Gauge freedom for Gravitational Wave problems in tensor-scalar theories of gravity
Wavy Strings Black or Bright
McGill 96–44 WATPHYS-TH-96/17
Wavy Strings: Black or Bright?
arXiv:hep-th/9612248v1 30 Dec 1996
Nemanja Kaloper,a,1 Robert C. Myersb,2 and Harold Roussedevelopments in string theory have brought forth a considerable interest in time-dependent hair on extended objects. This novel new hair is typically characterized by a wave profile along the horizon and angular momentum quantum numbers l, m in the transverse space. In this work, we present an extensive treatment of such oscillating black objects, focusing on their geometric properties. We first give a theorem of purely geometric nature, stating that such wavy hair cannot be detected by any scalar invariant built out of the curvature and/or matter fields. However, we show that the tidal forces detected by an infalling observer diverge at the ‘horizon’ of a black string superposed with a vibration in any mode with l ≥ 1. The same argument applied to longitudinal (l = 0) waves detects only finite tidal forces. We also provide an example with a manifestly smooth metric, proving that at least a certain class of these longitudinal waves have regular horizons.
大气波导环境中折射率指数模式的统计特征
大气波导环境中折射率指数模式的统计特征刘成国1)王元1)吴迅英2)1) 武汉理工大学理学院，湖北武汉，4300702) 中国气象局国家气象信息中心，北京，100081摘要：本文详细说明了大气波导环境下空气折射率指数剖面的建模方法，并用地面上一公里大气折射率的值、折射率平均梯度两个特征参数和它们与地面空气折射率的相关性分析了大气波导环境的折射率剖面的统计特征。
得到了具有实用的统计信息。
对70年代5年波导出现的数据和90年12月份的全部数据的研究表明：根据70年代5年的数据，贴地波导出现时，它们的值及其和N s指数关系的都常数分别是110.6 、0.0029和-8.6、0.0047，地面上一公里处的折射率N1k及地面上第一公里内的平均折射率梯度dN1和地面折射率N s的相关性比没有波导出现的情况好；而这两者相比，前者的结果又比后者好。
关键词：无线电气象，空气折射率，大气波导，电波传播Statistical Characteristics of the Exponential Refractivity Profiles under Atmospheric DuctEnvironmentLiu Chengguo1 Wang Yuan1 Wu Xunying21 Science School, Wuhan University of Technology, Wuhan Hubei, 4300702 National Meteorological Information Center, CMA, Beijing, 100081Abstract: The characteristics of exponential atmospheric refractivity profile under atmospheric duct are investigated with air refractivity at height of 1km and the average gradient of refractivity 1km above ground as the characteristic parameters, their correlation with surface refractivity included also. The methods of modeling and statistic are elaborated; the results depicted in detail are applicable. Based on the data of 5 years in 1970s with duct present and those of December 1990, refractivity at height of 1km, the average gradient of refractivity and surface refractivity are obtained by regression of the refractivity profiles to exponential models. And it is found that the constants in the exponential relation of refractivity of 1km above ground and the mean vertical refractivity gradient in the first kilometer height with the surface value of refractivity are 110.6, 0.0029 and -8.6, 0.0047 respectively according the data of the 1970s’ surface ducts, and the correlations under duct environment are better than under other environment.Key words: radio meteorology, atmospheric refractivity, atmospheric duct, radio wave propagation1.引言大气波导会使电波偏离原来的传播方向传播，使通信、导航、探测等应用系统出现一些特殊的传播特性，如某些方向上的传输距离延伸、而在另外方向的传播盲区等。
时间计算方法
Architecture and Performance Methods ofA Knowledge Support System ofUbiquitous Time ComputationYinsheng ZhangInstitute of Scientific & Technical Information of China, Beijing, ChinaCity University of Hong Kong,Hong Kong, ChinaEmail: zhangyinshengnet@Abstract— An architecture and main performance methods of a knowledge support system of ubiquitous time computation based on relativity are proposed. As main results, modern time theories are described as certain relations of term-nodes in a tree, and some space-time computation models in a large scale and time computation models in different time measurement systems (institutions) are programmed as interfaces for time computation in complex conditions such as time-anisotropic movement systems or gravity-anisotropic environments.Index Terms—Space-Time, Relativity, Real Time Communication, Time Ontology, Time MeasurementI.I NTRODUCTIONTime computation is so ubiquitous nowadays, not only in analyzing texts with time terms, but also in real time computation even in circumstance across time zones or in quantum application such as satellite positioning systems, time-anisotropic movement systems, gravity-anisotropic environments, or space scale in the cosmos. As the relativity theory and quantum mechanics, which we call modern time theories, have made great advances, time computation is desirable to be made on the new time knowledge. It is well known that an ontology made up of specific terms in relations can succinctly represent knowledge homogeneously structured in syntactic pattern and stratified in entailments or in contents with stem-branch relations, and easily be applied to navigate knowledge by relational calculus, so a time knowledge support system based on time ontology with some computational models is proposed here to suffice requirement of time computation based on modern time theories.II.E XTENSION OF T IME E XPRESSIONTime mostly is expressed in a form of natural number and suitable for a unified time measure system in the Earth. For example, Dan Ionescu & Cristian Lambiri[1], E.