Relativistic Conic Beams and Spatial Distribution of Gamma-Ray Bursts
共轭聚合物 有机半导体 英文
共轭聚合物有机半导体英文英文回答：Conjugated polymers are a class of organic semiconductors that have alternating single and double bonds along their backbone. This unique structure gives conjugated polymers interesting electrical and optical properties, making them promising candidates for use in various electronic applications.Conjugated polymers are typically synthesized via chemical polymerization techniques, such as oxidative coupling or Heck reaction. The resulting polymers are typically soluble in organic solvents and can be processed into thin films using techniques such as spin coating or drop casting.The electrical properties of conjugated polymers are highly dependent on the degree of conjugation, which is the length of the alternating single and double bond sequence.Longer conjugation lengths lead to higher charge carrier mobility and lower bandgap, making the polymer more conductive and semiconducting, respectively.The optical properties of conjugated polymers are also affected by the degree of conjugation. Longer conjugation lengths lead to absorption and emission of light at longer wavelengths, resulting in a red shift in the polymer's absorption and emission spectra.Conjugated polymers have been used in a variety of electronic applications, including organic solar cells, organic light-emitting diodes (OLEDs), and transistors. In organic solar cells, conjugated polymers act as the active layer, absorbing light and generating charge carriers that are then collected by the electrodes. In OLEDs, conjugated polymers are used as the emitting layer, emitting light when an electric current is applied. In transistors, conjugated polymers are used as the semiconductor channel, controlling the flow of current between the source and drain electrodes.Conjugated polymers are a promising class of materials for use in electronic applications due to their unique electrical and optical properties. Further research is needed to improve the performance and stability of conjugated polymers, but they have the potential to revolutionize the field of electronics.中文回答：共轭聚合物是有机半导体的一种，其主链上交替排列着单键和双键。
Superconducting qubits II Decoherence
The transition from quantum to classical physics, now known as decoherence, has intrigued physicists since the formulation of quantum mechanics (Giulini et al., 1996; Leggett, 2002; Peres, 1993; Feynman and Vernon, 1963; Zurek, 1993). It has been put into the poignant Schr¨ odinger cat paradox (Schr¨ odinger, 1935) and was considered an open fundamental question for a long time.
and compare it to the corresponding classical mixture leading to the same expectation value of σz 1 1 0 ρmix = (2) 2 0 1 we can see that the von-Neumann entropy ρ = −kB Tr [ρ log ρ] rises from Spure = 0 to Smix = kB ln 2. Hence, decoherence taking ρpure to ρmix creates entropy and is irreversible. Quantum mechanics, on the other hand, is always reversible. It can be shown, that any isolated quantum system is described by the Liouville von-Neumann equation i¯ hρ ˙ = [H, ρ] (3)
超表面共形至马鞍面 rcs缩减 文献
超表面共形至马鞍面 rcs缩减文献超表面共形至马鞍面 RCS缩减超表面是一种新型的人工结构，通过调控电磁波的传播和辐射，实现对电磁波的精确控制。
超表面的设计和制备可以实现对电磁波的各向异性调控，具有较高的灵活性和可调性。
超表面在通信、雷达、光学等领域都有广泛的应用前景。
共形变换是一种保持角度不变的变换，可以将一个几何形状映射到另一个几何形状上。
在电磁学中，共形变换可以用于设计新型的超表面结构，实现对电磁波的控制和调整。
而马鞍面是一种特殊的曲面，它具有非常特殊的几何形状和性质。
研究人员通过共形变换的方法将超表面的结构从原来的形状变换到马鞍面的形状上，实现了对超表面的 RCS（radar cross section，雷达截面）的缩减。
RCS是物体对雷达波的反射截面，是衡量物体在雷达系统中的探测能力的重要指标。
通过缩减超表面的RCS，可以减小物体在雷达系统中的探测范围，提高隐身性能。
在超表面共形至马鞍面的研究中，研究人员首先通过数学建模和仿真分析，确定了超表面的结构参数和性能指标。
然后，利用共形变换的理论和方法，将超表面的结构从原来的形状变换到马鞍面的形状上。
通过调整超表面的结构参数，可以实现对电磁波的各向异性调控，从而达到缩减RCS的效果。
研究人员还通过实验验证了超表面共形至马鞍面的效果。
他们利用微波实验系统对超表面的RCS进行了测量，结果显示相比原始的超表面结构，共形至马鞍面的结构在一定的频率范围内能够实现显著的RCS缩减。
这表明通过共形变换的方法可以有效地改变超表面的性能，实现对电磁波的精确控制。
超表面共形至马鞍面的研究不仅对于提高雷达隐身性能具有重要意义，还为其他领域的电磁波控制提供了新的思路和方法。
未来的研究可以进一步探索超表面共形变换的机理和方法，优化超表面的设计和制备技术，进一步提高超表面的性能和应用范围。
超表面共形至马鞍面的研究为电磁波的精确控制提供了新的思路和方法。
通过共形变换的方法，可以将超表面的结构从原来的形状变换到马鞍面的形状上，实现对电磁波的控制和调整。
物理专业 词汇C2
cometograph 彗星照相仪
command 命令
command guidance 指令制导
commensurate incommensurate transition 适应不适应转变
commensurate structure 适应结构
common emitter circuit 共同发射电路
compressive strength 抗压强度
compressive stress 压应力
compressor 压缩机
compton effect 康普顿效应
compton electron 康普顿电子
compton scattering 康普顿散射
compton wavelength 康普顿波长
complete orthogonal system 完全正交系
complete polarization 全极化
complete system 完全系
completed shell 满壳层
completely elastic 完善弹性的
completeness 完备性
complex 络合物
configuration space 组态空间
configurational energy 组态能量
configurational entropy 构形熵
confirmation 确认
confocal resonator 共焦谐振器
conformal field theory 共形场理论
computer language 计算机语言
computer network 计算机网络
固体物理英语
固体物理英语固体物理基本词汇（汉英对照）一画一维晶格 One-dimensional crystal lattice一维单原子链 One-dimensional monatomic chain 一维双原子链 One-dimensional diatomic chain 一维复式格子One-dimensional compound lattice 二画二维晶格 Two-dimensional crystal lattice二度轴 Twofold axis二度对称轴 Twofold axis of symmetry几何结构因子 Geometrical structure factor三画三斜晶系 Triclinic system三方晶系 Trigonal system三斜晶系 Triclinic system刃位错 Edge dislocation小角晶界 Low angle grain boundary马德隆常数 Madelung constant四画元素晶体 Element crystal元素的电负性 Electronegativities of elements元素的电离能 Ionization energies of the elements 元素的结合能 Cohesive energies of the elements 六方密堆积 Hexagonal close-packed六方晶系 Hexagonal system反演 Inversion分子晶体 Molecular Crystal切变模量 Shear module双原子链 Diatomic linear chain介电常数 Dielectric constant化学势 Chemical potential内能 Internal energy分布函数 Distribution function夫伦克耳缺陷 Frenkel defect比热 Specific heat中子散射 Neutron scattering五画布喇菲格子 Bravais lattice布洛赫函数 Bloch function布洛赫定理 Bloch theorem布拉格反射 Bragg reflection布里渊区 Brillouin zone布里渊区边界 Brillouin zone boundary 布里渊散射 Brillouin scattering正格子 Direct lattice正交晶系 Orthorhombic crystal system正则振动 Normal vibration正则坐标 Normal coordinates立方晶系 Cubic crystal system立方密堆积 Cubic close-packed四方晶系 Tetragonal crystal system对称操作 Symmetry operation对称群 Symmetric group正交化平面波 Orthogonalized plane wave电子-晶格相互作用 Electron-lattice interaction 电子热容量 Electronic heat capacity电阻率 Electrical resistivity电导率 Conductivity电子亲合势 Electron affinity电子气的动能 Kinetic energy of electron gas 电子气的压力 Pressure of electron gas电子分布函数 Electron distribution function 电负性 Electronegativity电磁声子 Electromagnetic phonon功函数 Work function长程力 Long-range force立方晶系 Cubic system平面波方法 plane wave method平移对称性 Translation symmetry平移对称操作 Translation symmetry operator 平移不变性 Translation invariance石墨结构 Graphite structure闪锌矿结构 Blende structure六画负电性 Electronegativity共价结合 Covalent binding共价键 Covalent bond共价晶体 Covalent crystals共价键的饱和 Saturation of covalent bonds 光学模 Optical modes光学支 Optical branch光散射 Light scattering红外吸收 Infrared absorption压缩系数 Compressibility扩散系数 Diffusion coefficient扩散的激活能 Activation energy of diffusion 共价晶体 Covalent Crystal价带 Valence band导带 Conduction band自扩散 Self-diffusion有效质量 Effective mass有效电荷 Effective charges弛豫时间 Relaxation time弛豫时间近似 Relaxation-time approximation扩展能区图式 Extended zone scheme自由电子模型 Free electron model自由能 Free energy杂化轨道 Hybrid orbit七画纯金属 Ideal metal体心立方 Body-centered cubic体心四方布喇菲格子 Body-centered tetragonal Bravais lattices 卤化碱晶体 Alkali-halide crystal劳厄衍射 Laue diffraction间隙原子 Interstitial atom间隙式扩散 Interstitial diffusion肖特基缺陷 Schottky defect位错 Dislocation滑移 Slip晶界 Grain boundaries伯格斯矢量 Burgers vector杜隆-珀替定律 Dulong-Petit’s law粉末衍射 Powder diffraction里查孙-杜师曼方程 Richardson-Dushman equation 克利斯托夫方程 Christofell equation克利斯托夫模量Christofell module位移极化 Displacement polarization声子 Phonon声学支 Acoustic branch应力 Stress 应变 Strain切应力 Shear stress切应变 Shear strain八画周期性重复单元 Periodic repeated unit底心正交格子 Base-centered orthorhombic lattice 底心单斜格工 Base-centered monoclinic lattices 单斜晶系 Monoclinic crystal system金刚石结构 Diamond structure金属的结合能 Cohesive energy of metals金属晶体 Metallic Crystal转动轴 Rotation axes转动-反演轴 Rotation-inversion axes转动晶体法 Rotating crystal method空间群 Space group空位 Vacancy范德瓦耳斯相互作用 Van der Waals interaction 金属性结合 Metallic binding单斜晶系 Monoclinic system单电子近似 Single-erection approximation极化声子 Polarization phonon拉曼散射 Raman scattering态密度 Density of states铁电软模 Ferroelectrics soft mode空穴 Hole万尼尔函数 Wannier function平移矢量 Translation vector非谐效应 Anharmonic effect周期性边界条件 Periodic boundary condition九画玻尔兹曼方程 Boltzman equation点群 Point groups迪. 哈斯－范. 阿耳芬效应 De Hass－Van Alphen effect胡克定律Hooke’s law氢键 Hydrogen bond亲合势 Affinity重迭排斥能 Overlap repulsive energy结合能 Cohesive energy玻恩-卡门边界条件 Born-Karman boundary condition费密-狄喇克分布函数 Fermi-Dirac distribution function费密电子气的简并性 Degeneracy of free electron Fermi gas 费密 Fermi费密能 Fermi energy费密能级 Fermi level费密球 Fermi sphere费密面 Fermi surface费密温度 Fermi temperature费密速度 Fermi velocity费密半径 Fermi radius恢复力常数 Constant of restorable force绝热近似 Adiabatic approximation十画原胞 Primitive cell原胞基矢 Primitive vectors倒格子 Reciprocal lattice倒格子原胞 Primitive cell of the reciprocal lattice 倒格子空间 Reciprocal space倒格点 Reciprocal lattice point倒格子基矢Primitive translation vectors of the reciprocal lattice倒格矢 Reciprocal lattice vector倒逆散射 Umklapp scattering粉末法 Powder method原子散射因子 Atomic scattering factor配位数 Coordination number原子和离子半径 Atomic and ionic radii原子轨道线性组合 Linear combination of atomic orbits离子晶体的结合能 Cohesive energy of inert crystals离解能 Dissociation energy离子键 Ionic bond离子晶体 Ionic Crystal离子性导电 Ionic conduction洛伦兹比 Lorenz ratio魏德曼－佛兰兹比 Weidemann－Franz ratio 缺陷的迁移 Migration of defects缺陷的浓度 Concentrations of lattice defects 爱因斯坦 Einstein爱因斯坦频率 Einstein frequency爱因斯坦温度 Einstein temperature格波 Lattice wave格林爱森常数 Gruneisen constant索末菲理论 Sommerfeld theory热电子发射 Thermionic emission热容量 Heat capacity热导率 Thermal conductivity热膨胀 Thermal expansion能带 Energy band能隙 Energy gap能带的简约能区图式 Reduced zone scheme of energy band 能带的周期能区图式 Repeated zone scheme of energy band 能带的扩展能区图式 Extended zone scheme of energy band 配分函数 Partition function准粒子 Quasi- particle准动量 Quasi- momentum准自由电子近似 Nearly free electron approximation十一画第一布里渊区 First Brillouin zone密堆积 Close-packing密勒指数 Miller indices接触电势差 Contact potential difference基元 Basis基矢 Basis vector弹性形变 Elastic deformation排斥能Repulsive energy弹性波 Elastic wave弹性应变张量 Elastic strain tensor弹性劲度常数 Elastic stiffness constant弹性顺度常数 Elastic compliance constant 弹性模量 Elastic module弹性动力学方程 Elastic-dynamics equation 弹性散射 Elastic scattering十二画等能面 Constant energy surface晶体 Crystal晶体结构 Crystal structure晶体缺陷 Crystal defect晶体衍射 Crystal diffraction晶列 Crystal array晶面 Crystal plane晶面指数 Crystal plane indices晶带 Crystal band晶向 direction晶格 lattice晶格常数 Lattice constant晶格周期势 Lattice-periodic potential 晶格周期性 Lattice-periodicity晶胞 Cell, Unit cell晶面间距 Interplanar spacing晶系 Crystal system晶体 Crystal晶体点群 Crystallographic point groups晶格振动 Latticevibration晶格散射 Lattice scattering散射 Scattering等能面 surface of constant energy十三画隋性气体晶体的结合能 Cohesive energy of inert gas crystals 滑移 Slip滑移面 Slip plane简单立方晶格 Simple cubic lattice简单晶格 Simple lattice简单单斜格子 Simple monoclinic lattice简单四方格子 Simple tetragonal lattice简单正交格子 Simple orthorhombic lattice简谐近似 Harmonic approximation简正坐标 Normal coordinates简正振动 Normal vibration简正模 Normal modes简约波矢 Reduced wave vector简约布里渊区 Reduced Brillouin zone禁带 Forbidden band紧束缚方法 Tight－binding method零点振动能 Zero-point vibration energy 雷纳德－琼斯势 Lenard－Jones potential 满带 Filled band十四画磁致电阻 Magnetoresistance模式密度 Density of modes漂移速度 Drift velocity漂移迁移率 Drift mobility十五至十七画德拜 Debye德拜近似 Debye approximation德拜截止频率 Debye cut-off frequency 德拜温度 Debye temperature霍耳效应 Hall effect螺位错 Screw dislocation赝势 Pseudopotential。
356602729_高电大纲07
ADVANCED ELECTRODYNAMICSElectromagnetic Theory for Microwaves and Optoelectronics 高等电动力学 -- 微波与光电子学中的电磁理论1 Maxwell's equations, wave equations, Helmholtz equations and boundary conditions麦克斯韦方程，波动方程，亥姆霍兹方程及边界条件(第I版 p.1–23, 第II版 p.1–28)2 Boundary value problems for time-varying fields, Uniqueness时变电磁场的边值问题，唯一性定理(第I版 p.235–239,第II版 p.173-179)3 Solution of vector Helmholtz's equations in orthogonal curvilinear coordinates矢量亥姆霍兹方程在正交曲坐标中的的求解(第I版 p.239–249, 第II版 p.179-192)4 Sepration of variables, electromagnetic waves in cylindrical systems分离变量，柱形系统中的电磁波(第I版 p.249–255, 第II版 p.192-197)5 Solution of Helmholtz's equations in rectangular coordinates, rectangular waveguides and cavities矩坐标系中的求解，矩形波导和谐振腔(第I版 p.255-258,279-293, 第II版 p.197–202,239-254)6 Solution of Helmholtz's equations in rectangular and circular cylindrical coordinates, waveguides and cavities 圆柱坐标系中的求解，圆柱形波导和谐振腔(第I版 p.258-260, 293-314, 第II版 p.202–206, 254-277)7 Solution of Helmholtz's equations in spherical coordinates, spherical cavity球坐标系中的求解，球形谐振腔(第I版 p.260-265, 314–318, 第II版 p.206-213,277-284)8 Solution of Helmholtz's equations with complicated boundary conditions，reentrant cavity复杂边界条件下的求解，重入谐振腔(第I版 p.265-270, 319–327, 第II版 p.220-226, 284-293)9 Dielectric waveguides and resonators介质波导和介质谐振器(第I版 p.343–394, 第II版 p.314-379)10 Uniform slow-wave systems, Corrugated conductor surface均匀慢波系统，褶皱导体表面(第I版 p.397–401, 第II版 p.382-387)11 Periodic systems and space harmonics, artificial photonic crystals周期系统与空间谐波(第I版 p.405–412, 第II版 p.392-403)12 Disk loaded waveguide盘荷波导(第I版 p.401-404, 416–418, 第II版 p.387-392, 406-410)13 Helix螺旋线(第I版 p.418–433, 第II版 p.410-428)14 Mode coupling theory模式耦合(第I版 p.441–449, 第II版 p.437-448)15 Distributed Feedback (DFB) Structures周期性分布反馈结构(第I版 p.449–456, 第II版 p.448-457)16 Electromagnetic waves in disperssive media电磁波在色散媒质中的传播(第I版 p.460–473, 第II版 p.461-477)17 Anisotropic media各向异性媒质(第I版 p.474–483, 第II版 p.477-489)18 Electromagnetic waves in reciprocal crystal media互易晶体介质中的电磁波(第I版 p.483–505, 第II版 p.489-516)19 Waves in electron beams, space charge wave电子束中的波，空间电荷波(第I版 p.505–511, 第II版 p.516-524)20 Gyrotropic media -- magnetized plasma回旋媒质--磁化等离子体(第I版 p.511–516, 第II版 p.524-529)21 Gyrotropic media -- magnetized ferrite回旋媒质--磁化铁氧体(第I版 p.516–525, 第II版 p.529-539)22 Electromagnetic wave propagation in gyrotropic media回旋媒质中的电磁波(第I版 p.525–537, 第II版 p.539-554)Texts 教科书Chinese 中文, 张克潜, 李德杰, 《微波与光电子学中的电磁理论》, 电子工业出版社, 第 I 版, 1994, 第 II 版，2001English 英文, Keqian Zhang and Dejie Li, Electromagnetic Theory for Microwaves and Optoelectronics, Springer-Verlag, 1998References 参考书[1] S. Ramo J.R. Whinnery, T. Van-Duzer, Fields and Waves in Communication Electronics, John Wiley & Sons, 1st. Ed. 1965, 2nd. Ed. 1984[2] H.A. Haus, Waves and Fields in Optoelectronics, prentice- Hall, 1984[3] A. Yariv, Optical Electronics, Holt, Rinehart and Winston, 1991, 1985.[4] T. Tamir (Ed), Guided-Wave Optoelectronics, Spring-Verlag, 1988[5] D. Marcuse, Theory of Dielectric Optical Waveguides, Academic Press, 1991, 1974[6] 吴伯瑜,张克潜:《微波电子学》,电子工业出版社,1986[7] 王一平,陈达章,刘鹏程,《工程电动力学》,西北电讯工程学院出版社,1985。
Observations and Simulations of Relativistic Jets
a r X i v :a s t r o -p h /0109338v 2 24 Se p21Observations and Simulations of Relativistic Jets Jos´e -Luis G´o mez Instituto de Astrof ´ısica de Andaluc ´ıa (CSIC),Apartado 3004,Granada 18008,Spain Abstract.The recent improvement in VLBI arrays is providing information of the emission and magnetic field structure of relativistic jets,both extragalactic and galac-tic (microquasars),with unprecedented spatial and temporal resolution.These obser-vations are revealing the importance of the hydrodynamical processes that govern the jet evolution,which can be studied by the recently developed time–dependent rela-tivistic hydrodynamical putation of the non–thermal emission from these hydrodynamical models,and its comparison with actual sources,is proving as one of the most powerful tools in the understanding of the physical processes taking place in these jets.This paper reviews some of the recent observational results,as well as the numerical models used to interpret them.1Introduction Since the classical works of [11]and [13],our knowledge of the jet physics in AGNs and microquasars have improved significantly by analytical and numerical models.The analytical efforts provided the basic frame work to understand the non–thermal synchrotron and inverse Compton emission of inhomogeneous jets ([93],[85]);spectral evolution of shock waves,associated with the superluminal components ([12],[94],[63]);and polarization (e.g.,[20]).The implementation of these analytical results into numerical models have allowed testing of the basic jet model hypotheses,as well as a more detailed comparison with the observations ([70],[64],[65],[43],[44],[45]).However,these early numerical models are limited by the lack of a detailed non–linear model to study the relativistic jet dynamics,being forced to adopt simplified stationary relativistic hydrodynamical models.On the other hand,Newtonian hydrodynamical numerical models have been used to obtain a more detailed study of the jet dynamics,and its influencein the jet observational properties.These models explored with great success the morphology,dynamics and stability of jets (see e.g.reviews [109],[27]),mainly aimed to study the large scale jet structure.However,these models cannot account for the relativistic effects that are of special importance in the overall emission of jets in AGNs and microquasars.First studies of relativistic (magneto)hydrodynamical jets were obtained for stationary flows ([136],[24],[17]).A significant step forward in the field of nu-merical simulations came with the development of modern high–resolution tech-niques in numerical hydrodynamics,mading feasible the computation of time–dependent simulations of relativistic jets ([127],[99],[100],[102],[25],[83],and reviews [101],[103],[104],[7]).These models are capable,for the first time,to2Jos´e-Luis G´o mezstudy the jet dynamics with unprecedented detail,and under very similar condi-tions as it is thought are taking place in real sources(strong shocks,relativistic internal energies and bulkflow velocities,etc.).Some of the latest simulations have started to explore three dimensional relativistic jets([4],[5],[6],[59]),mag-netized relativistic jets([84]),as well as jet formation and collimation making use of thefirst general relativity magnetohydrodynamical codes([79],[80],[81], [105],[106]).However,The emission structure that we observe in our VLBI images is not just a direct mapping of the jet hydrodynamical variables(pressure,den-sity,velocity).Thefinal radiation reaching our detectors is greatly determined by other several processes,like Faraday rotation,opacity,particle acceleration, radiative losses,and,most importantly,by relativistic effects such as light aber-ration and light travel time delays.For relativistic speeds(and small viewing angles)time delays can be of such importance as to render the emission images with no apparent relationship to the hydrodynamical jet structure.Therefore, the state of the art in the simulation of relativistic jets involves the computation of the emission,taking into account the appropriate relativistic and transfer of radiation processes,from the relativistic time-dependent hydrodynamical results ([46],[47],[48],[49],[66],[82],[107],[83],[5],[6],[71],[1],and review[57]).Com-parison of these simulations with actual observations should provide a better understanding of the relativistic jets in AGNs and microquasars.2Relativistic HD and Emission modelsMost of the energy transported in relativistic jets is assumed to be carried out by a population of thermal electrons.This population determines the hydrody-namical evolution of the jet,and can be simulated by the relativistic HD codes. However,the non-thermal emission observed from these jets is originated by a second population of high energy,non-thermal particles.Detection of circular polarization in the jet of3C279([133]),as well as in3C84,PKS0528+134,and 3C273([60]),suggests that this non-thermal population is mainly composed by pairs electron–positron.It is still unclear how this non-thermal population is originated([96]),perhaps by pair cascades([91],[14]),neutron decay([26], [42]),or by acceleration of the thermal electrons at a strong recollimation shock presumably associated with the VLBI core([22],[98],[89],[90]).This population of non-thermal electrons is subsequently re-accelerated at shocks along the jet ([77],[38],[78],[39]),and incremented with contributions from thermal electrons accelerated at the same shocks.In order to compute the expected emission from the hydrodynamical models is necessary to establish a relationship between the thermal and non-thermal jet populations.A common assumption considers that the particle and energy den-sity of the non-thermal electrons is a constant fraction of the thermal electrons ([113],[135],[46],[49],[6],[107],[83]).The population of non-thermal electrons is assumed to share the same dynamics as the thermal population,which can therefore be computed using the hydrodynamical simulations.Any exchange be-Observations and Simulations of Relativistic Jets 3tween internal and kinetic energy along the jet will maintain the proportionality between thermal and non-thermal populations.Only non-adiabatic processes,such as gains by particle acceleration in shocks or losses by radiation can modify this proportionality.Radiative losses at radio wavelengths are expected to be small,except at strong shocks,such as the terminal hot spots and jet cocoon.It is therefore expected that computation of parsec scale radio emission will not be severely in-fluenced by changes in the non-thermal population produced by radiative losses or particle accelerations.At higher energies (i.e.,optical)and at sites of strong shocks it is possible to trace the electron non-thermal population gains and losses of energy by computing the electron energy transport during the jet evo-lution.This has beenrecentlyconsideredfornon-relativistic magnetohydrody-namic simulations ([71]),allowing the exploration of the effects induced in the emission by synchrotron aging and electron energy gains at strong shocks.To compute the synchrotron emission is necessary to distribute the inter-nal energy calculated from the hydrodynamic codes among the relativistic non-thermal electrons.This is done by assuming a power low energy distribution in the form N (E )d E =N o E −γd E ,with E min ≤E ≤E max ,and spectral index γ.Neglecting radiative energy losses and particle accelerations,the ratio C E between the maximum and minimum energy remains constant trough the com-putational domain and can be considered a free parameter of the model.The power law is then fully determined by the equation ([46])N o =U (γ−2)N (γ−1) γ−2(1)andE min =Uγ−11−C 1−γE U .Once the magnetic fieldis considered dynamically negligible,ad-hoc magnetic field structures can be considered.To account for the small degree of linear polarization observed in many sources,the magnetic field is commonly considered to be predominantly turbulent.4Jos´e-Luis G´o mez2.1Synchrotron Radiation TransferThe transfer of synchrotron radiation have been considered in detail previously under different astrophysical scenarios,see e.g.,[111],[68],[69],[64].Its im-plementation for computing the polarized emission from the hydrodynamical models can be summarized as follows([43],[44],[45],[46]).To obtain the emission and absorption coefficients for the transfer of polarized synchrotron radiation let consider the direction of the component of the magnetic field in the plane of the sky at a given computational cell be specified as direction 2,and let the axis1,2,and the direction toward the observer be directions which form a right-handed orthogonal system in that order.In this system,the emission and absorption coefficients,respectively,are then computed in thefluid frame using(see e.g.,[111])ε(i)ν=√16πe33e34πm3c5x=νObservations and Simulations of Relativistic Jets 5I (a )−I (b ).Provided jets in blazars exhibit very low circular polarization we can assume V =0.I is the total intensity,and Q and U determine the degree of polarizationΠ=Q 2+U 2 1/2andthe polarization position angle χ=1Q .The change of the parameters I (a ),I (b )and U characterizing the radiation passing through a volume element of length d s can be obtained by solving the transfer equations in the (1,2)system and transforming to the (a,b )system,given byd I (a )2κνsin 22χB+U 1d s =I (b ) −κ(1)νcos 4χB −κ(2)νsin 4χB −14(κ(1)ν−κ(2)ν)sin 2χB −d χF /d s+ε(1)νcos 2χB +ε(2)νsin 2χB (6)d U 2(κ(1)ν−κ(2)ν)sin 2χB −2d χF /d s+I (b ) 16Jos´e-Luis G´o mezbeing p the thermal pressure andαthe spectral index.The total intensity can then be integrated using([19])ενI=I0e−τν+(13)cwhere−→x is the position vector of the cell,−→l denotes the line of sight unity vector,and c is the speed of light.We can investigate the observational consequences of light travel delays by considering the effects produced in the emission of shocked jet material([95], [45]).Because of the time delays between the far and near sides of a shock front, it appears rotated in the observed frame by an angle arccosβ.Depending on the pattern velocity of the shock front and viewing angle,time delays have a tendencyObservations and Simulations of Relativistic Jets7 towards aligning the shock front with the visual.This may have relevant effects in the emission time variability of material being heated by a shock by producing a“phasing”effect of the emission as measured by the observed,thus allowing for very rapid variability([117]).Light travel delays between the forward and reverse shocks produce a length-ening of the shocked material region in the observers