Probing the topological structure of the QCD vacuum with overlap fermions
串联电池组电感电容储能主动均衡方法
cost advantage of the novel topology was analyzed. Finally, a series battery pack composed of four cells
离,但绕组变压器的设计比较复杂,且电池组单体数
量变化,绕组变压器需要重新设计。
综合电感储能均衡精度高、电压差异较大时电
容储能均衡速度快的特点,基于电感电容( Inductorcapacitor, LC) 储能的拓扑近年来得到了更多的关
注。 文献[15] 提出三种基于 LC 储能的单开关升降
压电路均衡拓扑,开关管数量较少,但其三个拓扑每
第 27 卷 第 5 期
2023 年 5 月
电 机 与 控 制 学 报
Electri c Machines and Control
Vol. 27 No. 5
May 2023
串联电池组电感电容储能主动均衡方法
郭向伟, 吴齐, 邢程, 谢东垒, 朱军
for series battery pack
GUO Xiangwei, WU Qi, XING Cheng, XIE Donglei, ZHU Jun
( School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China)
收稿日期: 2021 - 09 - 19
基金项目:国家自然科学基金(52177039) ;河南省科技攻关项目(232102240078) ;河南省高校基本科研业务费青年探索项目( NSFRF210332) ;
现代桥梁 屡创“世界第一”的港珠澳大桥 英文介绍
World-Leading BridgeThe Hong Kong-Zhuhai-Macao BridgeThe world’s longest sea-spanning bridge, the highway-railway bridge with the longest span in the world, the first sea-spanning dual-use bridge in the world –t hese are just some of the “world firsts” China has created in the sphere of bridge building. But the one which best represents China’s modern industrial power is the Hong Kong-Zhuhai-Macao Bridge.The construction of the Hong Kong-Zhuhai-Macao Bridge began on December 15, 2009. As soon as the ceremony for the commencement of the project was over, the chief engineer, Su Quanke (苏权科), convened a meeting at which he laid out a high-speed plan for the construction work.Engineer Lin was the first to speak: “The topological features of the site for the Hong Kong-Zhuhai-Macao Bridge are very special: The bridge will span the busiest sea lane in Lingdingyng Bay, and possibly block it at its narrowest part. Also, it will be built near a busy airport. So we have to build it in a way that does not interfere with either sea or air traffic, don’t we?”The conference hall fell silent as the delegates all looked at each other. All the plans they came up with had some flaw or other. Inside the conference hall, sighs could be heard, and Su Quanke himself was racked with anxiety, when his gaze happened to fall on a photograph of an ancient Chinese bridge which was lying on a desk –w hy not get inspiration from the experience of ancient Chinese bridge builders? China has a multiplicity of complicated rivers and landforms, and the ancients took local conditions into account and used local resources to ensure a perfect addition to Nature.Excitedly, Su Quanke shared his idea with the other engineers: “Why don’t we work in harmony with the local natural conditions? Now, the bearing capacity of the bridge will be excessive if we build it directly across the sea, and the sea itself here has many winding bays, so why don’t we build the bridge to connect several different spots, and thus ensure unimpeded transportation both on the sea and in the air?” Even before his words had died away, his colleagues started to applaud. This was the first instance of innovative objective thinking in Chinese bridge building, based on the rich heritage of Chinese bridge building.Although the problem of the design for the structure of the bridge had been overcome, there still remained many difficulties concerning its actual construction. For instance, there were thirty-three sections of tunnel to be joined up. When the first section was laid, nobody was confident that it could be placed in the proper position, because this was the first attempt to do this in the history of Chinese bridge building, and, in fact, it would be the first attempt in the world. The engineers did not