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.     

水平均质表面上液滴聚合过程的可视化实验研究

对水平均匀表面上液滴的聚合过程及特性进行了可视化实验研究,获得了液滴半径和液滴物性等参数对液滴聚合过程中液滴液桥半径和接触角变化特性的影响规律。实验结果表明:液滴聚合中液桥半径和接触角都呈衰减振荡变化; 聚合前液滴半径越小,液桥半径振荡频率越大,振幅越小,振荡时间越短;液滴的粘度越大,液桥半径的振荡频率越小, 振幅越小,振荡时间越短;液滴聚合前的接触角明显大于聚合液滴静止后的接触角,其差值与固体界面状况和气、固、液物性相关。     

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.     

D维空间Cs2分子X1Σ+g态精确解析解

使用完全量子化规则法计算了D维空间中具有任意转动量子数Morse势的Schrödinger方程,得到了Cs2分子X1Σ+g态旋转-振动能谱,讨论了能谱与维度D和振动量子数之间的关系。结果表明：(1)具有不同转动量子数和振动量子数的能谱随维度D的增大而趋于相同;(2)高维Cs2分子X1Σ+g态的振动能特性与三维相似。     

D维空间Cs_2分子X~1Σ_g~+态精确解析解

使用完全量子化规则法计算了D维空间中具有任意转动量子数Morse势的Schrdinger方程,得到了Cs_2分子X~1Σ_g~+态旋转-振动能谱,讨论了能谱与维度D和振动量子数之间的关系.结果表明:(1)具有不同转动量子数和振动量子数的能谱随维度D的增大而趋于相同;(2)高维Cs_2分子X~1Σ_g~+态的振动能特性与三维相似.     

(1+2)维空间光孤子在非局域克尔介质中的传输特性

 从非局域非线性薛定谔方程出发,采用分步傅里叶算法数值讨论了在一定的非局域程度条件下,（1+2）维空间光孤子的传输特性, 数值求解了光孤子各特性参量。假定非局域克尔介质的响应函数为高斯型,得出了在一定的非局域程度条件下空间光孤子的数值解,并数值证明了它们的稳定性。结果表明:（1+2）维光孤子对非局域程度依赖性很强。在一定的非局域程度下,光束能以光孤子态在非局域克尔介质中稳定传输。强非局域时,光孤子的波形是高斯型,其它的非局域程度下,不是高斯型。当非局域程度较弱时,不存在孤子解。     

带电聚合电介质表面吸附理论研究

摘要：应用聚合电介质吸附的定标理论,根据介质和表面电介质常数的比率,考虑多化合价吸附电介质之间强相关性作用,我们提出一种表面排斥电荷的近似定标理论方法,根据这种方法把电介质表面吸附层的相图分为本质上不同的两大类。从相图可知：当表面电荷密度低（或体带相反电荷离子密度高）,这时表面和体带相反电荷离子密度几乎相同;一旦表面电荷密度足够高,就使带相反电荷的离子在表面上浓缩。据此,可确定在这个区域内,低化合价聚合电介质形成一个相关的多链状态,当化合价足够高时,由于近邻链之间的更强排斥增强,使状态转变成单链。     

(1+2)维空间光孤子在非局域克尔介质中的传输特性

从非局域非线性薛定谔方程出发,采用分步傅里叶算法数值讨论了在一定的非局域程度条件下,（1+2）维空间光孤子的传输特性, 数值求解了光孤子各特性参量。假定非局域克尔介质的响应函数为高斯型,得出了在一定的非局域程度条件下空间光孤子的数值解,并数值证明了它们的稳定性。结果表明:（1+2）维光孤子对非局域程度依赖性很强。在一定的非局域程度下,光束能以光孤子态在非局域克尔介质中稳定传输。强非局域时,光孤子的波形是高斯型,其它的非局域程度下,不是高斯型。当非局域程度较弱时,不存在孤子解。     

倾斜均质表面上非等径液滴的聚合特性

对倾斜均匀表面上非等径液滴的聚合过程及特性进行了可视化实验研究,获得了液滴半径和表面倾角等参数对液滴聚合过程中液滴液桥半径、接触角和接触线变化特性的影响规律,进一步说明了倾斜表面上液滴聚合可以加快液滴的运动.     