frame by a factor sinθ/(1−βcosθ)([45],[41]).Therefore,it is possible to obtain estimations of the shocked material size in the source frame from the measured sizes,velocities,and view-ing angles of superluminal components.High resolution VLBI observations([72], [50],[52],[89],[56],[37])reveal components sizes in some cases of the order of the jet width.If we assume commonly estimated values ofΓ∼10andθ=10◦,this implies that the emitting material associated with the superluminal component must be∼1/9smaller than the jet width.Thus,either shocks are very thin in the source frame,or radiative losses limit the emitting region in shocks to a thin layer([97]).It is also possible that,instead,multiple superluminal components may be associated with a single moving shock(see section3.1).3Hydrodynamical Models of Superluminal Sources Shock-in-jet models([12],[94],[63])have been proven to provide a general ex-planation for the emission variability observed in components of relativistic jets. Numerical relativistic HD and emission simulations provide a new powerful tool to improve upon these previous analytical models.With these new numerical techniques it is now possible to study with great detail the generation,struc-ture,and evolution of strong shocks,and analyze its importance in the overall dynamical evolution and emission of jets through comparison with recent high resolution VLBI observations.3.1Relativist ShocksSuperluminal components as associated with moving shock waves have been studied by relativistic hydrodynamical and emission models([49],[83],[107]).In these models,moving shocks are induced by the introduction of perturbations in steady relativistic jets,studying the subsequent jet evolution.In[49]thefluid jet dynamics are computed using a relativistic,axially–symmetric jet model obtained by means of a high–resolution shock capturing scheme([100],[102])to solve the equations of relativistic hydrodynamics in cylin-drical coordinates.The jet material is represented by an ideal gas of adiabatic exponent4/3and the quiescent state corresponds to a diffuse(ρb/ρa=10−3), relativistic(Γb=4),overpressured(p b=3p a/2),cylindrical beam with(local) Mach number M b=1.69(subscripts a and b refer,respectively,to atmosphere and beam).The jet propagates through a pressure–decreasing atmosphere which allows the jet to expand radially.The initial pressure mismatch in the model causes recollimation shocks and expansions in the jetflow([46]).The formation and evolution of shock waves is studied by introducing a square–wave increase8Jos´e-Luis G´o mezFig.1.Pressure distribution at six epochs(0to200R b/c in steps of40)after the introduction of a square-wave perturbation to theflow Lorentz factor for the jet model discussed in the text.The simulation has been performed over a grid of1600×80cells, with a spatial resolution of8cells/R b in both radial and axial directions.Reprinted from[49].of the beamflow velocity from the quiescent valueΓb=4,toΓp=10during a short period of timeτp=0.75R b/c.Because of the fasterflow velocity in the perturbation,thefluid in front piles up,creating a shocked state,which is trailed by a rarefaction.The resulting dynamical evolution of the perturbation along the jet is shown in Fig.1,which contains a set of panels showing the pressure distribution at dif-ferent epochs.Thefirst panel corresponds to the quiescent jet.Both the shocked and rarefied regions in the perturbation are clearly seen.When the perturba-tion passes through a standing shock,the latter is“dragged”downstream for some distance before returning to its initial position as the steady jet becomes reestablished.Figure2shows the total intensity maps corresponding to the stationary model(top panels),and four epochs in the evolution of the disturbance along the jet.Left and right image sequences of Fig.2represent the same data,but with different components identification.By looking at the unconvolved station-ary total intensity image we observe a regular pattern of knots of high emission, associated with the increased specific internal energy and rest-mass density of internal oblique shocks produced by the initial overpressure in this model.VLBI cores can be interpreted as afirst strong recollimation shock in the steady jet ([22],[98],[46],[89]).The regular pattern of knots should remain constant influx and position as long as the jet inlet hydrodynamical variables remain unchanged. Therefore,these components resulting from the recollimation shocks may rep-resent an alternative explanation for the stationary jet components commonly observed in many sources([86],[134],[72],[53],[55])as opposed to jet bendings ([2],[51]).The time evolution of the convolved maps in Fig.2shows the usual core–jet VLBI structure of a blazar,with a single well–defined traveling component associated with the moving shock.The unconvolved maps show a much more complex jet structure.Due to time delays,the shocked region appears as a very extended region of higher emission(see section2.2),which is moving and inter-acting with the quiescent jet.A tentative identification of components throughObservations and Simulations of Relativistic Jets9Fig.2.Simulated total intensity maps of the hydrodynamical model presented in Fig. 1atfive different epochs.Both,left and right image sequences,represent the same data but with different components identification(see text).Grey scale(normalized to the maximum of allfive epochs)shows the emission maps with the full resolution provided by the simulations.Contours show the same images once convolved with a Gaussian beam to resemble actual VLBI observations.Top panels show the stationary model. Maps are obtained for an optically thin observing frequency,and a viewing angle of 10◦.Reprinted from[49].epochs is shown in the right sequence of images of Fig.2,where components are connected by dashed lines.Without further information from the simulations, this would seem the most plausible identification of components,since it would conclude the existence of multiple superluminal components with similar ap-parent motions to that of the main single superluminal component obtained by analyzing the lower resolution images,that is,the convolved maps.However,this identification of components is completely wrong.When analyzing the simula-tions through intermediate epochs to those shown in Fig.2we obtain the correct identification of components,marked on the left sequence of images of Fig.2. This shows the importance of a well time sampled monitoring when studying and identifying superluminal components through epochs.It puts in evidence how easily a wrong identification of components may result from a sparse time10Jos´e-Luis G´o mezmonitoring.Most of the information obtained from analyzing VLBI images is deduced from the measured apparent motions,which,as shown here,may easily be completely wrong,and so the obtained conclusions.By analyzing the structural changes in the correctly identified images of Fig. 2we observe that the interaction of the moving shock with the underlying jet produces a temporary“dragging”of the previously stationary features,accompa-nied by an increase in theirflponents later on come to a stop,followed by upstream motions of the inner components.This upstream motion does not represent actual upstream movement of the jetfluid,but a re-positioning of the recollimation shock closer to the jet inlet.As the images of Fig.2show,detection of this predicted dragging and up-stream motion of components requires high linear resolution images.Some ev-idence of this behavior has been found in the jet of3C454.3([98]),where43 GHz VLBA observations have revealed the existence of a stationary component that moves downstream slightly before returning back upstream as a moving component passes it.Other evidence has been found in the jets of3C120([50], [54]),0735+178([30]),3C279([134]),and may be expected in other sources as more high–frequency images become available.In[107]the appearance of VLBI knots is studied by obtaining the total intensity emission from relativisticflows computed using the relativistic hydro-dynamical code of[25].Computation of the synchrotron radiation is obtained by computing the emission and absorption coefficients(Eqs.8and9),taking into account opacity effects to integrate the transfer equation(Eq.10).Time delay effects are ignored because the jet structures are found to move at barely relativistic speeds.Making use of this numerical model,perturbations in the jet are studied in [107]by introducing a sinusoidal modulation of the inflow Lorentz factor be-tween1and10.Figure3shows the obtained density plots before,and after the perturbations are introduced.The relative dominance of the intrinsic emissiv-ity and Doppler boosting in the intensity images is studied by computing the emission at different observing viewing angles.For small viewing angles the im-age morphology is found to be determined primarily by the Doppler boosting of the high-velocity jet,whereas at larger angles the intrinsic emissivity is more important.Blazars are assumed to be observed along small viewing angles,and therefore the appearance of VLBI knots is determined primarily by the Doppler boosting of fast moving jet perturbations.3.2Trailing shocksThe evolution of a strong shock wave cannot ideally be isolated from the un-derlying jetflow.During its motion along the jet the shock wave interacts with the ambient jet medium,as well as the quiescentflow.This highly non–linear interactions trigger a local pinch instability([59])that leads to the formation of a series of conical shocks.Some of these shocks are present in the simulations of Fig.1and have been studied in detail by[1].Observations and Simulations of Relativistic Jets11Fig.3.Schlieren-type images of laboratory frame density gradient for a jet with a Lorentz factor of10and adiabatic index of4/3.Bottom image shows the same jet after the inflow Lorentz factor has been sinusoidally modulated between1and10to induce perturbations.Reprinted from[107].Figure4shows the Lorentz factor distribution for a jet simulation after the passage of a strong shock.Multiple conical recollimation shocks(“trailing shocks”)can be found to follow the main perturbation.Although their strength is a function of the distance from the jet inlet,simulated total intensity maps show that they should be strong enough as to be detectable by present VLBI arrays([1]).These trailing shocks can be easily distinguished because they appear in the simulated maps as components being released on the wake of primary superlu-minal component(associated with the leading shock),instead of being ejected from the core of the jet.Those trailing components appearing closer to the core show small apparent motions and a very slow secular decrease in brightness, from which they could be identified as stationary components.Those appearing farther downstream are weaker and can reach superluminal apparent motions. Their oblique nature should also result in different polarization properties from that of the main planar leading shock.The existence of these trailing components indicates that not all observed components necessarily represent a major pertur-bation at the jet inlet;rather,multiple emission components can be generated by a single disturbance in the jet.A sample of42γ–ray blazars observed at high frequencies with the VLBA has revealed that stationary components are more common than previously thought ([75]).In27of those sources at least one non–core stationary component has been observed.By analyzing the properties of these stationary features two dif-ferent classes of stationary components are established([75]):those within about12Jos´e-Luis G´o mezFig.4.Relative variation with respect to the quiescent jet of the Lorentz factor(log-arithmic scale).Multiple conical recollimation shocks(“trailing shocks”)are found to follow the main shock labeled“M”.Reprinted from[1].2mas of the core,probably associated with standing hydrodynamical compres-sions,and those farther down the jet,probably associated with bends in the jet. These inner stationary features are in good agreement with the properties pre-dicted for the trailing shocks,and therefore their association seems a plausible interpretation for their nature.Polarimetric high resolution VLBI observations should provide the necessary information as to confirm or rule out this hypoth-esis.3.3Jet Instabilities and the Formation of KnotsRelativistic jets in AGNs and microquasars are thought to be subject to instabili-ties,perhaps due to changes in their feeding from unstable accretion disks.These jet instabilities have been studied with great detail by linear stability analysis of the linearizedfluid equations and by non–linear hydrodynamical simulations (e.g.,[16],[102],[58],[115],[59],[137]).Numerical simulations by[137]have revealed that mode–mode interactions in3D,such as helical surface and helical body mode interactions and coupling to pinch modes,may lead to the formation of relatively stationary knots along the jet beam.In particular,wave–wave interactions are shown to lead to the formation of internal to the jet beam nearly stationary knots close to the jetObservations and Simulations of Relativistic Jets13 inlet,but to move and develop shock spurs at larger distances.These mode–mode interactions,as well as the trailing shocks,may explain some of the puzzling knots evolution observed in the galactic superluminal GRO J1655-40([61]).4Magnetic Fields in Relativistic JetsAlthough recent polarimetric VLBI observations are providing added informa-tion on the magneticfield strength and structure at different jet scales,it is still largely unknown the role played by the magneticfield in the jet dynamics.In order to have a dynamically important magneticfield we should look for jet re-gions where the magnetic pressure B2/8πdominates over the thermal jet plasma pressure.This can be found in the inner jet regions,where magnetic pressure should be of importance for the initial jet formation and collimation.4.1Formation,Collimation,and Acceleration of JetsObservation of the inner jet regions,where jets are formed,collimated and ac-celerated,requires of the highest possible linear resolution in terms of the black hole Schwarzschild radii,which determines the scale length for the system.It is therefore in nearby sources with known massive central black hole where high fre-quency VLBI observations can provide the necessary linear resolution.This has been achieved by global43GHz VLBI observations of the jet in M87([74]),re-vealing that the strong collimation of the jet takes place at30-100Schwarzschild radii(r s)from the black hole,continuing out to∼1000r s.Thanks to the development of recent general relativistic magnetohydrody-namic(GRMHD)numerical codes([79],[80],[81])it is now possible to study the production of relativistic jet by numerical simulations(see e.g.,reviews by [105],[106]).The common scenario for jet production requires a differentially rotating accretion disk surrounding the massive central object.The disk is also threaded with an axial magneticfield of sufficient strength to exert a braking force on the rotating plasma,removing angular momentum and transfering it along the magneticfield lines.These rotating magnetic twists push out and pinch the plasma into a jet.This sweeping pinch mechanism appears to be nearly uni-versal([106]).Numerical GRMHD simulations of jet formation in a rapidly rotation Kerr black hole have been performed for the cases of a co–rotating and counter–rotating Keplerian accretion disk([81],Fig.5).For the co–rotating disk case, a pressure driven jet is formed by a shock in the disk,together with a weaker magnetically driven jet outside the pressure driven jet.However,for the counter–rotating disk case,a powerful magnetically driven jet is formed inside the pres-sure driven jet.This magnetically driven jet is accelerated by a strong magnetic field created by frame dragging in the ergosphere of the black hole.14Jos´e-Luis G´o mezFig.5.Numerical models of jet formation for the case of a counter–rotating(left)and co–rotating disk(right).Grey scale shows the logarithm of the proper mass density; vectors indicate velocity;solid lines show the poloidal magneticfield.Reprinted from [81].4.2Intrinsic Polarimetric Differences in Jets of AGNsPolarimetric VLBI observations have revealed intrinsic differences in the jets of BL Lacertae type objects and QSOs that cannot be explained solely by dif-ferences in the viewing angle to theflow axis.First evidence for these intrin-sic differences were observed in the polarization properties of the jets in the Pearson–Readhead sample through VLBI observations at6cm([29],[21]).These observations have shown that the magneticfields in BL Lac jet components are commonly perpendicular to the jet structural axis,while for QSOs the orien-tation is typically aligned to the jet axes.Recent observations([31],[35],[34]) confirm these differences,but also provide evidence that about30%of the BL Lac sources in the sample present aligned magneticfields,similar to those found in QSOs.This difference in the polarization properties of BL Lacs and QSOs is interpreted by associating the observed knots with moving transverse shocks in jets containing mainly tangled magneticfields.Shocks would be stronger and more commonly observed in BL Lacs,leading to the observed perpendicular fields in the knots.On the contrary,QSOs would be required to be less active, with weaker shocks that would never dominate in polarization.This larger activity in BL Lacs is also supported by the University of Michi-gan long–term total and polarization monitoring program([3]).BL Lacs are found to be more highly variable in totalflux than QSOs,and to present quasi simultaneous variations at different frequencies.This also suggests the existence of intrinsic opacity differences between the two classes of objects.The analysis of the polarized light curves is indicative of the existence of propagating shocks。
基于动态超表面天线的雷达通信一体化设计
doi:10.3969/j.issn.1003-3114.2023.05.021引用格式:高克,张海洋,王保云.基于动态超表面天线的雷达通信一体化设计[J].无线电通信技术,2023,49(5):946-952.[GAO Ke,ZHANG Haiyang,WANG Baoyun.Beamforming Design for Dual-functional Radar-communication Systems with Dynamic Metasurface Antennas[J].Radio Communications Technology,2023,49(5):946-952.]基于动态超表面天线的雷达通信一体化设计高㊀克,张海洋,王保云(南京邮电大学通信与信息工程学院,江苏南京210003)摘㊀要:雷达通信一体化(Dual-Functional Radar-Communication,DFRC)利用相同的硬件平台㊁频谱资源同时实现雷达感知和无线通信双功能,是当前无线通信领域研究的热点技术㊂针对动态超表面天线(Dynamic Metasurface Antenna,DMA)辅助的雷达通信一体化系统,研究了最优波束成形设计问题㊂最优波束成形设计是一个非凸优化问题,很难直接求解㊂设计全数字天线架构下的最优波束,将动态超表面天线雷达波束设计转换为拟合最优编码矩阵问题㊂转换后的波束设计问题仍为非凸,为此将其分解为两个子问题交替最小化,其中两个子问题分别采用黎曼共轭梯度和半正定松弛算法求解㊂数值仿真表明,满足通信质量约束的情况下,动态超表面天线架构的DFRC 雷达波束性能接近于无频谱共享时的纯雷达波束性能㊂关键词:雷达通信一体化;动态超表面天线;交替最小化;黎曼共轭梯度;半正定松弛中图分类号:TN929.5㊀㊀㊀文献标志码:A㊀㊀㊀开放科学(资源服务)标识码(OSID):文章编号:1003-3114(2023)05-0946-07Beamforming Design for Dual-functional Radar-communicationSystems with Dynamic Metasurface AntennasGAO Ke,ZHANG Haiyang,WANG Baoyun(Communication and Information Engineering,Nanjing University of Posts and Telecommunications,Nanjing 210003,China)Abstract :Dual-Functional Radar-Communication (DFRC)uses same hardware platform and spectrum re-sources to realize dualfunctions of radar detection and wireless communication simultaneously,which is a hot topic in the field of wireless communications.Forthe Dynamic Metasurface Antennas (DMA)-assisted DFRC system,an optimal beamforming design problem is studied.The optimalbeamforming design is a non-convex optimization problem that is difficult to solve directly.In this paper,an optimal beam with a digitalantenna architecture is designed first,and then the dynamic metamaterial antenna radar beam design is converted into a fitting optimalcoding matrix problem.Though the resulting design problem is still non-convex.it can be decom-posed into two sub-problems and then been solved alternately.In particular,the two sub-problems are solved by riemannian conjugate gradient and semidefinite relaxation algo-rithms,respectively.Finally,numerical results show that the performance of our proposed beamforming design for DMA-assisted DFRC system is close to that of the radar only beamforming without communication requirement.Keywords :DFRC;DMA;alternate minimization;riemannian conjugate gradient;semidefinite relaxation收稿日期:2023-05-050 引言随着5G 时代的到来,无线设备数量和种类均呈现出了爆发性增长,全球通信产业对无线频谱的需求日益迫切㊂有很多场景需要感知与通信联合设计,例如:自动驾驶㊁智慧城市和智能家居等[1]㊂与此同时,随着无线通信速率需求的不断提高,载波频率被推向了传统上分配给雷达系统的毫米波频率频段[2]㊂未来后5G 及6G 时代,为提高频谱效率以及降低雷达与通信系统之间的电磁干扰问题,雷达通信一体化(Dual-Functional Radar-Communication,DFRC)系统成为了一个有前途的热门研究领域㊂在雷达通信一体化系统中,雷达与通信系统之间共享相同的硬件平台和频谱资源,同时实现通信和雷达感知的双功能㊂在雷达通信一体化系统中,由于雷达和通信具有不同的需求且共享相同的资源,因此需要精心设计传输波束以平衡二者的性能㊂为了在保证通信用户服务质量的同时提高雷达的性能,文献[3]研究了发射波束成形优化设计㊂针对全数字天线架构,文献[4]考虑波束之间的相互干扰因素,设计了性能更优的雷达波束㊂考虑到全数字天线功耗大㊁成本高的问题,目前对雷达通信一体化系统研究比较广泛的是基于相移器的混合波束天线架构[5-10],其中文献[5-6]研究了设计模拟和数字预编码矩阵,使其与最优通信预编码矩阵和最优雷达波束预编码矩阵之间误差的加权总和最小;文献[7-8]研究主要集中在雷达波束与理想波束差距小于一定阈值作为约束条件,最大化用户通信质量;文献[9-10]研究了在保证用户通信质量前提下,最优化雷达波束性能,其雷达的波束性能直接由雷达接收机的信干扰加噪声比(Signal to Interference plus Noise Ratio, SINR)决定㊂智能超表面是当前无线通信领域的另外一个研究热点,其可用于增强无线通信盲区覆盖㊁物理层辅助安全通信㊁大规模D2D(Device-to-Device)通信㊁物联网中无线携能通信以及室内覆盖等领域[11]㊂然而,智能超表面除了用来做被动的反射外,还可以用来实现低功耗的主动收发天线㊂动态超表面天线(Dynamic Metasurface Antennas,DMA)是一种典型的基于超表面天线的收发天线㊂在基于DMA的收发器中,每个超表面天线单元是由低功耗的超表面组成,且每个天线单元的幅频特性可以动态实时调控[12]㊂DMA天线架构可以被视为混合模拟数字天线架构,即它不需要额外的专用模拟相移器网络,仅利用自身的信号处理功能便可实现模拟预编码[13]㊂此外,DMA可以包含大量可调谐的超表面天线元件,并且其天线单元之间的距离可以是亚波长,DMA需要的物理面积可以更小,有助于设备的小型化[14]㊂1㊀系统模型和问题描述1.1㊀系统模型雷达通信一体化系统场景示意图如图1所示,一个雷达通信一体化基站拥有N T根天线,为K个单天线用户提供通信服务并探测区域内目标㊂基站使用的动态超表面天线架构,其由数字预编码矩阵㊁L T条射频链路和模拟预编码矩阵组成㊂图1㊀雷达通信一体化系统场景示意图Fig.1㊀Schematic diagram of DFRC基带信号表示为sɪKˑ1,s i~(0,1),iɪ{1, 2, ,K}为第i个用户接收到的信息符号㊂发射信号可以表示为:y=UF DMA F BB s,(1)式中:F DMAɪN TˑL T为DMA天线模拟预编码矩阵, F BBɪN DMAˑK为数字预编码矩阵,DMA微带内的信号传播公式为:u i,j=e-ρi,j(αi+jβi),∀i,j,其中αi为波导衰减系数,βi为波数,ρi,j表示第i微带中第l个单元的位置,其中U((i-1)L+l,(i-1)L+l)=u i,l,L为每条微带上单元的个数[13]㊂功率约束条件为 UF DMA F BB 2FɤP max,P max为基带最大分配功率㊂F DMA矩阵满足以下形式[15]:F DMA=t10 00t2 0︙︙︙00 t L Téëêêêêêùûúúúúú,(2)式中:t iɪN TN DMAˑ1,非零相q i,l=j+e jφi,l2,{φi,lɪ[0,2π]}ɪF DMA,∀i,l㊂雷达在θ角方向的传输功率波束图可以表示为:P(θ;R)=a H(θ)Ra(θ),(3)式中:RɪN TˑN T为传输波束的协方差矩阵,R= UF DMA F BB ss H F H BB F H DMA U-H=UF DMA F BB F H BB F H DMA U H㊂对于N个天线单元的均匀线性天线阵列,其导向矢量为:a(θ)=1N[1,e j2πλdsin(θ), ,e j2πλd(N-1)sin(θ)]T,(4)式中:λ为信号波长,d=λ/2为天线单元间距㊂雷达在θ1和θ2两角之间的波束互相关可以表示为:P c(θ1,θ2;R)=a H(θ1)Ra T(θ2)㊂(5)由式(3)和式(5)可以看出,雷达的传输功率波束图和波束互相关都是由传输波束的协方差矩阵R决定㊂通过波束方向误差和波束互相关两部分的加权和组成一个损失函数,用损失函数评估雷达性能㊂第一部分可以用接收到的波束与理想波束之间的均方差来评估:L r,1(R,α)=1LðL l=1|αd(θl)-P(θl;R)|2,(6)式中:α为比例因子,d(θl)为θl方向理想接收波束㊂第二部分用波束互相关均方差来评估:L r,2(R)=2P2-PðP-1p=1㊀ðP q=p+1|P c(θ-p,θ-q);R|2㊂(7)㊀㊀将以上两部分加权和后,雷达波束图的损失函数表示为:L r(R,α)=L r,1(R,α)+ωL r,2(R)㊂(8)在本文雷达通信一体化系统中,假设通信用户是单天线的,则第k个用户接收信号为:y k=h H k UF DMA F BB,k s k+ðK iʂk h H k UF DMA F BB,i s i+n k,(9)式中:h kɪN Tˑ1为基站与第k个用户之间的下行通道,n k~(0,σ2k)为第k个用户加性高斯白噪声(Additive White Gaussian Noise,AWGN)㊂第k个用户接收信号的SINR可以表示为:γk=|h H k UF DMA F BB,k|2σ2k+ðK iʂk|h H k UF DMA F BB,i|2㊂(10)1.2㊀问题描述雷达通信一体化系统需要权衡通信和雷达之间的性能㊂基于动态超表面天线的雷达通信一体化系统,在保证每个通信用户的SINR高于给定阈值前提下的式(10),使雷达传输波束的性能达到最优的式(8)㊂另外,加上预编码矩阵有功率限制和模拟预编码矩阵相位限制的式(2),雷达通信一体化系统传输波束成形设计问题可以表示为:㊀min FBB,F DMA L r(R,α)㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀s.t.㊀ UF DMA F BB 2FɤP max,F DMA(i,l)=j+e jφi,l2,φi,lɪ[0,2π],|h H k UF DMA F BB,k|2σ2k+ðK iʂk|h H k UF DMA F BB,i|2ȡΓ,(11)式中:Γ为给定用户的SINR阈值㊂式(11)涉及到数字预编码矩阵和模拟预编码矩阵的联合设计,并且问题本身也是非凸的,很难求解㊂当天线架构为全数字天线架构时,该问题对应的问题容易求解,并且在用户SINR满足一定阈值时,其最优预编码矩阵获得的波束与理想波束十分相似㊂因此可以先求出全数字天线最优预编码矩阵,然后将动态超表面天线的模拟预编码矩阵和数字预编码矩阵拟合全数字天线的最优预编码矩阵,由此得到动态超表面天线的模拟与数字最优预编码矩阵㊂2㊀雷达通信一体化波束成形设计2.1㊀基于全数字天线架构先设计基于全数字天线架构的雷达通信一体化系统预编码矩阵W,使其在满足功率约束和用户SINR高于一定阈值前提下,雷达波束性能达到最优㊂其问题表示为:㊀㊀㊀min R L r(R,α)s.t.㊀R=WW HɪS+MW 2FɤP max|h H k w k|2σ2k+ðK iʂk|h H k w i|2ȡΓ,(12)式中:w i为W的第i列,W=(w1,w2 ,w K)㊂将第三个约束化简后的问题为:min R,RkL r(R,α)s.t.㊀R=WW HɪS+MW 2FɤP maxRkɪS+M,rank(R k)=1,k=1,2, ,K(1-Γ-1)h H k R k h kȡh H k Rh k+σ2k,(13)式中:R k=w k w H k,R=ðK k=1R k㊂由于其中的约束条件rank(R k)=1,k=1,2, , K是非凸的,可以先将其松弛掉,松弛后的问题是凸问题:min R,RkL r(R,α)s.t.㊀R=WW HɪS+MW 2FɤP maxRkɪS+M,k=1,2, ,K(1-Γ-1)h H k R k h kȡh H k Rh k+σ2kW=(w1,w2, ,w K),R k=w k w H k㊂(14)可以用Matlab中CVX工具箱求得最优解:R^, R^k,k=1,2, ,K㊂如果式(14)全局最优解满足R^kɪS+M,k=1,2, ,K 秩为1,那么求解式(13)中使用的松弛就是紧的,即松弛后问题的解也是原非凸问题的解㊂定理1㊀式(13)存在最优解R ~,R ~k ,k =1,2, ,K ,满足rank(R ~k )=1,k =1,2, ,K ㊂证明㊀R ^,R ^i ,i =1,2, ,K 为式(14)的全局最优解,将R ^,R ^i,i =1,2, ,K 做以下变换:R ~=R ^,w ~i =(h H i R ^i h i )-1/2R ^i h i ,R ~i =w ~i w ~H i ,R ~,R ~i ,i =1,2, ,K 为半正定矩阵且秩为一㊂因为R ~=R^,并且式(13)和式(14)的最终问题是相同的,所以R ~是式(13)全局最优解㊂现在只要证明R ~,R ~i ,i =1,2, ,K 为式(13)的可行解,则R ~,R ~i ,i =1,2, ,K 为式(13)的全局最优解㊂由于h H kR ~k h k =h H kw ~k w ~H k h k =h H k R ^k h k ,将其带入到(1-Γ-1)h H k R ~k h k=(1-Γ-1)h H k R ^k h k ȡh H k R ^k h k +σ2k =h H k R ~k h k +σ2k 满足式(13)的限制条件㊂所以R ~,R ~i ,i =1,2, ,K 为原问题的全局最优解㊂由定理1可知将式(14)最优解做以下变换:R ~=R ^,w ~k =(h H k R ^k h k )-1/2R ^k h k ,R ~k=w ~k w ~H k ,R ~k ɪS +M ,k=1,2, ,K 且秩为1,并且R ~仍为原问题的解㊂由此可以求解得到全数字天线最优预编码矩阵的列向量w k ,全数字天线架构的最优预编码矩阵W 也就可以求出㊂2.2㊀基于动态超表面天线架构在上节求解得到了全数字天线最优预编码矩阵,本节设计动态超表面天线架构预编码矩阵,使雷达通信一体化系统在满足功率约束㊁模拟预编码矩阵相位约束和通信用户信干扰加噪声比高于一定阈值前提下,最优拟合全数字天线预编码矩阵,其问题表示为:min F BB ,F DMAUF DMA F BB -W ~2Fs.t.