dare make the slightest slip. It took ninety-six continuous hours to lay the first section. When it was finally perfectly placed in its designated position, some of the workers were so tired that they slumped to the ground and slept right away where they lay. Finally, after innumerable difficulties had been overcome, on July 7, 2017 the Hong Kong-Zhuhai-Macao Bridge was fully opened. Seen from the air, the winding bridge looks like a long dragon. From Zhuhai Bay, the bridge stretches for over thirty kilometers above the sea, together with six-point-seven kilometers of tunnels under the seabed, to end in Hong Kong. On the way, there are three specially modeled cable-stayed bridges, named “China Connection,”“Dolphin”and “Sail,” respectively, capable of sustaining a total of three hundred thousand tons of wheeled cargo.Su Quanke remarked, “The bridge not only links the three geographical regions, it also forms a link between our thoughts and feelings, including the creative superiority we have developed over centuries.”When we look at this magnificent sea-spanning bridge, as a great achievement of the century, we can see a combination of the millennia-long history of bridge building in China and modern technology, and the glitter of the Chinese people’s diligence and wisdom.The Moral of This StoryChina’s modern bridge construction is not just an embodiment of the development of modern industrial technology. It is even more an expression of the development of the heritage of China’s bridge-building industry and culture. It manifests China’s historical heritage, spirit of determination to overcome difficulties, and boldness in a pioneering way.现代桥梁屡创“世界第一”的港珠澳大桥世界最长跨海大桥、跨度最大的公路铁路两用桥、首座公路铁路两用跨海大桥……中国桥梁界为世界桥梁创造了众多的“世界第一”，而其中最能代表中国现代工业实力的，当属港珠澳大桥。
三相电压型PWM整流器直接功率控制方法综述
三相电压型PWM整流器直接功率控制方法综述/tech/intro.aspx?id=565点击数：260刘永奎，伍文俊（西安理工大学自动化学院电气工程系，陕西西安710048）摘要首先介绍了三相电压型PWM整流器的拓扑结构，在此基础上，对当前应用于PWM 整流器的直接功率控制策略进行了对比分析，介绍了其实现机理和优缺点，最后，对直接功率控制在三相电压型PWM整流器中的控制技术进行了展望。
关键字 PWM整流器；直接功率控制；综述Summary about Direct Power Control Scheme of Three-Phase Voltage Source PWM RectifiersLIU Yongkui，WU Wenjun（Xi'an University of Technology，Xi'an Shannxi 710048 China）Abstract The topological structure of three-phase PWM rectifiers is introduced. On this basis, several DPC methods of three-phase voltage source PWM rectifiers were introduced and compared. At last, the pros原per of the control scheme development trends in three-phase PWM rectifiers is presented.Keywords three-phase PWM rectifiers；direct power control；summary1 概述三相电压型PWM整流器具有能量双向流动、网侧电流正弦化、低谐波输入电流、恒定直流电压控制、较小容量滤波器及高功率因数（近似为单位功率因数）等特征，有效地消除了传统整流器输入电流谐波含量大、功率因数低等问题，被广泛应用于四象限交流传动、有源电力滤波、超导储能、新能源发电等工业领域。
一种反激式开关电源的设计与仿真
第38卷第4期计算机仿真2021年4月文章编号：1006 -9348(2021 )04 -0083-06一种反激式开关电源的设计与仿真王强\王槐生U，田宏伟1(1.苏州大学应用技术学院，江苏苏州215325;2.苏州大学电子信息学院，江苏苏州215006)摘要：为实现小功率开关电源的小型化、高效化和低成本，提出了一种基于电流型PW M芯片UC3842控制下双路输出的反激式开关电源。
研究了电源的拓扑结构和工作原理，详细分析了EM1滤波器和整流滤波电路、功率变换电路、PW M控制电 路、反馈检测电路的关键参数和设计过程。
利用Sabei•软件的仿真工具箱搭建了电路闭环仿真模型，模拟反激式电路的环路控制，实现两路直流输出5V/1A和15V/1A，效率髙达90%。
仿真结果证明了设计的正确性和可行性。
