用格子Boltzmann方法研究Burgers方程

提出了用于Burgers方程的格子Boltzmann模型。应用Chapman-Enskog展开和多重尺度技术，通过选择平衡态分布函数的高阶矩，得到了几种精度的Burgers方程，模型中的参数通过分析耗散性质和色散性质给出。

Parameter-transformation relations for traveling-wave solutions of kdv-burgers equation

 Burgers suggested that the main properties of free-turbulence in the boundless area without basic flow might be understood with the aid of the following equation, which was much simpler than those of fluid dynamics, 更多还原

对流扩散方程的变步长摄动有限差分格式

摄动有限差分(PFD)方法是构造高精度差分格式的一种新方法。变步长摄动有限差分方法是等步长摄动有限差分方法的发展和推广。对需要局部加密网格的计算问题，变步长PFD格式不需要对自变量进行数学变换，且和等步长PFD格式一样，具有如下的共同特点：从变步长一阶迎风格式出发，通过把非微商项(对流系数和源项)作变步长摄动展开，展开幂级数系数通过消去摄动格式修正微分方程的截断误差项求出，由此获得高精度变步长PFD格式。该格式在一、二和三维情况下分别仅使用三、五和七个基点，且具有迎风性。文中利用变步长PFD格式对对流扩散反应模型方程，变系数方程及Burgers方程等进行了数值模拟，并与一阶迎风和二阶中心格式及其问题的精确解作了比较。数值试验表明，与一阶迎风和二阶中心格式相比，变步长PFD格式具有精度高，稳定性与收敛性好的特点。变步长PFD格式与等步长PFD格式相比，变步长PFD解在薄边界层型区域的分辨率得到了明显的提高。

粘性流动有限差分计算的新策略

对粘性流动计算，提出有限离散单元流动的流体分析(理论)和耦合离散流体理论(CDFT)的差分格式。利用CDFT差分格式计算Burgers方程和计算激波边界层干扰流动的数值实验表明：对计算精度和计算效率的提高，CDFT格式比提高常用差分格式(即离散流体力学方程得到的格式)精度和改进常用格式形式等更有效，且运算量小。

Calculations of longitudinal and transverse velocity structure functions using a vortex model of isotropic turbulence

The longitudinal structure function (LSF) and the transverse structure function (TSF) in isotropic turbulence are calculated using a vortex model. The vortex model is composed of the Rankine and Burgers vortices which have the exponential distributions in the vortex Reynolds number and vortex radii. This model exhibits a power law in the inertial range and satisfies the minimal condition of isotropy that the second-order exponent of the LSF in the inertial range is equal to that of the TSF. Also observed are differences between longitudinal and transverse structure functions caused by intermittency. These differences are related to their scaling differences which have been previously observed in experiments and numerical simulations.

NS方程激波计算的摄动有限差分方法

摄动有限差分（PFD）方法从一阶迎风差分格式出发，将差分系数展开为网格步长的幂级数，通过提高修正微分方程的逼近精度来获得更高精度的差分格式。由于格式基于一阶迎风格式，因此具有迎风效应、网格节点少等特点。本文首先通过对Burgers方程的摄动差分格式的推导，将摄动有限差分格式引入时间相关法的计算，并构造了守恒形式的摄动有限差分格式，然后推广到一维Navier-Stokes方程组的计算。数值比较研究表明：本文构造的NS方程摄动有限差分格式具有比一阶迎风较高的精度和分辨率，而且保持了一阶迎风格式的无振荡性质。

约化摄动法和非线性波远场分析

<正> 一、引言 如所周知,摄动法(特别是奇异摄动法)在研究弱非线性波方面有着广泛的应用[1—5]。其中,近年来发展形成的约化摄动法已经成了分析各种非线性波远场的有力工具[6—8]。 约化摄动法的实质是,对于一般的描述非线性波的复杂方程组,通过适当的坐标变形和摄动展开,在一阶近似下,把方程组约化成较为简单可解的单个非线性方程(例如Burgers方程、Korteweg-de Vries方程、非线性Schrodinger方程等),从而可以分析远离波的相互作用区的远场。

On the unstable stacking criterion for ideal and cracked copper-crystals

The unstable stacking criteria for an ideal copper crystal under homogeneous shearing and for a cracked copper crystal under pure mode II loading are analysed. For the ideal crystal under homogeneous shearing, the unstable stacking energy gamma(us) defined by Rice in 1992 results from shear with no relaxation in the direction normal to the slip plane. For the relaxed shear configuration, the critical condition for unstable stacking does not correspond to the relative displacement Delta = b(p)/2, where b(p) is the Burgers vector magnitude of the Shockley partial dislocation, but to the maximum shear stress. Based on this result, the unstable stacking energy Gamma(us) is defined for the relaxed lattice. For the cracked crystal under pure mode II loading, the dislocation configuration corresponding to Delta = b(p)/2 is a stable state and no instability occurs during the process of dislocation nucleation. The instability takes place at approximately Delta = 3b(p)/4. An unstable stacking energy Pi(us) is defined which corresponds to the unstable stacking state at which the dislocation emission takes place. A molecular dynamics method is applied to study this in an atomistic model and the results verify the analysis above.