㊀ UF DMA F BB 2F ɤP maxq i ,l =j +ej φi ,l2,φi ,l ɪ[0,2π]}{ɪF DMA ,∀i ,l|h H kUF DMA F BB,k|2σ2k+ðKi ʂk|h H kUF DMA F BB,i|2ȡΓ㊂(15)由于此问题不是凸问题,故将问题分解成设计两个子问题相互迭代来求解,两个子问题分别设计数字和模拟预编码矩阵㊂然而,数字和模拟预编码矩阵的设计问题都是非凸问题㊂为此,本文分别采用半正定松弛(Semidefinite Relaxation,SDR )技术[16-17]和黎曼共轭梯度(Riemannian Conjugate Gra-dient,RCG)算法[18]分别设计最优数字和模拟预编码矩阵㊂2.2.1设计模拟预编码矩阵当固定数字预编码矩阵F BB 设计最优模拟预编码矩阵时,限制条件只有模拟预编码矩阵的相位限制㊂其问题为:min FDMAUF DMA F BB -W ~2Fs.t.㊀q i ,l =j +ej φi ,l2,φi ,l ɪ[0,2π]}{ɪF DMA ,∀i ,l ㊂(16)由于问题是矩阵形式,不方便求解,所以将矩阵向量化:min FDMAUF DMA F BB -W ~2F =min F DMA(F T BB U )vec(F DMA )-w 2F ,式中:w =vec(W ~)㊂因为vec(F DMA )中的元素除了相位限制元素,其他为零元素㊂由于零元素的具体位置是已知的,所以可以先将零元素剔除掉㊂令q 为vec(F DMA )去除零元素后的向量,A 为(F T BB U )去除掉与vec(F DMA )零元素相对应的列向量㊂此时的问题转换为:㊀min F DMA(F T BB U )vec(F DMA )-w 2F =min q(Aq -w )H (Aq -w )=min qq H A H Aq -2q H A H w +w H w ㊂(17)由于模拟预编码矩阵的非零元素q i ,l 可以描述为圆心点为0,12e j π2(),半径为12的复平面圆上:q i ,l -12e j π2=12,定义向量b 为:b k =2q k -e j π2,所以q =12b +e j π21(),|b k |=1㊂最终可以将问题转换为关于向量b 的问题:min bq H A H Aq -2q H A H w +w H w =min b 14b +e j π21()H A H A b +e j π21()-b +e j π21()H A H w +w H w s.t.㊀|b k |=1ɪb ,(18)这时搜索空间为N T 个复数圆上,是一个N T的黎曼子流形,可以通过RCG 求得最优解b opt ㊂其中该问题的黎曼梯度为Δf (bt +1k)=AH㊃12A b t +1k +e j π21()-w ()㊂由于F DMA 非零位置是已知的,所以将最优解bopt扩展成矩阵形式,可以得到最优模拟预编码矩阵F opt DMA ㊂2.2.2设计模拟预编码矩阵当固定模拟预编码矩阵F DMA 时,限制条件为预编码矩阵功率约束和通信SINR 阈值约束,其问题为:㊀㊀㊀㊀min F BBUF DMA F BB -W ~ 2F㊀㊀㊀㊀s.t.㊀ UF DMA F BB 2FɤP maxh H k UF DMA F BB,k2σ2k+ðKi ʂk|h H kUF DMA F BB,i |2ȡΓ㊂(19)由于式(19)中第二个限制条件F BB 是按列展开的,所以将问题中的矩阵F BB 和W ~也按列展开:ðKk =1UF DMA F BB,k-W ~k 2F =ðK k =1F H BB,k F H DMA U H UF DMA F BB,k -2F H BB,k F H DMA U H W ~k +W ~Hk W ~k ㊂(20)展开后的问题并不容易求解,引入辅助变量t 2=1,可以化解成二次约束二次规划问题(Quadrati-cally Constrained Quadratic Programs,QCQP):v -k =F BB,kt(),Q k =F H DMA U H UF DMA ,-F H DMA U HW ~k ㊀㊀-W ~H k UF DMA ,W ~H k W ~k(),F H BB,k F H DMA U H U F DMA F BB,k -2F H BB,k F H DMA U H W ~k +W ~H k W ~k=v -H k Q v -k ㊂但此时,由于式(20)中第二个限制条件是非凸的,所以该问题也是非凸的㊂引用SDR 技术将问题进行化简,令V k =v -k v -H k ,rank(V k )=1,可以将问题简化为SDR 的标准形式:min V k ðKk =1tr(Q k V k )s.t.㊀ðKk =1trF H DMA U HUF DMA ,00,()V k ()ɤP max ,∀k ,trH k ,00,0()V k ()Γ-ðKi ʂktrH k ,00,()V i ()ȡσ2k ,tr0K ∗K ,00,1()V k ()=1,V k ȡ0,rank(V k )=1,H k =F H DMA U H h k h Hk UF DMA ㊂(21)由于约束项rank(V k )=1是非凸的,先将其松弛掉,之后的问题是凸问题,可以用Matlab 中CVX 工具箱求最优解V opt k ㊂如果该问题可解或有界,则ðKk =1[rank(V opt k )]ɤK +1,又因为每个用户的SINR 阈值限制,最优解满足:rank (V opt k )ȡ1,所以其最优解满足rank(V opt k )=1㊂由此证得rank(V k )=1的松弛是紧的,V opt k是原问题的最优解㊂F opt BB,k 是V optk的最大特征向量乘以最大特征值的平方根,因此,可以得到最优数字预编码矩阵F opt BB ㊂3 仿真分析本节采用数值仿真验证DMA 雷达通信一体化设计算法的性能,并且与全数字天线架构㊁基于相移器的混合波束天线架构和理想雷达波束进行对比㊂考虑雷达通信一体化基站的天线为均匀线性天线阵列,总发射功率为1W 和天线数量为24,其为用户提供通信服务并探测区域内目标㊂在探测区域内设置了方向为-40㊁0ʎ和40ʎ的3个理想目标,其波束表达式为:d (θ)=1,θ0-Δ2ɤθɤθ0+Δ20,㊀㊀otherwise{,(22)式中:Δ为理想波束的宽度,设置为2ʎ㊂当系统设计的DMA 射频链路为12个,信噪比设置为20dB 时,不同天线架构随角度变化的波速比较如图2所示㊂不同天线架构在满足用户需求前提下,使雷达波束达到最优的仿真,图中K =0㊁FD㊁DMA 和BP 线分别为理想目标波束㊁全数字天线架构波束㊁DMA 天线架构波束和基于相移器架构波束㊂可以看出,全数字天线的雷达波束图基本与理想的波束重合,DMA 天线架构和基于相移器架构也很好地还原了最优波束图,并且从中很容易查找出在-40ʎ㊁0ʎ和40ʎ方向有目标,因为这3个方向的波束峰值明显高于其他方向㊂图3是在4个通信用户SINR 的阈值从6dB 调整到14dB,不同天线架构随角度变化的波束比较㊂图2与图3对比可知,在通信用户阈值提高的情况下,DMA 架构和基于相移器的混合架构的目标雷达波束图峰值有明显的变差㊂图4是在6个通信用户信SINR 的阈值为6dB 情况下,不同天线架构随角度变化的波束比较㊂图2与图4对比可知,服务通信用户增加,目标雷达波束图峰值会变差㊂图5是在4个通信用户信SINR 的阈值为6dB,功率约束调整为2W 情况下,不同天线架构随角度变化的波束比较㊂图2与图5对比可知,增加发射功率,图5中目标雷达波束图峰值接近图2中目标峰值的2倍㊂图2㊀不同天线架构随角度变化的波束比较Fig.2㊀Comparison of beams varying by angle fordifferent antennaarchitectures图3㊀调整用户SINR 后的波束比较Fig.3㊀Beam comparison after adjusting theuser sSINR图4㊀调整用户个数后的波束比较Fig.4㊀Beam comparison after adjusting the number ofusers图5㊀调整功率约束后的波束比较Fig.5㊀Beam comparison after adjusting power constraints图6展示了基于DMA 的雷达一体化系统在不同发射功率情况下,用户SINR 阈值约束和雷达波束性能之间的权衡㊂可以看出,在发射功率一定时,随着用户SINR 阈值的增加,DMA 天线预编码矩阵与全数字天线预编码矩阵之间的均方差也在增加,并且发射功率为2W 时的均方差明显大于功率为1W 的设计㊂这是因为当通信质量要求增加时,为满足用户质量需要消耗更多的功率,而生成雷达波束的功率会变少,雷达波束性能也会变差㊂因此,降低通信质量要求,可以提高雷达波束性能㊂图6㊀用户SINR 阈值与雷达波束均方差之间关系Fig.6㊀Relationship between the user s SINR threshold andthe mean square deviation of the radarbeam4 结束语本文研究了基于动态超表面天线的雷达通信一体化系统,设计了相应的最优波束成形策略㊂采用了数字预编码矩阵与模拟预编码矩阵设计联合交替优化设计,分别应用半正定松弛和黎曼共轭梯度算法求解㊂数值仿真结果表明,所提算法设计的动态超表面天线架构的雷达通信一体化系统,在满足通信用户性能的前提下,其雷达性能接近理想雷达波束㊂动态超表面天线架构与基于相移器的混合波束天线架构整体性能相似,其雷达通信一体化系统中雷达与通信性能之间存在负相关,雷达性能随着通信性能的提高而降低㊂参考文献[1]㊀刘凡,袁伟杰,原进宏,等.雷达通信频谱共享及一体化:综述与展望[J].雷达学报,2020,10(3):467-484. [2]㊀ZHENG L,LOPS M,ELDAR Y C,et al.Radar and Com-munication Coexistence:An Overview:A Review of RecentMethods[J].IEEE Signal Processing Magazine,2019,36(5):85-99.[3]㊀CHU J,LIU R,LIU Y,et al.AN-aided Secure Beamform-ing Design for Dual-functional Radar-communication Sys-tems[C]ʊ2021IEEE/CIC International Conference onCommunications in China(ICCC Workshops).Xiamen:IEEE,2021:54-59.[4]㊀LIU X,HUANG T,SHLEZINGER N,et al.Joint TransmitBeamforming for Multiuser MIMO Communications andMIMO Radar[J].IEEE Transactions on Signal Process-ing,2020,68:3929-3944.[5]㊀KAUSHIK A,MASOUROS C,LIU F.Hardware EfficientJoint Radar-communications with Hybrid Precoding andRF Chain Optimization[C]ʊICC2021-IEEE InternationalConference on Communications.Montreal:IEEE,2021:1-6.[6]㊀LIU F,MASOUROS C.Hybrid Beamforming with Sub-arrayed MIMO Radar:Enabling Joint Sensing and Commu-nication at mmWave Band[C]ʊICASSP2019-2019IEEE International Conference on Acoustics,Speech andSignal Processing(ICASSP).Brighton:IEEE,2019:7770-7774.[7]㊀CHENG Z,LIAO B,HE Z.Hybrid Transceiver Design forDual-functional Radar-communication System[C]ʊ2020IEEE11th Sensor Array and Multichannel Signal Process-ing Workshop(SAM).Hangzhou:IEEE,2020:1-5. [8]㊀CHENG Z,HE Z,LIAO B.Hybrid Beamforming for Multi-carrier Dual-function Radar-communication System[J].IEEE Transactions on Cognitive Communications and Net-working,2021,7(3):1002-1015.[9]㊀CHEN C Y,VAIDYANATHAN P.MIMO Radar Wave-form Optimization with Prior Information of the ExtendedTarget and Clutter[J].IEEE Transactions on Signal Pro-cessing,2009,57(9):3533-3544.[10]DAI Y,HAN K,WEI G,et al.Hybrid Beamforming forDFRC System Based on SINR Performance Metric[C]ʊ2021IEEE/CIC International Conference on Communicationsin China(ICCC Workshops).Xiamen,IEEE,2021:82-87.[11]LAN G,IMANI M F,DEL HOUGNE P,et al.WirelessSensing Using Dynamic Metasurface Antennas:Challengesand Opportunities[J].IEEE Communications Magazine,2020,58(6):66-71.[12]SMITH D R,YURDUSEVEN O,MANCERA L P,et al.Analysis of a Waveguide-fed Metasurface Antenna[J].Physical Review Applied,2017,8(5):054048. [13]ZHANG H,SHLEZINGER N,GUIDI F,et al.Beam Focu-sing for Near-field Multiuser MIMO Communications[J].IEEE Transactions on Wireless Communications,2022,21(9):7476-7490.[14]SHLEZINGER N,ALEXANDROPOULOS G C,IMANI M F,et al.Dynamic Metasurface Antennas for6G ExtremeMassive MIMO Communications[J].IEEE WirelessCommunications,2021,28(2):106-113. [15]SHLEZINGER N,DICKER O,ELDAR Y C,et al.Dynam-ic Metasurface Antennas for Uplink Massive MIMO Sys-tems[J].IEEE Transactions on Communications,2019,67(10):6829-6843.[16]LUO Z Q,MA W K,SO A M C,et al.Semidefinite Relax-ation of Quadratic Optimization Problems[J].IEEE Sig-nal Processing Magazine,2010,27(3):20-34. [17]ZHANG S.Quadratic Maximization and Semidefinite Re-lax-ation[J].Mathematical Programming,2000,87:453-465.[18]YU X,SHEN J C,ZHANG J,et al.Alternating Minimiza-tion Algorithms for Hybrid Precoding in Millimeter WaveMIMO Systems[J].IEEE Journal of Selected Topics inSignal Processing,2016,10(3):485-500.作者简介:㊀㊀高㊀克㊀男,(1994 ),硕士研究生㊂主要研究方向:雷达通信信号处理㊂张海洋㊀男,(1987 ),博士研究生㊂主要研究方向:无线通信信号处理㊁面向6G近场无线通信㊂王保云㊀男,(1967 ),博士,教授㊂主要研究方向:香农信息论㊁无线通信中的博弈与协作㊁无线通信中的信号处理技术㊁视频信息的分析与理解㊂。
半导体物理与器件——Terms汉译英
半导体物理与器件——Terms(术语)U1 Terms:Semiconductor physics and devices半导体物理与器件,Space lattice空间晶格, unit cell晶胞, primitive cell原胞,basic crystal structures 基本晶格结构(five), Miller indices密勒指数, atomic bonding原子价键U2 Terms:quantum mechanics量子力学,energy quanta能量子, wave-particle duality波粒二象性,the uncertainty principle测不准原理/海森堡不确定原理Schrodinger's wave equation薛定谔波动方程, eletrons in free Space自由空间中的电子the infinite potential well无限深势阱, the step potential function 阶跃势函数, the potential barrier势垒.U3 Terms:Pauli exclusion principle泡利不相容原理, quantum state量子态. allowed energy band允带, forbidden energy band禁带.conduction band导带, valence band价带,hole空穴, electron 电子.effective mass有效质量.density of states function状态密度函数,the Fermi-Dirac probability function费米-狄拉克概率函数,the Boltzmann approximation波尔兹曼近似,the Fermi energy费米能级.U4 Terms:charge carriers载流子, effective density of states function有效状态密度函数,intrinsic本征的,the intrinsic carrier concentration本征载流子浓度, the intrinsic Fermi level本征费米能级.charge neutrality电中性状态, compensated semiconductor补偿半导体, degenerate简并的,non-degenerate非简并的, position of E F费米能级的位置U5 Terms:drift current漂移电流, diffusion current 扩散电流,mobility迁移率, lattice scattering晶格散射, ionized impurity scattering 电离杂质散射, velocity saturation饱和速度,conductivity电导率,resistivity电阻率.graded impurity distribution杂质梯度分布,the induced electric field感生电场, the Einstein relation爱因斯坦关系, the hall effect霍尔效应U6 Terms:nonequilibrium excess carriers非平衡过剩载流子,carrier generation and recombination载流子的产生与复合,excess minority carrier过剩少子,lifetime寿命,low-level injection小注入,ambipolar transport双极输运, quasi-Fermi energy准费米能级.U7 Terms:the space charge region空间电荷区,the built-in potential内建电势, the built-in potential barrier内建电势差,the space charge width空间电荷区宽度, zero applied bias零偏压, reverse applied bias反偏, onesided junction单边突变结.U8 Terms:the PN junction diode PN结二极管, minority carrier distribution少数载流子分布, the ideal-diode equation理想二极管方程, the reverse saturation current density反向饱和电流密度.a short diode短二极管,generation-recombination current产生-复合电流,the Zener effect齐纳效应, the avalanche effect雪崩效应, breakdown击穿.U9 Terms:Schottky barrier diode (SBD)肖特基势垒二极管,Schottky barrier height肖特基势垒高度.Ohomic contact欧姆接触,heterojunction异质结, homojunction单质结,turn-on voltage开启电压,narrow-bandgap窄带隙, wide-bandgap宽带隙,2-D electron gas二维电子气U10 Terms:bipolar transistor双极晶体管,base基极, emitter发射极, collector集电极.forward active region正向有源区, inverse active region反向有源区, cut-off截止, saturation饱和,current gain电流增益,common-base共基, common-emitter共射.base width modulation基区宽度调制效应, Early effect厄利效应, Early voltage厄利电压U11 Terms:Gate栅极, source源极, drain漏极, substrate基底.work function difference功函数差threshold voltage阈值电压, flat-band voltage平带电压enhancement mode增强型, depletion mode耗尽型strong inversion强反型, weak inversion弱反型,transconductance跨导, I-V relationship电流-电压关系。
电磁场微波词汇汉英对照表
【一画】一致性几何绕射理论UTD （Uniform Geometrical Theory of Diffraction）【二画】二端口网络two port network二重傅立叶级数double Fourier series入射场incident field入射波incident wave几何绕射理论GTD （Geometrical Theory of Diffraction）【三画】小波wavelet【四画】无功功率reactive power无限（界）区域unbound region无源网络passive network互易性reciprocity互阻抗mutual impedance互耦合mutual coupling互连interconnect天线antennas天线方向性图pattern of antenna匹配负载matched load孔aperture孔（缝）隙天线aperture antennas内阻抗internal impedance介电常数permittivity介质dielectric介质波导dielectric guide介质损耗dielectric loss介质损耗角dielectric loss angle介电常数dielectric constant反射reflection反射系数reflection coefficient分离变量法separation of variables【五画】主模dominant mode正交性orthogonality正弦的sinusoidal右手定则right hand rule平行板波导parallel plate waveguide平面波plane wave功率密度density of power功率流（通量）密度density of power flux 布魯斯特角Brewster angle本征值eigen value本征函数eigen function边值问题boundary value problem四端口网络four terminal network矢量位vector potential电压voltage电压源voltage source电导率conductivity电流元current element电流密度electric current density电荷守恒定律law of conservation of charge 电荷密度electric charge density电容器capacitor电路尺寸circuit dimension电路元件circuit element电场强度electric field intensity电偶极子electric dipole电磁兼容electromagnetic compatibility矢量vector矢径radius vector失真distortions平移translation击穿功率breakdown power节点node【六画】安培电流定律Ampere’s circuital law传播常数propagation constant亥姆霍兹方程Helmholtz equation动态场dynamic field共轭问题conjugate problem共面波导coplanar waveguide （CPW）有限区域finite region有源网络active network有耗介质lossy dielectric导纳率admittivity同轴线coaxial line全反射total reflection全透射total transmission各向同性物质isotropic matter各向异性nonisotropy行波traveling wave光纤optic fiber色散dispersion网格mesh全向天线omnidirectional antennas阵列arrays【七画】串扰cross-talk回波echo良导体good conductor均匀平面波uniform plane wave均匀传输线uniform transmission line近场near-field麦克斯韦方程Maxwell equation克希荷夫电流定律Kirchhoff’s current law 环行器circulator贝塞尔函数Bessel function时谐time harmonic时延time delay位移电流electric displacement current芯片chip芯片组chipset远场far-field【八画】变分法variational method定向耦合器directional coupler取向orientation法拉第感应定律Faraday’s law of induction 实部real part空间分量spatial components波导waveguide波导波长guide wave length波导相速度guide phase velocity波阻抗wave impedance波函数wave function波数wave number泊松方程Poisson’s equation拉普拉斯方程Laplace’s equation坡印亭矢量Poynting vector奇异性singularity阻抗矩阵impedance matrix表面电阻surface resistance表面阻抗surface impedance表面波surface wave直角坐标rectangular coordinate极化电流polarization current极点pole非均匀媒质inhomogeneous media非可逆器件nonreciprocal devices固有（本征）阻抗intrinsic impedance单位矢量unit vector单位法线unit normal单位切线unit tangent单极天线monopole antenna单模single mode环行器circulator驻波standing wave驻波比standing wave ratio直流偏置DC bias【九画】标量位scalar potential品质因子quality factor差分法difference method矩量法method of moment洛伦兹互易定理Lorentz reciprocity theorem 屏蔽shield带状线stripline标量格林定理scalar Green’s theorem面积分surface integral相对磁导率relative permeability相位常数phase constant相移器phase shifter相速度phase velocity红外频谱infra-red frequency spectrum矩形波导rectangular waveguide柱面坐标cylindrical coordinates脉冲函数impulse function复介电常数complex permittivity复功率密度complex power density复磁导率complex permeability复矢量波动方程complex vector wave equation 贴片patch信号完整性signal integrity信道channel寄生效应parasite effect指向天线directional antennas喇叭天线horn antennas【十画】准静态quasi-static旁路电流shunt current高阶模high order mode高斯定律Gauss law格林函数Green’s function连续性方程equation of continuity耗散电流dissipative current耗散功率dissipative power偶极子dipole脊形波导ridge waveguide径向波导radial waveguide径向波radial wave径向模radial mode能量守恒conservation of energy能量储存energy storage能量密度power density衰减常数attenuation constant特性阻抗characteristic impedance特征值characteristic value特解particular solution勒让德多项式Legendre polynomial积分方程integral equation涂层coating谐振resonance谐振长度resonance length【十一画】混合模hybrid mode部分填充波导partially filled waveguide 递推公式recurrence formula探针馈电probe feed接头junction基本单位fundamental unit理想介质perfect dielectric理想导体perfect conductor唯一性uniqueness虚部imaginary part透射波transmission wave透射系数transmission coefficient球形腔spherical cavity球面波spherical wave球面坐标spherical coordinate终端termination终端电压terminal voltage射频radio frequency探针probe【十二画】涡旋vortices散度方程divergence equation散射scattering散杂电容stray capacitance散射矩阵scattering matrix斯托克斯定理Stoke’s theorem斯涅尔折射定律Snell’s law of refraction阴影区shadow region超越方程transcendental equation超增益天线supergain antenna喇叭horn幅角argument最速下降法method of steepest descent趋肤效应skin effect趋肤深度skin depth微扰法perturbational method等相面equi-phase surface等幅面equi-amplitude surface等效原理equivalence principle短路板shorting plate短截线stub傅立叶级数Fourier series傅立叶变换Fourier transformation第一类贝塞耳函数Bessel function of the first kind第二类汉克尔函数Hankel function of the second kind 解析函数analytic function激励excitation集中参数元件lumped-element场方程field equation场源field source场量field quantity遥感remote sensing振荡器oscillators滤波器filter【十三画】隔离器isolator雷达反射截面radar cross section （RCS）损耗角loss angle感应电流induced current感应场induction field圆波导circular waveguide圆极化circularly polarized圆柱腔circular cavity铁磁性ferromagnetic铁氧体陶瓷ferrite ceramics传导电流conducting current传导损耗conduction loss传播常数propagation constant传播模式propagation mode传输线模式transmission line mode传输矩阵transmission matrix零点Zero静态场static field算子operator输入阻抗input impedance椭圆极化elliptically polarized微带microstrip微波microwave微波单片集成电路microwave monolithicintegrated circuit MMIC毫米波单片集成电路millimeter wave monolithic integrated circuit M3IC 【十四画】漏电电流leakage current渐进表示式asymptotic expression模式mode模式展开mode expansion模式函数mode模式图mode pattern截止波长cut off wavelength截止频率cut off frequency鞍点saddle频谱spectrum线性极化linearly polarized线积分line integral磁矢量位magnetic vector potential磁通magnetic flux磁场强度magnetic intensity磁矩magnetic moment磁损耗角magnetic loss angle磁滞损耗magnetic hysteresis磁导率permeability【十五画】辐射radiate增益gain横电场transverse electric field横电磁波transverse electromagnetic wave 劈wedge【十六画】雕落场evanescent field雕落模式evanescent mode霍尔效应Hall effect辐射电阻radiation resistance辐射电导radiation conductance辐射功率radiation power辐射方向性图radiation pattern谱域方法spectral method【十七画以上】瞬时量insaneous quantity镜像image峰值peak valueδ函数delta function。
2007自然杂志石墨烯诺贝尔得奖者文章
THE RISE OF GRAPHENEA.K. Geim and K.S. NovoselovManchester Centre for Mesoscience and Nanotechnology,University of Manchester, Oxford Road M13 9PL, United KingdomGraphene is a rapidly rising star on the horizon of materials science and condensed matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of “relativistic” condensed matter physics, where quantum relativistic phenomena, some of which are unobservable in high energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.Graphene is the name given to a flat monolayer of carbon atoms tightly packed into a two-dimensional (2D) honeycomb lattice, and is a basic building block for graphitic materials of all other dimensionalities (Figure 1). It can be wrapped up into 0D fullerenes, rolled into 1D nanotubes or stacked into 3D graphite. Theoretically, graphene (or “2D graphite”) has been studied for sixty years1-3 and widely used for describing properties of various carbon-based materials. Forty years later, it was realized that graphene also provides an excellent condensed-matter analogue of (2+1)-dimensional quantum electrodynamics4-6, which propelled graphene into a thriving theoretical toy model. On the other hand, although known as integral part of 3D materials, graphene was presumed not to exist in the free state, being described as an “academic” material5 and believed to be unstable with respect to the formation of curved structures such as soot, fullerenes and nanotubes. All of a sudden, the vintage model turned into reality, when free-standing graphene was unexpectedly found three years ago7,8 and, especially, when the follow-up experiments9,10 confirmed that its charge carriers were indeed massless Dirac fermions. So, the graphene “gold rush” has begun.MATERIALS THAT SHOULD NOT EXISTMore than 70 years ago, Landau and Peierls argued that strictly two-dimensional (2D) crystals were thermodynamically unstable and could not exist11,12. Their theory pointed out that a divergent contribution of thermal fluctuations in low-dimensional crystal lattices should lead to such displacements of atoms that they become comparable to interatomic distances at any finite temperature13. The argument was later extended by Mermin14 and is strongly supported by a whole omnibus of experimental observations. Indeed, the melting temperature of thin films rapidly decreases with decreasing thickness, and they become unstable (segregate into islands or decompose) at a thickness of, typically, dozens of atomic layers15,16. For this reason, atomic monolayers have so far been known only as an integral part of larger 3D structures, usually grown epitaxially on top of monocrystals with matching crystal lattices15,16. Without such a 3D base, 2D materials were presumed not to exist until 2004, when the common wisdom was flaunted by the experimental discovery of graphene7 and other free-standing 2D atomic crystals (for example, single-layer boron nitride and half-layer BSCCO)8. These crystals could be obtained on top of non-crystalline substrates8-10, in liquid suspension7,17 and as suspended membranes18.Importantly, the 2D crystals were found not only to be continuous but to exhibit high crystal quality7-10,17,18. The latter is most obvious for the case of graphene, in which charge carriers can travel thousands interatomic distances without scattering7-10. With the benefit of hindsight, the existence of such one-atom-thick crystals can be reconciled with theory. Indeed, it can be argued that the obtained 2D crystallites are quenched in a metastable state because they are extracted from 3D materials, whereas their small size (<<1mm) and strong interatomic bonds assure that thermal fluctuations cannot lead to the generation of dislocations or other crystal defects even at elevated temperature13,14.Figure 1. Mother of all graphitic forms. Graphene is a 2D building material for carbon materials of all other dimensionalities. It can be wrapped up into 0D buckyballs, rolled into 1D nanotubes or stacked into 3D graphite.A complementary viewpoint is that the extracted 2D crystals become intrinsically stable by gentle crumpling in the third dimension on a lateral scale of ≈10nm 18,19. Such 3D warping observed experimentally 18 leads to a gain in elastic energy but suppresses thermal vibrations (anomalously large in 2D), which above a certain temperature can minimize the total free energy 19.BRIEF HISTORY OF GRAPHENEBefore reviewing the earlier work on graphene, it is useful to define what 2D crystals are. Obviously, a single atomic plane is a 2D crystal, whereas 100 layers should be considered as a thin film of a 3D material. But how many layers are needed to make a 3D structure? For the case of graphene, the situation has recently become reasonably clear. It was shown that the electronic structure rapidly evolves with the number of layers, approaching the 3D limit of graphite already at 10 layers 20. Moreover, only graphene and, to a good approximation, its bilayer have simple electronic spectra: they are both zero-gap semiconductors (can also be referred to as zero-overlap semimetals) with one type of electrons and one type of holes. For 3 and more layers, the spectra become increasingly complicated: Several charge carriers appear 7,21, and the conduction and valence bands start notably overlapping 7,20. This allows one to distinguish between single-, double- and few- (3 to <10) layer graphene as three different types of 2D crystals (“graphenes”). Thicker structures should be considered, to all intents and purposes, as thin films of graphite. From the experimental point of view, such a definition is also sensible. The screening length in graphite is only ≈5Å (that is, less than 2 layers in thickness)21 and, hence, one must differentiate between the surface and the bulk even for films as thin as 5 layers.21,22Earlier attempts to isolate graphene concentrated on chemical exfoliation. To this end, bulk graphite was first intercalated (to stage I)23so that graphene planes became separated by layers of intervening atoms or molecules.This usually resulted in new 3D materials23. However, in certain cases, large molecules could be inserted between atomic planes, providing greater separation such that the resulting compounds could be considered as isolated graphene layers embedded in a 3D matrix. Furthermore, one can often get rid of intercalating molecules in a chemical reaction to obtain a sludge consisting of restacked and scrolled graphene sheets24-26. Because of its uncontrollable character, graphitic sludge has so far attracted only limited interest.There have also been a small number of attempts to grow graphene. The same approach as generally used for growth of carbon nanotubes so far allowed graphite films only thicker than ≈100 layers27. On the other hand, single- and few-layer graphene have been grown epitaxially by chemical vapour deposition of hydrocarbons on metal substrates28,29 and by thermal decomposition of SiC30-34. Such films were studied by surface science techniques, and their quality and continuity remained unknown. Only lately, few-layer graphene obtained on SiC was characterized with respect to its electronic properties, revealing high-mobility charge carriers32,33. Epitaxial growth of graphene offers probably the only viable route towards electronic applications and, with so much at stake, a rapid progress in this direction is expected. The approach that seems promising but has not been attempted yet is the use of the previously demonstrated epitaxy on catalytic surfaces28,29 (such as Ni or Pt) followed by the deposition of an insulating support on top of graphene and chemical removal of the primary metallic substrate.THE ART OF GRAPHITE DRAWINGIn the absence of quality graphene wafers, most experimental groups are currently using samples obtained by micromechanical cleavage of bulk graphite, the same technique that allowed the isolation of graphene for the first time7,8. After fine-tuning, the technique8 now provides high-quality graphene crystallites up to 100 µm in size, which is sufficient for most research purposes (see Figure 2). Superficially, the technique looks as nothing more sophisticated than drawing by a piece of graphite8 or its repeated peeling with adhesive tape7 until the thinnest flakes are found. A similar approach was tried by other groups (earlier35 and independently22,36) but only graphite flakes 20 to 100 layers thick were found. The problem is that graphene crystallites left on a substrate are extremely rare and hidden in a “haystack” of thousands thick (graphite) flakes. So, even if one were deliberately searching for graphene by using modern techniques for studying atomically thin materials, it would be impossible to find those several micron-size crystallites dispersed over, typically, a 1-cm2 area. For example, scanning-probe microscopy has too low throughput to search for graphene, whereas scanning electron microscopy is unsuitable because of the absence of clear signatures for the number of atomic layers.The critical ingredient for success was the observation7,8 that graphene becomes visible in an optical microscope if placed on top of a Si wafer with a carefully chosen thickness of SiO2, owing to a feeble interference-like contrast with respect to an empty wafer. If not for this simple yet effective way to scan substrates in search of graphene crystallites, they would probably remain undiscovered today. Indeed, even knowing the exact recipe7,8, it requires special care and perseverance to find graphene. For example, only a 5% difference in SiO2 thickness (315 nm instead of the current standard of 300 nm) can make single-layer graphene completely invisible. Careful selection of the initial graphite material (so that it has largest possible grains) and the use of freshly -cleaved and -cleaned surfaces of graphite and SiO2 can also make all the difference. Note that graphene was recently37,38 found to have a clear signature in Raman microscopy, which makes this technique useful for quick thickness inspection, even though potential crystallites still have to be first hunted for in an optical microscope.Similar stories could be told about other 2D crystals (particularly, dichalcogenides monolayers) where many attempts were made to split these strongly layered materials into individual planes39,40. However, the crucial step of isolating monolayers to assess their properties individually was never achieved. Now, by using the same approach as demonstrated for graphene, it is possible to investigate potentially hundreds of different 2D crystals8 in search of new phenomena and applications.FERMIONS GO BALLISTICAlthough there is a whole class of new 2D materials, all experimental and theoretical efforts have so far focused on graphene, somehow ignoring the existence of other 2D crystals. It remains to be seen whether this bias is justified but the primary reason for it is clear: It is the exceptional electronic quality exhibited by the isolated graphene crystallites7-10. From experience, people know that high-quality samples always yield new physics, and this understanding has played a major role in focusing attention on graphene.Figure 2. One-atom-thick single crystals: the thinnest material you will ever see. a, Graphene visualized by atomic-force microscopy (adapted from ref. 8). The folded region exhibiting a relative height of ≈4Å clearly indicates that it is a single layer. b, A graphene sheet freely suspended on a micron-size metallic scaffold. The transmission-electron-microscopy image is adapted from ref. 18. c, scanning-electron micrograph of a relatively large graphene crystal, which shows that most of the crystal’s faces are zigzag and armchair edges as indicated by blue and red lines and illustrated in the inset (T.J. Booth, K.S.N, P. Blake & A.K.G. unpublished). 