关键词.•开关电源;反激式;电路设计;建模与仿真中图分类号:TP391.9 文献标识码：BDesign and Simulation of a Flyback Switching Power SupplyWANG Qiang1,WANG Huai - sheng12 ,TIAN H ong-w ei1(1. Applied Technology College,Soochow University,Suzhou Jiangsu 215325 ,China；2.School of Electronic and Information Engineering,Soochow University,Suzhou Jiangsu 215006,China)A B S T R A C T：For the r e a l ization of small switching power supply miniaturization,high efficiency,and low cost,a f l yback switching power supply controlled dual output was designed based on the current - mode P W M chip U C3842.The topological structure and working principle of the power supply were studied.The key parameters and the design process of EMI f i l t e r s and r e c t i f i e r f i l t e r circuit,power conversion circuit,PWM control circuit,feedback detection c i rc u i t were analyzed in ing the simulation toolbox of Saber software t o build the closed - loop simulation mode l simulating the loop control of the flyback c i r c u i t and achieving the two - channel DC output of 5V/1A and 15 V/1A,the efficiency can reach 90%.The simulation resu l t s prove the correctness and f e a s i b i l i t y of the design.K E Y W O R D S：Switching power supply； Flyback； Circuit design； Modeling and simulationi引言近年来，随着电子电路仿真技术应用领域的不断扩展，对仿真技术也提出新的要求，如何提高仿真的可靠性和准确性，提高建模和仿真的效率对于电子电路设计具有重要意义[|]。
连续体结构的拓扑优化设计
连续体结构的拓扑优化设计一、本文概述Overview of this article随着科技的不断进步和工程需求的日益增长，连续体结构的拓扑优化设计已成为现代工程领域的研究热点。
拓扑优化旨在通过改变结构的内部布局和连接方式，实现结构性能的最优化，从而提高工程结构的承载能力和效率。
本文将对连续体结构的拓扑优化设计进行深入研究，探讨其基本原理、方法、应用以及未来的发展趋势。
With the continuous progress of technology and the increasing demand for engineering, the topology optimization design of continuum structures has become a research hotspot in the field of modern engineering. Topology optimization aims to optimize the structural performance by changing the internal layout and connection methods of the structure, thereby improving the load-bearing capacity and efficiency of engineering structures. This article will conduct in-depth research on the topology optimization design of continuum structures, exploring their basic principles, methods,applications, and future development trends.本文将介绍连续体结构拓扑优化的基本概念和原理，包括拓扑优化的定义、目标函数和约束条件等。
天然气管网仿真分层计算方法
第50卷第1期工程设计随着经济的持续发展，我国对能源的需求越来越大[1]。
由于天然气具有高热值、低碳、清洁等优点[2-3]，其消费量逐年增长。
预计到2030年，全国天然气消费量将达到（5500~6000）×108m 3[4]。
出于经济原因，天然气通常通过管道进行大规模输送[5-6]。
通过对天然气管网进行仿真，可以明确天然气在管网内部流动过程中的水热力变化情况，为天然气管网的优化、管理、调度及运行提供技术支持[7-10]。
截至2021年，我国主干天然气管道总里程达到11.6×104km [11]。
天然气管网规模的不断扩大对管网仿真提出了越来越高的要求。
对于大规模天然气管网，采用隐式差分法离散水热力系统得到的代数方程组规模较大。
受限于代数方程组巨大的规模，LU 分解等直接解法的[12]求解速度慢。
童睿康等[13]采用迭代法替代高斯消元法来求解水热力方程组，有效提高了求解速度。
然而，使用迭代法仍要对整个方程组进行求解操作，这对大规模管网来说仍是个较大的挑战。
为提高天然气管网的求解速度与效率，提出了一种管网分层求解的算法。
该算法将管网划分为不同层次的子管网，自下而上传递变量关系式，自上而下传递变量值，最终实现整个管网仿真过程的快速求解。
1管网数学模型天然气管网由管道、阀门、压缩机等元件组DOI ：10.3969/j.issn.1001-2206.2024.01.012天然气管网仿真分层计算方法阎涛1，刘天尧1，王雪莉1，薛向东1，2，康阳1，朱峰11.国家管网集团科学技术研究总院分公司，河北廊坊0650002.西安交通大学软件学院，陕西西安710049摘要：随着用气需求的日益增加，天然气管网的规模逐渐复杂化，管网仿真消耗的计算资源和计算时间亦趋庞大。
对于管网仿真过程中出现的大型代数方程组，结合天然气管网的拓扑结构特征，提出一种分层计算方法，该方法将管网自上而下分解为若干层，每层又包含若干独立的子管网，从而使得每个子管网的计算可以独立执行。
20kW三电平并网变流器主电路参数的设计
第38卷第20期电力系统保护与控制Vol.38 No.20 2010年10月16日Power System Protection and Control Oct. 16, 201020 kW三电平并网变流器主电路参数的设计易映萍 1 ，刘 刚2，胡四全2（1.上海理工大学，上海 200093；2.许继柔性输电有限公司，河南 许昌 461000）摘要：提出了采用三电平并网技术研制可再生能源发电高压并网变流器，介绍了三电平并网变流器主电路的拓扑结构，并对其主电路参数的选择进行了研究，给出了主电路功率器件IGBT、箝位二极管和直流侧电容的设计方法。
采用LCL滤波器抑制注入电网谐波，并对其工作原理和滤波特性进行了分析，建立了LCL滤波器设计的数学模型。
在此基础上，设计出了20 kW 三电平并网变流器的实验样机，实验结果表明所提出的设计方法正确实用。
关键词：三电平；并网变流器；主电路；IGBT；滤波器Design of main circuit parameters for 20 kW three-level grid-connected converterYI Ying-ping1，LIU Gang2，HU Si-quan2（1. University of Shanghai for Science and Technology，Shanghai 200093，China；2. Xuji Flexible Transmission System Corporation，Xuchang 461000，China）Abstract：This paper presents that using three-level grid-connected technology to study renewable energy generation high-voltage grid-connected converter, introduces the topological structure of main circuit of three-level grid-connected converter, and studies the parameters selection of main circuit. The design methods of the