Universal Large-Deviation Function of the Kardar–Parisi–Zhang Equation in One Dimension

Using the Bethe ansatz, we calculate the whole large-deviation function of the displacement of particles in the asymmetric simple exclusion process (ASEP) on a ring. When the size of the ring is large, the central part of this large deviation function takes a scaling form independent of the density of particles. We suggest that this scaling function found for the ASEP is universal and should be characteristic of all the systems described by the Kardar–Parisi–Zhang equation in 1+1 dimension. Simulations done on two simple growth models are in reasonable agreement with this conjecture.     

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     

A fluctuating lattice Boltzmann scheme for the one-dimensional KPZ equation

Based on the well-known mapping between the Burgers equation with noise and the Kardar–Parisi–Zhang (KPZ) equation for fluctuating interfaces, we develop a fluctuating lattice Boltzmann (LB) scheme for growth phenomena, as described by the KPZ formalism. A very simple LB-KPZ scheme is demonstrated in 1+1 spacetime dimensions, and is shown to reproduce the scaling exponents characterizing the growth of one-dimensional fluctuating interfaces.     

Directed polymer melts and quantum critical phenomena

The statistical mechanics of directed linelike objects, such as directed polymers in an external field, strands of dipoles in both ferro- and electrorheological fluids, and flux lines in high-T_c superconductors, bears a close resemblance to the quantum mechanics of bosons in 2+1 dimensions. We show that single-component and binary mixture critical phenomena in these systems are in the universality class of three-dimensional uniaxial dipolar ferromagnets and ferroelectrics. Our results also apply to films of two superfluid species undergoing phase separation well below their -points near T=0. In the case of directed polymers and electrorheological fluids we analyze the effects of free ends occurring in the sample as well as a novel directionally-dependent compressibility.     

Simulations of Co‐GISAXS during kinetic roughening of growth surfaces

The recent development of surface growth studies using X‐ray photon correlation spectroscopy in a grazing‐incidence small‐angle X‐ray scattering (Co‐GISAXS) geometry enables the investigation of dynamical processes during kinetic roughening in greater detail than was previously possible. In order to investigate the Co‐GISAXS behavior expected from existing growth models, calculations and (2+1)‐dimension simulations of linear Kuramoto–Sivashinsky and non‐linear Kardar–Parisi–Zhang surface growth equations are presented which analyze the temporal correlation functions of the height–height structure factor. Calculations of the GISAXS intensity auto‐correlation functions are also performed within the Born/distorted‐wave Born approximation for comparison with the scaling behavior of the height–height structure factor and its correlation functions.     

Effective potential for the massless KPZ equation

In previous work we have developed a general method for casting a classical field theory subject to Gaussian noise (that is, a stochastic partial differential equation (SPDE)) into a functional integral formalism that exhibits many of the properties more commonly associated with quantum field theories (QFTs). In particular, we demonstrated how to derive the one-loop effective potential. In this paper we apply the formalism to a specific field theory of considerable interest, the massless KPZ equation (massless noisy Burgers equation), and analyze its behavior in the ultraviolet (short-distance) regime. When this field theory is subject to white noise we can calculate the one-loop effective potential and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, and fails to be ultraviolet renormalizable in higher dimensions. We show that the one-loop effective potential for the massless KPZ equation is closely related to that for λφ⁴ QFT. In particular, we prove that the massless KPZ equation exhibits one-loop dynamical symmetry breaking (via an analog of the Coleman–Weinberg mechanism) in 1 and 2 space dimensions, and that this behavior does not persist in 3 space dimensions.     

Continuously Varying Exponents in a Sandpile Model with Dissipation Near Surface

We consider the directed Abelian sandpile model in the presence of sink sites whose density f_t at depth t below the top surface varies as ct^–. For >1 the disorder is irrelevant. For <1, it is relevant and the model is no longer critical for any nonzero c. For =1 the exponents of the avalanche distributions depend continuously on the amplitude c of the disorder. We calculate this dependence exactly, and verify the results with simulations.     

Determination of the Kardar–Parisi–Zhang equation from experimental data with a small number of configurations

We introduce an inverse method to determine the parameters of the Kardar–Parisi–Zhang equation corresponding to an evolving interface which requires a small number of configurations as input data. Our approach presents advantages for applications in real world scenarios since it does not require small time intervals between fronts. The method is applied to a restricted solid-on-solid model and a stochastic cellular automata model for fire front propagation.     

Spectral Properties of Burgers and KPZ Turbulence

This paper presents the higher-order spectral densities of non-Gaussian random fields arising as scaling limits in the Burgers and KPZ turbulence problems with strongly dependent non-Gaussian initial conditions.