A discrete duality finite volume discretization of the vorticity‐velocity‐pressure stokes problem on almost arbitrary two‐dimensional grids

We present an application of the discrete duality finite volume method to the numerical approximation of the vorticity‐velocity‐pressure formulation of the two‐dimensional Stokes equations, associated to various nonstandard boundary conditions. The finite volume method is based on the use of discrete differential operators obeying some discrete duality principles. The scheme may be seen as an extension of the classical Marker and Cell scheme to almost arbitrary meshes, thanks to an appropriate choice of degrees of freedom. The efficiency of the scheme is illustrated by numerical examples over unstructured triangular and locally refined nonconforming meshes, which confirm the theoretical convergence analysis led in the article. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1–30, 2015     

Highly sensitive optical humidity probe

A highly sensitive optical humidity probe based on reflectance measurements has been developed using Nafion^®-crystal violet (CV) films. This sensor can be used to calibrate relative humidity (RH) in the range 0-0.25% with a detection limit (blank signal + 3σ_b, where σ_b = the standard deviation (S.D.) of the blank signal) of 0.018% RH (∼4.37 ppm) and exhibited low hysteresis. The sensor films were fully reversible in dry nitrogen and reversal times were shown to be dependent on exposure time and % RH. The response to 1% RH was highly reproducible (S.D. = 1.67%, number of samples (n) = 5). Hydrogen chloride gas did not interfere with the response of the sensor to RH but did reduce sensor reversal times. This sensor displayed sufficient sensitivity that it could be used to detect ppm levels of moisture in process gases such as nitrogen and HCl.     

任意随机多元函数序列的一类强偏差定理

本文通过概率空间上的任意测度与另一任意测度相比较,研究了任意随机多元函数序列普遍成立的一类强偏差定理.利用网微分法与分析运算法,获得了若干任意信源的Shannon-Mcmillan随机逼近定理,并将已有的关于随机多地函数序列及离散信源的结果加以推广.     

色散方程的一类具任意稳定性的显格式

本文对色散方程u_r=au_xxx构造了一类中间层包含四个结点,带两个参数m和θ的三层显式差分格式。当m和θ满足一定的关系时,其稳定性条件为|γ|≤(m+1)/(4(m-1))(|m|>1),从而当取m充分接近1时,可得到任意大的稳定性条件,并且保持截断误差阶不变。数值例子验证了理论分析的结果。     

任意空间曲面三元叶轮叶片厚度对气动性能的影响

以任意空间曲面三元闭式叶轮为对象,研究了不同展向和流向叶片厚度分布方案对离心压缩机气动性能的影响。数值结果表明:对等厚叶片沿展向和流向进行合理地削薄,均能在基本不改变小流量工况性能的情况下,显著提升大流量工况的性能。展向削薄叶片和流向削薄叶片带来的性能提升幅度可以叠加,通过组合叶片厚度分布改型,本文压缩机设计工况点等熵效率提升了约2.08%。相比于沿流向削薄前缘和尾缘厚度,沿展向削薄叶尖厚度具有更大的性能提升能力。研究工作为三元闭式离心压缩机叶轮的优化设计提供了有益的参考。     

Matrix Projection Exposure Using an Analogue Liquid Crystal Display Panel in Place of a Reticle

The most serious problems for the matrix projection exposure using a liquid crystal display (LCD) panel in place of a reticle are largely solved by a new breakthrough method. LCD matrix exposure is effective for small volume productions of print circuits, screen masks, micromachine parts, and other items. Since no reticles are needed, all reticle costs are saved, and turnaround times required for changing the patterns are greatly shortened. However, in the conventional method, pattern widths and positions were strictly restricted depending on the geometric size and pitch of the liquid crystal cells. In this paper, a new concept appointing the cell brightness grades continuously using an analogue interface LCD panel is proposed. Calculating the image intensity distributions for various appointments of cell brightness balances to print same wide patterns, it is clarified that the pattern widths and positions are not much different if the pattern widths are wider than 2 cell pitches of the LCD panel. Maximum width and position variations are less than ± 10% even when the patterns are printed at arbitrary positions, of course including halfway ones. The calculated results are proved by experiments using an analogue LCD panel with a cell pitch of 15 μm. Though the cell size are 13 × 10 μm², and different in x and y directions, almost same wide line-and-space patterns are successfully printed at all positions by only one exposure. It is not necessary to shift the reticle for overlapping exposures to print smooth patterns. Oblique patterns and complicated Chinese character patterns are also printed at arbitrary positions. The new breakthrough technology will make the LCD matrix exposure promising for wide uses of printing various rough patterns easily at small costs.     

Analytical Solutions of the Kratzer-Fues Potential in an Arbitrary Number of Dimensions

No Heading Some aspects of the N dimensional Kratzer-Fues potential are discussed, which is an extension of the combined Coulomb-like potential with inverse quadratic potential in N dimensions. The analytical solutions obtained (eigenfunctions and eigenvalues) are dimensionally dependent, so also, the solutions depend on the value of the coefficient of the inverse quadratic term. The expectation values for < r^–2 >, < r^–1 > and the virial theorem for this potential are obtained and the values are also dimensions and parameter dependent.     

非Lipschitz条件下严格伪压缩映射不动点的逼近

Abstract. Without the Lipschitz assumption and boundedness of K in arbitrary Banach spaces,the Ishikawa iteration     

On the statistical mechanics of rigid particles

In this paper, generalized functions are used in the configuration partition function for fluids composed of arbitrarily shaped, rigid particles. This leads to new expressions for the basic statistical thermodynamic functions and some equations that may be useful in developing approximate theories, such as the scaled particle theory, for such fluids. The results are applicable to a large class of arbitrarily shaped, rigid particles and reduce exactly to the usual hard-sphere expressions.     

Correlation inequalities for antiferromagnets

We prove several correlation inequalities for a class of antiferromagnets with pair interaction and arbitrary fields. To do this we use the Ginibre-Percus method of double variables.