IGBT, clamped diode and DC bus capacitor in the main circuit are given. The paper uses LCL filter to restrain the harmonics injected into power system, and analyses the principle and filter characteristics and builds the mathematic model of the LCL filter. On these basis, experimental circuit of 20 kW three-level grid-connected converter is designed, and experimental results prove the correctness and practicability of the design method.Key words：three-level；grid-connected converter；main circuit； IGBT； filter中图分类号： TM46 文献标识码：A 文章编号： 1674-3415(2010)20-0193-030 引言本文所研制的三电平并网变流器交流侧接380 V三相交流电网，直流侧能量通过并网变流器后经滤波器后送入电网。
数学专业英语词汇（T）_数学物理英语词汇
t distribution 学生t分布t number t数t statistic t统计量t test t检验t1topological space t1拓扑空间t2topological space t2拓扑空间t3topological space 分离空间t4topological space 正则拓扑空间t5 topological space 正规空间t6topological space 遗传正规空间table 表table of random numbers 随机数表table of sines 正弦表table of square roots 平方根表table of values 值表tabular 表的tabular value 表值tabulate 制表tabulation 造表tabulator 制表机tacnode 互切点tag 标签tame 驯顺嵌入tame distribution 缓增广义函数tamely imbedded 驯顺嵌入tangency 接触tangent 正切tangent bundle 切丛tangent cone 切线锥面tangent curve 正切曲线tangent function 正切tangent line 切线tangent of an angle 角的正切tangent plane 切平面tangent plane method 切面法tangent surface 切曲面tangent vector 切向量tangent vector field 切向量场tangent vector space 切向量空间tangential approximation 切线逼近tangential component 切线分量tangential curve 正切曲线tangential equation 切线方程tangential stress 切向应力tangents method 切线法tape 纸带tape inscription 纸带记录tariff 税tautology 重言taylor circle 泰勒圆taylor expansion 泰勒展开taylor formula 泰勒公式taylor series 泰勒级数technics 技术technique 技术telegraph equation 电报方程teleparallelism 绝对平行性temperature 温度tempered distribution 缓增广义函数tend 倾向tendency 瞧tension 张力tensor 张量tensor algebra 张量代数tensor analysis 张量分析tensor bundle 张量丛tensor calculus 张量演算法tensor density 张量密度tensor differential equation 张量微分方程tensor field 张量场tensor form 张量形式tensor form of the first kind 第一张量形式tensor function 张量函数tensor of torsion 挠率张量tensor product 张量乘积tensor product functor 张量乘积函子tensor representation 张量表示tensor space 张量空间tensor subspace 张量子空间tensor surface 张量曲面tensorial multiplication 张量乘法term 项term of higher degree 高次项term of higher order 高次项term of series 级数的项terminability 有限性terminable 有限的terminal decision 最后判决terminal edge 终结边terminal point 终点terminal unit 级端设备terminal vertex 悬挂点terminate 终止terminating chain 可终止的链terminating continued fraction 有尽连分数terminating decimal 有尽小数termination 终止terminology 专门名词termwise 逐项的termwise addition 逐项加法termwise differentiation 逐项微分termwise integration 逐项积分ternary 三元的ternary connective 三元联结ternary form 三元形式ternary notation 三进制记数法ternary number system 三进制数系ternary operation 三项运算ternary relation 三项关系ternary representation og numbers 三进制记数法tertiary obstruction 第三障碍tesseral harmonic 田形函数tesseral legendre function 田形函数test 检验test for additivity 加性检验test for uniform convergence 一致收敛检验test function 测试函数test of dispersion 色散检验test of goodness of fit 拟合优度检验test of hypothesis 假设检验test of independence 独立性检验test of linearity 线性检验test of normality 正规性检验test point 测试点test routine 检验程序test statistic 检验统计量tetracyclic coordinates 四圆坐标tetrad 四元组tetragon 四角形tetragonal 正方的tetrahedral 四面角tetrahedral angle 四面角tetrahedral co ordinates 四面坐标tetrahedral group 四面体群tetrahedral surface 四面曲面tetrahedroid 四面体tetrahedron 四面形tetrahedron equation 四面体方程theorem 定理theorem for damping 阻尼定理theorem of alternative 择一定理theorem of identity for power series 幂级数的一致定理theorem of implicit functions 隐函数定理theorem of mean value 平均值定理theorem of principal axes 轴定理theorem of residues 残数定理theorem