-R.Orderog & H.Dierks[2], and Merlin [3] respectively gave time definitions or expressions for the real-time system, which, however, relativity of time, time computation models which define how to calculate time units, are omitted. In contrast to some software application fields’ research, some time science organizations give serial time expressions based on modern time theories, among which the International Astronomical Union (IAU,1991) made time definition widely accepted in a reality frame [4] . Thus we need to integrate these definitions and expressions in a complete and standard form for ubiquitous time. To do this, we give a time expression as follows.The physical quantity of time can be expressed as a 4-tuple:T=< D,U,M,I > (1) where,D: Data about time in quantity, it may be numbers or circle physical signals indicating time, or symbols expressing a time in quantity; that is, D∈{ time reading, tick, time number expression}.U: Unit, the measure unit such as “second”,” day”.M: Model, the mathematical formulae, using which you get a time quantity by mathematical computations.I: Institution, it may be indicated by a code which stipulates what unit U is meaningful, from which start time point S an interval can be fixed, according to what model M about time can be computed. So we use I( ) to indicate determining a time physical quantity by some parameters.For example, you say “2 seconds”, you might refer to two units of the Universal Time i.e., of coordinated universal time (CUT, or UTC) set by IAU and the finally arbitrated by the International Telecommunication Union (ITU). Of course, you probably might not refer to that, but to an atomic time (AT), as it may. Both the quantities can be computed by the corresponding models issued by the related organizations. Here, the institution determines the meanings of the time as a physical quantity and gives the computation methods, so we can give an expression similar with a programming expression as T=I(D,U,M), here, T serves as a return value ,and I, a function for the other parameters.Clearly, to set up a knowledge support system, we need to consider this time expression, its elements in the tuple will constitute the main profiles.© 2013 ACADEMY PUBLISHER doi:10.4304/jsw.8.11.2947-2955Figure 1. The architecture of the knowledge support system ofubiquitous time computation.III. A RCHITECTURE OF THE K NOWLEDGE S UPPORTS YSTEM We designed such an architecture for the knowledge support system developed by the author for the time computation in the complex systems.The system mainly made up of the 4 components that ①Time Knowledge Navigation, ② Time Measurement and Computation Models, ③ Time Expression Semantics Computation Models,④ Time Institution Knowledge Texts.Component ① accepts users’ requests for knowledge relating to the time measuring data, for example, a user requests for a model for computing the derivation between its time readings and a time unit in another space or in a time measurement system. The kernel of Component ① is a tree describing time knowledge profiles, say its branches are classifications of the time knowledge in certain relations. It is a catalogue of classification and relations of time knowledge, and also mappings between the classification and the knowledge in Component ② and Component ③. It contains institutions I in (1), which determines Component ② and Component ③ in logic, however, Component ② and Component ③ are listed for directing call not through the nodes of institutions.Component ② is the mathematical models for time measurement and computation, written in software programs and can be called for other time computation programs.Component ③ and ④ are discussed in number V and VI.IV. T IME ONTOLOGY.4. 