1D transport along zigzag edges and edge-related magnetism are expected to attract significant attention.Graphene’s quality clearly reveals itself in a pronounced ambipolar electric field effect (Fig. 3a) such that charge carriers can be tuned continuously between electrons and holes in concentrations n as high as 1013cm-2 and their mobilities µ can exceed 15,000 cm2/Vs even under ambient conditions7-10. Moreover, the observed mobilities weakly depend on temperature T, which means that µ at 300K is still limited by impurity scattering and, therefore, can be improved significantly, perhaps, even up to ≈100,000 cm2/Vs. Although some semiconductors exhibit room-temperature µ as high as ≈77,000 cm2/Vs (namely, InSb), those values are quoted for undoped bulk semiconductors. In graphene, µ remains high even at high n (>1012cm-2) in both electrically- and chemically- doped devices41, which translates into ballistic transport on submicron scale (up to ≈0.3 µm at 300K). A further indication of the system’s extreme electronic quality is the quantum Hall effect (QHE) that can be observed in graphene even at room temperature (Fig. 3b), extending the previous temperature range for the QHE by a factor of 10.An equally important reason for the interest in graphene is a unique nature of its charge carriers. In condensed matter physics, the Schrödinger equation rules the world, usually being quite sufficient to describe electronic properties of materials. Graphene is an exception: Its charge carriers mimic relativistic particles and are easier and more natural to describe starting with the Dirac equation rather than the Schrödinger equation4-6,42-47. Although there is nothing particularly relativistic about electrons moving around carbon atoms, their interaction with a periodic potential of graphene’s honeycomb lattice gives rise to new quasiparticles that at low energies EFigure 3. Ballistic electron transport in graphene. a , Ambipolar electric field effect in single-layer graphene. The insets show its conical low-energy spectrum E (k ), indicating changes in the position of the Fermi energy E F with changing gate voltage V g . Positive (negative) V g induce electrons (holes) in concentrations n =αV g where the coefficient α ≈7.2⋅1010cm -2/V for field-effect devices with a 300 nm SiO 2 layer used as a dielectric 7-9. The rapid decrease in resistivity ρwith adding charge carriers indicates their high mobility (in this case, µ ≈5,000cm 2/Vs and does not noticeably change with temperature up to 300K). b , Room-temperature quantum Hall effect (K.S.N., Z. Jiang, Y. Zhang, S.V. Morozov, H.L. Stormer, U. Zeitler,J.C. Maan, G.S. Boebinger, P. Kim & A.K.G. Science 2007, in the press). Because quasiparticles in graphene are massless and also exhibit little scattering even under ambient conditions, the QHE survives up to room T . Shown in red is the Hall conductivity σxy that exhibits clear plateaux at 2e 2/h for both electrons and holes. The longitudinal conductivity ρxx (blue) reaches zero at the same gate voltages. The inset illustrates the quantized spectrum of graphene where the largest cyclotron gap is described by δE (K)≈420⋅B (T). are accurately described by the (2+1)-dimensionalDirac equation with an effective speed of lightv F ≈106m/s. These quasiparticles, called masslessDirac fermions, can be seen as electrons that losttheir rest mass m 0 or as neutrinos that acquired theelectron charge e . The relativistic-like descriptionof electron waves on honeycomb lattices has beenknown theoretically for many years, never failingto attract attention, and the experimental discoveryof graphene now provides a way to probe quantumelectrodynamics (QED) phenomena by measuringgraphene’s electronic properties.QED IN A PENCIL TRACEFrom the point of view of its electronic properties,graphene is a zero-gap semiconductor, in whichlow-E quasiparticles within each valley canformally be described by the Dirac-likeHamiltoniank v ik k ik k v H F y x y x F r r h h ⋅=⎟⎟⎠⎞⎜⎜⎝⎛+−=σ00ˆwhere k r is the quasiparticle momentum, σr the2D Pauli matrix and the k -independent Fermivelocity v F plays the role of the speed of light. TheDirac equation is a direct consequence ofgraphene’s crystal symmetry. Its honeycomblattice is made up of two equivalent carbonsublattices A and B , and cosine-like energy bandsassociated with the sublattices intersect at zero Enear the edges of the Brillouin zone, giving rise toconical sections of the energy spectrum for |E | <1eV (Fig. 3).We emphasize that the linear spectrumk v E F h = is not the only essential feature of the band structure. Indeed, electronic states near zeroE (where the bands intersect) are composed ofstates belonging to the different sublattices, andtheir relative contributions in quasiparticles’make-up have to be taken into account by, forexample, using two-component wavefunctions(spinors). This requires an index to indicatesublattices A and B , which is similar to the spinindex (up and down) in QED and, therefore, isreferred to as pseudospin. Accordingly, in theformal description of graphene’s quasiparticles bythe Dirac-like Hamiltonian above, σr refers topseudospin rather than the real spin of electrons(the latter must be described by additional terms inthe Hamiltonian). Importantly, QED-specificphenomena are often inversely proportional to thespeed of light c and, therefore, enhanced ingraphene by a factor c /v F ≈300. In particular, thisρ(kΩ)n(1012 cm-2)σ(4e2/h)277321−21+23255-82-2-4-664Vg(V)σ2EDEdecEFigure 4. Chiral quantum Hall effects.a, The hallmark of massless Dirac fermions is QHE plateaux in σxy at half integers of 4e2/h (adapted from ref. 9). b, Anomalous QHE for massive Dirac fermions in bilayer graphene is more subtle (red curve55): σxy exhibits the standard QHE sequence with plateaux at all integer N of 4e2/h except for N=0. The missing plateau is indicated by the red arrow. The zero-N plateau can be recovered after chemical doping, which shifts the neutrality point to high V g so that an asymmetry gap (≈0.1eV in this case) is opened by the electric field effect (green curve; adapted from ref.59). c-e, Different types of Landau quantization in graphene. The sequence of Landau levels in the density of states D isdescribed by NEN∝ for massless Dirac fermions in single-layer graphene (c) and by )1(−∝NNENfor massive Dirac fermions in bilayer graphene (d). The standard LL sequence )(21+∝NENis expected to recover if an electronic gap is opened in the bilayer (e).means that pseudospin-related effects should generally dominate those due to the real spin.By analogy with QED, one can also introduce a quantity called chirality6 that is formally a projection of σr on the direction of motion kr and is positive (negative) for electrons (holes). In essence, chirality in graphene signifies the fact that k electron and -k hole states are intricately connected by originating from the same carbon sublattices. The concepts of chirality and pseudospin are important because many electronic processes in graphene can be understood as due to conservation of these quantities.6,42-47It is interesting to note that in some narrow-gap 3D semiconductors, the gap can be closed by compositional changes or by applying high pressure. Generally, zero gap does not necessitate Dirac fermions (that imply conjugated electron and hole states) but, in some cases, they may appear5. The difficulties of tuning the gap to zero, while keeping carrier mobilities high, the lack of possibility to control electronic properties of 3D materials by the electric field effect and, generally, less pronounced quantum effects in 3D limited studies of such semiconductors mostly to measuring the concentration dependence of their effective masses m (for a review, see ref. 48). It is tempting to have a fresh look at zero-gap bulk semiconductors, especially because Dirac fermions were recently reported even in such a well-studied (small-overlap) 3D material as graphite.49,50CHIRAL QUANTUM HALL EFFECTSAt this early stage, the main experimental efforts have been focused on electronic properties of graphene, trying to understand the consequences of its QED-like spectrum. Among the most spectacular phenomena reported so far, there are two new (“chiral”) quantum Hall effects, minimum quantum conductivity in the limit of vanishing concentrations of charge carriers and strong suppression of quantum interference effects.Figure 4 shows three types of the QHE behaviour observed in graphene. The first one is a relativistic analogue of the integer QHE and characteristic to single-layer graphene9,10. It shows up as an uninterrupted ladder of equidistant steps in Hall conductivity σxy which persists through the neutrality (Dirac) point, where charge carriers change from electrons to holes (Fig. 4a). The sequence is shifted with respect to the standard QHE sequence by ½, so that σxy= ±4e2/h(N + ½) where N is the Landau level (LL) index and factor 4 appears due to double valley and double spin degeneracy. This QHE has been dubbed “half-integer” to reflect both the shift and the fact that, although it is not a new fractional QHE, it is not the standard integer QHE either. The unusual sequence is now well understood as arising due to the QED-like quantization of graphene’s electronic spectrumin magnetic field B , which is described 44,51-53 by BN e v E F N h 2±= where sign ± refers to electrons and holes. The existence of a quantized level at zero E , which is shared by electrons and holes (Fig. 4c), is essentially everything one needs to know to explain the anomalous QHE sequence.51-55 An alternative explanation for the half-integer QHE is to invoke the coupling between pseudospin and orbital motion, which gives rise to a geometrical phase of π accumulated along cyclotron trajectories and often referred to as Berry’s phase.9,10,56 The additional phase leads to a π-shift in the phase of quantum oscillations and, in the QHE limit, to a half-step shift. Bilayer graphene exhibits an equally anomalous QHE (Fig 4b)55. Experimentally, it shows up less spectacular: One measures the standard sequence of Hall plateaux σxy = ±N 4e 2/h but the very first plateau at N =0 is missing, which also implies that bilayer graphene remains metallic at the neutrality point.55 The origin of this anomaly lies in a rather bizarre nature of quasiparticles in bilayer graphene, which are described 57 by⎟⎟⎠⎞⎜⎜⎝⎛+−−=0)()(02ˆ222y x y x ik k ik k m H h This Hamiltonian combines the off-diagonal structure, similar to the Dirac equation, with Schrödinger-like terms m p2ˆ2. The resulting quasiparticles are chiral, similar to massless Dirac fermions, but have a finite mass m ≈0.05m 0. Such massive chiral particles would be an oxymoron in relativistic quantum theory. The Landau quantization of “massive Dirac fermions” is given 57 by )1(−±=N N E c N ωh with two degenerate levels N =0 and 1 at zero E (c ω is the cyclotron frequency). This additional degeneracy leads to the missing zero-E plateau and the double-height step in Fig. 4b. There is also a pseudospin associated with massive Dirac fermions, and its orbital rotation leads to a geometrical phase of 2π. This phase is indistinguishable from zero in the quasiclassical limit (N >>1) but reveals itself in the double degeneracy of the zero-E LL (Fig. 4d).55It is interesting that the “standard” QHE with all the plateaux present can be recovered in bilayer graphene by the electric field effect (Fig. 4b). Indeed, gate voltage not only changes n but simultaneously induces an asymmetry between the two graphene layers, which results in a semiconducting gap 58,59. The electric-field-induced gap eliminates the additional degeneracy of the zero-E LL and leads to the uninterrupted QHE sequence by splitting the double step into two (Fig. 4e)58,59. However, to observe this splitting in the QHE measurements, one needs to probe the region near the neutrality point at finite V g , which can be achieved by additional chemical doping 59. Note that bilayer graphene is the only known material in which the electronic band structure changes significantly by the electric field effect and the semiconducting gap ∆E can be tuned continuously from zero to ≈0.3eV if SiO 2 is used as a dielectric.CONDUCTIVITY “WITHOUT” CHARGE CARRIERSAnother important observation is that graphene’s zero-field conductivity σ does not disappear in the limit of vanishing n but instead exhibits values close to the conductivity quantum e 2/h per carrier type 9. Figure 5 shows the lowest conductivity σmin measured near the neutrality point for nearly 50 single-layer devices. For all other known materials, such a low conductivity unavoidably leads to a metal-insulator transition at low T but no sign of the transition has been observed in graphene down to liquid-helium T . Moreover, although it is the persistence of the metallic state with σ of the order of e 2/h that is most exceptional and counterintuitive, a relatively small spread of the observed conductivity values (see Fig. 5) also allows one to speculate about the quantization of σmin . We emphasize that it is the resistivity (conductivity) that is quantized in graphene, in contrast to the resistance (conductance) quantization known in many other transport phenomena.Minimum quantum conductivity has been predicted for Dirac fermions by a number of theories 5,44,45,47,60-64. Some of them rely on a vanishing density of states at zero E for the linear 2D spectrum. However, comparison between the experimental behaviour of massless and massive Dirac fermions in graphene and its bilayer allows one to distinguish between chirality- and masslessness- related effects. To this end, bilayer graphene also exhibits a minimum conductivity of the order of e 2/h per carrier type,55,65 which indicates that it is chirality, rather than the linear spectrum, that is more important. Most theories suggest σmin =4e 2/h π, which is of about π times smaller than the typical values observed experimentally. One can see in Fig. 5 that the experimental data do not approach this theoretical value and mostly cluster around σmin =4e 2/h (except for one low-µ sample that is rather unusual by also exhibiting 100%-normal weak localization behaviour at high n ; see below). This disagreement has become known as “the mystery of a missing pie”, and it remains unclear whether it is due toσm i n (4e 2/h )11/µ(cm 2/Vs)012,0004,0008,0000Figure 5. Minimum conductivity of graphene.Independent of their carrier mobility µ, different graphene devices exhibited approximately the same conductivity at the neutrality point (open circles) with most data clusteringaround ≈4e 2/h indicated for clarity by the dashed line (A.K.G. & K.S.N. unpublished; includes the published datapoints from ref. 9). The high-conductivity tail is attributed to macroscopic inhomogeneity: by improving samples’ homogeneity, σmin generally decreases, moving closer to ≈4e 2/h . The green arrow and symbols show one of the devices that initially exhibited an anomalously large value of σmin but after thermal annealing at 400K its σmin moved closer to the rest of the statistical ensemble. Most of thedata are taken in the bend resistance geometry where themacroscopic inhomogeneity plays the least role.theoretical approximations about electron scatteringin graphene or because the experiments probed onlya limited range of possible sample parameters (e.g., length-to-width ratios 47). To this end, note that close to the neutrality point (n ≤1011cm -2) graphene islikely to conduct as a random network of electronand hole puddles (A.K.G. & K.S.N . unpublished).Such microscopic inhomogeneity is probablyinherent to graphene (because of graphene sheet’swarping/rippling)18,66 but so far has not been taken into account by theory. Furthermore, macroscopicinhomogeneity (on the scale larger than the meanfree path l ) also plays an important role in measurements of σmin . The latter inhomogeneity canexplain a high-σ tail in the data scatter in Fig. 5 by the fact that σ reached its lowest values at slightly different V g in different parts of a sample, whichyields effectively higher values of experimentally measured σmin .WEAK LOCALIZATION IN SHORT SUPPLYAt low temperatures, all metallic systems with high resistivity should inevitably exhibit large quantum-interference (localization) magnetoresistance,eventually leading to the metal-insulator transition at σ ≈e 2/h . Until now, such behaviour has been absolutely universal but it was found missing in graphene. Even near the neutrality point, no significant low-field (B <1T) magnetoresistance has been observed down to liquid-helium temperatures 66 and, although sub-100 nm Hall crosses did exhibit giant resistance fluctuations (S.V. Morozov, K.S.N., A.K.G. et al , unpublished), those could be attributed to changes in the distribution of electron and holepuddles and size quantization. It remains to be seen whether localization effects at the Dirac point recover at lower T , as the phase-breaking length becomes increasingly longer,67 or the observed behaviour indicates a “marginal Fermi liquid”68,43, in which the phase-breaking length goes to zero with decreasing E . Further experimental studies are much needed in this regime but it is difficult to probe because of microscopic inhomogeneity.Away from the Dirac point (where graphene becomes a good metal), the situation has recently become reasonably clear. Universal conductance fluctuations (UCF) were reported to be qualitatively normal in this regime, whereas weak localization (WL) magnetoresistance was found to be somewhat random, varying for different samples from being virtually absent to showing the standard behaviour 66. On the other hand, early theories had also predicted every possible type of WL magnetoresistance in graphene, from positive to negative to zero. Now it is understood that, for large n and in the absence of inter-valley scattering, there should be no magnetoresistance, because the triangular warping of graphene’s Fermi surface destroys time-reversal symmetry within each valley.69 With increasing inter-valley scattering, the normal (negative) WL should recover. Changes in inter-valley scattering rates by, for example, varying microfabrication procedures can explain the observed sample-dependent behaviour. A complementary explanation is that a sufficient inter-valley scattering is already present in the studied samples but the time-reversal symmetry is destroyed by elastic strain due to microscopic warping 66,70. The strain in graphene has turned out to be equivalent to a random magnetic field, which also destroys time-reversal symmetry and suppresses WL. Whatever the mechanism, theory expects (approximately 71) normal UCF at high n , in agreement with the experiment 66.。
Thermal emission from three-dimensional arrays of gold nanoparticles