of riemann roch type 黎曼洛赫型定理theorem on embedding 嵌入定理theorems for limits 极限定理theoretical curve 理论曲线theoretical model 理论模型theory of automata 自动机理论theory of cardinals 基数论theory of complex multiplication 复数乘法论theory of complexity of computations 计算的复杂性理论theory of correlation 相关论theory of differential equations 微分方程论theory of dimensions 维数论theory of elementary divisors 初等因子理论theory of elementary particles 基本粒子论theory of equations 方程论theory of errors 误差论theory of estimation 估计论theory of functions 函数论theory of games 对策论theory of hyperbolic functions 双曲函数论theory of judgment 判断论theory of numbers 数论theory of ordinals 序数论theory of perturbations 摄动理论theory of probability 概率论theory of proportions 比例论theory of relativity 相对论theory of reliability 可靠性理论theory of representations 表示论theory of sets 集论theory of sheaves 层理论theory of singularities 奇点理论theory of testing 检验论theory of time series 时间序列论theory of transversals 横断线论theory of types 类型论thermal 热的thermodynamic 热力学的thermodynamics 热力学theta function 函数theta series 级数thick 厚的thickness 厚度thin 薄的thin set 薄集third boundary condition 第三边界条件third boundary value problem 第三边界值问题third fundamental form 第三基本形式third isomorphism theorem 第三同构定理third proportional 比例第三项third root 立方根thom class 汤姆类thom complex 汤姆复形three body problem 三体问题three dimensional 三维的three dimensional space 三维空间three dimensional torus 三维环面three eighths rule 八分之三法three faced 三面的three figur 三位的three place 三位的three point problem 三点问题three series theorem 三级数定理three sheeted 三叶的three sided 三面的three sigma rule 三规则three termed 三项的three valued 三值的three valued logic 三值逻辑three valued logic calculus 三值逻辑学threshold logic 阈逻辑time interval 时程time lag 时滞time series analysis 时序分析timesharing 分时toeplitz matrix 托普利兹矩阵tolerance 容许tolerance distribution 容许分布tolerance estimation 容许估计tolerance factor 容许因子tolerance level 耐受水平tolerance limit 容许界限tolerance region 容许区域top digit 最高位数字topological 拓扑的topological abelian group 拓扑阿贝耳群topological algebra 拓扑代数topological cell 拓扑胞腔topological circle 拓扑圆topological completeness 拓扑完备性topological complex 拓扑复形topological convergence 拓扑收敛topological dimension 拓扑维topological direct sum 拓扑直和topological dynamics 拓扑动力学topological embedding 拓扑嵌入topological field 拓扑域topological group 拓扑群topological homeomorphism 拓扑同胚topological index 拓扑指数topological invariant 拓扑不变量topological limit 拓扑极限topological linear space 拓扑线性空间topological manifold 拓扑廖topological mapping 拓扑同胚topological pair 拓扑偶topological polyhedron 曲多面体topological product 拓扑积topological residue class ring 拓扑剩余类环topological ring 拓扑环topological simplex 拓扑单形topological skew field 拓扑非交换域topological space 拓扑空间topological sphere 拓扑球面topological structure 拓扑结构topological sum 拓扑和topological type 拓扑型topologically complete set 拓扑完备集topologically complete space 拓扑完备空间topologically equivalent space 拓扑等价空间topologically nilpotent element 拓扑幂零元topologically ringed space 拓扑环式空间topologically solvable group 拓扑可解群topologico differential invariant 拓扑微分不变式topologize 拓扑化topology 拓扑topology of bounded convergence 有界收敛拓扑topology of compact convergence 紧收敛拓扑topology of uniform convergence 一致收敛拓扑toroid 超环面toroidal coordinates 圆环坐标toroidal function 圆环函数torque 转矩torsion 挠率torsion coefficient 挠系数torsion form 挠率形式torsion free group 非挠群torsion group 挠群torsion module 挠模torsion of a curve 曲线的挠率torsion product 挠积torsion subgroup 挠子群torsion tensor 挠率张量torsion vector 挠向量torsionfree connection 非挠联络torsionfree module 无挠模torsionfree ring 无挠环torus 环面torus function 圆环函数torus group 环面群torusknot 环面纽结total 总和total correlation 全相关total curvature 全曲率total degree 全次数total differential 全微分total