质过程,利用双线性插值算法将凝固参数传递给微观组织模型. 采用元胞自动机法模拟随机取向的枝晶在熔池凝固条件下的竞争生长过程. 模拟结果表明,所建立的微观模型能够精确模拟任意生长取向的枝晶. 凝固条件中最大温度梯度方向对枝晶竞争过程有明显选择作用,生长方向与最大温度梯度方向相同或接近的枝晶在竞争中具有更大优势. 焊缝中的晶粒组织由枝晶簇发展形成,晶粒组织的形貌演变取决于相邻枝晶簇之间的竞争过程,具有择优取向的枝晶簇会逐渐排挤非择优取向的枝晶簇并最终将其阻挡在凝固组织内部,宏观晶粒的取向与其内部枝晶簇的生长方向并不一定相同. 熔池中心线附近区域在焊接过程中具有更小的温度梯度、更大的凝固速率以及更大的局部冷却速率,凝固后可以获得更加细小的焊缝枝晶组织. 枝晶间距的模拟结果与相应凝固条件下的试验数据符合较好. 关键词： 焊接熔池 枝晶形貌 竞争生长 元胞自动机     

基于元胞自动机方法的定向凝固枝晶竞争生长数值模拟

通过耦合温度场模型、溶质扩散方程以及枝晶生长动力学方程等重要因素,建立了一种改进的元胞自动机模型.该模型通过采用偏心算法消除网格各向异性,实现了二维尺度上任意角度枝晶生长的模拟,同时适用于模拟三维尺度上枝晶的生长过程.利用建立的模型开展了定向凝固枝晶竞争生长过程的数值模拟.为了体现本模型的有效性,模拟了透明合金的竞争生长过程,并与实验结果符合良好.镍基高温合金汇聚竞争和发散竞争的模拟结果清楚地展现了不同抽拉速度和枝晶优先生长角度下枝晶的竞争生长过程,并且模拟结果与理论模型相符合.三维枝晶生长的模拟结果表明本模型可以用来模拟三维枝晶一次臂间距的调整过程.     

A dynamic scaling assumption for phase separation

A review of the dynamics of phase separation is presented, which focuses on the scaling assumption of the problem. Conventional linear and nonlinear theories are briefly reviewed. The problems with these conventional theories, and how the scaling idea can be used to overcome them are discussed. The growth rates of the droplets, domains, or grains are discussed in terms of the scaling assumption, and experimental tests of the scaling assumption for growth laws and scattering intensities are reviewed. To explain singular properties of the structure function and growth rate, which are observed experimentally, a strong correlation among droplets or grains on phase separations is postulated. A nonconventional form of the scattering function and a nonconventional droplet growth rate are explained qualitatively.     

Influence of the angular distribution function of incident particles on the microstructure and anomalous scaling behavior of thin films

The microstructure and the scaling properties of films grown by plasma enhanced chemical vapor deposition are reproduced with a discrete model that takes into account the angular distribution function of the particles and the lateral growth of the films. Both the experimental and simulated surfaces exhibit a granular microstructure and an anomalous scaling behavior characterized by values of the growth exponent beta that vary with the scale of measurement. Depending on the angular distribution function used in the model, values of beta ranging from 0.86 to 0.2 are obtained.     

Network analysis of the state space of discrete dynamical systems

We study networks representing the dynamics of elementary 1D cellular automata (CA) on finite lattices. We analyze scaling behaviors of both local and global network properties as a function of system size. The scaling of the largest node in-degree is obtained analytically for a variety of CA including rules 22, 54, and 110. We further define the path diversity as a global network measure. The coappearance of nontrivial scaling in both the hub size and the path diversity separates simple dynamics from the more complex behaviors typically found in Wolfram's class IV and some class III CA.     

界面能各向异性对定向凝固枝晶生长的影响

采用元胞自动机 (cellular automaton, CA) 模型研究了界面能各向异性对二维定向凝固枝晶生长的影响. 模拟结果显示当晶体的择优生长方向与热流方向一致时, 随着界面能各向异性强度的增大, 凝固组织形态由弱界面能各向异性时的海藻晶转变为强界面能各向异性时的树枝晶. 同时, 界面能各向异性强度会影响稳态枝晶尖端状态的选择, 界面能各向异性越强, 定向凝固稳态枝晶尖端半径越小, 尖端界面前沿的液相浓度和过冷度越小. 稳态枝晶生长的尖端状态选择参数与界面能各向异性强度也存在标度律的指数关系, 而枝晶一次间距则受界面能各向异性强度影响较弱. 当晶体的择优生长方向与热流方向呈-40°夹角时随着界面能各向异性强度的增大, 凝固组织形态由海藻晶逐渐转变为退化枝晶, 后又逐渐转变为倾斜枝晶. 关键词： 元胞自动机 枝晶 界面能各向异性     

Universal scaling of wave propagation failure in arrays of coupled nonlinear cells

We study the onset of the propagation failure of wave fronts in systems of coupled cells. We introduce a new method to analyze the scaling of the critical external field at which fronts cease to propagate, as a function of intercellular coupling. We find the universal scaling of the field throughout the range of couplings and show that the field becomes exponentially small for large couplings. Our method is generic and applicable to a wide class of cellular dynamics in chemical, biological, and engineering systems. We confirm our results by direct numerical simulations.     