a r X i v :c o n d -m a t /0602674v 1 [c o n d -m a t .o t h e r ] 28 F eb 2006Thermal emission from three-dimensional arrays of goldnanoparticlesVassilios Yannopapas ∗Department of Materials Science,School of Natural Sciences,University of Patras,GR-26504Patras,Greece Abstract We study the blackbody spectrum from slabs of three-dimensional metallodielectric photonic crystals consisting of gold nanoparticles using an ab initio multiple-scattering method.The spectra are calculated for different photonic-crystal slab thicknesses,particle radii and hosting materials.We find in particular that such crystals exhibit a broadband emission spectrum above a specific cutofffrequency with emissivity of about 90%.The studied photonic crystals can be used as efficient selective emitters and can therefore find application in thermophotovoltaics and sensing.The main feature of photonic crystals is the ability to tailor the photon density of states and this way control the spontaneous emission of light,aiming at the realization of new opto-electronic devices.In this context,there has been considerable effort to design and fabricate photonic crystals which allow for control of thermal emission of light,i.e.thermally driven spontaneous emission,promising applications in imaging,sensing and most importantly,in thermophotovoltaics(TPV).1,2,3,4,5,6,7,8,9Control of thermal emission can also be achieved by means of microstructured engineering on silicon10,11,12,13or metal surfaces.14Depending on the type of application,photonic crystals and structured surfaces can act as narrow-or wide-band,directional or isotropic thermal emitters.For example,in TPV applications15a quasi-monochromatic emission is preferable whilst in radiation cooling16a broad emission spectrum is desired.In this work we investigate the emission properties of three-dimensional metallodielectric photonic crystals consisting of gold nanoparticles.Wefind,in particular, that the emission spectrum of these crystals can be such that photons are emitted in all directions only when their energies lie above a specific cutofffrequency,with emissivity as large as90%.Photonic crystals of spherical scatterers have been theoretically studied using multiple scattering theory17,18which is ideally suited for the calculation of the transmission,reflection and absorption coefficients of an electromagnetic(EM)wave incident on a composite slab consisting of a number of planes of non-overlapping particles with the same two-dimensional (2D)periodicity.For each plane of particles,the method calculates the full multipole expan-sion of the total multiply scattered wavefield and deduces the corresponding transmission and reflection matrices in the plane-wave basis.The transmission and reflection matrices of the composite slab are evaluated from those of the constituent layers.Having calculated these matrices one can evaluate the transmittance T(ω,θ,φ),reflectance R(ω,θ,φ),and from those two,the absorbance A(ω,θ,φ)of the composite slab as functions of the incident photon energy ωand incident anglesθandφ.Transmittance and reflectance are defined as the ratio of the transmitted,respectively the reflected,energyflux to the energyflux as-sociated with the incident wave.The method applies equally well to non-absorbing systems and to absorbing ones.In terms of speed,convergence and accuracy,the multiple scattering method is the best method to treat photonic structures of spherical particles.The emittanceE(ω,θ,φ)is calculated indirectly by application of Kirchoff’s law,19,20i.e.fromE(ω,θ,φ)=A(ω,θ,φ)=1−R(ω,θ,φ)−T(ω,θ,φ)(1) Note that recent direct calculations of the thermal emission from photonic crystals have verified the validity of Kirchoff’s law for the case of photonic crystals.21 In this work we deal with gold spheres with radius of a few nanometres.Traditionally, the gold spheres are treated as plasma spheres whose dielectric function is given by Drude’s formulaǫp(ω)=1−ω2pω(ω+iτ−1b )−ω2pdielectric function,i.e.Eq.(4),has successfully reproduced experimentally obtained light absorption and scattering spectra of monolayers of gold nanoparticles.27 To begin with,we consider an fcc photonic crystal whose lattice sites are occupied by gold nanospheres of radius S=5nm.The lattice constant of the crystal is a=19.11nm corresponding to a volumefilling fraction occupied by the spheres,f=0.3.The spheres are supposed to be suspended in air.The crystal is viewed as a succession of planes of spheres(layers)parallel to the(001)surface of fcc.In Fig.1we show the transmittance, reflectance and absorbance vs energy for light incident normally on afinite slab of the crystal consisting of128layers of spheres.We observe that for energies above2.2eV almost all light (92%-98%)that is incident on the crystal slab is absorbed from the gold spheres.Therefore, from Kirchoff’s law,i.e.E(ω,θ,φ)=A(ω,θ,φ),we can infer that the blackbody radiation is strong above this energy.Indeed,the blackbody radiation intensity of the photonic crystal is given byI P C(ω,θ,φ,T)=E(ω,θ,φ)I BB(ω,T)(5) where I BB(ω,θ,φ,T)is the blackbody radiation intensity(Planck distribution)I BB(ω,T)= ω3exp( ω/k B T)−1.(6)k B is the Boltzmann constant and c is the speed of light in vacuum.In a metal particle of nanoscale radius,there are two principal sources of light emission/absorption:thefirst one is the dipole oscillations due to the surface plasmon resonances and the second is the interband transitions that take place in bulk gold contributing to its dielectric function.In terms of thefirst source of emission,the crystal can be viewed as a lattice of interacting oscillating dipoles where each one of the dipoles emits light around the surface plasma resonance frequencyωSP=ωp/√interested in the spectral hemispherical (SH)radiative properties of the photonic crystal.More specifically,we are interested in the SH emissivity s (ω)which is the ratio of the SH emissive power of a photonic-crystal slab to the SH emissive power of a perfect blackbody at the same temperature T .For a slab infinitely extended in two dimensions:s (ω)= 2π0dφ π/20dθI P C (ω,θ,φ,T )cos θsin θπ 2π0dφ π/2dθE (ω,θ,φ)cos θsin θ(7)Note that E (ω,θ,φ)in the above equation is the arithmetical average of both polarization modes.In Fig.2we show the SH emissivity from slabs of the photonic crystal of Fig.1for different slab thicknesses (number of layers).It is evident that as the number of layers increases the SH emissivity increases accordingly until it reaches a saturation plateau for slabs of 64layers and above.Indeed,for energies above 2.2eV the emissivity curves for 64and 128layers are practically the same.This fact implies that,if we measure the emission from one of the surfaces of a 128layers-thick slab,then the emitted radiation must be coming from the 64outmost layers (relative to a given surface)whilst radiation coming from the 64innermost layers is almost totally absorbed from the 64outmost layers by the time it reaches the surface of the slab.The most important finding of Fig.2is the fact that the photonic crystal behaves more or less as gray body (emissivity ranging from 88%to 92%)for energies above 2.2eV while,at the same time,emits small amounts of radiation for energies below this cutoff.A similar emission spectrum is observed for the Salisbury screen 13but with significantly lower values of the SH emissivity.So far,we have assumed that the gold nanospheres are suspended in air.In order to provide a manufacturable structure it is necessary to examine the case where the spheres are embedded in a host material of dielectric function ǫh .In Fig.3we show the SH emissivity from a 64-layer slab of an fcc photonic crystal of gold nanospheres with f =0.3where the spheres are surrounded by air (ǫh =1),silica (ǫh =1.88)and gelatine (ǫh =2.37).The introduction of a host material does not change the picture drastically except that it lowers the emission cutoffenergy.This is due to thelowering of the surface plasmon frequency according to ωSP =ωp /√emission region and a distinct local minimum appears.This is evident from the emissivity spectra of Fig.3for silica and gelatine host materials.The shift of the surface plasmon energy with respect to the host materialǫh allows for tuning of the cutoffenergy so that it coincides with the band gap of the photodiode of a TPV device.Next we study the effect of the volumefilling fraction f on the emission properties of the photonic structure under study.In Fig.4we show the SH emissivity spectra for photonic crystals of different values of f.We have kept the lattice constant the same and changed the sphere radii accordingly.Note that for each value of f we obtain a different value of τ−1from Eq.(3).We observe that the maximum emissivity in the region above the cutoffenergy is achieved for f=0.3.Since our calculations show that the SH reflectivity assumes higher values for f=0.5,0.7,the radiation emitted from the innermost layers is reflected back and reabsorbed before it reaches the surface of the slab.Finally we address the issue of spatial order/disorder of the photonic crystal under investigation.As it has been both theoretically30,31and experimentally32shown,the pres-ence of disorder does not changes practically the absorption/emission properties of three-dimensional photonic crystals of metal nanoparticles since these quantities mostly depend on single sphere properties such as surface plasmon resonances,and less on the particular spatial arrangement of the spheres.Note that this not true for one-or two-dimensional structures,e.g.a linear chain or a monolayer of nanospheres,where the presence of dis-order changes dramatically the absorption/emission spectra.31So,since we deal with a three-dimensional structure,a disordered crystal might be easier and cheaper to fabricate.In summary,we have shown that a metallodielectric crystal consisting of gold nanospheres can act as a90%gray body for energies above a cutoff.The cutofffrequency can be tuned by appropriate choice of the material hosting the nanospheres.Optimal emissivity is obtained for moderate volumefilling fractions and slab thicknesses.ACKNOWLEDGEMENTSThis work was supported by the‘Karatheodory’research fund of University of Patras.∗Electronic address:vyannop@upatras.gr1 C.M.Cornelius and J.P.Dowling,Phys.Rev.A59,4736(1999).2S.Y.Lin,J.G.Fleming,E.Chow,J.Bur,K.K.Choi,and A.Goldberg,Phys.Rev.B62, R2243(2000).3J.G.Fleming,S.Y.Lin,I.El-Kady,R.Biswas,and K.M.Ho,Nature(London)417,52(2002). 4M.U.Pralle,N.Moelders,M.P.McNeal,I.Puscasu,A.C.Greenwald,J.T.Daly,E.A.Johnson, T.George,D.S.Choi,I.El-Kady,and R.Biswas,Appl.Phys.Lett.81,4685(2002).5S.Y.Lin,J.G.Fleming,and I.El-Kady,Opt.Lett.28,1909(2003).6I.Celanovic,F.O’Sullivan,M.Ilak,J.Kassakian,and D.Perreault,Opt.Lett.29,863(2004).7 A.Narayanaswamy,and G.Chen,Phys.Rev.B70,125101(2004).8S.Enoch,J.-J.Simon,L.Escoubas,Z.Elalmy,F.Lemarquis,P.Torchio,and G.Albrand, 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69,075108(2004).1234560.00.20.40.60.81.0Photon Energy (eV) Transmittance Reflectance Absorbance FIG.1:Transmittance,reflectance,and absorbance of light incident normally on a 128-layers thick slab of a fcc crystal consisting of gold spheres (S =5nm)in air (ǫh =1),with f =0.3.1234560.00.20.40.60.81.0E m i s s i v i t y Photon Energy (eV) N=128 N= 64 N= 32 N= 16 N= 8 N= 4 N= 2 N= 1FIG.2:SH emissivity for different numbers of layers (slab thicknesses)of the photonic crystal described in Fig.1.1234560.00.20.40.60.81.0E m i s s i v i t y Photon Energy (eV) In Air In SiO In gelatine FIG.3:SH emissivity of a 64-layer thick slab of an fcc crystal of gold spheres (S =5nm)in air (ǫh =1-solid line),silica (ǫh =1.88-dashed line)and gelatine (ǫh =2.37-dotted line),with f =0.3.We have assumed that the host medium surrounding the spheres also covers the whole space.1234560.00.20.40.60.81.0E m i s s i v i t y Photon Energy (eV) f=0.1 f=0.3 f=0.5 f=0.7FIG.4:SH emissivity of a 64-layer thick slab of an fcc crystal of gold spheres (S =5nm)in air,for different volume filling fractions f (fixed lattice constant and different sphere radii).。
弹性力学专业英语英汉互译词汇
弹性力学elasticity弹性理论theory of elasticity 均匀应力状态homogeneous state of stress 应力不变量stress invariant应变不变量strain invariant应变椭球strain ellipsoid 均匀应变状态homogeneous state ofstrain 应变协调方程equation of straincompatibility 拉梅常量Lame constants 各向同性弹性isotropic elasticity 旋转圆盘rotating circular disk 楔wedge开尔文问题Kelvin problem 布西内斯克问题Boussinesq problem艾里应力函数Airy stress function克罗索夫--穆斯赫利什维Kolosoff-利法Muskhelishvili method 基尔霍夫假设Kirchhoff hypothesis 板Plate矩形板Rectangular plate圆板Circular plate环板Annular plate波纹板Corrugated plate加劲板Stiffened plate,reinforcedPlate 中厚板Plate of moderate thickness 弯[曲]应力函数Stress function of bending 壳Shell扁壳Shallow shell旋转壳Revolutionary shell球壳Spherical shell [圆]柱壳Cylindrical shell 锥壳Conical shell环壳Toroidal shell封闭壳Closed shell波纹壳Corrugated shell扭[转]应力函数Stress function of torsion 翘曲函数Warping function半逆解法semi-inverse method瑞利--里茨法Rayleigh-Ritz method 松弛法Relaxation method莱维法Levy method松弛Relaxation 量纲分析Dimensional analysis自相似[性] self-similarity 影响面Influence surface接触应力Contact stress赫兹理论Hertz theory协调接触Conforming contact滑动接触Sliding contact滚动接触Rolling contact压入Indentation各向异性弹性Anisotropic elasticity 颗粒材料Granular material散体力学Mechanics of granular media 热弹性Thermoelasticity超弹性Hyperelasticity粘弹性Viscoelasticity对应原理Correspondence principle 褶皱Wrinkle塑性全量理论Total theory of plasticity 滑动Sliding微滑Microslip粗糙度Roughness非线性弹性Nonlinear elasticity 大挠度Large deflection突弹跳变snap-through有限变形Finite deformation格林应变Green strain阿尔曼西应变Almansi strain弹性动力学Dynamic elasticity运动方程Equation of motion准静态的Quasi-static气动弹性Aeroelasticity水弹性Hydroelasticity颤振Flutter弹性波Elastic wave简单波Simple wave柱面波Cylindrical wave水平剪切波Horizontal shear wave竖直剪切波Vertical shear wave 体波body wave无旋波Irrotational wave畸变波Distortion wave膨胀波Dilatation wave瑞利波Rayleigh wave等容波Equivoluminal wave勒夫波Love wave界面波Interfacial wave边缘效应edge effect塑性力学Plasticity可成形性Formability金属成形Metal forming耐撞性Crashworthiness结构抗撞毁性Structural crashworthiness 拉拔Drawing 破坏机构Collapse mechanism 回弹Springback挤压Extrusion冲压Stamping穿透Perforation层裂Spalling 塑性理论Theory of plasticity安定[性]理论Shake-down theory运动安定定理kinematic shake-down theorem静力安定定理Static shake-down theorem 率相关理论rate dependent theorem 载荷因子load factor加载准则Loading criterion加载函数Loading function加载面Loading surface塑性加载Plastic loading塑性加载波Plastic loading wave 简单加载Simple loading比例加载Proportional loading 卸载Unloading卸载波Unloading wave冲击载荷Impulsive load阶跃载荷step load脉冲载荷pulse load极限载荷limit load中性变载nentral loading拉抻失稳instability in tension 加速度波acceleration wave本构方程constitutive equation 完全解complete solution名义应力nominal stress过应力over-stress真应力true stress等效应力equivalent stress流动应力flow stress应力间断stress discontinuity应力空间stress space主应力空间principal stress space静水应力状态hydrostatic state of stress 对数应变logarithmic strain工程应变engineering strain等效应变equivalent strain应变局部化strain localization 应变率strain rate应变率敏感性strain rate sensitivity 应变空间strain space有限应变finite strain塑性应变增量plastic strain increment 累积塑性应变accumulated plastic strain 永久变形permanent deformation内变量internal variable应变软化strain-softening理想刚塑性材料rigid-perfectly plasticMaterial刚塑性材料rigid-plastic material理想塑性材料perfectl plastic material 材料稳定性stability of material应变偏张量deviatoric tensor of strain 应力偏张量deviatori tensor of stress 应变球张量spherical tensor of strain 应力球张量spherical tensor of stress 路径相关性path-dependency线性强化linear strain-hardening应变强化strain-hardening随动强化kinematic hardening各向同性强化isotropic hardening 强化模量strain-hardening modulus幂强化power hardening塑性极限弯矩plastic limit bendingMoment塑性极限扭矩plastic limit torque弹塑性弯曲elastic-plastic bending弹塑性交界面elastic-plastic interface 弹塑性扭转elastic-plastic torsion 粘塑性Viscoplasticity非弹性Inelasticity理想弹塑性材料elastic-perfectly plasticMaterial 极限分析limit analysis极限设计limit design极限面limit surface上限定理upper bound theorem上屈服点upper yield point下限定理lower bound theorem下屈服点lower yield point界限定理bound theorem初始屈服面initial yield surface后继屈服面subsequent yield surface屈服面[的]外凸性convexity of yield surface 截面形状因子shape factor of cross-section沙堆比拟sand heap analogy 屈服Yield 屈服条件yield condition屈服准则yield criterion屈服函数yield function屈服面yield surface塑性势plastic potential 能量吸收装置energy absorbing device 能量耗散率energy absorbing device 塑性动力学dynamic plasticity 塑性动力屈曲dynamic plastic buckling 塑性动力响应dynamic plastic response 塑性波plastic wave 运动容许场kinematically admissibleField 静力容许场statically admissibleField 流动法则flow rule速度间断velocity discontinuity滑移线slip-lines滑移线场slip-lines field移行塑性铰travelling plastic hinge 塑性增量理论incremental theory ofPlasticity 米泽斯屈服准则Mises yield criterion 普朗特--罗伊斯关系prandtl- Reuss relation 特雷斯卡屈服准则Tresca yield criterion洛德应力参数Lode stress parameter莱维--米泽斯关系Levy-Mises relation亨基应力方程Hencky stress equation赫艾--韦斯特加德应力空Haigh-Westergaard 间stress space洛德应变参数Lode strain parameter德鲁克公设Drucker postulate盖林格速度方程Geiringer velocityEquation结构力学structural mechanics结构分析structural analysis结构动力学structural dynamics拱Arch三铰拱three-hinged arch抛物线拱parabolic arch圆拱circular arch穹顶Dome空间结构space structure空间桁架space truss雪载[荷] snow load风载[荷] wind load土压力earth pressure地震载荷earthquake loading弹簧支座spring support支座位移support displacement支座沉降support settlement超静定次数degree of indeterminacy机动分析kinematic analysis结点法method of joints截面法method of sections结点力joint forces共轭位移conjugate displacement影响线influence line 三弯矩方程three-moment equation单位虚力unit virtual force刚度系数stiffness coefficient柔度系数flexibility coefficient力矩分配moment distribution力矩分配法moment distribution method 力矩再分配moment redistribution分配系数distribution factor矩阵位移法matri displacement method 单元刚度矩阵element stiffness matrix 单元应变矩阵element strain matrix 总体坐标global coordinates贝蒂定理Betti theorem高斯--若尔当消去法Gauss-Jordan eliminationMethod 屈曲模态buckling mode 复合材料力学mechanics of composites 复合材料composite material 纤维复合材料fibrous composite单向复合材料unidirectional composite泡沫复合材料foamed composite颗粒复合材料particulate composite 层板Laminate夹层板sandwich panel正交层板cross-ply laminate 斜交层板angle-ply laminate 层片Ply 多胞固体cellular solid 膨胀Expansion压实Debulk劣化Degradation脱层Delamination脱粘Debond 纤维应力fiber stress层应力ply stress层应变ply strain层间应力interlaminar stress比强度specific strength强度折减系数strength reduction factor 强度应力比strength -stress ratio 横向剪切模量transverse shear modulus 横观各向同性transverse isotropy正交各向异Orthotropy剪滞分析shear lag analysis短纤维chopped fiber长纤维continuous fiber纤维方向fiber direction纤维断裂fiber break纤维拔脱fiber pull-out纤维增强fiber reinforcement致密化Densification最小重量设计optimum weight design网格分析法netting analysis 混合律rule of mixture失效准则failure criterion蔡--吴失效准则Tsai-W u failure criterion 达格代尔模型Dugdale model 断裂力学fracture mechanics概率断裂力学probabilistic fractureMechanics格里菲思理论Griffith theory线弹性断裂力学linear elastic fracturemechanics, LEFM弹塑性断裂力学elastic-plastic fracturemecha-nics, EPFM 断裂Fracture 脆性断裂brittle fracture解理断裂cleavage fracture蠕变断裂creep fracture延性断裂ductile fracture晶间断裂inter-granular fracture 准解理断裂quasi-cleavage fracture 穿晶断裂trans-granular fracture 裂纹Crack裂缝Flaw缺陷Defect割缝Slit微裂纹Microcrack折裂Kink 椭圆裂纹elliptical crack深埋裂纹embedded crack[钱]币状裂纹penny-shape crack 预制裂纹Precrack短裂纹short crack表面裂纹surface crack裂纹钝化crack blunting裂纹分叉crack branching裂纹闭合crack closure裂纹前缘crack front裂纹嘴crack mouth裂纹张开角crack opening angle,COA 裂纹张开位移crack opening displacement,COD 裂纹阻力crack resistance裂纹面crack surface裂纹尖端crack tip裂尖张角crack tip opening angle,CTOA裂尖张开位移crack tip openingdisplacement, CTOD裂尖奇异场crack tip singularityField裂纹扩展速率crack growth rate稳定裂纹扩展stable crack growth定常裂纹扩展steady crack growth亚临界裂纹扩展subcritical crack growth 裂纹[扩展]减速crack retardation 止裂crack arrest 止裂韧度arrest toughness断裂类型fracture mode滑开型sliding mode张开型opening mode撕开型tearing mode复合型mixed mode撕裂Tearing 撕裂模量tearing modulus断裂准则fracture criterionJ积分J-integral J阻力曲线J-resistance curve断裂韧度fracture toughness应力强度因子stress intensity factor HRR场Hutchinson-Rice-RosengrenField 守恒积分conservation integral 有效应力张量effective stress tensor 应变能密度strain energy density 能量释放率energy release rate 内聚区cohesive zone塑性区plastic zone张拉区stretched zone热影响区heat affected zone, HAZ 延脆转变温度brittle-ductile transitiontempe- rature 剪切带shear band剪切唇shear lip无损检测non-destructive inspection 双边缺口试件double edge notchedspecimen, DEN specimen 单边缺口试件single edge notchedspecimen, SEN specimen 三点弯曲试件three point bendingspecimen, TPB specimen 中心裂纹拉伸试件center cracked tensionspecimen, CCT specimen 中心裂纹板试件center cracked panelspecimen, CCP specimen 紧凑拉伸试件compact tension specimen,CT specimen 大范围屈服large scale yielding小范围攻屈服small scale yielding 韦布尔分布Weibull distribution 帕里斯公式paris formula 空穴化Cavitation应力腐蚀stress corrosion概率风险判定probabilistic riskassessment, PRA 损伤力学damage mechanics 损伤Damage连续介质损伤力学continuum damage mechanics 细观损伤力学microscopic damage mechanics 累积损伤accumulated damage脆性损伤brittle damage延性损伤ductile damage宏观损伤macroscopic damage细观损伤microscopic damage微观损伤microscopic damage损伤准则damage criterion损伤演化方程damage evolution equation 损伤软化damage softening损伤强化damage strengthening损伤张量damage tensor损伤阈值damage threshold损伤变量damage variable损伤矢量damage vector损伤区damage zone疲劳Fatigue 低周疲劳low cycle fatigue应力疲劳stress fatigue随机疲劳random fatigue蠕变疲劳creep fatigue腐蚀疲劳corrosion fatigue疲劳损伤fatigue damage疲劳失效fatigue failure 疲劳断裂fatigue fracture 疲劳裂纹fatigue crack 疲劳寿命fatigue life疲劳破坏fatigue rupture 疲劳强度fatigue strength 疲劳辉纹fatigue striations 疲劳阈值fatigue threshold 交变载荷alternating load 交变应力alternating stress 应力幅值stress amplitude 应变疲劳strain fatigue 应力循环stress cycle应力比stress ratio安全寿命safe life过载效应overloading effect 循环硬化cyclic hardening 循环软化cyclic softening 环境效应environmental effect 裂纹片crack gage裂纹扩展crack growth, crackPropagation 裂纹萌生crack initiation 循环比cycle ratio实验应力分析experimental stressAnalysis工作[应变]片active[strain] gage基底材料backing material应力计stress gage 零[点]飘移zero shift, zero drift 应变测量strain measurement应变计strain gage 应变指示器strain indicator 应变花strain rosette 应变灵敏度strain sensitivity机械式应变仪mechanical strain gage 直角应变花rectangular rosette 引伸仪Extensometer应变遥测telemetering of strain 横向灵敏系数transverse gage factor 横向灵敏度transverse sensitivity 焊接式应变计weldable strain gage 平衡电桥balanced bridge粘贴式应变计bonded strain gage粘贴箔式应变计bonded foiled gage粘贴丝式应变计bonded wire gage 桥路平衡bridge balancing电容应变计capacitance strain gage 补偿片compensation technique 补偿技术compensation technique 基准电桥reference bridge电阻应变计resistance strain gage 温度自补偿应变计self-temperaturecompensating gage半导体应变计semiconductor strainGage 集流器slip ring应变放大镜strain amplifier疲劳寿命计fatigue life gage电感应变计inductance [strain] gage 光[测]力学Photomechanics 光弹性Photoelasticity光塑性Photoplasticity杨氏条纹Young fringe双折射效应birefrigent effect 等位移线contour of equalDisplacement 暗条纹dark fringe条纹倍增fringe multiplication 干涉条纹interference fringe 等差线Isochromatic等倾线Isoclinic等和线isopachic应力光学定律stress- optic law主应力迹线Isostatic 亮条纹light fringe光程差optical path difference 热光弹性photo-thermo -elasticity 光弹性贴片法photoelastic coatingMethod光弹性夹片法photoelastic sandwichMethod动态光弹性dynamic photo-elasticity 空间滤波spatial filtering空间频率spatial frequency起偏镜Polarizer反射式光弹性仪reflection polariscope残余双折射效应residual birefringentEffect应变条纹值strain fringe value应变光学灵敏度strain-optic sensitivity 应力冻结效应stress freezing effect应力条纹值stress fringe value应力光图stress-optic pattern暂时双折射效应temporary birefringentEffect脉冲全息法pulsed holography透射式光弹性仪transmission polariscope 实时全息干涉法real-time holographicinterfero - metry 网格法grid method全息光弹性法holo-photoelasticity 全息图Hologram全息照相Holograph全息干涉法holographic interferometry 全息云纹法holographic moire technique 全息术Holography全场分析法whole-field analysis散斑干涉法speckle interferometry 散斑Speckle错位散斑干涉法speckle-shearinginterferometry, shearography 散斑图Specklegram白光散斑法white-light speckle method 云纹干涉法moire interferometry [叠栅]云纹moire fringe[叠栅]云纹法moire method 云纹图moire pattern 离面云纹法off-plane moire method 参考栅reference grating试件栅specimen grating分析栅analyzer grating面内云纹法in-plane moire method脆性涂层法brittle-coating method 条带法strip coating method坐标变换transformation ofCoordinates计算结构力学computational structuralmecha-nics加权残量法weighted residual method 有限差分法finite difference method 有限[单]元法finite element method 配点法point collocation里茨法Ritz method广义变分原理generalized variationalPrinciple 最小二乘法least square method胡[海昌]一鹫津原理Hu-Washizu principle赫林格-赖斯纳原理Hellinger-ReissnerPrinciple 修正变分原理modified variationalPrinciple 约束变分原理constrained variationalPrinciple 混合法mixed method杂交法hybrid method边界解法boundary solution method 有限条法finite strip method半解析法semi-analytical method协调元conforming element非协调元non-conforming element混合元mixed element杂交元hybrid element边界元boundary element 强迫边界条件forced boundary condition 自然边界条件natural boundary condition 离散化Discretization离散系统discrete system连续问题continuous problem广义位移generalized displacement 广义载荷generalized load广义应变generalized strain广义应力generalized stress界面变量interface variable 节点node, nodal point[单]元Element角节点corner node边节点mid-side node内节点internal node无节点变量nodeless variable 杆元bar element桁架杆元truss element 梁元beam element二维元two-dimensional element 一维元one-dimensional element 三维元three-dimensional element 轴对称元axisymmetric element 板元plate element壳元shell element厚板元thick plate element三角形元triangular element四边形元quadrilateral element 四面体元tetrahedral element 曲线元curved element二次元quadratic element线性元linear element三次元cubic element四次元quartic element等参[数]元isoparametric element超参数元super-parametric element 亚参数元sub-parametric element节点数可变元variable-number-node element 拉格朗日元Lagrange element拉格朗日族Lagrange family巧凑边点元serendipity element巧凑边点族serendipity family 无限元infinite element单元分析element analysis单元特性element characteristics 刚度矩阵stiffness matrix几何矩阵geometric matrix等效节点力equivalent nodal force 节点位移nodal displacement节点载荷nodal load位移矢量displacement vector载荷矢量load vector质量矩阵mass matrix集总质量矩阵lumped mass matrix相容质量矩阵consistent mass matrix 阻尼矩阵damping matrix瑞利阻尼Rayleigh damping刚度矩阵的组集assembly of stiffnessMatrices载荷矢量的组集consistent mass matrix质量矩阵的组集assembly of mass matrices 单元的组集assembly of elements局部坐标系local coordinate system局部坐标local coordinate面积坐标area coordinates体积坐标volume coordinates曲线坐标curvilinear coordinates 静凝聚static condensation合同变换contragradient transformation 形状函数shape function试探函数trial function检验函数test function权函数weight function样条函数spline function代用函数substitute function降阶积分reduced integration零能模式zero-energy modeP收敛p-convergenceH收敛h-convergence掺混插值blended interpolation等参数映射isoparametric mapping双线性插值bilinear interpolation小块检验patch test非协调模式incompatible mode 节点号node number单元号element number带宽band width带状矩阵banded matrix变带状矩阵profile matrix带宽最小化minimization of band width 波前法frontal method子空间迭代法subspace iteration method 行列式搜索法determinant search method 逐步法step-by-step method 纽马克法Newmark威尔逊法Wilson拟牛顿法quasi-Newton method牛顿-拉弗森法Newton-Raphson method 增量法incremental method初应变initial strain初应力initial stress切线刚度矩阵tangent stiffness matrix 割线刚度矩阵secant stiffness matrix 模态叠加法mode superposition method 平衡迭代equilibrium iteration子结构Substructure子结构法substructure technique 超单元super-element网格生成mesh generation结构分析程序structural analysis program 前处理pre-processing后处理post-processing网格细化mesh refinement应力光顺stress smoothing组合结构composite structure。
物理学名词
中文又称
[coefficient of] stiffness 劲度[系数]
又称刚度系数 (rigidity);曾称:倔 强系数
[constant] current source 恒流源 [constant] voltage source 恒压源 [crystal] lattice [crystal] whisker [crystalline] grain [electric] bridge [electric] polarization [electron] avalanche ionization 晶格 晶须 晶粒 电桥 [电]极化强度 [电子]雪崩电离
accelerated reference frame accelerating tube accelerating voltage acceleration acceleration mechanism acceleration of gravity accelerator Accelerator mass spectrometer, AMS accelerometer acceptance angle acceptor acceptor acceptor acceptor density acceptor doping acceptor impurity acceptor ionization energy acceptor level accessible state accidental accuracy accidental coincidence accidental degeneracy accidental error accommodation accretion accretion disk accumulated dose accumulated error accumulation layer accumulator, [storage] battery accuracy acetylene
洛伦兹线形近似光学响应
洛伦兹线形近似光学响应全文共四篇示例，供读者参考第一篇示例：洛伦兹线形近似光学响应是指在一定条件下，材料的电磁响应可以用洛伦兹线形来描述。
这种线形近似在材料的电磁性质研究中起到了至关重要的作用，对于理解材料的光学性质和设计光学器件具有重要意义。
洛伦兹线形近似的提出源于对物质的电磁响应的研究。
在材料中，原子或分子通过自由电子和束缚电子来响应外加电磁场。
当外加电磁场的频率接近原子或分子的振动频率时，会发生共振吸收现象，这就是典型的洛伦兹线形近似的特征之一。
在洛伦兹线形近似中，材料的电磁响应可以用由若干个谐波振子组成的复杂振动体系来模拟。
每个振子对应材料中的一个原子或分子，它们的共振频率和阻尼常数决定了其电磁响应的特性。
在假设谐振子相互独立且不耦合的情况下，可以建立出描述材料光学性质的洛伦兹线形模型。
洛伦兹线形近似的具体形式可以表示为：ε(ω) = ε∞ + ∑ [ (ω0^2 - ω^2 - iγω)/(ω0^2 - ω^2 + iγω) ]ε(ω)表示材料的介电常数随频率的变化，ε∞是高频介电常数，ω0是振子的共振频率，γ是阻尼常数。
上述公式描述了材料在不同频率下的响应情况，其中各个振子的共振频率和阻尼常数决定了材料在特定波长下的吸收和透射特性。
洛伦兹线形近似的优点是可以很好地描述材料的光学性质，并且能够通过调节振子的参数来模拟不同的光学响应。
这种近似方法在材料结构设计和光学器件性能优化中得到了广泛应用。
洛伦兹线形近似也存在一些局限性。
该近似方法是基于线性响应理论的，而实际材料的电磁响应往往是非线性的，因此在高光强或频率较高的情况下可能会失效。
实际材料中的振子通常是相互耦合的，而洛伦兹线形近似假设振子之间相互独立，这也限制了其适用范围。
第二篇示例：洛伦兹线形近似是描述一种物质在光学响应中的特性的理论模型，它常被用于研究原子、分子和固态材料的光学性质。
本文将探讨洛伦兹线形近似的基本原理、应用以及一些相关的研究进展。
中英文力学对准