differential equation 全微分方程total error 全误差total graph 全图total image 全象total inspection 全检查total instability 全不稳定性total inverse image 全逆象total matrix algebra 全阵环total matrix ring 全阵环total order 全序total predicate 全谓词total probability 总概率total probability formula 总概率公式total regression 总回归total relation 通用关系total space 全空间total stability 全稳定性total step iteration 整步迭代法total step method 整步迭代法total stiefel whitney class 全斯蒂费尔惠特尼类total subset 全子集total sum 总和total variation 全变差totally bounded set 准紧集totally bounded space 准紧空间totally differentiable 完全可微分的totally differentiable function 完全可微函数totally disconnected 完全不连通的totally disconnected graph 完全不连通图totally disconnected groupoid 完全不连通广群totally disconnected set 完全不连通集totally disconnected space 完全不连通空间totally geodesic 全测地的totally nonnegative matrix 全非负矩阵totally ordered group 全有序群totally ordered set 线性有序集totally positive 全正的totally positive matrix 全正矩阵totally quasi ordered set 完全拟有序集totally real field 全实域totally reflexive relation 完全自反关系totally regular matrix method 完全正则矩阵法totally singular subspace 全奇异子空间totally symmetric loop 完全对称圈totally symmetric quasigroup 完全对称拟群touch 相切tournament 竞赛图trace 迹trace form 迹型trace function 迹函数trace of dyadic 并向量的迹trace of matrix 矩阵的迹trace of tensor 张量的迹tracing point 追迹点track 轨迹tractrix 曳物线trajectory 轨道transcendence 超越性transcendence basis 超越基transcendence degree 超越次数transcendency 超越性transcendental element 超越元素transcendental equation 超越方程transcendental function 超越函数transcendental integral function 超越整函数transcendental number 超越数transcendental singularity 超越奇点transcendental surface 超越曲面transfer 转移transfer function 转移函数transfinite 超限的transfinite diameter 超限直径transfinite induction 超限归纳法transfinite number 超限序数transfinite ordinal 超限序数transform 变换transformation 变换transformation equation 变换方程transformation factor 变换因子transformation formulas of the coordinates 坐标的变换公式transformation function 变换函数transformation group 变换群transformation of air mass 气团变性transformation of coordinates 坐标的变换transformation of parameter 参数变换transformation of state 状态变换transformation of the variable 变量的更换transformation rules 变换规则transformation theory 变换论transformation to principal axes 轴变换transgression 超渡transient response 瞬态响应transient stability 瞬态稳定性transient state 瞬态transient time 过渡时间transition function 转移函数transition graph 转换图transition matrix 转移矩阵transition probability 转移函数transitive closure 传递闭包transitive graph 传递图transitive group of motions 可迁运动群transitive law 可迁律transitive permutation group 可迁置换群transitive relation 传递关系transitive set 可递集transitivity 可递性transitivity laws 可迁律translatable design 可旋转试验设计translate 转移translation 平移translation curve 平移曲线translation group 平移群translation invariant 平移不变的translation invariant metric 平移不变度量translation number 殆周期translation of axes 坐标轴的平移translation operator 平移算子translation surface 平移曲面translation symmetry 平移对称translation theorem 平移定理transmission channel 传输通道transmission ratio 传输比transport problem 运输问题transportation algorithm 运输算法transportation matrix 运输矩阵transportation network 运输网络transportation problem 运输问题transpose 转置transposed inverse matrix 转置逆矩阵transposed kernel 转置核transposed map 转置映射transposed matrix 转置阵transposition 对换transversal 横截矩阵胚transversal curve 横截曲线transversal field 模截场transversal lines 截线transversality 横截性transversality condition 横截条件transverse axis 横截轴transverse surface 横截曲面trapezium 不规则四边形trapezoid 不规则四边形trapezoid formula 梯形公式trapezoid method 梯形公式traveling salesman problem 转播塞尔斯曼问题tree 树trefoil 三叶形trefoil knot 三叶形纽结trend 瞧trend line 瞧直线triad 三元组trial 试验triangle 三角形triangle axiom 三角形公理triangle condition 三角形公理triangle