Duality in parameter space and approximation of measures for mixing repellers

For one-dimensional expanding mapsT with an invariant measure we consider, in a parameter space, the envelope _n of the real lines associated to any couple of points of the orbit, connected byn iterations ofT. If the map hass inverses and is piecewise linear, then the sets _n are just the union ofs ⁿ points and converge to the invariant Cantor set ofT. A correspondence between all the sets and their measures is established and allows one to associate the atomic measure on ₁ to the completly continuous measure on the Cantor set. If the map is nonlinear, hyperbolic, and hass inverses, the sets _n are homeomorphic to the Cantor set; they converge to the Cantor set ofT and their measures converge to the measure of the Cantor set whenn. The correspondence between the sets _n allows one to define converging approximation schemes for the map an its measure: one replaces each of thes ⁿ disjoint sets with a point in a convenient neighborhood and a probability equal to its measure and transforms it back to the original set ₁. All the approximations with linear Cantor systems previously proposed are recovered, the converging proprties being straightforward in the present scheme. Moreover, extensions to higher dimensionality and to nondisconnected repellers arte possible and are briefly examined.     

基于水平集方法二维模型的软性磨粒两相流流场特性分析方法

两相流场特性分析是软性磨粒流精密加工方法的技术关键. 针对此问题, 利用水平集方法(LSM)结构拓扑变换原理, 建立了描述磨粒流在另一流体中运动变化的二维模型. 该模型中, 用LSM捕捉两相流之间的界面, 从而对两相流的运动情况和相关参数进行模拟仿真, 深入讨论了磨粒流加工机理. 研究表明: 以LSM原理建立的二维模型, 成功地仿真模拟了两相流相变过程; 利用k-ε湍流模型与Preston方程相结合的数值分析方法, 对流道内各区域的速度等流场特性进行讨论, 为软性磨粒流加工提供了前期基础性研究. 关键词： 水平集方法 结构化表面 软性磨粒流 k-ε湍流模型')" href="#">k-ε湍流模型     

A nonlinear PDE model for reconstructing a regular surface from sampled data using a level set formulation on triangular meshes

In this paper, we propose a nonlinear PDE model for reconstructing a regular surface from sampled data. At first, we show the existence and the uniqueness of a viscosity solution to this problem. Then we propose a numerical scheme for solving the nonlinear level set equation on unstructured triangulations adapted to the data sample. We show the consistency of this scheme. In addition, we show how to compute nodewise first and second order derivatives. Some application examples of curve or surface construction are provided to illustrate the potential and to demonstrate the accuracy of this method.     

A robust numerical model for premixed flames with high density ratios based on new pressure correction and IMEX schemes

In this study we present a model for the interaction of premixed flames with obstacles in a channel flow. Although the flow equations are solved with Direct Numerical Simulation using a low Mach number approximation, the resolution used in the computation is limited (∼1 mm) hence the inner structure of the flame and the chemical scales are not solved. The species equations are substituted with a source term in the energy equation that simulates a one-step global reaction. A level set method is applied to track the position of the flame and its zero level is used to activate the source term in the energy equation only at the flame front. An immersed boundary method reproduces the geometry of the obstacles. The main contribution of the paper is represented by the proposed numerical approach: an IMEX (implicit–explicit) Runge–Kutta scheme is used for the time integration of the energy equation and a new pressure correction algorithm is introduced for the time integration of the momentum equations. The approach presented here allows to calculate flames which produce high density ratios between burnt and unburnt regions. The model is verified by simulating first simple solutions for one- and two-dimensional flames. At last, the experiments performed by Masri and Ibrahim with square and rectangular bodies are calculated.     

关于刚体转动惯量测定的计时方法研究

本文给出了在刚体转动惯量的测定中测定时间的计时装置，减小了计量时间所带来的误差。     

全相对论多组态原子结构及物理量的精密计算——构建准完备基以及组态相互作用

从第一原理出发计算原子结构有多种理论方法,它们都是基于变分原理的,其关键是构建一组最适合描述真实物理体系的且适用于变分原理的准完备基.本文阐明了如何利用全相对论计算程序GRASPVU,通过单组态Dirac-Fock计算以及多组态Dirac-Fock自洽场计算建立准完备基.然后利用该准完备基进行组态相互作用计算以充分考虑关联作用;在此基础上,进一步考虑电磁相互作用的延迟效应和量子电动力学等修正.该准完备基对原子结构和电磁跃迁等物理量可进行精密的理论计算.最简单的He体系的能级和跃迁速率等物理量的计算值与目前最准确的理论计算值以及精密的实验测量值符合很好,验证了本文提出的方案的适用性.本文计算是全相对论的,可推广到相对论效应很重要的高Z类He体系,以面向重离子储存环相关实验测量.同时该方案也适用于其他任何多电子原子体系;对Mg进行了精密理论计算,阐明了其33D,43D精细结构次序变化的机理.     

整数小波的有损与无损图像压缩

提出了基于整数小波变换的有损与无损图像编码方案。有损编码采用无链表的SPIHT零树编码算法,它不同于SPIHT和LZC算法的零树分割策略和状态比特表结构。该算法所需的存储空间小,有损压缩性能高,易于硬件的实现。无损编码根据不同子带小波系数的分布特性,采用带间预测编码,不同方向的子带采用不同的预测方式,预测误差采用霍夫曼编码。测试结果证明,基于整数小波的无链表有损压缩方案不仅优于LZC,接近于SPIHT,而且易于硬件的实现。     

Three types of maximally entangled states for a two-particle system

Foratwo-particle(spin1/2)systemthespinstateisdescribedusingavectorinafour-dimensionalHilbertspace.Inangularmomentumcouplingtheory[1],theangularmomentumuncouplingandcouplingrepresentationsareusuallyadopted.WhilethesimultaneouseigenstatesoftheCSCO(s1z,s2z),12,12,12and12,arechosenasthebasisofangularmomentumuncouplingscheme,thesimultaneouseigenstatesoftheCSCO(2,zSS),,SM(12=+Sss),arechosenasthebasisofangularmomentumcouplingscheme,1212100,2轾=-臌1212110,2轾=+臌121211,1,1.=-=Thefo…     

A joint shape evolution approach to medical image segmentation using expectation-maximization algorithm

This study proposes an expectation–maximization (EM)-based curve evolution algorithm for segmentation of magnetic resonance brain images. In the proposed algorithm, the evolution curve is constrained not only by a shape-based statistical model but also by a hidden variable model from image observation. The hidden variable model herein is defined by the local voxel labeling, which is unknown and estimated by the expected likelihood function derived from the image data and prior anatomical knowledge. In the M-step, the shapes of the structures are estimated jointly by encoding the hidden variable model and the statistical prior model obtained from the training stage. In the E-step, the expected observation likelihood and the prior distribution of the hidden variables are estimated. In experiments, the proposed automatic segmentation algorithm is applied to multiple gray nuclei structures such as caudate, putamens and thalamus of three-dimensional magnetic resonance imaging in volunteers and patients. As for the robustness and accuracy of the segmentation algorithm, the results of the proposed EM-joint shape-based algorithm outperformed those obtained using the statistical shape model-based techniques in the same framework and a current state-of-the-art region competition level set method.     

用电磁打点计时器进行受迫振动实验--介绍我校的一个自学物理实验

介绍一种用简单的方法进行的受迫振动实验。