一般力学类：分析力学 analytical mechanics拉格朗日乘子 Lagrange multiplier拉格朗日[量] Lagrangian拉格朗日括号 Lagrange bracket循环坐标 cyclic coordinate循环积分 cyclic integral哈密顿[量] Hamiltonian哈密顿函数 Hamiltonian function正则方程 canonical equation正则摄动 canonical perturbation正则变换 canonical transformation正则变量 canonical variable哈密顿原理 Hamilton principle作用量积分 action integral哈密顿-雅可比方程 Hamilton-Jacobi equation作用--角度变量 action-angle variables阿佩尔方程 Appell equation劳斯方程 Routh equation拉格朗日函数 Lagrangian function诺特定理 Noether theorem泊松括号 poisson bracket边界积分法 boundary integral method并矢 dyad运动稳定性 stability of motion轨道稳定性 orbital stability李雅普诺夫函数 Lyapunov function渐近稳定性 asymptotic stability结构稳定性 structural stability久期不稳定性 secular instability弗洛凯定理 Floquet theorem倾覆力矩 capsizing moment自由振动 free vibration固有振动 natural vibration暂态 transient state环境振动 ambient vibration反共振 anti-resonance衰减 attenuation库仑阻尼 Coulomb damping同相分量 in-phase component非同相分量 out-of -phase component超调量 overshoot 参量[激励]振动 parametric vibration模糊振动 fuzzy vibration临界转速 critical speed of rotation阻尼器 damper半峰宽度 half-peak width集总参量系统 lumped parameter system 相平面法 phase plane method相轨迹 phase trajectory等倾线法 isocline method跳跃现象 jump phenomenon负阻尼 negative damping达芬方程 Duffing equation希尔方程 Hill equationKBM方法 KBM method, Krylov-Bogoliu- bov-Mitropol'skii method马蒂厄方程 Mathieu equation平均法 averaging method组合音调 combination tone解谐 detuning耗散函数 dissipative function硬激励 hard excitation硬弹簧 hard spring, hardening spring谐波平衡法harmonic balance method久期项 secular term自激振动 self-excited vibration分界线 separatrix亚谐波 subharmonic软弹簧 soft spring ,softening spring软激励 soft excitation邓克利公式 Dunkerley formula瑞利定理 Rayleigh theorem分布参量系统 distributed parameter system优势频率 dominant frequency模态分析 modal analysis固有模态natural mode of vibration同步 synchronization超谐波 ultraharmonic范德波尔方程 van der pol equation频谱 frequency spectrum基频 fundamental frequencyWKB方法 WKB methodWKB方法Wentzel-Kramers-Brillouin method缓冲器 buffer风激振动 aeolian vibration嗡鸣 buzz倒谱cepstrum颤动 chatter蛇行 hunting阻抗匹配 impedance matching机械导纳 mechanical admittance机械效率 mechanical efficiency机械阻抗 mechanical impedance随机振动 stochastic vibration, random vibration隔振 vibration isolation减振 vibration reduction应力过冲 stress overshoot喘振surge摆振shimmy起伏运动 phugoid motion起伏振荡 phugoid oscillation驰振 galloping陀螺动力学 gyrodynamics陀螺摆 gyropendulum陀螺平台 gyroplatform陀螺力矩 gyroscoopic torque陀螺稳定器 gyrostabilizer陀螺体 gyrostat惯性导航 inertial guidance 姿态角 attitude angle方位角 azimuthal angle舒勒周期 Schuler period机器人动力学 robot dynamics多体系统 multibody system多刚体系统 multi-rigid-body system机动性 maneuverability凯恩方法Kane method转子[系统]动力学 rotor dynamics转子[一支承一基础]系统 rotor-support- foundation system静平衡 static balancing动平衡 dynamic balancing静不平衡 static unbalance动不平衡 dynamic unbalance现场平衡 field balancing不平衡 unbalance不平衡量 unbalance互耦力 cross force挠性转子 flexible rotor分频进动 fractional frequency precession半频进动half frequency precession油膜振荡 oil whip转子临界转速 rotor critical speed自动定心 self-alignment亚临界转速 subcritical speed涡动 whirl固体力学类：弹性力学 elasticity弹性理论 theory of elasticity均匀应力状态 homogeneous state of stress 应力不变量 stress invariant应变不变量 strain invariant应变椭球 strain ellipsoid均匀应变状态 homogeneous state of strain应变协调方程 equation of strain compatibility拉梅常量 Lame constants各向同性弹性 isotropic elasticity旋转圆盘 rotating circular disk 楔wedge开尔文问题 Kelvin problem布西内斯克问题 Boussinesq problem艾里应力函数 Airy stress function克罗索夫--穆斯赫利什维利法 Kolosoff- Muskhelishvili method基尔霍夫假设 Kirchhoff hypothesis板 Plate矩形板 Rectangular plate圆板 Circular plate环板 Annular plate波纹板 Corrugated plate加劲板 Stiffened plate,reinforcedPlate中厚板 Plate of moderate thickness弯[曲]应力函数 Stress function of bending 壳Shell扁壳 Shallow shell旋转壳 Revolutionary shell球壳 Spherical shell[圆]柱壳 Cylindrical shell锥壳Conical shell环壳 Toroidal shell封闭壳 Closed shell波纹壳 Corrugated shell扭[转]应力函数 Stress function of torsion 翘曲函数 Warping function半逆解法 semi-inverse method瑞利--里茨法 Rayleigh-Ritz method松弛法 Relaxation method莱维法 Levy method松弛 Relaxation量纲分析 Dimensional analysis自相似[性] self-similarity影响面 Influence surface接触应力 Contact stress赫兹理论 Hertz theory协调接触 Conforming contact滑动接触 Sliding contact滚动接触 Rolling contact压入 Indentation各向异性弹性 Anisotropic elasticity颗粒材料 Granular material散体力学 Mechanics of granular media热弹性 Thermoelasticity超弹性 Hyperelasticity粘弹性 Viscoelasticity对应原理 Correspondence principle褶皱Wrinkle塑性全量理论 Total theory of plasticity滑动 Sliding微滑Microslip粗糙度 Roughness非线性弹性 Nonlinear elasticity大挠度 Large deflection突弹跳变 snap-through有限变形 Finite deformation 格林应变 Green strain阿尔曼西应变 Almansi strain弹性动力学 Dynamic elasticity运动方程 Equation of motion准静态的Quasi-static气动弹性 Aeroelasticity水弹性 Hydroelasticity颤振Flutter弹性波Elastic wave简单波Simple wave柱面波 Cylindrical wave水平剪切波 Horizontal shear wave竖直剪切波Vertical shear wave体波 body wave无旋波 Irrotational wave畸变波 Distortion wave膨胀波 Dilatation wave瑞利波 Rayleigh wave等容波 Equivoluminal wave勒夫波Love wave界面波 Interfacial wave边缘效应 edge effect塑性力学 Plasticity可成形性 Formability金属成形 Metal forming耐撞性 Crashworthiness结构抗撞毁性 Structural crashworthiness 拉拔Drawing破坏机构 Collapse mechanism回弹 Springback挤压 Extrusion冲压 Stamping穿透Perforation层裂Spalling塑性理论 Theory of plasticity安定[性]理论 Shake-down theory运动安定定理 kinematic shake-down theorem静力安定定理 Static shake-down theorem 率相关理论 rate dependent theorem载荷因子load factor加载准则 Loading criterion加载函数 Loading function加载面 Loading surface塑性加载 Plastic loading塑性加载波 Plastic loading wave简单加载 Simple loading比例加载 Proportional loading卸载 Unloading卸载波 Unloading wave冲击载荷 Impulsive load阶跃载荷step load脉冲载荷 pulse load极限载荷 limit load中性变载 nentral loading拉抻失稳 instability in tension加速度波 acceleration wave本构方程 constitutive equation完全解 complete solution名义应力 nominal stress过应力 over-stress真应力 true stress等效应力 equivalent stress流动应力 flow stress应力间断 stress discontinuity应力空间 stress space主应力空间 principal stress space静水应力状态hydrostatic state of stress对数应变 logarithmic strain工程应变 engineering strain等效应变 equivalent strain应变局部化 strain localization应变率 strain rate应变率敏感性 strain rate sensitivity应变空间 strain space有限应变 finite strain塑性应变增量 plastic strain increment 累积塑性应变 accumulated plastic strain 永久变形 permanent deformation内变量 internal variable应变软化 strain-softening理想刚塑性材料 rigid-perfectly plastic Material刚塑性材料 rigid-plastic material理想塑性材料 perfectl plastic material 材料稳定性stability of material应变偏张量deviatoric tensor of strain应力偏张量deviatori tensor of stress 应变球张量spherical tensor of strain应力球张量spherical tensor of stress路径相关性 path-dependency线性强化 linear strain-hardening应变强化 strain-hardening随动强化 kinematic hardening各向同性强化 isotropic hardening强化模量 strain-hardening modulus幂强化 power hardening塑性极限弯矩 plastic limit bending Moment塑性极限扭矩 plastic limit torque弹塑性弯曲 elastic-plastic bending弹塑性交界面 elastic-plastic interface弹塑性扭转 elastic-plastic torsion粘塑性 Viscoplasticity非弹性 Inelasticity理想弹塑性材料 elastic-perfectly plastic Material极限分析 limit analysis极限设计 limit design极限面limit surface上限定理 upper bound theorem上屈服点upper yield point下限定理 lower bound theorem下屈服点 lower yield point界限定理 bound theorem初始屈服面initial yield surface后继屈服面 subsequent yield surface屈服面[的]外凸性 convexity of yield surface截面形状因子 shape factor of cross-section 沙堆比拟 sand heap analogy屈服Yield屈服条件 yield condition屈服准则 yield criterion屈服函数 yield function屈服面 yield surface塑性势 plastic potential能量吸收装置 energy absorbing device能量耗散率 energy absorbing device塑性动力学 dynamic plasticity塑性动力屈曲 dynamic plastic buckling塑性动力响应 dynamic plastic response塑性波 plastic wave运动容许场 kinematically admissible Field静力容许场 statically admissibleField流动法则 flow rule速度间断 velocity discontinuity滑移线 slip-lines滑移线场 slip-lines field移行塑性铰 travelling plastic hinge塑性增量理论 incremental theory ofPlasticity米泽斯屈服准则 Mises yield criterion普朗特--罗伊斯关系 prandtl- Reuss relation特雷斯卡屈服准则 Tresca yield criterion洛德应力参数 Lode stress parameter莱维--米泽斯关系 Levy-Mises relation亨基应力方程 Hencky stress equation赫艾--韦斯特加德应力空间Haigh-Westergaard stress space洛德应变参数 Lode strain parameter德鲁克公设 Drucker postulate盖林格速度方程Geiringer velocity Equation结构力学 structural mechanics结构分析 structural analysis结构动力学 structural dynamics拱 Arch三铰拱 three-hinged arch抛物线拱 parabolic arch圆拱 circular arch穹顶Dome空间结构 space structure空间桁架 space truss雪载[荷] snow load风载[荷] wind load土压力 earth pressure地震载荷 earthquake loading弹簧支座 spring support支座位移 support displacement支座沉降 support settlement超静定次数 degree of indeterminacy机动分析 kinematic analysis 结点法 method of joints截面法 method of sections结点力 joint forces共轭位移 conjugate displacement影响线 influence line三弯矩方程 three-moment equation单位虚力 unit virtual force刚度系数 stiffness coefficient柔度系数 flexibility coefficient力矩分配 moment distribution力矩分配法moment distribution method力矩再分配 moment redistribution分配系数 distribution factor矩阵位移法matri displacement method单元刚度矩阵 element stiffness matrix单元应变矩阵 element strain matrix总体坐标 global coordinates贝蒂定理 Betti theorem高斯--若尔当消去法 Gauss-Jordan elimination Method屈曲模态 buckling mode复合材料力学 mechanics of composites 复合材料composite material纤维复合材料 fibrous composite单向复合材料 unidirectional composite泡沫复合材料foamed composite颗粒复合材料 particulate composite层板Laminate夹层板 sandwich panel正交层板 cross-ply laminate斜交层板 angle-ply laminate层片Ply多胞固体 cellular solid膨胀 Expansion压实Debulk劣化 Degradation脱层 Delamination脱粘 Debond纤维应力 fiber stress层应力 ply stress层应变ply strain层间应力 interlaminar stress比强度 specific strength强度折减系数 strength reduction factor强度应力比 strength -stress ratio横向剪切模量 transverse shear modulus 横观各向同性 transverse isotropy正交各向异 Orthotropy剪滞分析 shear lag analysis短纤维 chopped fiber长纤维 continuous fiber纤维方向 fiber direction纤维断裂 fiber break纤维拔脱 fiber pull-out纤维增强 fiber reinforcement致密化 Densification最小重量设计 optimum weight design网格分析法 netting analysis混合律 rule of mixture失效准则 failure criterion蔡--吴失效准则 Tsai-W u failure criterion 达格代尔模型 Dugdale model断裂力学 fracture mechanics概率断裂力学 probabilistic fracture Mechanics格里菲思理论 Griffith theory线弹性断裂力学 linear elastic fracturemechanics, LEFM弹塑性断裂力学 elastic-plastic fracture mecha-nics, EPFM断裂 Fracture脆性断裂 brittle fracture解理断裂 cleavage fracture蠕变断裂 creep fracture延性断裂 ductile fracture晶间断裂 inter-granular fracture准解理断裂 quasi-cleavage fracture穿晶断裂 trans-granular fracture裂纹Crack裂缝Flaw缺陷Defect割缝Slit微裂纹Microcrack折裂Kink椭圆裂纹 elliptical crack深埋裂纹 embedded crack[钱]币状裂纹 penny-shape crack预制裂纹 Precrack 短裂纹 short crack表面裂纹 surface crack裂纹钝化 crack blunting裂纹分叉 crack branching裂纹闭合 crack closure裂纹前缘 crack front裂纹嘴 crack mouth裂纹张开角crack opening angle,COA裂纹张开位移 crack opening displacement, COD裂纹阻力 crack resistance裂纹面 crack surface裂纹尖端 crack tip裂尖张角 crack tip opening angle,CTOA裂尖张开位移 crack tip openingdisplacement, CTOD裂尖奇异场crack tip singularity Field裂纹扩展速率 crack growth rate稳定裂纹扩展 stable crack growth定常裂纹扩展 steady crack growth亚临界裂纹扩展 subcritical crack growth 裂纹[扩展]减速 crack retardation止裂crack arrest止裂韧度 arrest toughness断裂类型 fracture mode滑开型 sliding mode张开型 opening mode撕开型 tearing mode复合型 mixed mode撕裂 Tearing撕裂模量 tearing modulus断裂准则 fracture criterionJ积分 J-integralJ阻力曲线 J-resistance curve断裂韧度 fracture toughness应力强度因子 stress intensity factorHRR场 Hutchinson-Rice-Rosengren Field守恒积分 conservation integral有效应力张量 effective stress tensor应变能密度strain energy density能量释放率 energy release rate内聚区 cohesive zone塑性区 plastic zone张拉区 stretched zone热影响区heat affected zone, HAZ延脆转变温度 brittle-ductile transitiontemperature剪切带shear band剪切唇shear lip无损检测 non-destructive inspection双边缺口试件double edge notchedspecimen, DEN specimen单边缺口试件 single edge notchedspecimen, SEN specimen三点弯曲试件 three point bendingspecimen, TPB specimen中心裂纹拉伸试件 center cracked tension specimen, CCT specimen中心裂纹板试件 center cracked panelspecimen, CCP specimen紧凑拉伸试件 compact tension specimen, CT specimen大范围屈服large scale yielding小范围攻屈服 small scale yielding韦布尔分布 Weibull distribution帕里斯公式 paris formula空穴化 Cavitation应力腐蚀 stress corrosion概率风险判定 probabilistic riskassessment, PRA损伤力学 damage mechanics损伤Damage连续介质损伤力学 continuum damage mechanics细观损伤力学 microscopic damage mechanics累积损伤 accumulated damage脆性损伤 brittle damage延性损伤 ductile damage宏观损伤 macroscopic damage细观损伤 microscopic damage微观损伤 microscopic damage损伤准则 damage criterion损伤演化方程 damage evolution equation 损伤软化 damage softening损伤强化 damage strengthening 损伤张量 damage tensor损伤阈值 damage threshold损伤变量 damage variable损伤矢量 damage vector损伤区 damage zone疲劳Fatigue低周疲劳 low cycle fatigue应力疲劳 stress fatigue随机疲劳 random fatigue蠕变疲劳 creep fatigue腐蚀疲劳 corrosion fatigue疲劳损伤 fatigue damage疲劳失效 fatigue failure疲劳断裂 fatigue fracture疲劳裂纹 fatigue crack疲劳寿命 fatigue life疲劳破坏 fatigue rupture疲劳强度 fatigue strength疲劳辉纹 fatigue striations疲劳阈值 fatigue threshold交变载荷 alternating load交变应力 alternating stress应力幅值 stress amplitude应变疲劳 strain fatigue应力循环 stress cycle应力比 stress ratio安全寿命 safe life过载效应 overloading effect循环硬化 cyclic hardening循环软化 cyclic softening环境效应 environmental effect裂纹片crack gage裂纹扩展 crack growth, crack Propagation裂纹萌生 crack initiation循环比 cycle ratio实验应力分析 experimental stressAnalysis工作[应变]片 active[strain] gage基底材料 backing material应力计stress gage零[点]飘移zero shift, zero drift应变测量 strain measurement应变计strain gage应变指示器 strain indicator应变花 strain rosette应变灵敏度 strain sensitivity机械式应变仪 mechanical strain gage 直角应变花 rectangular rosette引伸仪 Extensometer应变遥测 telemetering of strain横向灵敏系数 transverse gage factor 横向灵敏度 transverse sensitivity焊接式应变计 weldable strain gage 平衡电桥 balanced bridge粘贴式应变计 bonded strain gage粘贴箔式应变计bonded foiled gage粘贴丝式应变计 bonded wire gage 桥路平衡 bridge balancing电容应变计 capacitance strain gage 补偿片 compensation technique补偿技术 compensation technique基准电桥 reference bridge电阻应变计 resistance strain gage温度自补偿应变计 self-temperature compensating gage半导体应变计 semiconductor strain Gage集流器slip ring应变放大镜 strain amplifier疲劳寿命计 fatigue life gage电感应变计 inductance [strain] gage 光[测]力学 Photomechanics光弹性 Photoelasticity光塑性 Photoplasticity杨氏条纹 Young fringe双折射效应 birefrigent effect等位移线 contour of equalDisplacement暗条纹 dark fringe条纹倍增 fringe multiplication干涉条纹 interference fringe等差线 Isochromatic等倾线 Isoclinic等和线 isopachic应力光学定律 stress- optic law主应力迹线 Isostatic亮条纹 light fringe 光程差optical path difference热光弹性 photo-thermo -elasticity光弹性贴片法 photoelastic coating Method光弹性夹片法 photoelastic sandwich Method动态光弹性 dynamic photo-elasticity空间滤波 spatial filtering空间频率 spatial frequency起偏镜 Polarizer反射式光弹性仪 reflection polariscope残余双折射效应 residual birefringent Effect应变条纹值 strain fringe value应变光学灵敏度 strain-optic sensitivity 应力冻结效应 stress freezing effect应力条纹值 stress fringe value应力光图 stress-optic pattern暂时双折射效应 temporary birefringent Effect脉冲全息法 pulsed holography透射式光弹性仪 transmission polariscope 实时全息干涉法 real-time holographicinterfero - metry网格法 grid method全息光弹性法 holo-photoelasticity全息图Hologram全息照相 Holograph全息干涉法 holographic interferometry 全息云纹法 holographic moire technique 全息术 Holography全场分析法 whole-field analysis散斑干涉法 speckle interferometry散斑Speckle错位散斑干涉法 speckle-shearinginterferometry, shearography散斑图Specklegram白光散斑法white-light speckle method云纹干涉法 moire interferometry[叠栅]云纹 moire fringe[叠栅]云纹法 moire method云纹图 moire pattern离面云纹法 off-plane moire method参考栅 reference grating试件栅 specimen grating分析栅 analyzer grating面内云纹法 in-plane moire method脆性涂层法 brittle-coating method条带法 strip coating method坐标变换 transformation ofCoordinates计算结构力学 computational structuralmecha-nics加权残量法weighted residual method有限差分法 finite difference method有限[单]元法 finite element method配点法 point collocation里茨法 Ritz method广义变分原理 generalized variational Principle最小二乘法 least square method胡[海昌]一鹫津原理 Hu-Washizu principle 赫林格-赖斯纳原理 Hellinger-Reissner Principle修正变分原理 modified variational Principle约束变分原理 constrained variational Principle混合法 mixed method杂交法 hybrid method边界解法boundary solution method有限条法 finite strip method半解析法 semi-analytical method协调元 conforming element非协调元 non-conforming element混合元 mixed element杂交元 hybrid element边界元 boundary element强迫边界条件 forced boundary condition 自然边界条件 natural boundary condition 离散化 Discretization离散系统 discrete system连续问题 continuous problem广义位移 generalized displacement广义载荷 generalized load广义应变 generalized strain广义应力 generalized stress界面变量 interface variable 节点 node, nodal point[单]元 Element角节点 corner node边节点 mid-side node内节点 internal node无节点变量 nodeless variable杆元 bar element桁架杆元 truss element梁元 beam element二维元 two-dimensional element一维元 one-dimensional element三维元 three-dimensional element轴对称元 axisymmetric element板元 plate element壳元 shell element厚板元 thick plate element三角形元 triangular element四边形元 quadrilateral element四面体元 tetrahedral element曲线元 curved element二次元 quadratic element线性元 linear element三次元 cubic element四次元 quartic element等参[数]元 isoparametric element超参数元 super-parametric element亚参数元 sub-parametric element节点数可变元 variable-number-node element拉格朗日元 Lagrange element拉格朗日族 Lagrange family巧凑边点元 serendipity element巧凑边点族 serendipity family无限元 infinite element单元分析 element analysis单元特性 element characteristics刚度矩阵 stiffness matrix几何矩阵 geometric matrix等效节点力 equivalent nodal force节点位移 nodal displacement节点载荷 nodal load位移矢量 displacement vector载荷矢量 load vector质量矩阵 mass matrix集总质量矩阵 lumped mass matrix相容质量矩阵 consistent mass matrix阻尼矩阵 damping matrix瑞利阻尼 Rayleigh damping刚度矩阵的组集 assembly of stiffnessMatrices载荷矢量的组集 consistent mass matrix质量矩阵的组集 assembly of mass matrices 单元的组集 assembly of elements局部坐标系 local coordinate system局部坐标 local coordinate面积坐标 area coordinates体积坐标 volume coordinates曲线坐标 curvilinear coordinates静凝聚 static condensation合同变换 contragradient transformation形状函数 shape function试探函数 trial function检验函数test function权函数 weight function样条函数 spline function代用函数 substitute function降阶积分 reduced integration零能模式 zero-energy modeP收敛 p-convergenceH收敛 h-convergence掺混插值 blended interpolation等参数映射 isoparametric mapping双线性插值 bilinear interpolation小块检验 patch test非协调模式 incompatible mode 节点号 node number单元号 element number带宽 band width带状矩阵 banded matrix变带状矩阵 profile matrix带宽最小化minimization of band width波前法 frontal method子空间迭代法 subspace iteration method 行列式搜索法determinant search method逐步法 step-by-step method纽马克法Newmark威尔逊法 Wilson拟牛顿法 quasi-Newton method牛顿-拉弗森法 Newton-Raphson method 增量法 incremental method初应变 initial strain初应力 initial stress切线刚度矩阵 tangent stiffness matrix割线刚度矩阵 secant stiffness matrix模态叠加法mode superposition method平衡迭代 equilibrium iteration子结构 Substructure子结构法 substructure technique超单元 super-element网格生成 mesh generation结构分析程序 structural analysis program 前处理 pre-processing后处理 post-processing网格细化 mesh refinement应力光顺 stress smoothing组合结构 composite structure流体动力学类：流体动力学 fluid dynamics连续介质力学 mechanics of continuous media介质medium流体质点 fluid particle无粘性流体 nonviscous fluid, inviscid fluid连续介质假设 continuous medium hypothesis流体运动学 fluid kinematics水静力学 hydrostatics 液体静力学 hydrostatics支配方程 governing equation伯努利方程 Bernoulli equation伯努利定理 Bernonlli theorem毕奥-萨伐尔定律 Biot-Savart law欧拉方程Euler equation亥姆霍兹定理 Helmholtz theorem开尔文定理 Kelvin theorem涡片 vortex sheet库塔-茹可夫斯基条件 Kutta-Zhoukowskicondition布拉休斯解 Blasius solution达朗贝尔佯廖 d'Alembert paradox 雷诺数 Reynolds number施特鲁哈尔数 Strouhal number随体导数 material derivative不可压缩流体 incompressible fluid 质量守恒 conservation of mass动量守恒 conservation of momentum 能量守恒 conservation of energy动量方程 momentum equation能量方程 energy equation控制体积 control volume液体静压 hydrostatic pressure涡量拟能 enstrophy压差 differential pressure流[动] flow流线stream line流面 stream surface流管stream tube迹线path, path line流场 flow field流态 flow regime流动参量 flow parameter流量 flow rate, flow discharge涡旋 vortex涡量 vorticity涡丝 vortex filament涡线 vortex line涡面 vortex surface涡层 vortex layer涡环 vortex ring涡对 vortex pair涡管 vortex tube涡街 vortex street卡门涡街 Karman vortex street马蹄涡 horseshoe vortex对流涡胞 convective cell卷筒涡胞 roll cell涡 eddy涡粘性 eddy viscosity环流 circulation环量 circulation速度环量 velocity circulation 偶极子 doublet, dipole驻点 stagnation point总压[力] total pressure总压头 total head静压头 static head总焓 total enthalpy能量输运 energy transport速度剖面 velocity profile库埃特流 Couette flow单相流 single phase flow单组份流 single-component flow均匀流 uniform flow非均匀流 nonuniform flow二维流 two-dimensional flow三维流 three-dimensional flow准定常流 quasi-steady flow非定常流unsteady flow, non-steady flow 暂态流transient flow周期流 periodic flow振荡流 oscillatory flow分层流 stratified flow无旋流 irrotational flow有旋流 rotational flow轴对称流 axisymmetric flow不可压缩性 incompressibility不可压缩流[动] incompressible flow 浮体 floating body定倾中心metacenter阻力 drag, resistance减阻 drag reduction表面力 surface force表面张力 surface tension毛细[管]作用 capillarity来流 incoming flow自由流 free stream自由流线 free stream line外流 external flow进口 entrance, inlet出口exit, outlet扰动 disturbance, perturbation分布 distribution传播 propagation色散 dispersion弥散 dispersion附加质量added mass ,associated mass收缩 contraction镜象法 image method无量纲参数 dimensionless parameter几何相似 geometric similarity运动相似 kinematic similarity动力相似[性] dynamic similarity平面流 plane flow势 potential势流 potential flow速度势 velocity potential复势 complex potential复速度 complex velocity流函数 stream function源source汇sink速度[水]头 velocity head拐角流 corner flow空泡流cavity flow超空泡 supercavity超空泡流 supercavity flow空气动力学 aerodynamics低速空气动力学 low-speed aerodynamics 高速空气动力学 high-speed aerodynamics 气动热力学 aerothermodynamics亚声速流[动] subsonic flow跨声速流[动] transonic flow超声速流[动] supersonic flow锥形流 conical flow楔流wedge flow叶栅流 cascade flow非平衡流[动] non-equilibrium flow细长体 slender body细长度 slenderness钝头体 bluff body钝体 blunt body翼型 airfoil翼弦 chord薄翼理论 thin-airfoil theory构型 configuration后缘 trailing edge迎角 angle of attack失速stall脱体激波detached shock wave 波阻wave drag诱导阻力 induced drag诱导速度 induced velocity临界雷诺数critical Reynolds number前缘涡 leading edge vortex附着涡 bound vortex约束涡 confined vortex气动中心 aerodynamic center气动力 aerodynamic force气动噪声 aerodynamic noise气动加热 aerodynamic heating离解 dissociation地面效应 ground effect气体动力学 gas dynamics稀疏波 rarefaction wave热状态方程thermal equation of state喷管Nozzle普朗特-迈耶流 Prandtl-Meyer flow瑞利流 Rayleigh flow可压缩流[动] compressible flow可压缩流体 compressible fluid绝热流 adiabatic flow非绝热流 diabatic flow未扰动流 undisturbed flow等熵流 isentropic flow匀熵流 homoentropic flow兰金-于戈尼奥条件 Rankine-Hugoniot condition状态方程 equation of state量热状态方程 caloric equation of state完全气体 perfect gas拉瓦尔喷管 Laval nozzle马赫角 Mach angle马赫锥 Mach cone马赫线Mach line马赫数Mach number马赫波Mach wave当地马赫数 local Mach number冲击波 shock wave激波 shock wave正激波normal shock wave斜激波oblique shock wave头波 bow wave附体激波 attached shock wave激波阵面 shock front激波层 shock layer压缩波 compression wave反射 reflection折射 refraction散射scattering衍射 diffraction绕射 diffraction出口压力 exit pressure超压[强] over pressure反压 back pressure爆炸 explosion爆轰 detonation缓燃 deflagration水动力学 hydrodynamics液体动力学 hydrodynamics泰勒不稳定性 Taylor instability 盖斯特纳波 Gerstner wave斯托克斯波 Stokes wave瑞利数 Rayleigh number自由面 free surface波速 wave speed, wave velocity 波高 wave height波列wave train波群 wave group波能wave energy表面波 surface wave表面张力波 capillary wave规则波 regular wave不规则波 irregular wave浅水波 shallow water wave深水波deep water wave重力波 gravity wave椭圆余弦波 cnoidal wave潮波tidal wave涌波surge wave破碎波 breaking wave船波ship wave非线性波 nonlinear wave孤立子 soliton水动[力]噪声 hydrodynamic noise 水击 water hammer空化 cavitation空化数 cavitation number 空蚀 cavitation damage超空化流 supercavitating flow水翼 hydrofoil水力学 hydraulics洪水波 flood wave涟漪ripple消能 energy dissipation海洋水动力学 marine hydrodynamics谢齐公式 Chezy formula欧拉数 Euler number弗劳德数 Froude number水力半径 hydraulic radius水力坡度 hvdraulic slope高度水头 elevating head水头损失 head loss水位 water level水跃 hydraulic jump含水层 aquifer排水 drainage排放量 discharge壅水曲线back water curve压[强水]头 pressure head过水断面 flow cross-section明槽流open channel flow孔流 orifice flow无压流 free surface flow有压流 pressure flow缓流 subcritical flow急流 supercritical flow渐变流gradually varied flow急变流 rapidly varied flow临界流 critical flow异重流density current, gravity flow堰流weir flow掺气流 aerated flow含沙流 sediment-laden stream降水曲线 dropdown curve沉积物 sediment, deposit沉[降堆]积 sedimentation, deposition沉降速度 settling velocity流动稳定性 flow stability不稳定性 instability奥尔-索末菲方程 Orr-Sommerfeld equation 涡量方程 vorticity equation泊肃叶流 Poiseuille flow奥辛流 Oseen flow剪切流 shear flow粘性流[动] viscous flow层流 laminar flow分离流 separated flow二次流 secondary flow近场流near field flow远场流 far field flow滞止流 stagnation flow尾流 wake [flow]回流 back flow反流 reverse flow射流 jet自由射流 free jet管流pipe flow, tube flow内流 internal flow拟序结构 coherent structure 猝发过程 bursting process表观粘度 apparent viscosity 运动粘性 kinematic viscosity 动力粘性 dynamic viscosity 泊 poise厘泊 centipoise厘沱 centistoke剪切层 shear layer次层 sublayer流动分离 flow separation层流分离 laminar separation 湍流分离 turbulent separation 分离点 separation point附着点 attachment point再附 reattachment再层流化 relaminarization起动涡starting vortex驻涡 standing vortex涡旋破碎 vortex breakdown 涡旋脱落 vortex shedding压[力]降 pressure drop压差阻力 pressure drag压力能 pressure energy型阻 profile drag滑移速度 slip velocity无滑移条件 non-slip condition 壁剪应力 skin friction, frictional drag壁剪切速度 friction velocity磨擦损失 friction loss磨擦因子 friction factor耗散 dissipation滞后lag相似性解 similar solution局域相似 local similarity气体润滑 gas lubrication液体动力润滑 hydrodynamic lubrication 浆体 slurry泰勒数 Taylor number纳维-斯托克斯方程 Navier-Stokes equation 牛顿流体 Newtonian fluid边界层理论boundary later theory边界层方程boundary layer equation边界层 boundary layer附面层 boundary layer层流边界层laminar boundary layer湍流边界层turbulent boundary layer温度边界层thermal boundary layer边界层转捩boundary layer transition边界层分离boundary layer separation边界层厚度boundary layer thickness位移厚度 displacement thickness动量厚度 momentum thickness能量厚度 energy thickness焓厚度 enthalpy thickness注入 injection吸出suction泰勒涡 Taylor vortex速度亏损律 velocity defect law形状因子 shape factor测速法 anemometry粘度测定法 visco[si] metry流动显示 flow visualization油烟显示 oil smoke visualization孔板流量计 orifice meter频率响应 frequency response油膜显示oil film visualization阴影法 shadow method纹影法 schlieren method烟丝法smoke wire method丝线法 tuft method。
(光电信息工程专业英语)专业英语第七讲Geometrical Optics
牛顿1672年使用的6英寸反射式望远镜复制品，为皇 家学会所拥有。
1994年，不列颠哥伦比亚大学开始建造一台 口径为6米的旋转水银面望远镜——大型天 顶望远镜（LZT），并于2003年建成
1.9 Lens Aberrations
9. By choosing materials with indices of refraction that depend in different ways on the color of the light, lens designers can ensure that positive and negative lens elements compensate for each other by having equal but opposite chromatic effects.
