Ellipse detection and phase demodulation for wood grain orientation measurement based on the tracheid effect

The methods of ellipse detection and phase demodulation for determining wood grain orientation are proposed. These methods are based on the tracheid effect—laser beam impinging upon a wood surface forms an elongated laser spot with its direction indicative of the grain orientation. Experimental results show that the method of ellipse detection is suitable for the grain orientation measurement on planed softwood surfaces, while the method of phase demodulation is capable of extracting the grain orientation precisely from laser images with low signal-to-noise ratio, such as the images on the surfaces of hardwood species or roughsawn materials.     

关于非退化的二阶曲线的分类研究

从抛物线的一种判定方法出发,借助于欧氏平面上非退化的二阶曲线的度量性质,通过对欧氏平面上非退化二阶曲线类型的研究,探究出确定非退化二阶曲线类型的若干定理。     

Uniform and refinable grids on elliptic domains and on some surfaces of revolution

We construct a bijection from R² to R², which maps rectangles centered at the origin O onto ellipses centered at O, and preserves area. This bijection allows us to construct uniform and refinable grids on elliptic domains. Then, we combine a particular case of this bijection (i.e. that bijection that maps squares into circles) with another area preserving projection from R² to a surface of revolution around Oz. This yields uniform and refinable grids on this surface of revolution. The lines of these grids are situated in horizontal planes, if they are images of squares centered at O. We consider the particular case of the hemisphere and show how the northern hemisphere of the Earth is projected onto a square. Thus, our equiareal maps can be useful for constructing geographical maps of one hemisphere of the Earth onto rectangles.     

基于均分配焦椭流线法的LED匀光管菲涅尔反射器设计

基于边光原理和椭流线理论提出了均分配焦椭流线的非成像光学设计方法,通过对LED光源的能量均分、椭流线虚实焦点的配对和光学仿真优化三个规范步骤实现了应用于LED匀光管均匀配光的菲涅尔反射器的光学设计.分析了光源、反射器和投射目标面三者之间的复杂关系,为LED照明设计的优化提供了方便.仿真结果表明,LED匀光管管壁照度的均匀度超过0.93,有效降低了LED光源的眩光性.     

Transverse conductivity and longitudinal shear of elliptic fiber composite with imperfect interface

The paper addresses the problem of calculating the local fields and effective transport properties and longitudinal shear stiffness of elliptic fiber composite with imperfect interface. The Rayleigh type representative unit cell approach has been used. The micro geometry of composite is modeled by a periodic structure with a unit cell containing multiple elliptic inclusions. The developed method combines the superposition principle, the technique of complex potentials and certain new results in the theory of special functions. An appropriate choice of the potentials provides reducing the boundary-value problem to an ordinary, well-posed set of linear algebraic equations. The exact finite form expression of the effective stiffness tensor has been obtained by analytical averaging the local gradient and flux fields. The convergence of solution has been verified and the parametric study of the model has been performed. The obtained accurate, statistically meaningful results illustrate a substantial effect of imperfect interface on the effective behavior of composite.     

BiGlobal stability analysis in curvilinear coordinates of massively separated lifting bodies

A methodology based on spectral collocation numerical methods for global flow stability analysis of incompressible external flows is presented. A potential shortcoming of spectral methods, namely the handling of the complex geometries encountered in global stability analysis, has been dealt with successfully in past works by the development of spectral-element methods on unstructured meshes. The present contribution shows that a certain degree of regularity of the geometry may be exploited in order to build a global stability analysis approach based on a regular spectral rectangular grid in curvilinear coordinates and conformal mappings. The derivation of the stability linear operator in curvilinear coordinates is presented along with the discretisation method. Unlike common practice to the solution of the same problem, the matrix discretising the eigenvalue problem is formed and stored. Subspace iteration and massive parallelisation are used in order to recover a wide window of its leading Ritz system. The method is applied to two external flows, both of which are lifting bodies with separation occurring just downstream of the leading edge. Specifically the flow configurations are a NACA 0015 airfoil, and an ellipse of aspect ratio 8 chosen to closely approximate the geometry of the airfoil. Both flow configurations are at an angle of attack of 18° with a Reynolds number based on the chord length of 200. The results of the stability analysis for both geometries are presented and illustrate analogous features.     

Binary fluid mixture of hard ellipses: Integral equation and weighted density functional theory

We study a two-dimensional (2D) classical fluid mixture of hard convex shapes. The components of the mixture are two kinds of hard ellipses with different aspect ratios. Two different approaches are used to calculate the direct, pair and total correlation functions of this fluid and results are compared. We first use a formalism based on the weighted density functional theory (WDFT), introduced by Chamoux and Perera [Phys. Rev. E 58 (1998) 1933]. Second, in general the Percus-Yevick (PY) and the hypernetted chain (HNC) integral equations are solved numerically for the 2D fluid mixtures of hard noncircular particles. Explicit results are obtained for the fluid mixtures of hard ellipses and comparisons are made by the two approaches. Also, the results are compared with the recent Monte Carlo simulation for the one-component fluids of hard ellipses. Finally we obtained the equation of state of hard ellipses for the aspect ratio sufficiently close to 1 and compared our results with the simulations of the fluid mixtures of hard disks.     

椭圆法测量接触角

接触角在胶体与表面化学,矿物浮选,洗涤和油气开采等领域是一项重要的物性参数。接触角的测量方法很多,其中固滴法因只需少量试样,简便易行而应用较广。人们为避免人为因素对固滴法中作切线的影响,在此基础上提出了各种通过测量液滴尺寸计算接触角的间接方法,并以圆法,即半角法应用最广。这些方法将液滴剖面视为圆形,液滴剖面受重力影响偏离圆形,使计算结果产生误差,在液滴体积较大和界面张力较低时尤为明显。Ryley建议将油滴剖面视为椭圆,在其轮廓线上选择三点,测量六个数据计算接触角,该法不受重力影响,较圆法优越,缺点是需要测量的数据较多,计算公式复杂,难以推广应用。本文提出只需在椭圆轮廓线上选择两点,测量四个数据计算接触角的方法,计算公式比较简单,便于推广应用。     

数学建模在多元统计分析教学中的应用

本利用数学建模的思想对多元统计分析特别是主成分分析方法的教学进行改革，通过使用统计软件SPSS进行计算和分析，使学生对十分抽象的统计概念和深奥的多元统计理论有直现的认识和理解，为掌握多元统计分析方法提供了较好的手段。     

Flow separation behind ellipses at Reynolds numbers less than 10

Flow separation behind two-dimensional ellipses with aspect ratios ranging from 0, a flat plate, to 1, a circular cylinder, were investigated for Reynolds numbers less than 10 using both a cellular automata model and a commercial computational fluid dynamics software program. The relationship between the critical aspect ratio for flow separation and Reynolds number was determined to be linear for Reynolds numbers greater than one. At slower velocities, the critical aspect ratio decreases more quickly as the Reynolds number approaches zero. The critical Reynolds numbers estimated for flow separation behind a flat plate and circular cylinder agree with extrapolations from experimental observations. Fluctuations in the values of the stream function for laminar flow behind the ellipses were found at combinations of Reynolds number and aspect ratio near the critical values for separation.