Corners of self-conjugate (s,s + 1)-cores and (s‾,s+1‾)-cores

In this paper, we describe a result on self-conjugate $(s,s+1)$-core partitions with the fixed number of corners. We also define shifted corners of a distinct partition and find formulas for the number of $(\stackrel{￣}{s},\stackrel{￣}{s+1})$-core partitions and the number of $(s,s+1)$-core shifted Young diagrams with the fixed number of shifted corners.     

锥体棱镜的加工

本文简单地叙述了锥体棱镜两种加工工艺。重点介绍直接成型法加工中对角度误差~1″的控制。并提出了角度超差零件返修时的光胶方法。     

角锥棱镜谐振腔激光模式模拟研究

为了探究角锥棱镜谐振腔激光模式,以角锥-平面镜腔为例,将角锥棱镜等效为衍射光栅,考虑角锥镜棱宽在谐振腔中的衍射效应以及二面角误差引起的附加相位分布对谐振腔激光模式的影响,在光学谐振腔理论的基础上,建立了求解本征模式的理论分析模型.采用快速傅里叶法数值模拟不同腔长、角锥镜棱宽和二面角误差情况下该无源谐振腔激光输出模式分布情况.结果表明,在腔长30 cm、角锥镜棱宽小于75μm、二面角误差在-10′~5′之间时,可实现光斑完整的圆形分布输出模式,且有较好的光束质量;棱宽不小于0.4 mm,二面角误差在-40′~10′之间时,光斑为TEM 03阶横模,光场呈六瓣分布;当角锥镜棱宽为0.4 mm、二面角误差为3′,腔长从30~90 cm范围内增加时,该谐振腔输出的激光模式从TEM 03转换成TEM 10.     

Modification of Spalart-Allmaras model with consideration of turbulence energy backscatter using velocity helicity

The correlation between the velocity helicity and the energy backscatter is proved in a DNS case of 256³-grid homogeneous isotropic decaying turbulence. The helicity is then proposed to be employed to improve turbulence models and SGS models. Then Spalart-Allmaras turbulence model (SA) is modified with the helicity to take account of the energy backscatter, which is significant in the region of corner separation in compressors. By comparing the numerical results with experiments, it can be concluded that the modification for SA model with helicity can appropriately represent the energy backscatter, and greatly improves the predictive accuracy for simulating the corner separation flow in compressors.     

Fatigue crack growth behavior of Al7050-T7451 attachment lugs under flight spectrum variation

This paper discusses an analytical and experimental investigations of the fatigue crack growth behavior in attachment lugs subjected to a randomized flight-by-flight spectrum. In the analysis, the stress intensity factors for through-the-thickness cracks initiating from lug holes were compared by weight function method, boundary element method (BEM), the interpolation of Brussat’s solution. The stress intensity factors of a corner crack at a transition region were obtained using two parameter weight function method and correction factors. Fatigue life under a load spectrum was predicted using stress intensity factors and Willenborg retardation model considering the effects of a tensile overload. Experiments were performed under a load spectrum and compared with the fatigue life prediction using the stress intensity factors by different methods. Changes of fatigue life and aspect ratio according to the clipping level of the spectrum were discussed through experiment and prediction. Effect of the spectrum clipping level on the fatigue life was experimentally evaluated by using beach marks of fractured surface.     

Optimal estimates of the field enhancement in presence of a bow-tie structure of perfectly conducting inclusions in two dimensions

This paper deals with the field enhancement due to insertion of a bow-tie structure of perfectly conducting inclusions into the two-dimensional space with a given field. The field enhancement is represented by the gradient blow-up of a solution to the conductivity problem. The bow-tie structure consists of two disjoint bounded domains which have corners with possibly different aperture angles. The domains are parts of cones near the vertices which are nearly touching to each other. We construct functions explicitly which characterize the field enhancement. As consequences, we derive optimal estimates of the gradient in terms of the distance between two inclusions and aperture angles of the corners. The estimates show in quantitatively precise way that the field is enhanced beyond the corner singularities due to the interaction between two inclusions, and the blow-up rate is much higher than the one for the case of inclusions with smooth boundaries.     

Universal quadratures for boundary integral equations on two-dimensional domains with corners

We describe the construction of a collection of quadrature formulae suitable for the efficient discretization of certain boundary integral equations on a very general class of two-dimensional domains with corner points. The resulting quadrature rules allow for the rapid high-accuracy solution of Dirichlet boundary value problems for Laplace’s equation and the Helmholtz equation on such domains under a mild assumption on the boundary data. Our approach can be adapted to other boundary value problems and certain aspects of our scheme generalize to the case of surfaces with singularities in three dimensions. The performance of the quadrature rules is illustrated with several numerical examples.     

基于改进Harris角点算法的摄像机标定技术研究

针对传统的Harris焦点提取算法对噪声敏感,执行效率低等不足,提出了一种改进的Harris焦点提取方法。以Harris焦点提取算法为基础,通过优化角点响应函数,消除系数 K,提高焦点提取算法的执行效率。采用改进的 Harris 算法对黑白棋盘表格进行内角点提取,利用张正友摄像机标定法计算USB摄像机的内外参数。实验结果证明了该方法可以有效的对黑白棋盘格内角点进行提取,准确高效,提高了摄像机的标定精度和准确性,是一种可行的摄像机标定方法。     

Hermite Subdivision Schemes and Taylor Polynomials

We propose a general study of the convergence of a Hermite subdivision scheme ℋ of degree d>0 in dimension 1. This is done by linking Hermite subdivision schemes and Taylor polynomials and by associating a so-called Taylor subdivision (vector) scheme . The main point of investigation is a spectral condition. If the subdivision scheme of the finite differences of is contractive, then is C ⁰ and ℋ is C ^d . We apply this result to two families of Hermite subdivision schemes. The first one is interpolatory; the second one is a kind of corner cutting. Both of them use the Tchakalov-Obreshkov interpolation polynomial.