H4 exponential finite-difference scheme for convective diffusion-equations

Perturbations are applied to the convective coefficients and source term of a convection-diffusion equation so that second-order corrections may be applied to a second-order exponential scheme. The basic Structure of the equations in the resulting fourth-order scheme is identical to that for the second order. Furthermore, the calculations are quite simple as the second-order corrections may be obtained in a single pass using a second-order scheme. For one to three dimensions, the fourth-order exponential scheme is unconditionally stable. As examples, the method is applied to Burgers' and other fluid mechanics problems. Compared with schemes normally used, the accuracies are found to be good and the method is applicable to regions with large gradients.

Numerical experiments on one-dimensional model of turbulence

The initial-value problem of a forced Burgers equation is numerically solved by the Fourier expansion method. It is found that its solutions finally reach a steady state of 'laminar flow' which has no randomness and is stable to disturbances. Hence, strictly speaking, the so-called Burgers turbulence is not a turbulence. A new one-dimensional model is proposed to simulate the Navier-Stokes turbulence. A series of numerical experiments on this one-dimensional turbulence is made and is successful in obtaining Kolmogorov's (1941) k exp(-5/3) inertial-range spectrum. The (one-dimensional) Kolmogorov constant ranges from 0.5 to 0.65.

迎风紧致格式与热流计算

该文在朱庆勇、马延文(1998)一文的基础上给出了利用迎风紧致格式求解NS方程.它是UCGVC格式在粘性流计算中的推广.对于方程中的无粘部分利用Steger-Warming的通量分裂技术将流通向量分裂成两部分,在此基础上据风向构造逼近于无粘项的三阶迎风紧致格式.对方程中的粘性部分采用通常的二阶中心差分格式.该文利用对Burgers方程的特征分析,研究了为正确模拟边界层内的流动特征对网格雷诺数的限制条件.通过对超声速粘性球头绕流的数值模拟表明:迎风紧致格式能在较大的网格雷诺数的条件下计算热流值,结果是令人满意的.

Generation and behavior of pure-edge threading misfit dislocations in InxGa1-xN/GaN multiple quantum wells

The relaxation of the misfit strain by the formation of misfit dislocations in InxGa1-xN/GaN multiple quantum wells grown by metal-organic chemical-vapor deposition was investigated by the cross-sectional transmission electron microscopy, double crystal x-ray diffraction, and temperature-dependent photoluminescence. It is found that the misfit dislocations generated from strain relaxation are all pure-edge threading dislocations with burgers vectors of b=1/3<11 (2) over bar0>. The misfit dislocations arise from the strain relaxation due to the thickness of strained layer greater than the critical thickness. The relaxation of strained layer was mainly achieved by the formation of dislocations and localization of In, while the dislocations changed their slip planes from {0001} to {10 (1) over bar0}. With the increasing temperature, the efficiency of photoluminescence decrease sharply. It indicates that the relaxation of the misfit strain has a strong effect on optical efficiency of film. (C) 2004 American Institute of Physics.

Development of cross-hatch grid morphology and its effect on ordering growth of quantum dots

We investigate the development of cross-hatch grid surface morphology in growing mismatched layers and its effect on ordering growth of quantum dots (QDs). For a 60degrees dislocation (MD), the effective part in strain relaxation is the part with the Burgers vector parallel to the film/substrate interface within its b(edge) component; so the surface stress over a MD is asymmetric. When the strained layer is relatively thin, the surface morphology is cross-hatch grid with asymmetric ridges and valleys. When the strained layer is relatively thick, the ridges become nearly symmetrical, and the dislocations and the ridges inclined-aligned. In the following growth of InAs, QDs prefer to nucleate on top of the ridges. By selecting ultra-thin In0.15Ga0.85As layer (50nm) and controlling the QDs layer at just formed QDs, we obtained ordered InAs QDs. (C) 2004 Elsevier B.V. All rights reserved.

Measurement of threading dislocation densities in GaN by wet chemical etching

We demonstrate a technique based on wet chemical etching that enables quick and accurate evaluation of edge- and screw/mixed-type threading dislocations (TDs) in GaN. Large and small etch pits are formed by phosphoric acid on the etched surfaces. The large etch pits are attributed to screw/mixed TDs and the small ones to edge TDs, according to their locations on the surface and Burgers vectors of TDs. Additionally, the origin of small etch pits is confirmed by a transmission electron microscopy. The difference in the size of etch pits is discussed in view of their origin and merging. Overetching at elevated temperatures or for a long time may result in merging of individual etch pits and underestimating of the density of TDs. Wet chemical etching has also been proved efficient in revealing the distribution of TDs in epitaxial lateral overgrowth GaN.

Two-dimensional network of dislocations and nanocavities in hydrogen-implanted and two-step annealed silicon

Conventional transmission electron microscopy and energy-filtering were used to study the dislocations and nanocavities in proton-implanted [001] silicon. A two-dimensional network of dislocations and nanocavities was found after a two-step annealing, while only isolated cavities were present in single-step annealed Si. In addition, two-step annealing increased materially the size and density of the nanocavities. The Burgers vector of the dislocations was mainly the 1/2[110] type. The gettering of oxygen at the nanocavities was demonstrated. (C) 1998 American Institute of Physics. [S0003-6951(98)00620-2].