Identification of source terms in wave equation with dynamic boundary conditions

This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fréchet differentiability of the Tikhonov functional is studied, and a gradient formula is obtained via the solution of an associated adjoint problem. Then, the Lipschitz continuity of the gradient is proved. Furthermore, the existence and the uniqueness for the minimization problem are discussed. Finally, some numerical experiments for the reconstruction of an internal wave force are implemented via a conjugate gradient algorithm.     

Jacobi矩阵特征值反问题

研究如下一类Jacobi矩阵特征值反问题:问题IEP:给定两个互异实数λ,μ(λ<μ)和两个n维非零实向量x,y,求n阶Jacobi矩阵J,使得(λ,x),(μ,y)分别恰是J的第i,j(i≠j)个特征对。还分析了Jacobi矩阵的特征性质,给出了一个特征对恰是Jacobi矩阵J的第i个特征对的充分必要条件,由此导出了问题IEP有解的充分必要条件。     

电容量及损耗角的一种测量方法

介绍了在微机控制的自动测量装置中采用的双极性电容器的测试方法。这种方法用反相运算放大器微分电路获得与电容器相关的两个工频电压,并通过对它们数字化输入微机内存,最后通过对数字化后的两个周期信号进行处理求得电容量和损耗角正切。     

~ Transform Demonstration of Dark Soliton Solutions Found by Inverse Scattering

One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions.     

空气开关等离子体干涉条纹图像的处理

利用Mach-Zehnder干涉仪测量了空气开关中等离子体电子密度分布,使用高速分幅相机拍摄记录不同时延下的干涉条纹图像。针对实验获得的干涉条纹图像的特点,提出了一种首先进行频域FFT滤波去噪,然后进行空域二值化、细化的处理方法。该方法能够很好的消除图像噪声的影响,提取出单像素的亮条纹中心线,从而能够准确读取条纹坐标信息,再通过对干涉条纹偏移量进行Abel逆变换,得到等离子体电子密度分布。     

基于奇异值分解的运动模糊图像广义逆恢复方法

当线性模型应用于运动模糊模糊图像的恢复时,方程的最小二乘解是恢复图像的最优线性无偏估计。由于图像退化过程的不适定性,当观测值受到噪声干扰时,该解往往会远偏离真值。为了克服这个问题,通过对退化矩阵的奇异值分解,提取其不易受干扰的子空间,用该空间重构的逆矩阵具有良好抑噪能力,使图像在较长的运动模糊尺度内恢复时保持较低的失真。     

Analytical predictions of shapes of laminar diffusion flames in microgravity and earth gravity

Flame shape is an important observed characteristic of flames that can be used to scale flame properties such as heat release rates and radiation. Flame shape is affected by fuel type, oxygen levels in the oxidiser, inverse burning and gravity. The objective of this study is to understand the effect of high oxygen concentrations, inverse burning, and gravity on the predictions of flame shapes. Flame shapes are obtained from recent analytical models and compared with experimental data for a number of inverse and normal ethane flame configurations with varying oxygen concentrations in the oxidiser and under earth gravity and microgravity conditions. The Roper flame shape model was extended to predict the complete flame shapes of laminar gas jet normal and inverse diffusion flames on round burners. The Spalding model was extended to inverse diffusion flames. The results show that the extended Roper model results in reasonable predictions for all microgravity and earth gravity flames except for enhanced oxygen normal diffusion flames under earth gravity conditions. The results also show trends towards cooler flames in microgravity that are in line with past experimental observations. Some key characteristics of the predicted flame shapes and parameters needed to describe the flame shape using the extended Roper model are discussed.     

0.14 THz高分辨力成像雷达信号处理

为适应0.14 THz超高分辨雷达实时成像的需求,开发了基于CPU+GPU+FPGA的硬件架构和成像处理算法,算法以距离-多普勒为原型,引入L类维格纳分布变换提高横向分辨力,用Keystone变换方法对越距离单元徙动进行校正,并开发了系统非线性补偿算法。在载频0.14 THz、带宽5 GHz雷达样机上进行了逆合成孔径雷达成像试验,获得了3 cm3 cm的成像分辨力和实时成像能力,验证了信号处理方法的有效性。     

晶体中隐含的半群结构

序列性和莫比吾思反演已应用到物理中各类逆问题,诸如黑体辐射逆问题、比热逆问题和各类费米体系逆问题.文章要介绍这种方法对提取体材料中原子相互作用势的结合能逆问题的应用,以及对提取界面两侧原子间相互作用势的界面粘结能逆问题的应用.这些方法的关键是要发现对象体系中的半群结构.     

非线性薛定谔模型边界场算子的形式因子

讨论了可积开边界条件下的非线性薛定谔模型，给出了其贝特本征态的内积和模长.在此基础上得到了边界场算子的形式因子. 这些结果均被表达成由谱参量的函数所构成的行列式. 关键词： 可积模型 形式因子 反散射