Numerical Study on an RBF-FD Tangent Plane Based Method for Convection–Diffusion Equations on Anisotropic Evolving Surfaces

In this paper, we present a fully Lagrangian method based on the radial basis function (RBF) finite difference (FD) method for solving convection–diffusion partial differential equations (PDEs) on evolving surfaces. Surface differential operators are discretized by the tangent plane approach using Gaussian RBFs augmented with two-dimensional (2D) polynomials. The main advantage of our method is the simplicity of calculating differentiation weights. Additionally, we couple the method with anisotropic RBFs (ARBFs) to obtain more accurate numerical solutions for the anisotropic growth of surfaces. In the ARBF interpolation, the Euclidean distance is replaced with a suitable metric that matches the anisotropic surface geometry. Therefore, it will lead to a good result on the aspects of stability and accuracy of the RBF-FD method for this type of problem. The performance of this method is shown for various convection–diffusion equations on evolving surfaces, which include the anisotropic growth of surfaces and growth coupled with the solutions of PDEs.     

一种基于新型小波包阈值的图像去噪方法

提出了一种基于小波包理论去除图像噪声的方法,用小波包把图像分解为高频分量和低频分量,根据高频分量估计噪声的标准差,并利用该标准差以及Birge-Massart惩罚函数计算阈值.鉴于传统软硬阈值的缺陷,采用一种新型阈值量化方法,用三次多项式在硬阈值的基础上插值,使新的阈值函数保持了连续性和可导性.通过这种方法既消除了图像的振铃现象,又保留了细节成分.实验表明：与传统方法相比,新方法使图像视觉效果和峰值信噪比均获得提高.     

基于一维标定物和改进进化策略的相机标定

为了解决运动参数光电探测过程中的相机标定问题,制作一种两端及中间各安装一个红外反光标记球的一维标定物.不需要其它复杂标定装置,只要将这种特制的一维标定物在测量空间内多次随意移动并摄取其图像,即可实现标定.算法首先假定主点位于像面中心附近的某个位置,再求出焦距、旋转矩阵、平移向量和比例因子,最后通过评价函数将相机标定转换成寻找两相机最佳主点对的非线性最小化问题.在传统进化策略中引进个体的自我改进系数、个体间距离等概念,提出了求取子代个体间的欧式距离并排序的方法,设计了搜索最佳主点对的改进型进化策略算法.与传统标定方法相比,基于一维标定物的方法克服了多相机场合的遮挡问题,改进进化策略的引入打破了一维标定物需做某种特殊运动的限制,使一维标定物自由运动时相机内、外参数的同时求解成为可能,改进的模拟退火进化策略改善了算法的全局收敛性能并加快了收敛速度.     

Mural inspection by vibration measurements with TV-holography

A commonly encountered problem in the conservation of historical murals is the identification of sections in the plaster that have detached from the wall and thus threaten to fall off. Commonly, walls are inspected by the acoustic response to a gentle finger-tapping (percussion method). Since this is a costly and cumbersome technique, means for a more automatic inspection are searched for. A TV-holography system of increased sensitivity in combination with acoustic excitation of the object is shown to be a new and powerful tool for monitoring of loose areas. It has the advantage of non-contact and remote operation which, for example, is extremely useful in large buildings. Principles of the method, experimental results obtained at an artificial wall in the laboratory, and a thorough comparison of results from historical sites gained by the traditional percussion method and the new technique are presented. The latter shows very good agreement in the assessment of wall quality and thus is evidence of the suitability of the optical equipment for tasks in conservation.     

LIMITED MEMORY BFGS METHOD FOR NONLINEAR MONOTONE EQUATIONS

In this paper, we propose an algorithm for solving nonlinear monotone equations by combining the limited memory BFGS method （L-BFGS） with a projection method. We show that the method is globally convergent if the equation involves a Lipschitz continuous monotone function. We also present some preliminary numerical results.     

Spin Transport in a Rashba Ring-Quantum Dot System Pumped by Microwave Fields

We report a theoretical study on producing electrically spin-polarized current in the Rashba ring with parallel double dots embedded, which are subject to two time-dependent microwave fields. By means of the Keldysh Green's function method, we present an analytic result of the pumped current at adiabatic limit and demonstrate that the interplay between the quantum pumping effectand spin-dependent quantum interference can lead to an arbitrarily controllable spin-polarized current in the device. The magnitude and direction of the charge and spin current can be effectively modulated by system parameters such as the pumping phase difference, Rashba precession phase, and the dynamic phase difference of electron traveling in two arms of ring; moreover, thespin-polarization degree of the charge current can also be tuned in the range [-∞, +∞]. Our findings may shed light on the all-electric way to produce the controllable spin-polarized charge current in the field of spintronics.     

Spin-correlation function of the fully frustrated Ising model and ± J Ising spin glass on the square lattice

In this work we study the correlation function of the ground state of two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as correlation function. We estimate the exponent of spin correlation function for fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.     

基于溶液温度差谱分析的ATR-FTIR原位测量方法

作为一种原位、快速、无损坏的中红外光谱分析技术,ATR-FTIR已在很多工程领域得到越来越多的应用,尤其是针对结晶过程溶液浓度的原位实时测量。水是一种常用的结晶溶剂,在中红外波段具有强吸收峰,并且在不同温度下具有光谱吸收差异性,因而不能忽略溶剂水和温度对溶液浓度的中红外光谱测量带来的影响。以朗伯-比尔定律为基础,提出采用溶液光谱减去相应温度下的溶剂光谱的方法,从而能准确地测量溶液浓度。以L-谷氨酸溶液结晶过程为例,对L-谷氨酸水溶液的原始光谱数据、溶液光谱扣除常温(25℃)溶剂水的光谱数据以及溶液光谱对应温度扣除溶剂水的光谱数据分别进行建模。结果表明,提出的对应温度差谱法能有效消除溶剂水峰对溶质光谱测量的干扰,明显地降低了溶液浓度光谱标定模型的预测误差。该方法对提高原位ATR-FTIR光谱检测精度的实际应用具有一定的参考价值。     

寄生虚反射对外差干涉椭偏测量的影响

研究了一种采用横向塞曼激光器并且没有任何运动部件的外差干涉椭偏测量系统。由非理想的激光源、偏振分光镜等器件所产生的非线性误差,是影响纳米测量精度的主要因素。采用琼斯矢量法,分析并建立了光学系统寄生虚反射所引入的误差模型,讨论了虚反射对误差漂移的影响。在不考虑其它误差因素的前提下,同一光路内部产生的同频率虚反射波对测量结果没有影响;而不同频率的参考光束与测量光束之间的交叉虚反射所产生的膜厚测量误差为亚纳米量级。讨论了消除和抑制虚反射误差的方法。     

关于分布函数极大值位置的讨论

将关于某个变量的连续分布函数进行变数变换,除非新老变数为线性关系,否则变换前后的分布函数的极大值之间的关系一般会不同于新老变数之间的关系。