Kinetics of cell spreading

Cell spreading is a fundamental event where the contact area with a solid substrate increases because of actin polymerization. We propose in this Letter a physical model to study the growth of the contact area with time. This analysis is compared with experimental data using the ameoba Dictyostelium discoideum. Our model couples the stress, which builds up at the margin of the contact area when the cell spreads, to the biochemical processes of actin polymerization. This leads to a scaling analysis of experimental data with a characteristic time whose order of magnitude compares well with our experimental results.     

Superscaling in charged current neutrino quasielastic scattering in the relativistic impulse approximation

Superscaling of the quasielastic cross section in charged-current neutrino-nucleus reactions at energies of a few GeV is investigated within the framework of the relativistic impulse approximation. Several approaches are used to describe final-state interactions and comparisons are made with the plane-wave approximation. Superscaling is very successful in all cases. The scaling function obtained using a relativistic mean field for the final states shows an asymmetric shape with a long tail extending towards positive values of the scaling variable, in excellent agreement with the behavior presented by the experimental scaling function.     

激光快速凝固条件下Cu-31.4%Mn合金的微观组织特征

利用连续波CO2激光器对Cu 314%Mn进行了系列表面熔凝实验，对该合金的组织形态和胞晶间距选择规律进行了研究.结果表明：随着生长速度的提高，组织形态由低速平界面向展宽胞晶、规则胞晶、展宽胞晶、类平面晶和高速绝对稳定平界面转变.在快速凝固条件下，Cu 314%Mn合金的胞晶间距存在一个选择范围，最大、最小和平均胞晶间距与生长速度的关系分别为λmax=682v-033s，λmin=289v-028s和=435v-031s，实验结果与Hunt Lu模型的预测结果相吻合.     

Geometric scaling for the total gamma(*)p cross section in the low x region

We observe that the saturation model of deep inelastic scattering predicts a geometric scaling of the total gamma(*)p cross section in the region of small Bjorken variable x. The geometric scaling in this case means that the cross section is a function of only one dimensionless variable tau = Q(2)R(2)(0)(x), where the function R(0)(x) decreases with decreasing x. We show that the experimental data from HERA in the region x<0.01 confirm the expectations of this scaling over a very broad region of Q(2). We suggest that the geometric scaling is more general than the saturation model.     

Dynamical scaling of the quantum Hall plateau transition

Using different experimental techniques, we examine the dynamical scaling of the quantum Hall plateau transition in a frequency range f=0.1-55 GHz. We present a scheme that allows for a simultaneous scaling analysis of these experiments and all other data in literature. We observe a universal scaling function with an exponent kappa=0.5+/-0.1, yielding a dynamical exponent z=0.9+/-0.2.     

Scaling of ac susceptibility and the nonlinear response function of high-temperature superconductors

The amplitude-dependent ac susceptibility of high-temperature superconductors is shown to obey some empirical scaling relations. We try to analyze this behavior by extending a dc nonlinear response function of mixed state to the ac cases. The derived equations for critical current and ac susceptibility X(T) agree with the scaling relations of experimental data.     

参数不确定量子细胞神经网络与Lorenz超混沌系统的函数投影同步研究

研究了具有不确定参数的量子细胞神经网络系统与Lorenz超混沌系统的函数投影同步.设计了自适应追踪控制器来实现两个不同系统渐进同步到已知的比例函数,并运用Lyapunov稳定性方法进行了证明.理论分析了量子细胞神经网络系统不确定参数的系数向量线性无关性,实现了不确定参数的识别和估计.数值仿真结果验证了函数投影同步和参数估计的有效性.     

Crossover from hydrodynamics to the kinetic regime in confined nanoflows

We present an experimental study of a confined nanoflow, which is generated by a sphere oscillating in the proximity of a flat solid wall in a simple fluid. Varying the oscillation frequency, the confining length scale, and the fluid mean free path over a broad range provides a detailed map of the flow. We use this experimental map to construct a scaling function, which describes the nanoflow in the entire parameter space, including both the hydrodynamic and the kinetic regimes. Our scaling function unifies previous theories based on the slip boundary condition and the effective viscosity.     

Superscaling predictions for neutral current quasielastic neutrino-nucleus scattering

The application of superscaling ideas to predict neutral-current (NC) quasielastic (QE) neutrino cross sections is investigated. The relativistic impulse approximation (RIA) using the same relativistic mean field potential (RMF) for both initial and final nucleons - a model that reproduces the experimental (e,e(')) scaling function - is used to illustrate our findings. While NC reactions are apparently not well suited for scaling analyses, to a large extent, the RIA-RMF predictions do exhibit superscaling. Independence of the scaled response on the nuclear species is very well fulfilled. The RIA-RMF NC superscaling function is in good agreement with the experimental (e,e(')) one. The idea that electroweak processes can be described with a universal scaling function, provided that mild restrictions on the kinematics are assumed, is shown to be valid.