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.     

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.     

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。     

无穷积分余项与其被积函数比值的收敛阶

对一类函数的无穷积分余项与该函数的比值得到当x趋于无穷大时的收敛阶,这类函数是幂函数与指数函数的乘积函数,并将其应用到Mittag-Leffler函数.同时考虑了对应的级数情形.     

一个新的IEC61000-4-2标准ESD电流解析表达式

分析了两个ESD标准电流波形表达式,并提出一个新的基于脉冲函数来描述ESD标准电流的解析表达式,该表达式符合最新的标准IEC61000-4-2,在零时刻的电流及其微分部为0,且波形与实际测量波形基本吻合。     

电子束泵浦氩中高能电子分布的理论计算

改进了文献中报导的Boltzmann基本方程。与Boltzmann基本方程相比,改进后的Boltzmann方程更全面地描述了电子与基态氩原子碰撞的物理过程,并能计算出整个能量区间的电子分布。利用Boltzmann基本方程和改进的Boltzmann方程,对电子束泵浦氩中能量大于氩原子第一激发态能量(11.56eV)的高能电子分布函数进行了理论计算。计算中,选取了电子碰撞氩的微分电离截面和激发截面的解析表达式。对计算所得的稳态电子分布函数以及达到稳态分布所需的特征时间进行了分析和讨论。     

Electron energy-loss spectroscopy of V2O5 nanofibers synthesized by electro-spinning

The dielectric properties of V₂O₅ nanofibers, synthesized by the electrospinning method, are studied by analyzing the low-loss region of the electron energy loss spectroscopy (EELS) in a transmission electron microscope. A comparison of experimental EELS spectra and ab initio density-functional theory calculations (WIEN2k code) within the Generalized Gradient Approximation (GGA) is presented, having found an excellent agreement between them. Although the experimental EELS has been acquired for the nanoparticles composing the fibers, and numerical calculations were carried out for bulk material, agreement between experimental and calculated results shows that no difference exists between the electronic structure in calculated bulk material and the nanoparticles. Furthermore, our results from EELS confirm that we accomplished the expected crystalline phase. The origins of interband transitions are identified in the electronic band structure by calculating the partial imaginary part of the dielectric function and the partial density of states.