0 General Description sThe tree in Component ① is a time ontology based on modern time theories for logically showing and savingall the knowledge term nodes in certain relations.These relations are potential information for deeper application such as inference based on relational calculus. On time ontology, most studies focus on time expressions and computations of relations between these expressions. For example, Moen’s time ontology is about time concepts in linguistics [5][6].; Frank etc. came up with a plan and principles building space-time in 4 dimensions and 5 tiers [7]. The typical extant time ontology see WordNet in the part of time, DAML time sub-ontology [8],Time Ontology in OWL built by W3C [9] ,and NASASWEET (Semantic Web for Earth an Environmental Terminology)[10]. In addition, ISO 19111 [11] and ISO 19112[12] set out the conceptual schema for spatial references based on geographic identifiers. This work shows various profiles of data structure of time description, yet has the limitations that(1) Time it describes is in the periphery of the Earth, but not in cosmos large scales;(2) The time properties are unraveled only on non-symmetry (non-back as an arrow), a little on relativity, singularity and quantum property.This might lead to difficulties in computations based on modern time theories.In contrast with this work, the time knowledge tree in Component ① is a time ontology based on modern time theories (hereafter “TOboMTT”, the main branches see attachment) .The nodes between any two levels in top-bottom constitute relations which are propositions (note that when we say “A and B in a certain relation”, it just says a proposition) stating the main frame of modern time theories. So, in essence, we have :TOboMTT={N,R }={Propositions} （2）here, N,R refer to nodes and relations respectively.The root (0- level) and the nodes in the next (1-level) are as followingz TimeSpace-Time Type Time Type Time Property Time Measure Time ExpressionThe root “Time” constitutes “has ” relations with the nodes in the 1-level. That is, “Time has the Space-Time Types”, “Time has the Time Types”, “Time has the Time Properties”, “Time has the Time Measures”, “Time has the Time Expressions”. These relations are basic profiles of the up-to-date study on time.The relations of the nodes between the 1 and 2 levels continue such propositions of those relations between 0 and 1 levels, for example, we can say “Time has the Space-Time Types like Euclid Space-Time”, here, “Euclid Space-Time” just is a node in the 2nd level. Thus,© 2013 ACADEMY PUBLISHERthe relations between the 1 and 2 levels are “includes ”, like “Space-Time Type includes Euclid Space-Time”. In the following contexts, we intuitively explain the main nodes which express some important assertions of modern time theories.4. 1 SPACE-Time TYPEAccording to Einstein’s field equation, space andtime are integrated. So we must take space as a parameterof time considering the space-time type. Einstein’s fieldequation see (3) [13]1()+=82R Rg g T αβαβαβαβ−Λπ （3）Here, α and β are space-time dimensions, i.e., α, β=0,1,2,3 and 0 denotes time for the left expression; R αβ is Ricci tensor, it is a 4×4 matrix of the 16 components ofsecond order space-time curvature, R is scalar curvature, g αβ is a 4×4 matrix of metric tensor, Λ is cosmological constant, T αβ is energy-momentum tensor, a 4×4 matrixtoo.From (3), we get (4), i.e., the differentiation of square of space-time intervals:2=ds g dx dy αβαβ (4) here, x,y are curvilineal coordinates, s is space-time interval. (4) adopts Einstein summation convention, normally like in physics, that a repeated index (α or β ) implies summation over all values of that indexed. (3) and (4) are well confirmed by some experiments in the scale 10-13 cm (the radius of a fundamental particle) to 1028 cm (the radius of the universe). A space-time type normally defined by a solution of the equations (3) or (4).See some basic nodes: Space-Time Type Euclidean space-time (absolute time) Riemannian space-time Inertial reference frame space-time Non-inertial reference frame space-time Friedmann- Walke space-time…… If (3) or (4) are determined as the nonlinear partial differential equations about g αβ , we call s is Riemannian space-time, which means space-time is of curvature and might not be flat (flatness is just a special instance, i.e., Minkowski space-time, in which gravity is neglected, it is regarded as inertial). In (3) or (4), if the time in different space places is described as absolutely not different , and independently from its different places and velocities, the space-time is Euclidean space-time or Newton space-time. Friedmann-Lemaître-Robertson-Walker space-time, simply Robertson-Walker space-time [14][15] , put forwarded by Robertson and Walker, and meet the inference of Friedman [16] and Lamaitre [17] , describes homogeneous and isotropic space-time in a non-inertial system, for which, cosmological curvature k and cosmological time t are introduced into (3) or (4). k takes 3 constants 0,1,-1 representing 3 possible space-time types: flatness, positive curvature and negative curvature. If R in (3) is a constant, Robertson-Walker space-time will become some special instance: when R =0, itwill be Minkowski space-time; R >0, de_Sitter space-time;R <0, anti-de_Sitter space-time. Bianchy I space-time is more general than Robertson-Walker that the space-time is homogeneousbut might be anisotropic [18]. Taub-NUT space-time adds magnetic and electric parameters into (3) or (4) [19]. Godel space-time adds rotationally symmetric axis into (3) or (4) [20]. Rindler space-time expresses such space-time determined by inertial system and non-inertial system [21][22]. In some special cases, R is not easy to be determined. To solve (3) or (4), some parameters are given for specialtypes of space-time. These special types include spherical and axial space-time, and time’s elapse may be neglected for a space spot. For (4), Schwarzschild space-time [23] isspherically symmetric beyond a mass sphere. A spherewith great mass and a radius less than Schwarzschild radius is a black hole, which is thought to bear only 3 kinds of information of mass, charge and angular momentum. Schwarzschild black hole is considered as one with only mass, while Ressner-Nordstrom black hole, named as Ressner-Nordstrom space-time, with mass and charge [24][25]; Kerr black hole, named as Kerr space-time with mass and angular momentum [26]; Kerr-Newmanblack hole, named as Kerr-Newman space-time [27], simultaneously have information of mass, charge and angular momentum. Some spherically symmetric space-time like Vaidya space-time [28] and Tolman space-time [29] consider time as the variable of the function of mass and curvature. As an axial metric space-time, Weyl-Levi-Civita space-time [30] is typical. . 4. 2 Time TYPEWhen we solely study time, we can primarily dividetime into the 3 types: Proper time Coordinate time Cosmological time Proper time is the elapsed between two events as measured by a clock that passes through both events. In other words, proper time value is from the real readings of the clock set by an observer in a definite space spot (ifthe measured body moves, then the clock spot and the moved body’s end spot are considered as one area for the two spots are so near for a large scale space). © 2013 ACADEMY PUBLISHERCoordinate time is integrated time under a coordinate system. It is not a real readings for a special spot (the difference between the different spots in the system is neglected), but a stipulated (calculated that it should be) time in the system. Proper time multiplied by (1- v2/c2)-2 is coordinate time (v is the velocity of the body, in which an implied observer is, c is light velocity). If we set a clock in a universe coordinate system indicating the integrated time, it would indicate the universal time (t in Robertson-Walker equation).The proper time in the Earth can be expressed in various forms as the follows.Ephemeris Time (ET) [31] was defined in principle by the orbital motion of the Earth around the Sun. Here, ephemeris is based on Julian calendar which had been reformed to be Gregorian calendar lasted to the nowadays.True solar time (apparent solar time) is given by the daily apparent motion of the true, or observed, Sun. It is based on the apparent solar day, which is the interval between two successive returns of the Sun to the local meridian [32].Mean solar time is the mean values of measured time of the intervals between two Sun passing an identical meridian [33].Sidereal Time is based on a sidereal day; a sidereal day is a time scale that is based on the Earth's rate of rotation measured relative to the fixed stars, normally to the Sun [34]. Sidereal time may be Greenwich Sidereal Time (GST) which calculated by Greenwich Royal Observatory in mean data or Local Sidereal Time (LST) which is computed by adding or subtracting the numbers of timezone [35] .Universal Time (UT) is computed by truly measured time data based on rotation of the Earth, it is a Greenwich Mean Time (GMT) and computed from the start of a midnight of Prime Meridian at Greenwich, and it has different versions such as UT0,UT1,UT2 and Coordinated Universal Time (UTC) for the computations from varying data on non-exact time scales of the Earth rotation. UT0 is Universal Time determined at an observatory by observing the diurnal motion of stars or extragalactic radio sources. It is uncorrected for the displacement of Earth's geographic pole from its rotational pole. This displacement, called polar motion, causes the geographic position of any place on Earth to vary by several metres, and different observatories will find a different value for UT0 at the same moment.UT1 is the principal form of Universal Time. While conceptually it is mean solar time at 0° longitude, precise measurements of the Sun are difficult. UT1R is a smoothly tuned version of UT1, filtering out periodic variations