inequality 三角形公理triangulable 可三角剖分的triangular decomposition 三角分解triangular form 三角型triangular matrix 三角形矩阵triangular number 三角数triangular prism 三棱柱triangular pyramid 四面形triangular surface 三角曲面triangulate 分成三角形triangulation 三角剖分triaxial 三轴的triaxial ellipsoid 三维椭面trichotomy 三分法trident of newton 牛顿三叉线tridiagonal matrix 三对角线矩阵tridimensional 三维的trigammafunction 三函数trigonometric 三角的trigonometric approximation polynomial 三角近似多项式trigonometric equation 三角方程trigonometric function 三角函数trigonometric moment problem 三角矩问题trigonometric polynomial 三角多项式trigonometric series 三角级数trigonometrical interpolation 三角内插法trigonometry 三角学trihedral 三面形的trihedral angle 三面角trihedron 三面体trilateral 三边的trilinear 三线的trilinear coordinates 三线坐标trilinear form 三线性形式trinomial 三项式;三项式的trinomial equation 三项方程triplanar point 三切面重点 ?triple 三元组triple curve 三重曲线triple integral 三重积分triple point 三重点triple product 纯量三重积triple product of vectors 向量三重积triple root 三重根triple series 三重级数triple tangent 三重切线triply orthogonal system 三重正交系triply tangent 三重切线的trirectangular spherical triangle 三直角球面三角形trisecant 三度割线trisect 把...三等分trisection 三等分trisection of an angle 角的三等分trisectrix 三等分角线trivalent map 三价地图trivector 三向量trivial 平凡的trivial character 单位特贞trivial cohomology functor 平凡上同弹子trivial extension 平凡扩张trivial fibre bundle 平凡纤维丛trivial graph 平凡图trivial homogeneous ideal 平凡齐次理想trivial knot 平凡纽结trivial solution 平凡解trivial subset 平凡子集trivial topology 密着拓扑trivial valuation 平凡赋值triviality 平凡性trivialization 平凡化trochoid 摆线trochoidal 余摆线的trochoidal curve 摆线true error 真误差true formula 真公式true proposition 真命题true sign 直符号true value 真值truncated cone 截锥truncated cylinder 截柱truncated distribution 截尾分布truncated pyramid 截棱锥truncated sample 截样本truncated sequence 截序列truncation 舍位truncation error 舍位误差truncation point 舍位点truth 真值truth function 真值函项truth matrix 真值表truth set 真值集合truth symbol 真符号truth table 真值表truthvalue 真值tube 管tubular knot 管状纽结tubular neighborhood 管状邻域tubular surface 管状曲面turbulence 湍流turbulent 湍聊turing computability 图灵机可计算性turing computable 图灵机可计算的turing machine 图录机turn 转向turning point 转向点twice 再次twice differentiable function 二次可微函数twin primes 素数对twisted curve 空间曲线twisted torus 挠环面two address 二地址的two address code 二地址代码two address instruction 二地址指令two body problem 二体问题two decision problem 二判定问题two digit 二位的two dimensional 二维的two dimensional laplace transformation 二重拉普拉斯变换two dimensional normal distribution 二元正态分布two dimensional quadric 二维二次曲面two dimensional vector space 二维向量空间two fold transitive group 双重可迁群two person game 两人对策two person zero sum game 二人零和对策two phase sampling 二相抽样法two place 二位的two point distribution 二点分布two point form 两点式two sample method 二样本法two sample problem 二样本问题two sample test 双样本检验two sheet 双叶的two sided condition 双边条件two sided decomposition 双边分解two sided divisor 双边因子two sided ideal 双边理想two sided inverse 双边逆元two sided module 双边模two sided neighborhood 双侧邻域two sided surface 双侧曲面two sided test 双侧检定two stage sampling 两阶段抽样法two termed expression 二项式two valued logic 二值逻辑two valued measure 二值测度two variable matrix 双变量矩阵two way array 二向分类two way classification 二向分类twopoint boundary value problem 两点边值问题type 型type problem 类型问题typenumber 型数typical mean 典型平均。
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possibility to exactly define the index theorem on the lattice allow us to investigate the relationship of topological properties of gauge fields and the dynamics of fermions. A further advantage of overlap fermions, in contrast to Wilson fermions, is that they are automatically O(a) improved [4] and not plagued by exceptional configurations.