1.9 Lens Aberrations
4. Up to now, our discussion of lenses has not taken into account some of the optical imperfections that are inherent in single lenses made of uniform material with spherical surfaces. These failures of a lens to give a perfect image are known as aberrations. 句子结构： our discussion … has not taken into account … imperfections…
vt.提供；给予（provide的过去式）
参考翻译：
在上述的推导中，我们检验了物在会聚透镜焦点以外的特殊情况。 然而，如果遵守下述的符号规则，薄透镜公式对于会聚和发散薄透镜都是 有效的，且不论物体远近。
弹性力学专业英语词汇_elasticity
弹性力学elasticity弹性理论theory of elasticity均匀应力状态homogeneous state of stress应力不变量stress invariant应变不变量strain invariant应变椭球strain ellipsoid均匀应变状态homogeneous state of strain应变协调方程equation of strain compatibility拉梅常量Lame constants各向同性弹性isotropic elasticity旋转圆盘rotating circular disk楔wedge开尔文问题Kelvin problem布西内斯克问题Boussinesq problem艾里应力函数Airy stress function克罗索夫-穆斯赫利什维利法Kolosoff-Muskhelishvili method 基尔霍夫假设Kirchhoff hypothesis板Plate矩形板Rectangular plate圆板Circular plate环板Annular plate波纹板Corrugated plate加劲板Stiffened plate,reinforced Plate中厚板Plate of moderate thickness弯[曲]应力函数Stress function of bending 壳Shell扁壳Shallow shell旋转壳Revolutionary shell球壳Spherical shell[圆]柱壳Cylindrical shell锥壳Conical shell环壳Toroidal shell封闭壳Closed shell波纹壳Corrugated shell扭[转]应力函数Stress function of torsion 翘曲函数Warping function半逆解法semi-inverse method瑞利——里茨法Rayleigh-Ritz method松弛法Relaxation method莱维法Levy method松弛Relaxation量纲分析Dimensional analysis自相似[性] self-similarity影响面Influence surface接触应力Contact stress赫兹理论Hertz theory协调接触Conforming contact滑动接触Sliding contact滚动接触Rolling contact压入Indentation各向异性弹性Anisotropic elasticity颗粒材料Granular material散体力学Mechanics of granular media 热弹性Thermoelasticity超弹性Hyperelasticity粘弹性Viscoelasticity对应原理Correspondence principle褶皱Wrinkle塑性全量理论Total theory of plasticity 滑动Sliding微滑Microslip粗糙度Roughness非线性弹性Nonlinear elasticity大挠度Large deflection突弹跳变snap-through有限变形Finite deformation格林应变Green strain阿尔曼西应变Almansi strain弹性动力学Dynamic elasticity运动方程Equation of motion准静态的Quasi-static气动弹性Aeroelasticity水弹性Hydroelasticity颤振Flutter弹性波Elastic wave简单波Simple wave柱面波Cylindrical wave水平剪切波Horizontal shear wave 竖直剪切波Vertical shear wave 体波body wave无旋波Irrotational wave畸变波Distortion wave膨胀波Dilatation wave瑞利波Rayleigh wave等容波Equivoluminal wave勒夫波Love wave界面波Interfacial wave边缘效应edge effect塑性力学Plasticity可成形性Formability金属成形Metal forming耐撞性Crashworthiness结构抗撞毁性Structural crashworthiness拉拔Drawing破坏机构Collapse mechanism回弹Springback挤压Extrusion冲压Stamping穿透Perforation层裂Spalling塑性理论Theory of plasticity安定[性]理论Shake-down theory运动安定定理kinematic shake-down theorem 静力安定定理Static shake-down theorem率相关理论rate dependent theorem载荷因子load factor加载准则Loading criterion加载函数Loading function加载面Loading surface塑性加载Plastic loading塑性加载波Plastic loading wave 简单加载Simple loading比例加载Proportional loading 卸载Unloading卸载波Unloading wave冲击载荷Impulsive load阶跃载荷step load脉冲载荷pulse load极限载荷limit load中性变载nentral loading拉抻失稳instability in tension加速度波acceleration wave本构方程constitutive equation 完全解complete solution名义应力nominal stress过应力over-stress真应力true stress等效应力equivalent stress流动应力flow stress应力间断stress discontinuity应力空间stress space主应力空间principal stress space静水应力状态hydrostatic state of stress对数应变logarithmic strain工程应变engineering strain等效应变equivalent strain应变局部化strain localization应变率strain rate应变率敏感性strain rate sensitivity应变空间strain space有限应变finite strain塑性应变增量plastic strain increment累积塑性应变accumulated plastic strain永久变形permanent deformation内变量internal variable应变软化strain-softening理想刚塑性材料rigid-perfectly plastic Material 刚塑性材料rigid-plastic material理想塑性材料perfectl plastic material材料稳定性stability of material应变偏张量deviatoric tensor of strain应力偏张量deviatori tensor of stress应变球张量spherical tensor of strain应力球张量spherical tensor of stress路径相关性path-dependency线性强化linear strain-hardening应变强化strain-hardening随动强化kinematic hardening各向同性强化isotropic hardening强化模量strain-hardening modulus幂强化power hardening塑性极限弯矩plastic limit bending Moment塑性极限扭矩plastic limit torque弹塑性弯曲elastic-plastic bending弹塑性交界面elastic-plastic interface弹塑性扭转elastic-plastic torsion粘塑性Viscoplasticity非弹性Inelasticity理想弹塑性材料elastic-perfectly plastic Material 极限分析limit analysis极限设计limit design极限面limit surface上限定理upper bound theorem上屈服点upper yield point下限定理lower bound theorem下屈服点lower yield point界限定理bound theorem初始屈服面initial yield surface后继屈服面subsequent yield surface屈服面[的]外凸性convexity of yield surface 截面形状因子shape factor of cross-section 沙堆比拟sand heap analogy屈服Yield屈服条件yield condition屈服准则yield criterion屈服函数yield function屈服面yield surface塑性势plastic potential能量吸收装置energy absorbing device能量耗散率energy absorbing device塑性动力学dynamic plasticity塑性动力屈曲dynamic plastic buckling塑性动力响应dynamic plastic response塑性波plastic wave运动容许场kinematically admissible Field 静力容许场statically admissible Field流动法则flow rule速度间断velocity discontinuity滑移线slip-lines滑移线场slip-lines field移行塑性铰travelling plastic hinge塑性增量理论incremental theory of Plasticity米泽斯屈服准则Mises yield criterion普朗特——罗伊斯关系prandtl- Reuss relation特雷斯卡屈服准则Tresca yield criterion洛德应力参数Lode stress parameter莱维——米泽斯关系Levy-Mises relation亨基应力方程Hencky stress equation赫艾——韦斯特加德应力空间Haigh-Westergaard stress space 洛德应变参数Lode strain parameter德鲁克公设Drucker postulate盖林格速度方程Geiringer velocity Equation结构力学structural mechanics结构分析structural analysis结构动力学structural dynamics拱Arch三铰拱three-hinged arch抛物线拱parabolic arch圆拱circular arch穹顶Dome空间结构space structure空间桁架space truss雪载[荷] snow load风载[荷] wind load土压力earth pressure地震载荷earthquake loading弹簧支座spring support支座位移support displacement支座沉降support settlement超静定次数degree of indeterminacy机动分析kinematic analysis结点法method of joints截面法method of sections结点力joint forces共轭位移conjugate displacement影响线influence line三弯矩方程three-moment equation单位虚力unit virtual force刚度系数stiffness coefficient柔度系数flexibility coefficient力矩分配moment distribution力矩分配法moment distribution method力矩再分配moment redistribution分配系数distribution factor矩阵位移法matri displacement method单元刚度矩阵element stiffness matrix单元应变矩阵element strain matrix总体坐标global coordinates贝蒂定理Betti theorem高斯——若尔当消去法Gauss-Jordan elimination Method 屈曲模态buckling mode复合材料力学mechanics of composites复合材料composite material纤维复合材料fibrous composite单向复合材料unidirectional composite泡沫复合材料foamed composite颗粒复合材料particulate composite层板Laminate夹层板sandwich panel正交层板cross-ply laminate斜交层板angle-ply laminate层片Ply多胞固体cellular solid膨胀Expansion压实Debulk劣化Degradation脱层Delamination脱粘Debond纤维应力fiber stress层应力ply stress层应变ply strain层间应力interlaminar stress比强度specific strength强度折减系数strength reduction factor 强度应力比strength -stress ratio横向剪切模量transverse shear modulus 横观各向同性transverse isotropy正交各向异Orthotropy剪滞分析shear lag analysis短纤维chopped fiber长纤维continuous fiber纤维方向fiber direction纤维断裂fiber break纤维拔脱fiber pull-out纤维增强fiber reinforcement致密化Densification最小重量设计optimum weight design网格分析法netting analysis混合律rule of mixture失效准则failure criterion蔡——吴失效准则Tsai-W u failure criterion达格代尔模型Dugdale model断裂力学fracture mechanics概率断裂力学probabilistic fracture Mechanics格里菲思理论Griffith theory线弹性断裂力学linear elastic fracture mechanics, LEFM 弹塑性断裂力学elastic-plastic fracture mecha-nics, EPFM 断裂Fracture脆性断裂brittle fracture解理断裂cleavage fracture蠕变断裂creep fracture延性断裂ductile fracture晶间断裂inter-granular fracture准解理断裂quasi-cleavage fracture穿晶断裂trans-granular fracture裂纹Crack裂缝Flaw缺陷Defect割缝Slit微裂纹Microcrack折裂Kink椭圆裂纹elliptical crack深埋裂纹embedded crack[钱]币状裂纹penny-shape crack预制裂纹Precrack短裂纹short crack表面裂纹surface crack裂纹钝化crack blunting裂纹分叉crack branching裂纹闭合crack closure裂纹前缘crack front裂纹嘴crack mouth裂纹张开角crack opening angle,COA裂纹张开位移crack opening displacement, COD裂纹阻力crack resistance裂纹面crack surface裂纹尖端crack tip裂尖张角crack tip opening angle, CTOA裂尖张开位移crack tip opening displacement, CTOD 裂尖奇异场crack tip singularity Field裂纹扩展速率crack growth rate稳定裂纹扩展stable crack growth定常裂纹扩展steady crack growth亚临界裂纹扩展subcritical crack growth 裂纹[扩展]减速crack retardation止裂crack arrest止裂韧度arrest toughness断裂类型fracture mode滑开型sliding mode张开型opening mode撕开型tearing mode复合型mixed mode撕裂Tearing撕裂模量tearing modulus断裂准则fracture criterionJ积分J-integralJ阻力曲线J-resistance curve断裂韧度fracture toughness应力强度因子stress intensity factor HRR场Hutchinson-Rice-Rosengren Field 守恒积分conservation integral有效应力张量effective stress tensor应变能密度strain energy density能量释放率energy release rate内聚区cohesive zone塑性区plastic zone张拉区stretched zone热影响区heat affected zone, HAZ延脆转变温度brittle-ductile transition temperature剪切带shear band剪切唇shear lip无损检测non-destructive inspection双边缺口试件double edge notched specimen, DEN specimen单边缺口试件single edge notched specimen, SEN specimen三点弯曲试件three point bending specimen, TPB specimen中心裂纹拉伸试件center cracked tension specimen, CCT specimen 中心裂纹板试件center cracked panel specimen, CCP specimen紧凑拉伸试件compact tension specimen, CT specimen大范围屈服large scale yielding小范围攻屈服small scale yielding韦布尔分布Weibull distribution帕里斯公式paris formula空穴化Cavitation应力腐蚀stress corrosion概率风险判定probabilistic risk assessment, PRA 损伤力学damage mechanics损伤Damage连续介质损伤力学continuum damage mechanics 细观损伤力学microscopic damage mechanics 累积损伤accumulated damage脆性损伤brittle damage延性损伤ductile damage宏观损伤macroscopic damage细观损伤microscopic damage微观损伤microscopic damage损伤准则damage criterion损伤演化方程damage evolution equation损伤软化damage softening损伤强化damage strengthening损伤张量damage tensor损伤阈值damage threshold损伤变量damage variable损伤矢量damage vector损伤区damage zone疲劳Fatigue低周疲劳low cycle fatigue应力疲劳stress fatigue随机疲劳random fatigue 蠕变疲劳creep fatigue腐蚀疲劳corrosion fatigue 疲劳损伤fatigue damage 疲劳失效fatigue failure疲劳断裂fatigue fracture 疲劳裂纹fatigue crack疲劳寿命fatigue life疲劳破坏fatigue rupture疲劳强度fatigue strength 疲劳辉纹fatigue striations 疲劳阈值fatigue threshold 交变载荷alternating load 交变应力alternating stress 应力幅值stress amplitude 应变疲劳strain fatigue应力循环stress cycle应力比stress ratio安全寿命safe life过载效应overloading effect 循环硬化cyclic hardening循环软化cyclic softening环境效应environmental effect裂纹片crack gage裂纹扩展crack growth, crack Propagation 裂纹萌生crack initiation循环比cycle ratio实验应力分析experimental stress Analysis 工作[应变]片active[strain] gage基底材料backing material应力计stress gage零[点]飘移zero shift, zero drift应变测量strain measurement应变计strain gage应变指示器strain indicator应变花strain rosette应变灵敏度strain sensitivity机械式应变仪mechanical strain gage直角应变花rectangular rosette引伸仪Extensometer应变遥测telemetering of strain横向灵敏系数transverse gage factor横向灵敏度transverse sensitivity焊接式应变计weldable strain gage平衡电桥balanced bridge粘贴式应变计bonded strain gage粘贴箔式应变计bonded foiled gage粘贴丝式应变计bonded wire gage桥路平衡bridge balancing电容应变计capacitance strain gage补偿片compensation technique补偿技术compensation technique基准电桥reference bridge电阻应变计resistance strain gage温度自补偿应变计self-temperature compensating gage 半导体应变计semiconductor strain Gage集流器slip ring应变放大镜strain amplifier疲劳寿命计fatigue life gage电感应变计inductance [strain] gage光[测]力学Photomechanics光弹性Photoelasticity光塑性Photoplasticity杨氏条纹Young fringe双折射效应birefrigent effect等位移线contour of equal Displacement暗条纹dark fringe条纹倍增fringe multiplication干涉条纹interference fringe等差线Isochromatic等倾线Isoclinic等和线isopachic应力光学定律stress- optic law主应力迹线Isostatic亮条纹light fringe光程差optical path difference热光弹性photo-thermo -elasticity光弹性贴片法photoelastic coating Method 光弹性夹片法photoelastic sandwich Method 动态光弹性dynamic photo-elasticity空间滤波spatial filtering空间频率spatial frequency起偏镜Polarizer反射式光弹性仪reflection polariscope残余双折射效应residual birefringent Effect 应变条纹值strain fringe value应变光学灵敏度strain-optic sensitivity应力冻结效应stress freezing effect应力条纹值stress fringe value应力光图stress-optic pattern暂时双折射效应temporary birefringent Effect脉冲全息法pulsed holography透射式光弹性仪transmission polariscope实时全息干涉法real-time holographic interferometry网格法grid method全息光弹性法holo-photoelasticity全息图Hologram全息照相Holograph全息干涉法holographic interferometry全息云纹法holographic moire technique全息术Holography全场分析法whole-field analysis散斑干涉法speckle interferometry散斑Speckle错位散斑干涉法speckle-shearing interferometry, shearography 散斑图Specklegram白光散斑法white-light speckle method云纹干涉法moire interferometry[叠栅]云纹moire fringe[叠栅]云纹法moire method云纹图moire pattern离面云纹法off-plane moire method参考栅reference grating试件栅specimen grating分析栅analyzer grating面内云纹法in-plane moire method脆性涂层法brittle-coating method条带法strip coating method坐标变换transformation of Coordinates计算结构力学computational structural mechanics 加权残量法weighted residual method有限差分法finite difference method有限[单]元法finite element method配点法point collocation里茨法Ritz method广义变分原理generalized variational Principle最小二乘法least square method胡[海昌]一鹫津原理Hu-Washizu principle赫林格-赖斯纳原理Hellinger-Reissner Principle修正变分原理modified variational Principle约束变分原理constrained variational Principle混合法mixed method杂交法hybrid method边界解法boundary solution method有限条法finite strip method半解析法semi-analytical method协调元conforming element非协调元non-conforming element混合元mixed element杂交元hybrid element边界元boundary element强迫边界条件forced boundary condition 自然边界条件natural boundary condition 离散化Discretization离散系统discrete system连续问题continuous problem广义位移generalized displacement广义载荷generalized load广义应变generalized strain广义应力generalized stress界面变量interface variable节点node, nodal point[单]元Element角节点corner node边节点mid-side node内节点internal node无节点变量nodeless variable杆元bar element桁架杆元truss element梁元beam element二维元two-dimensional element 一维元one-dimensional element 三维元three-dimensional element 轴对称元axisymmetric element 板元plate element壳元shell element厚板元thick plate element三角形元triangular element四边形元quadrilateral element四面体元tetrahedral element曲线元curved element二次元quadratic element线性元linear element三次元cubic element四次元quartic element等参[数]元isoparametric element超参数元super-parametric element亚参数元sub-parametric element节点数可变元variable-number-node element 拉格朗日元Lagrange element拉格朗日族Lagrange family巧凑边点元serendipity element巧凑边点族serendipity family无限元infinite element单元分析element analysis单元特性element characteristics刚度矩阵stiffness matrix几何矩阵geometric matrix等效节点力equivalent nodal force节点位移nodal displacement节点载荷nodal load位移矢量displacement vector载荷矢量load vector质量矩阵mass matrix集总质量矩阵lumped mass matrix相容质量矩阵consistent mass matrix阻尼矩阵damping matrix瑞利阻尼Rayleigh damping刚度矩阵的组集assembly of stiffness Matrices 载荷矢量的组集consistent mass matrix质量矩阵的组集assembly of mass matrices单元的组集assembly of elements局部坐标系local coordinate system局部坐标local coordinate面积坐标area coordinates体积坐标volume coordinates曲线坐标curvilinear coordinates静凝聚static condensation合同变换contragradient transformation形状函数shape function试探函数trial function检验函数test function权函数weight function样条函数spline function代用函数substitute function降阶积分reduced integration零能模式zero-energy modeP收敛p-convergenceH收敛h-convergence掺混插值blended interpolation等参数映射isoparametric mapping双线性插值bilinear interpolation小块检验patch test非协调模式incompatible mode节点号node number单元号element number带宽band width带状矩阵banded matrix变带状矩阵profile matrix带宽最小化minimization of band width 波前法frontal method子空间迭代法subspace iteration method 行列式搜索法determinant search method 逐步法step-by-step method纽马克法Newmark威尔逊法Wilson拟牛顿法quasi-Newton method牛顿-拉弗森法Newton-Raphson method 增量法incremental method初应变initial strain初应力initial stress切线刚度矩阵tangent stiffness matrix割线刚度矩阵secant stiffness matrix模态叠加法mode superposition method平衡迭代equilibrium iteration子结构Substructure子结构法substructure technique超单元super-element网格生成mesh generation结构分析程序structural analysis program 前处理pre-processing后处理post-processing网格细化mesh refinement应力光顺stress smoothing组合结构composite structure流体动力学fluid dynamics连续介质力学mechanics of continuous media 介质medium流体质点fluid particle无粘性流体nonviscous fluid, inviscid fluid连续介质假设continuous medium hypothesis 流体运动学fluid kinematics水静力学hydrostatics液体静力学hydrostatics支配方程governing equation伯努利方程Bernoulli equation伯努利定理Bernonlli theorem毕奥-萨伐尔定律Biot-Savart law欧拉方程Euler equation亥姆霍兹定理Helmholtz theorem开尔文定理Kelvin theorem涡片vortex sheet库塔-茹可夫斯基条件Kutta-Zhoukowski condition 布拉休斯解Blasius solution达朗贝尔佯廖d&;am #39;Alembert paradox雷诺数Reynolds number施特鲁哈尔数Strouhal number随体导数material derivative不可压缩流体incompre ible fluid质量守恒co ervation of ma动量守恒co ervation of momentum能量守恒co ervation of energy动量方程momentum equation能量方程energy equation控制体积control volume液体静压hydrostatic pre ure 涡量拟能e trophy压差differential pre ure流[动] flow流线stream line流面stream surface流管stream tube迹线path, path line流场flow field流态flow regime流动参量flow parameter流量flow rate, flow discharge 涡旋vortex涡量vorticity涡丝vortex filament涡线vortex line涡面vortex surface涡层vortex layer涡环vortex ring涡对vortex pair涡管vortex tube涡街vortex street卡门涡街Karman vortex street 马蹄涡horseshoe vortex对流涡胞convective cell卷筒涡胞roll cell涡eddy涡粘性eddy viscosity环流circulation环量circulation速度环量velocity circulation偶极子doublet, dipole驻点stagnation point总压[力] total pre ure总压头total head静压头static head总焓total enthalpy能量输运energy tra ort速度剖面velocity profile库埃特流Couette flow单相流single phase flow单组份流single-component flow 均匀流uniform flow非均匀流nonuniform flow二维流two-dime ional flow三维流three-dime ional flow准定常流quasi-steady flow非定常流u teady flow, non-steady flow 暂态流tra ient flow周期流periodic flow振荡流oscillatory flow分层流stratified flow无旋流irrotational flow有旋流rotational flow轴对称流axisymmetric flow不可压缩性incompre ibility不可压缩流[动] incompre ible flow浮体floating body定倾中心metacenter阻力drag, resistance减阻drag reduction表面力surface force表面张力surface te ion毛细[管]作用capillarity来流incoming flow自由流free stream自由流线free stream line外流external flow进口entrance, inlet出口exit, outlet扰动disturbance, perturbation分布distribution传播propagation色散di ersion弥散di ersion附加质量added ma ,a ociated ma 收缩contraction镜象法image method无量纲参数dime ionle parameter 几何相似geometric similarity运动相似kinematic similarity动力相似[性] dynamic similarity平面流plane flow势potential势流potential flow速度势velocity potential复势complex potential复速度complex velocity流函数stream function源source汇sink速度[水]头velocity head拐角流corner flow空泡流cavity flow超空泡supercavity超空泡流supercavity flow空气动力学aerodynamics低速空气动力学low- eed aerodynamics 高速空气动力学high- eed aerodynamics 气动热力学aerothermodynamics亚声速流[动] su onic flow跨声速流[动] tra onic flow超声速流[动] supersonic flow锥形流conical flow楔流wedge flow叶栅流cascade flow非平衡流[动] non-equilibrium flow细长体slender body细长度slenderne钝头体bluff body钝体blunt body翼型airfoil翼弦chord薄翼理论thin-airfoil theory构型configuration后缘trailing edge迎角angle of attack失速stall脱体激波detached shock wave波阻wave drag诱导阻力induced drag诱导速度induced velocity临界雷诺数critical Reynolds number 前缘涡leading edge vortex附着涡bound vortex约束涡confined vortex气动中心aerodynamic center气动力aerodynamic force气动噪声aerodynamic noise气动加热aerodynamic heating离解di ociation地面效应ground effect气体动力学gas dynamics稀疏波rarefaction wave热状态方程thermal equation of state喷管Nozzle普朗特-迈耶流Prandtl-Meyer flow瑞利流Rayleigh flow可压缩流[动] compre ible flow可压缩流体compre ible fluid绝热流adiabatic flow非绝热流diabatic flow未扰动流undisturbed flow等熵流isentropic flow匀熵流homoentropic flow兰金-于戈尼奥条件Rankine-Hugoniot condition 状态方程equation of state量热状态方程caloric equation of state完全气体perfect gas拉瓦尔喷管Laval nozzle马赫角Mach angle马赫锥Mach cone马赫线Mach line马赫数Mach number马赫波Mach wave当地马赫数local Mach number 冲击波shock wave激波shock wave正激波normal shock wave斜激波oblique shock wave头波bow wave附体激波attached shock wave 激波阵面shock front激波层shock layer压缩波compre ion wave反射reflection折射refraction散射scattering衍射diffraction绕射diffraction出口压力exit pre ure超压[强] over pre ure反压back pre ure爆炸explosion爆轰detonation缓燃deflagration水动力学hydrodynamics液体动力学hydrodynamics 泰勒不稳定性T aylor i tability 盖斯特纳波Gerstner wave斯托克斯波Stokes wave瑞利数Rayleigh number自由面free surface波速wave eed, wave velocity 波高wave height波列wave train波群wave group波能wave energy表面波surface wave表面张力波capillary wave规则波regular wave不规则波irregular wave浅水波shallow water wave 深水波deep water wave重力波gravity wave椭圆余弦波cnoidal wave潮波tidal wave涌波surge wave破碎波breaking wave船波ship wave非线性波nonlinear wave孤立子soliton水动[力]噪声hydrodynamic noise水击water hammer空化cavitation空化数cavitation number空蚀cavitation damage超空化流supercavitating flow水翼hydrofoil水力学hydraulics洪水波flood wave涟漪ri le消能energy di ipation海洋水动力学marine hydrodynamics 谢齐公式Chezy formula欧拉数Euler number弗劳德数Froude number水力半径hydraulic radius水力坡度hvdraulic slope高度水头elevating head水头损失head lo水位water level水跃hydraulic jump含水层aquifer排水drainage排放量discharge壅水曲线back water curve压[强水]头pre ure head过水断面flow cro -section明槽流open cha el flow孔流orifice flow无压流free surface flow有压流pre ure flow缓流subcritical flow急流supercritical flow渐变流gradually varied flow急变流rapidly varied flow临界流critical flow异重流de ity current, gravity flow 堰流weir flow掺气流aerated flow含沙流sediment-laden stream降水曲线dropdown curve沉积物sediment, deposit沉[降堆]积sedimentation, deposition沉降速度settling velocity流动稳定性flow stability不稳定性i tability奥尔-索末菲方程Orr-Sommerfeld equation 涡量方程vorticity equation泊肃叶流Poiseuille flow奥辛流Oseen flow剪切流shear flow粘性流[动] viscous flow层流laminar flow分离流separated flow二次流secondary flow近场流near field flow远场流far field flow滞止流stagnation flow尾流wake [flow]回流back flow反流reverse flow射流jet自由射流free jet管流pipe flow, tube flow内流internal flow拟序结构coherent structure 猝发过程bursting proce表观粘度a arent viscosity运动粘性kinematic viscosity 动力粘性dynamic viscosity 泊poise厘泊centipoise厘沱centistoke剪切层shear layer次层sublayer流动分离flow separation层流分离laminar separation 湍流分离turbulent separation 分离点separation point附着点attachment point再附reattachment再层流化relaminarization起动涡starting vortex驻涡standing vortex涡旋破碎vortex breakdown涡旋脱落vortex shedding压[力]降pre ure drop压差阻力pre ure drag压力能pre ure energy型阻profile drag滑移速度slip velocity无滑移条件non-slip condition壁剪应力skin friction, frictional drag壁剪切速度friction velocity磨擦损失friction lo磨擦因子friction factor耗散di ipation滞后lag相似性解similar solution局域相似local similarity气体润滑gas lubrication液体动力润滑hydrodynamic lubrication 浆体slurry泰勒数Taylor number纳维-斯托克斯方程Navier-Stokes equation 牛顿流体Newtonian fluid边界层理论boundary later theory边界层方程boundary layer equation 边界层boundary layer附面层boundary layer层流边界层laminar boundary layer 湍流边界层turbulent boundary layer 温度边界层thermal boundary layer 边界层转捩boundary layer tra ition 边界层分离boundary layer separation 边界层厚度boundary layer thickne位移厚度di lacement thickne动量厚度momentum thickne能量厚度energy thickne焓厚度enthalpy thickne注入injection吸出suction泰勒涡Taylor vortex速度亏损律velocity defect law形状因子shape factor测速法anemometry粘度测定法visco[si] metry流动显示flow visualization油烟显示oil smoke visualization孔板流量计orifice meter频率响应frequency re o e油膜显示oil film visualization阴影法shadow method纹影法schlieren method烟丝法smoke wire method丝线法tuft method氢泡法nydrogen bu le method相似理论similarity theory相似律similarity law部分相似partial similarity定理pi theorem, Buckingham theorem 静[态]校准static calibration动态校准dynamic calibration风洞wind tu el激波管shock tube激波管风洞shock tube wind tu el水洞water tu el拖曳水池towing tank旋臂水池rotating arm basin扩散段diffuser测压孔pre ure tap皮托管pitot tube普雷斯顿管preston tube斯坦顿管Stanton tube文丘里管Venturi tubeU形管U-tube压强计manometer微压计micromanometer多管压强计multiple manometer静压管static [pre ure]tube流速计anemometer风速管Pitot- static tube激光多普勒测速计laser Do ler anemometer, laser Do ler velocimeter 热线流速计hot-wire anemometer热膜流速计hot- film anemometer流量计flow meter粘度计visco[si] meter涡量计vorticity meter传感器tra ducer, se or压强传感器pre ure tra ducer热敏电阻thermistor示踪物tracer时间线time line脉线streak line尺度效应scale effect壁效应wall effect堵塞blockage堵寒效应blockage effect动态响应dynamic re o e响应频率re o e frequency底压base pre ure菲克定律Fick law巴塞特力Ba et force埃克特数Eckert number格拉斯霍夫数Grashof number努塞特数Nu elt number普朗特数prandtl number雷诺比拟Reynolds analogy施密特数schmidt number斯坦顿数Stanton number对流convection自由对流natural convection, free convec-tion 强迫对流forced convection热对流heat convection质量传递ma tra fer传质系数ma tra fer coefficient 热量传递heat tra fer传热系数heat tra fer coefficient 对流传热convective heat tra fer 辐射传热radiative heat tra fer 动量交换momentum tra fer能量传递energy tra fer传导conduction热传导conductive heat tra fer 热交换heat exchange临界热通量critical heat flux浓度concentration扩散diffusion扩散性diffusivity扩散率diffusivity扩散速度diffusion velocity分子扩散molecular diffusion 沸腾boiling蒸发evaporation气化gasification凝结conde ation。
