Spectral analysis and numerical simulation for second order elliptic operator with highly oscillating coefficients in perforated domains with a periodic structure

This paper discusses the spectral properties and numerical simulation for the second order elliptic operators with rapidly oscillating coefficients in the domains which may contain small cavities distributed periodically with period ε. A multiscale asymptotic analysis formula for this problem is obtained by constructing properly the boundary layer. Finally, numerical results are given, which provide a strong support for the analytical estimates     

红外探测器光电性能测量系统方案研究

本文提出了一种新型的由微机控制的全自动红外探测器件光电性能测量系统,针对系统的硬件组成部分及其设计思想做了详细的讨论.     

Spatial‐skin effect for eigenvibrations of a thick cascade junction with ‘heavy’ concentrated masses

A spectral problem for the Laplace operator in a thick cascade junction with concentrated masses is considered. This cascade junction consists of the junction's body and a great number of ?‐alternating thin rods belonging to two classes. One class consists of rods of finite length, and the second one consists of rods of small length of order . The density of the junction is of order on the rods from the second class and outside of them. The asymptotic behavior of eigenvalues and eigenfunctions of this problem is studied as ? → 0. There exist five qualitatively different cases in the asymptotic behavior of eigenmagnitudes as ? → 0, namely the case of ‘light’ concentrated (α ∈ (0,1)), ‘middle’ concentrated (α = 1), and ‘heavy’ concentrated masses (α ∈ (1, + ∞ )) that we divide into ‘slightly heavy’ concentrated (α ∈ (1,2)), ‘intermediate heavy’ concentrated (α = 2), and ‘very heavy’ concentrated masses (α > 2). In the paper, we study in detail the influence of the concentrated masses on the asymptotic behavior if α ∈ (1,2). We construct the leading terms of asymptotic expansions both for the eigenvalues and eigenfunctions and prove the corresponding asymptotic estimates. Copyright © 2013 John Wiley & Sons, Ltd.     

红外光谱结合线阵列检测技术研究聚合物分散液晶膜分子取向

采用偏振红外光谱和变温红外光谱研究聚合物分散液晶膜中液晶分子取向随外加电场及温度的变化.利用线阵列检测技术表征了聚合物与液晶界面处的成分分布.结果表明,线阵列检测技术能够快速而直观地给出成分分布图,通过该成分分布图可以解释PDLC在温度场作用下分子取向的变化.     

基于电致发光成像的太阳能电池缺陷检测

为了检测太阳能电池存在的缺陷,给太阳能电池施加一定的正向偏压,利用CCD相机在暗室中探测电池的发光。 探测分别在3种状态下进行:无滤光探测、过滤800 nm以下波长后探测和过滤800 nm以上波长后探测。研究发现:只有在过滤800 nm以下波长的镜片下探测效果最好,表明电池主要发红外光,其波长范围为850~1 200 nm。控制光探测器的探测时间,发现不同探测时间下电池的发光强度不同,探测时间相同但偏压不同则光强也不同。该方法可以检测出正向偏压下电池存在的各种缺陷类型。在反向电压下,薄膜电池会出现小光点,这表示缺陷区域和密度,研究证明薄膜电池也能发红外光且薄膜中存在区域缺陷。对低功率的电池片进行光探测发现,电池存在严重缺陷。上述结果表明,红外光探测可以直观、快速、方便地检测太阳能电池存在的缺陷。     

基于实时小波变换信号处理的相干检测布里渊光时域反射计

布里渊光时域反射计检测信号较微弱的自发布里渊散射光,其布里渊频移只有11 GHz左右.相干检测是一较好的方法,但其接收信号是一宽带的幅度调制信号,难以直接解调.采用实时小波变换对传感信号进行处理,设计了布里渊光时域反射计传感器实验系统,实现了25 km的分布式温度传感,在5 m的空间分辨率和1 min的响应时间下,达到40 με的应变分辨率.     

Multiscale asymptotic expansions and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients

In this paper, we discuss the multiscale analysis and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients. The formal multiscale asymptotic expansions of the solutions for these problems in four specific cases are presented. Higher order corrector methods are constructed and associated explicit convergence rates are obtained in some cases. A multiscale numerical method and a symplectic geometric scheme are introduced. Finally, some numerical results and unsolved problems are presented, and these numerical results support strongly the convergence theorem of this paper.     

Extended Mild-Slope Equation

ＩｎｔｒｏｄｕｃｔｉｏｎＡｃｃｕｒａｔｅｍｏｄｅｌｌｉｎｇｏｆｓｕｒｆａｃｅｗａｖｅｄｙｎａｍｉｃｓｉｎｃｏａｓｔａｌｒｅｇｉｏｎｓｈａｓｂｅｅｎｔｈｅｇｏａｌｏｆｍｕｃｈｒｅｃｅｎｔｒｅｓｅａｒｃｈ ,ｗｈｉｃｈｈａｓｂｅｅｎｓｕｍｍａｒｉｚｅｄｉｎｓｕｒｖｅｙｓｂｙＤｉｎｇｅｍａｎｓ( 1 997) [1]ａｎｄＫｉｒｂｙ( 1 997) [2 ].Ｔｈｅｒｉｃｈｎｅｓｓｏｆｃｏａｓｔａｌｗａｖｅｄｙｎａｍｉｃｓａｒｉｓｅｓｆｒｏｍｔｈｅｓｔｒｏｎｇａｍｂｉｅｎｔｃｕｒｒｅｎｔｓａｎｄｔｈｅｗｉｄｅｖａｒｉａｔｉｏｎｓ…     

缓坡方程的推广

为了描述水波和强烈的环境流在非平整海底上的相互作用,运用无旋运动的Lagrangian变分原理,对经典的Berkhoff缓坡方程进行了改进。假定水流沿水深方向基本上保持均匀性,这正如潮流运动的特征。海底地形由慢变、快变两个分量叠加构成;慢变分量满足缓坡逼近假定,快变分量的波长与表面波波长为同一量级,但其振幅小于表面波的振幅。在以上假定条件下,得到了适用于非平整海底的推广型浅水方程和应用性更加广泛的波－流－非平整海底相互作用的一般缓坡方程,并且从理论上证明一般缓坡方程包含了以下3种著名的缓坡型方程：经典的Berkhoff缓坡方程;波－流相互作用的Kirby缓坡方程、Dingemans关于沙纹海底的缓坡方程。最后,通过与Bragg反射实验数据的比较,表明该模型可以准确地反映快变海底的典型地貌特征。     

On Boundary-Value Problems for the Laplacian in Bounded Domains with Micro Inhomogeneous Structure of the Boundaries

We consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized （limit） problems depending on the ratio of small parameters, which characterize the diameter of parts of the boundary with different types of boundary conditions. Also we study the respective spectral problem of this type.