1. Introduction
The understanding of the vacuum structure of QCD is an important goal of elementary particle physics. The distribution of topological charge density is believed to describe nonperturbative phenomena like the large η′ mass, the axial U(1) anomaly, the θ dependence and the spontaneous breaking of chiral symmetry. In the traditional instanton picture the excitations of the QCD vacuum are phenomenologically modelled as an interacting ensemble of instantons and antiinstantons.
Recent advances in implementing chiral symmetry on the lattice have made it possible to directly clarify from first principles to what extent the instanton picture of localised solutions of the Euclidean Yang-Mills equations of motion realistically describes the QCD vacuum.
8.10 0.125 123 × 24 254 O(140)
2. Density and locality of the eigenmodes of the overlap operator
The spontaneous breaking of chiral symmetry by the dynamical creation of a nonvanishing chiral condensate, Ψ¯ Ψ , is related to the spectral density ρ(λ) of the Dirac operator near zero by the Banks-Casher relation [9] Ψ¯ Ψ = −π/V ρ(0).
a small condition numb the ‘sign function’
sgn(X) =
√X X†X
≡ γ5 sgn(H),
H
= γ5X,
(2)
we use the minmax polynomial approximation [5]. We compute the O(10) lowest eigenvalues of H and treat the sign function on the corresponding subspace exactly.
The Lu¨scher-Weisz gauge field action is given by
S[U ]
=
6 g2
c0
1 3
Re
Tr
(1
−
Uplaquette)
plaquette
+ c1
1 3
Re Tr (1
−
Urectangle)
(3)
rectangle
+ c2
1 3
Re
Tr
(1
−
Uparallelogram)
Using the Arnoldi-algorithm, we compute the O(50) − O(160) lowest eigenvalues on every con-
The mass parameter ρ is chosen to be 1.4,
which is a compromise between the physical re-
quirement of good locality properties of the over-
lap operator and the performance requirement of
,
parallelogram
with coefficients c1, c2 (c0 + 8c1 + 8c2 = 1) taken from tadpole improved perturbation theory [8].
To investigate the volume dependence of our data we have simulated at 3 different volumes at fixed coupling β = 8.45. To explore the a dependence of the results, we also employed a 123 × 24 lattice at β = 8.10 with approximately the same physical volume as the 163 × 32 lattice.
Topological studies using the Wilson gauge field action suffer from dislocations [6] and should be treated with caution. We therefore use the Lu¨scher-Weisz gauge field action [7], which suppresses dislocations and greatly reduces the number of unphysical zero modes.
The eigenvalues of DN lie on a circle around (ρ,0) with radius ρ in the complex plane. In
our spectral analysis we use the improved operator DNimp = (1 − aDN /2ρ)−1DN [10,11] , which projects the eigenvalues of DN stereographically onto the imaginary axis. The nonzero eigenvalues of DNimp come in pairs ±iλ¯, while the zero modes are untouched.
Overlap fermions [1,2] have an exact chiral symmetry on the lattice [3] and are the cleanest known theoretical description of lattice fermions. Their implementation of chiral symmetry and the
The overlap operator is defined by
ρ DN = a
1+ √X X†X
,X
=
DW
−
ρ a
,
(1)
where we use the Wilson-Dirac operator DW as the kernel of the overlap operator.
The operator DN has n− + n+ exact zero modes, DN ψn = 0, n− (n+) being the number of modes with negative (positive) chirality, γ5ψn = −ψn (γ5ψn = +ψn). The index of DN is given by Q = n− − n+. The nonzero modes λ with DN ψλ = λψλ come in complex conjugate pairs λ and λ∗ and satisfy (ψλ† , γ5ψλ) = 0.
Overlap fermions implement exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum. We study various chiral and topological aspects on Lu¨scher-Weisz-type quenched gauge field configurations using overlap fermions as a probe. Particular emphasis is placed upon the analysis of the spectral density and the localisation properties of the eigenmodes as well as on the local structure of topological charge fluctuations.