Measuring thickness change of transparent plate by electronic speckle pattern interferometry and digital image correlation

The thickness change of transparent plates was measured by electronic speckle pattern interferometry (ESPI) method and digital image correlation (DIC) method. An out-of-plane ESPI system was developed based on the Michelson interferometer, and a new thickness measurement method was designed, which is on the basis of Snell's law of refraction and DIC. The main principles and experimental procedures of these two methods were presented. The thickness change of polymethyl specimens under uniaxial tensile loading were measured by the optical techniques and compared with each other. The results reveal that the data obtained with DIC method achieve better linearity than ESPI.     

Effective method for preparation of oxide-free Ge2Sb2Te5 surface: An X-ray photoelectron spectroscopy study

Cleaning the surfaces of the as-deposited Ge₂Sb₂Te₅ was studied by X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM) and X-ray diffraction (XRD). The mixed native oxides on the as-deposited Ge₂Sb₂Te₅ surface can be easily removed by dipping Ge₂Sb₂Te₅ in de-ionized water for 1 min, while the surface morphology remains unchanged after cleaning. Native oxides only re-grow after exposure to air for more than 4 min. Although dipping in water leads to a surface layer deficient in Ge and Sb, the surface composition of Ge₂Sb₂Te₅ can recover to its stoichiometric value after annealing at 200 °C in vacuum. The phase remains amorphous at room temperature after dipping in water, and changes to fcc and hcp after annealing at 100 and 220 °C, respectively.     

线性比式和规划问题的输出空间分支定界算法

本文旨在针对线性比式和规划这一NP-Hard非线性规划问题提出新的全局优化算法.首先,通过引入p个辅助变量把原问题等价的转化为一个非线性规划问题,这个非线性规划问题的目标函数是乘积和的形式并给原问题增加了p个新的非线性约束,再通过构造凸凹包络的技巧对等价问题的目标函数和约束条件进行相应的线性放缩,构成等价问题的一个下界线性松弛规划问题,从而提出了一个求解原问题的分支定界算法,并证明了算法的收敛性.最后,通过数值结果比较表明所提出的算法是可行有效的.     

p-Euler equations and p-Navier–Stokes equations

We propose in this work new systems of equations which we call p-Euler equations and p-Navier–Stokes equations. p-Euler equations are derived as the Euler–Lagrange equations for the action represented by the Benamou–Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the ‘momentum’ is the signed ($p?1$)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier–Stokes equations. If $\gamma =p$, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier–Stokes equations in ${\mathbb{R}}^d$ for $\gamma =p$ and $p\ge d\ge 2$ through a compactness criterion.     

On a model for the Navier–Stokes equations using magnetization variables

It is known that in a classical setting, the Navier–Stokes equations can be reformulated in terms of so-called magnetization variables w that satisfy

(1)${?}_{t}w+(\mathbb{P}w?\mathrm{?})w+{(\mathrm{?}\mathbb{P}w)}^{?}w?\mathrm{\Delta }w=0,$

and relate to the velocity u via a Leray projection $u=\mathbb{P}w$. We will prove the equivalence of these formulations in the setting of weak solutions that are also in $L^{\infty }(0,T;H^{1/2})\cap L^2(0,T;H^{3/2})$ on the 3-dimensional torus.Our main focus is the proof of global well-posedness in $H^{1/2}$ for a new variant of (1), where $\mathbb{P}w$ is replaced by w in the second nonlinear term:

(2)${?}_{t}w+(\mathbb{P}w?\mathrm{?})w+\frac{1}{2}\mathrm{?}|w{|}^2?\mathrm{\Delta }w=0.$

This is based on a maximum principle, analogous to a similar property of the Burgers equations.     

不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法

针对带不等式约束的极大极小问题,借鉴一般约束优化问题的模松弛强次可行SQP算法思想,提出了求解不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法.首先,通过在QCQP子问题中选取合适的罚函数,保证了算法的可行性以及目标函数F(x)的下降性,同时简化QCQP子问题二次约束项参数α_k的选取,可保证算法的可行性和收敛性.其次,算法步长的选取合理简单.最后,在适当的假设条件下证明了算法具有全局收敛性及强收敛性.初步的数值试验结果表明算法是可行有效的.     

On well-posedness for some dispersive perturbations of Burgers' equation

We show that the Cauchy problem for a class of dispersive perturbations of Burgers' equations containing the low dispersion Benjamin–Ono equation

${?}_{t}u?D_x^{\alpha }{?}_{x}u={?}_x(u^2),0<\alpha \le 1,$

is locally well-posed in $H^s(\mathbb{R})$ when $s>s_{\alpha }:=\frac{3}{2}?\frac{5\alpha }{4}$. As a consequence, we obtain global well-posedness in the energy space $H^{\frac{\alpha }{2}}(\mathbb{R})$ as soon as $\frac{\alpha }{2}>s_{\alpha }$, i.e. $\alpha >\frac{6}{7}$.     

M估计的稳健平面标靶中心定位算法

标靶在地面激光扫描仪多测站点云配准,以及在全球卫星导航信号不良状况下改善移动激光雷达系统精度具有重要作用,标靶的精确提取与定位是关键问题之一。本文提出基于M估计的标靶中心定位方法：先根据标靶与周围环境反射强度差异,构建强度变化率特征,提取标靶边缘点云;再对标靶候选区域点云进行主成分分析,计算标靶平面法向量,对标靶边缘点云进行投影变换;最后通过M估计选权迭代法,剔除标靶噪声与粗差点云,拟合标靶形状,精确定位标靶中心。试验表明,本文算法能够在标靶存在冗余、缺损状态时排除非标靶圆形边缘的粗差点,获得高精度标靶中心。     

Global existence to the initial–boundary value problem for a system of nonlinear diffusion and wave equations

We prove the global existence of weak solution pair to the initial boundary value problem for a system of m-Laplacian type diffusion equation and nonlinear wave equation. The interaction of two equations is given through nonlinear source terms $f(u,v)$ and $g(u,v)$.