南开大学光学工程专业英语重点词汇汇总
光学专业英语部分refraction [rɪˈfrækʃn]n.衍射reflection [rɪˈflekʃn]n.反射monolayer['mɒnəleɪə]n.单层adj.单层的ellipsoid[ɪ'lɪpsɒɪd]n.椭圆体anisotropic[,ænaɪsə(ʊ)'trɒpɪk]adj.非均质的opaque[ə(ʊ)'peɪk]adj.不透明的；不传热的；迟钝的asymmetric[,æsɪ'metrɪk]adj.不对称的；非对称的intrinsic[ɪn'trɪnsɪk]adj.本质的，固有的homogeneous[,hɒmə(ʊ)'dʒiːnɪəs;-'dʒen-] adj.均匀的；齐次的；同种的；同类的，同质的incidentlight入射光permittivity[,pɜːmɪ'tɪvɪtɪ]n.电容率symmetric[sɪ'metrɪk]adj.对称的；匀称的emergentlight出射光；应急灯.ultrafast[,ʌltrə'fɑ:st,-'fæst]adj.超快的；超速的uniaxial[,juːnɪ'æksɪəl]adj.单轴的paraxial[pə'ræksɪəl]adj.旁轴的；近轴的periodicity[,pɪərɪə'dɪsɪtɪ]n.[数]周期性；频率；定期性soliton['sɔlitɔn]n.孤子，光孤子；孤立子；孤波discrete[dɪ'skriːt]adj.离散的，不连续的convolution[,kɒnvə'luːʃ(ə)n]n.卷积；回旋；盘旋；卷绕spontaneously:[spɒn'teɪnɪəslɪ] adv.自发地；自然地；不由自主地instantaneously:[,instən'teinjəsli]adv.即刻；突如其来地dielectricconstant[ˌdaiiˈlektrikˈkɔnstənt]介电常数，电容率chromatic[krə'mætɪk]adj.彩色的；色品的；易染色的aperture['æpətʃə;-tj(ʊ)ə]n.孔，穴；（照相机，望远镜等的）光圈，孔径；缝隙birefringence[,baɪrɪ'frɪndʒəns]n.[光]双折射radiant['reɪdɪənt]adj.辐射的；容光焕发的；光芒四射的; photomultiplier[,fəʊtəʊ'mʌltɪplaɪə]n.[电子]光电倍增管prism['prɪz(ə)m]n.棱镜；[晶体][数]棱柱theorem['θɪərəm]n.[数]定理；原理convex['kɒnveks]n.凸面体；凸状concave['kɒnkeɪv]n.凹面spin[spɪn]n.旋转；crystal['krɪst(ə)l]n.结晶，晶体；biconical[bai'kɔnik,bai'kɔnikəl] adj.双锥形的illumination[ɪ,ljuːmɪ'neɪʃən] n.照明；[光]照度；approximate[ə'prɒksɪmət] adj.[数]近似的；大概的clockwise['klɒkwaɪz]adj.顺时针方向的exponent[ɪk'spəʊnənt；ek-] n.[数]指数；even['iːv(ə)n]adj.[数]偶数的；平坦的；相等的eigenmoden.固有模式；eigenvalue['aɪgən,væljuː]n.[数]特征值cavity['kævɪtɪ]n.腔；洞，凹处groove[gruːv]n.[建]凹槽，槽；最佳状态；惯例；reciprocal[rɪ'sɪprək(ə)l]adj.互惠的；相互的；倒数的，彼此相反的essential[ɪ'senʃ(ə)l]adj.基本的；必要的；本质的；精华的isotropic[,aɪsə'trɑpɪk]adj,各向同性的；等方性的phonon['fəʊnɒn]n.[声]声子cone[kəʊn]n.圆锥体，圆锥形counter['kaʊntə]n.柜台；对立面；计数器；cutoff['kʌt,ɔːf]n.切掉；中断；捷径adj.截止的；中断的cladding['klædɪŋ]n.包层；interference[ɪntə'fɪər(ə)ns]n.干扰，冲突；干涉borderline['bɔːdəlaɪn]n.边界线，边界；界线quartz[kwɔːts]n.石英droplet['drɒplɪt]n.小滴，微滴precision[prɪ'sɪʒ(ə)n]n.精度，[数]精密度；精确inherently[ɪnˈhɪərəntlɪ]adv.内在地；固有地；holographic[,hɒlə'ɡræfɪk]adj.全息的；magnitude['mægnɪtjuːd]n.大小；量级；reciprocal[rɪ'sɪprək(ə)l]adj.互惠的；相互的；倒数的，彼此相反的stimulated['stimjə,letid]v.刺激（stimulate的过去式和过去分词）cylindrical[sɪ'lɪndrɪkəl]adj.圆柱形的；圆柱体的coordinates[kəu'ɔ:dineits]n.[数]坐标；external[ɪk'stɜːn(ə)l;ek-]n.外部；外观；scalar['skeɪlə]n.[数]标量；discretization[dɪs'kriːtaɪ'zeɪʃən]n.[数]离散化synthesize['sɪnθəsaɪz]vt.合成；综合isotropy[aɪ'sɑtrəpi]n.[物]各向同性；[物]无向性；[矿业]均质性pixel['pɪks(ə)l;-sel]n.（显示器或电视机图象的）像素（passive['pæsɪv]adj.被动的spiral['spaɪr(ə)l]n.螺旋；旋涡；equivalent[ɪ'kwɪv(ə)l(ə)nt]adj.等价的，相等的；同意义的; transverse[trænz'vɜːs;trɑːnz-;-ns-]adj.横向的；横断的；贯轴的;dielectric[,daɪɪ'lektrɪk]adj.非传导性的；诱电性的;n.电介质；绝缘体integral[ˈɪntɪɡrəl]adj.积分的；完整的criteria[kraɪ'tɪərɪə]n.标准，条件（criterion的复数）Dispersion:分散|光的色散spectroscopy[spek'trɒskəpɪ]n.[光]光谱学photovoltaic[,fəʊtəʊvɒl'teɪɪk]adj.[电子]光电伏打的，光电的polar['pəʊlə]adj.极地的；两极的；正好相反的transmittance[trænz'mɪt(ə)ns;trɑːnz-;-ns-] n.[光]透射比；透明度dichroic[daɪ'krəʊɪk]adj.二色性的；两向色性的confocal[kɒn'fəʊk(ə)l]adj.[数]共焦的；同焦点的rotation[rə(ʊ)'teɪʃ(ə)n]n.旋转；循环，轮流photoacoustic[,fəutəuə'ku:stik]adj.光声的exponential[,ekspə'nenʃ(ə)l]adj.指数的;fermion['fɜːmɪɒn]n.费密子（费密系统的粒子）semiconductor[,semɪkən'dʌktə]n.[电子][物]半导体calibration[kælɪ'breɪʃ(ə)n]n.校准；刻度；标度photodetector['fəʊtəʊdɪ,tektə]n.[电子]光电探测器interferometer[,ɪntəfə'rɒmɪtə]n.[光]干涉仪；干涉计static['stætɪk]adj.静态的；静电的；静力的;inverse相反的，反向的，逆的amplified['æmplifai]adj.放大的；扩充的horizontal[hɒrɪ'zɒnt(ə)l]n.水平线，水平面；水平位置longitudinal[,lɒn(d)ʒɪ'tjuːdɪn(ə)l;,lɒŋgɪ-] adj.长度的，纵向的；propagate['prɒpəgeɪt]vt.传播；传送；wavefront['weivfrʌnt]n.波前；波阵面scattering['skætərɪŋ]n.散射；分散telecommunication[,telɪkəmjuːnɪ'keɪʃ(ə)n] n.电讯；[通信]远程通信quantum['kwɒntəm]n.量子论mid-infrared中红外eigenvector['aɪgən,vektə]n.[数]特征向量；本征矢量numerical[njuː'merɪk(ə)l]adj.数值的；数字的ultraviolet[ʌltrə'vaɪələt]adj.紫外的；紫外线的harmonic[hɑː'mɒnɪk]n.[物]谐波。
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a rXiv:as tr o-ph/5302v42J un2RELATIVISTIC CONIC BEAMS AND SPATIAL DISTRIBUTION OF GAMMA-RAY BURSTS Heon-Young Chang and Insu Yi Korea Institute For Advanced Study,Seoul,130-012,Korea hyc@kias.re.kr,iyi@kias.re.kr ReceivedABSTRACTWe study the statistics of gamma-ray bursts,assuming that gamma-ray bursts are cosmological and they are beamed in the form of a conical jet with a large bulk Lorentz factor∼100.In such a conic beam,the relativistic ejecta may have a spatial variation in the bulk Lorentz factor and the density distribution of gamma-ray emitting jet material.An apparent luminosity function arises be-cause the axis of the cone is randomly oriented with respect to the observer’s line of sight.The width and the shape of the luminosity function are determined by the ratio of the beam opening angle of the conical jet to the inverse of the bulk Lorentz factor,when the bulk Lorentz factor and the jet material density is uniform on the photon emitting jet surface.We calculate effects of spatial variation of the Lorentz factor and the spatial densityfluctuations within the cone on the luminosity function and the statistics of gamma-ray bursts.In par-ticular,we focus on the redshift distribution of the observed gamma-ray bursts. The maximum distance to and the average redshift of the gamma-ray bursts are strongly affected by the beaming-induced luminosity function.The bursts with the angle-dependent Lorentz factor which peaks at the center of the cone have substantially higher average gamma-ray burst redshifts.When both the jet ma-terial density and the Lorentz factor are inhomogeneous in the conical beam, the average redshift of the bursts could be5times higher than that of the case in which relativistic jet is completely homogeneous and structureless.Even the simplest models for the gamma-ray burst jets and their apparent luminosity dis-tributions have a significant effect on the redshift distribution of the gamma-ray bursts.Subject headings:gamma rays:bursts1.INTRODUCTIONThe BATSE experiment on the Compton Gamma Ray Observatory and the studyof the afterglows(e.g.,Piran1999and references therein).have established that the gamma-ray bursts(GRBs)are cosmological(Mao and Paczy´n ski1992;Meegan et al. 1992;Piran1992).Even though the distance scale seems settled(Metzger et al.1997),it appears that uncertainties remain in the total energy and the burst rate of GRBs(Kumar 1999;Kumar and Piran1999).These two important issues depend on the level of beaming in GRB emission.That is,the issues critically depend on whether the geometry of the gamma-ray emitting ejecta is spherical or jet-like(Harrison et al.1999;Kulkarni et al.1999; M´e sz´a ros and Rees1999;Sari et al.1999).A number of authors have studied energetics and geometry of the ejecta(Mao and Yi1994;Rhoads1997;Panaitescu and M´e sz´a ros 1998;Rhoads1999;Moderski et al.2000).It is also important to put constraints on the width of the luminosity function by comparing the observed intensity distribution with those predicted by a physical model(Mao and Yi1994;Yi1994).In essence,the rate,the energy,and the luminosity function of GRBs are all closely related to whether or not the geometry of the ejecta is spherical.Two most frequently quoted statistics in GRB observations are<V/V max>and log N(>F)−log F,where F refers to the peakflux(or peak count rate)and N denotes the number of GRBs withfluxes higher than F(e.g.,Yi1994).These two quantities contain information on the lumonosity function of GRBs and the spatial number density of the sources.A value of<V/V max>consistent with that of an observed sample is a necessary condition but not a sufficient condition for a luminosity functionΦ(L)which is neither directly observable nor theoretically well undertood.The luminosity function of GRBs can be obtained for an assumed source distribution n(z)such that the calculated log N(>F)−log Ffits the observed distribution,and vice versa.The density n(z)refersto the rate of GRBs per unit time per unit comoving cosmological volume.However,due to the very nature of N(>F),which is the convolution of n(z)andΦ(L),one almost always obtains n(z)for a givenΦ(L)such that the theoretical log N(>F)−log F curvefits the observed intensity distribution.Therefore,in order to extract information concerning n(z) orΦ(L),one has to assume one of these two functions or to develop a techinique to separate the effects of these two unknown functions(Horack and Emslie1994;Horack et al.1994; Ulmer et al.1995;Ulmer and Wijers1995).It is therefore of great interest to construct Φ(L)on the basis of a physical model,which is one of our major goals in this Letter.Since there remain uncertainties in GRB engine models,we focus on the consequences of the conical beaming without specifying how a beam is formed in a physical engine model.Using thefirst BATSE catalog of gamma-ray bursts(Fishman et al.1994),Mao and Yi (1994)studied the effects of the relativistic bulk motion in a conical beam on the statistics of gamma-ray bursts.They found that the luminosity function is naturally introduced by the random distribution of the space orientation of the cone axis and that the case of the standard candle is not easily distinguished from that of the beaming-induced luminosity function with a sharp peak.This is especially the case for large beam opening angle and the large Lorentz factorγ,as one may expect.Different Lorentz factors and opening angles however result in non-trivial changes for the distances to GRBs and especially the highest redshift of or the maximum distance to the most distant GRB for a given sample.For instance,the maximum redshift z max increases as the ratio of the opening angle toγ−1 decreases.We modify the conical beam model by allowing a spatial variation ofγand the density profile of gamma-ray emitting electrons on the photon-emitting surface of the cone.From numerical simulations of relativistic jets(Marti et al.1997;Renaud and Henri 1998;Rosen et al.1999)and observations of the astrophysical jets(Zensus1997;Spruit 2000),it is clear that jets do have some significant structure in them and the bulk Lorentzfactors evolve as the jets propagate.Therefore,it is plausible to extend the simplest jet model such as that of Mao and Yi(1994).In a more realistic jet model,the bulk Lorentz factor has a spatial profile at the surface where the observed gamma-ray emission occurs and the spatial electron density distribution is significantly inhomogeneous.In§2we begin with a brief presention of data we use,which are parts of the BATSE 4B catalog(Paciesas et al.1999),and we describe our conical jet geometry,following Mao and Yi(1994),in§3we present results.Finally,we conclude with summary of our results and discussions in§4.2.OBSERVATIONAL DATA AND MODELThe BATSE4B catalog(Paciesas et al.1999)provides1637triggered GRBs detected from1991April through1996August.We use the bursts which are detected on the1024 ms trigger time scale.We choose the bursts of which peak count rates are above0.4 photons cm−2s−1in order to avoid the threshold effects(cf.Mao and Yi1994).Of those bursts,we select the GRBs whose C max/C min is greater than1.0,which gives a sample of 651bursts.The energy range in which the peakflux is measured is50−300keV.The peak fluxes of bursts vary by about2orders of magnitude in this data set.Throughout this Letter we adopt the simplest cosmological model;the universe isflat with the density parameterΩ0=1,the Hubble constant is65kms−1Mpc−1,the cosmological constant is absent,all the GRBs are’standard bursts’with an identical power-law spectrum,and the rate of bursts per unit comoving volume per unit comoving time is constant(cf.Mao and Paczy´n ski1992;Yi1994).In our beaming model,the ejecta isflowing outward relativistically in a cone with the geometrical opening angle∆θ.The observed gamma-ray emission is produced at radius Rfrom the central engine where the radiationfirst becomes optically thin.In the minimal beaming model of Mao and Yi(1994),the ejected material has the same bulk Lorentz factor γat this distance and the photon-emitting electrons’density at the surface of the cone is uniform.In this Letter those simplifications are relaxed as described below.In the cylindrical symmetry one may consider the colatitude alone,which is defined by the angle between the line of sight and the symmetry axis of the cone.Besides the spherical coordinate system centered on the central engine,we introduce an auxiliary spherical coordinate system with the z′-axis along the symmetry axis of the cone.It can be shown that the angleΘbetween a position of a direction within the cone and the line of sight is given bycosΘ=cosθ′cosθ−sinθ′sinφ′sinθ.(1)The monochromaticflux received by a local observer at a distance D from the source, taking the cosmological redshift effects into account,reads(1+z)R2F(ν,θ)=× ∆θsin θ′cos ΘΓ2+αdθ′.(3)The maximum local peak count rate is achieved at θ=0and can be obtained analytically :P loc,max (θ=0)= ν1−αdν2πR 2α(x αu −x αl )−12sin θdθ,(5)where θis between 0and π.Since the local peak count rate is a function of the orientation of the cone,one may translate the probability function of the cone’s angle into the probability function of the local peak count rate.In order to obtain the luminosity function and compare with observations,we calculate the local peak count rate in a fixed frequency range.We allow variations of γand the electron density at the surface of the cone by introducing a window function for γand electron density,N e .The window function is axisymmetric with respect to the symmetry axis of the cone.The window function we adopt is the Gaussian function centered at the center of the cone:W (θ′)=exp[−A (θ′3.RESULTSThe probability function of the local peak count rate is shown in Figure1for three different ratios of∆θtoγ−1,in the case whereγis uniform over the photon-emitting surface of the cone.For afixedγ,as the opening angle increases the peak of the probability of the local peak count rate becomes higher and narrower,as one may expect.A model with a large value of Lorentz factor(∆θ≫γ−1)essentially provides a luminosity function indistinguishable from that of the standard candle model.For a given value of the ratio, the whole distribution function moves vertically when the absolute value of the Lorentz factor changes.This is because the local peak count rate is decreasing faster with the angle for largerγ.In the extreme case where∆θ≪γ−1the distribution is a power law with the index of−1/3,as expected from the analytical result(Yi1993).In Figure2,we show the probability distribution functions for both the varying bulk Lorentz factor and the inhomogeneous electron density.We assume the axisymmetry of the Lorentz factor profile around the cone axis,γ=γ(θ′),and hence the Lorentz factor profile could mimic a simplified model for the jet-environment drag.At the center of the cone,γhas the maximum value and decreases withθ′.Asγdecreases more steeply withθ′,the log p L(log P loc)shows a smaller peak at log(P loc/P loc,max)=0,and a higher level of the’tail’of the log p L(log P loc).It is because this type ofγeffectively reduces the’average’value of γover the cone and the’effective opening angle’simultaneously.For a very narrow window function it essentially reduces to the pencil-beam case.The photon-emitting electrons are supposed to be distributed according to theγdistribution such that the local electron number density is inversely proportional to the square of the bulk Lorentz factor,γ.That is,the electron number density is a function of the angular position in the cone.In this profile,the electron number density increases outwards from the center of the cone,sinceγis a decreasing function.In effect,the cone is reminiscent of the hollow cone.Once the probability distribution is obtained,we are in a position to calculatelog N(>F)−log F with an assumed spatial distribution of GRBs,n(z).In Figure3,we compare the cumulative intensity distribution curve produced by our luminosity function with observational data.Since the goal of this study is looking at effects of the conic beam with varying distributions ofγand the electron density over the surface of the cone,we assume there is no source evolution,that is,n(z)=n0.We adopt the power law indexαof unity instead of2(cf.Mao and Yi,1994).This is a simplification in a sense that observed GRBs show various power-law indices.This value,however,represents the averaged power law indices of observed GRBs(Band et al.1993;Mallozzi et al.1996;Preece et al.2000). All the theoretical cumulative probability distribution with the luminosity functions shown in Figure2are plotted in Figure3along with the observed distribution.The curves shown in Figure3are best-fit functions determined by the Kolmogorov-Smirnov(K-S)test for each parameter set.Parameters in our model are not sensitive enough to constrain the luminosity function.For a given set of model paramters,z max plays a role of a parameter in the K-S test in that the luminosity function studied here optimizes log N(>F)−log F tofit observational data.The obtained z max’s in this procedure are shown in the Table1.These z max’s obtained with the4B BATSE catalog are greater than those for the1B BATSE catalog by about0.1 on average,which indicates that we are seeing fainter GRBs in the4B BATSE than in the 1B BATSE catalog and therefore more distant GRBs.It shows that the redshift of the most distant GRBs becomes larger asγfalls more steeply from the cone center.As shown in the Table1,our toy models with the narrow Gaussian profiles could easily reproduce z max values as high as the highest reportedz max=3.42(quoted from Bulik(1999),see references therein).This simple case indicates that the effects of the luminosity function have significant implications on the cosmologicalspatial distribution of GRBs.It is interesting to see that such a high redshift would be hard to explain in the homogeneous beam model with a constant n(z).The effects of the Gaussian window on the values of z max are substantial enough for further comments.The model for a narrow window with A=4gives z max=3.7(average redshift<z>=1.03)while the uniform beam model(i.e.without any variation ofγ)gives z max=1.6(<z>=0.51).The average value of redshifts,<z>,is taken over the cumulative redshift distribution function shown in Figure4.The cumulative redshift distribution is defined byN(z′<z<z max)N(z′)=n(z)r2(z)dr(z).(8)1+zThe cumulative redshift distributions shown in Figure4also indicate that the luminosity distribution induced by the beaming has a significant implication on the GRBs distances in the observed samples.When the beam is sharply peaked at the beam center (solid curves in the upper panel in Figure4)the fraction of the high redshift GRBs(e.g. z>3)could be as high as∼10%while the broad beam case(e.g.A=1/8)essentially rules out any high redshift GRBs.The cumulative distribution slowly decreases with the redshift when theγin the conic beam is decreasing rapidly in a sense that GRBs are spead out in a broader region beyond the averaged z for the highly concentrated beam.That is,the ratio of z max to<z>is3.59and3.14when A=4and A=1/8,respectively.The beams’electron density structure also has a similar effect on the redshifts of GRBs.The effects of the luminosity function have to be explicitly considered when observed high redshift values are interpreted(Krumholz et al.1998).For instance,in the standard candle case, a significant probability for high redshift GRBs could directly imply a substantial source evolution effect.However,the beaming induced luminosity function could make this simple interpretation much uncertain(Blain and Natarajan2000).4.DISCUSSIONThe theoretical models for GRBs are abundant.Despite remarkable progresses in understanding physical mechanisms involved in these models,the GRB prompt emission mechanisms and engine models have so far been unable to constrain the extent of beaming and the luminosity distribution of GRBs.This in turn has been a major uncertainty in interpreting the observedflux data in terms of the cosmological spatial distribution of the bursts.In this regard,the present work has shown that the simple beaming models and their resulting apparent luminosity functions have significant effects in interpreting the observed data.If the GRBs are indeed standard candles with a single well-defined luminosity,the spatial distribution of GRBs in connection with the cosmic star formation rate could be translated into the cosmological source evolution.However,the luminosity distributions we have considered affect the maximum redshift and the average redshift significantly.It is therefore important to derive a theoretical luminosity function for a given GRB model.The jet models we adopted are obviously over-simplified.Despite this major drawback, the models capture the essential ingredients of the beamed relativistic jets concerning the apparent luminosity function.One of the major uncertainties is that the jets and GRB sources differ greatly and GRB luminosities and jets’physical conditions are intrinsically different in each source.Given the wide range of burst durations and the diverse burst types(Fishman and Meegan1995,and references therein),such a possibility cannot be ruled out.If this is indeed the case,our standard source approach is not applicable.We thank C.Kim,H.Kim,and K.Kwak for useful discussions and especially C.Kim for her help with Figure3.IY is supported in part by the KRF grant 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Note that for∆θ=0◦.1case,it is basically a power-law function with the index of−1/4.Fig. 2.—Plots similar to Fig. 1.In the upper panel,values ofγvaries over the surface of the cone.The window function adopted is the Gaussian,exp[−A(θ′Table1:The maximum redshifts of GRBs which allow the best-fit of models to observed data,and the averaged redshifts.The parameter A determines the sharpness of the window function.Parameters adopted in the calculation areα=1,γ0=100,and∆θ=1◦.0.A z max<z>constantγ0N/A 1.600.51411.23 2.362 3.470.98varyingγand N e1 2.200.671/2 1.850.581/8 1.600.51-1.5-1-0.50-6-4-2-1.5-1-0.50-4.5-4-3.5-3-2.5-1.5-1-0.50-4.5-4-3.5-3-2.50.511.50.20.40.60.812468100.20.40.60.81z’1230.20.40.60.81z’。