Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation

In this paper a lattice Boltzmann (LB) model to simulate incompressible flow is developed. The main idea is to explicitly eliminate the terms of o(M ²), where M is the Mach number, due to the density fluctuation in the existing LB models. In the proposed incompressible LB model, the pressure p instead of the mass density ρ is the independent dynamic variable. The incompressible Navier–Stokes equations are derived from the incompressible LB model via Chapman–Enskog procedure. Numerical results of simulations of the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2D Womersley flow are presented. The numerical results are found to be in excellent agreement with theory.     

Equivalent boundary integral equations for plane elasticity

Indirect and direct boundary integral equations equivalent to the original boundary value problem of differential equation of plane elasticity are established rigorously. The unnecessity or deficiency of some customary boundary integral equations is indicated by examples and numerical comparison.     

气体放电击穿过程的物理和数值研究

本文对低气压（１０＾－２Ｐａ）热阴极气体放电的击穿过程给出了物理描述和相应的双流体数学型，并发展了一种选择和调整未知初始条件的有效算法，可以通过伴随试射法得到对初始条件十分敏感的非线性两点边值常微分方程组的数值解，从而给出这类气体放电中击穿过程的定量描述。     

Analysis of saltation characteristics of bed-load transport in flowing water

The study of bed-load transport is of great significance both in theory and in practice. This paper discusses the saltation of bed-load solid grains in flowing water. Experiments and theoretic analysis have been made by means of high-speed photographing and advanced data processing technique with a combined method based on mechanical and statistical theories. It indicates that the saltation is the main form of the bed-load transport under ordinary flowing conditions. In the meantime, taking successive saltation as the model of bed-load transport, systematic analysis has been made with regard to the kinematic properties and mechanism of saltation. The statistical analysis shows that the probability density functions of the relative height and length of saltation are in conformity with Γ-type distribution, while the probability density functions of the relative velocities of saltation are in conformity with the Gaussian distribution. The project supported by National Natural Science Foundation of China     

有序分组资料的线性趋势检验的确切概率计算

有序分组资料的线性趋势检验主要用于检验几个二项总体反应率的线性趋势；在医学与生物学中最典型的用途是研究剂量和反应的关系． 如果用Ｚ检验来代替通常在本检验中所用的卡方检验，就可容易地导出本检验的确切概率计算方法，和其他２×Ｃ有序列联表有着相同的形式．本文给出了该检验的确切概率计算方法．     

A comparison of master equation and Fokker-Planck equation in the thermodynamic limit

The master equation and the Fokker-Planck equation are compared thoroughly in both of the stationary and the time-dependent cases for a one-dimensional system. The comparison includes the master equation without detailed balance.     

纯生跳跃扩散型交换期权定价公式

在假定标的资产价格服从纯生跳跃过程的条件下,研究一类多资产期权——资产权重不同的交换期权,并在风险中性的条件下建立相应的定价方程,运用条件期望等相关知识得出交换期权的解析公式。文中最后列出一些特殊纯生跳跃扩散型交换期权的定价的例子.     

Matrix representation of three-dimensional astigmatic resonators

Three-dimensional astigmatic resonators, typical examples of which are the resonators bounded by cylindrical-spherical mirrors and cylindrical-cylindrical mirrors oriented at an arbitrary crossed angle, are investigated in detail by using a complex curvature tensor concept and generalized tensor ABCD law. Computerized numerical calculations illustrate some interesting characteristics of these astigmatic resonators.     

Effect of carbon content on the microstructure and the cracking susceptibility of Fe-based laser-clad layer

The laser cladding of Fe-based alloys on a medium carbon steel substrate was performed using a CO₂ laser and Ar shielding gas that was blown into a molten pool. The microstructure and cracking susceptibility of the laser-clad layers were studied in terms of carbon additions. Results show that the small change of the carbon content in the alloy powders can obviously change the microstructure and properties of the layers. When the carbon content is in the range of 0.3–0.4 wt.%, the decrease of the carbon content in alloy powders will increase the hardness and toughness of the layers simultaneously under the same process parameters. As a result, crack-free coatings with high hardness can be obtained. As the carbon content increases from 0.2 wt.% to 0.4 wt.%, the segregation ratio of chromium increases, while the segregation ratios of nickel, manganese, and silicon first decrease and then increase. At the same time, a new designing principle concerning the composition and microstructure has been put forward, and the principal mechanisms of strengthening and toughening of the layers are fine-grain strengthening and low carbon martensitic phase transformation strengthening.