due to tides. UT2 is a smoothed version of UT1, filtering out periodic seasonal variations. UTC is an atomic timescale that approximates UT1. It is the international standard on which civil time is based [36].Atomic time applies the principle of stimulated atom radiation in a constant frequency. The Thirteenth General Conference of Weights and Measures define a second that "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom [37] ". That is a unit of International Atomic Time (ATI).The results of atomic time computed by different local laboratories are called local atomic time.Dynamical Time (DT) [38] is inferred from the observed position of an astronomical object via a theory of its motion, ET is a DT based on revolution of the Earth in replace of UT based on rotation of the Earth meet Newton’s time theory; to meet Einstein’s time theory IAU builds two versions of ET respectively in the system of Terrestrial Dynamic Time (TDT) Barycentric Dynamical Time (TDB).Local civil time is the corrected version of UTC by adding timezone numbers and adjusting daylight saving time [35] .Coordinate time includes centroid coordinate time and Earth-centered coordinate time, they are set by IAU.4. 3 Time propertyThe time properties are divided into 4 kinds as follows.Time PropertyAsymmetryRelativitySingularityQuantum propertyAsymmetry is the property human first discovered, it refers to what seems to be an arrow went out in one direction and not back.Relativity means anisotropy against gravity or in a light-like velocity.Singularity is the property of some places, where the present physical laws break down, or it can be thought of as the property of edge of space-time [39].The quantum property of time refers to that of time in the particle-scale, where time appears the stranger phenomena far from the macro-scale as we see. For example, the former -latter sequence in macro-scale might be isochronous in the quantum –scale [40].4. 4 Time measure4. 4.1 CoordinatorThe space-time expressed in (3) or (4) can’t always be indicated by Cartesian system, mostly due to some properties which are difficult to be indicated by Cartesian system, and also due to the singularity in the space-time which normally cannot be indicated by the real number system. So two kinds of coordinates are mainly introduced, they are general coordinates and special coordinates. The former are popular in common sense, and transforming them for a special purpose we get the latter----special coordinates, which mainly for describing some new metrics -solutions of (3), (4) with some© 2013 ACADEMY PUBLISHERsingularity variables, or for some particular space-time areas.The coordinates special for the metrics are introduced as follows.Schwarzschild coordinate indicates spherical symmetry, it sometimes becomes degeneratation of some more general conditions. Schwarzschild coordinate uses sphere coordinate with the radius r≠2GM/C2 and r≠0, here , G is universal gravitational constant, M is the mass. The coordinate is divided into two areas by r >2GM/C2 and r <2GM/C2 and leads to the two metrics in (3): g00= - (1-2GM/rC2) and g11= (1-2GM/rC2) -1.In Schwarzschild coordinate, there is not the expression that r=2GM/C2 (this is a singularity), but tortoise coordinate covers this singularity.Eddington coordinate does not diverge in r=2GM/C2 and r=0 by the linear transformation of the variables.Kruskal coordinate covers r=2GM/C2 and r=0 too, and more general in indicating space-time than tortoise and Eddington coordinate .Lemaitre coordinate covers r=2GM/C2 with a different method to Kruskal coordinate.Rindler coordinate indicates the space-time determined by both inertial and non-inertial system.Weyl coordinate indicates the function of metric and allows to indicate imaginary numbers.Fermi normal coordinate indicates space-like geodesic which is the trajectory that its covariant differential is 0 for (4). “space-like” denotes the velocity in the area is far less than light speed. And its time axis indicates proper time for a non-inertial or locally inertial conditions.Harmonic coordinate indicates harmonic conditions that coordinates in curved space satisfy a D' Alembert equation, it is a Cartesian-coordinate-like one in curved space.Local inertial coordinate indicates Minkowski space-time.The special coordinates for the particular space-time areas are introduced as follows.Centroid coordinate (center-of-mass coordinate system) is one taking the centre of a space area as the origin of coordinate. These coordinates include non-rotating geocentric reference system, rotating geocentric reference system, Barycentric Celestial Reference System (BCRS), International Celestial Reference System (ICRS).Non-rotating geocentric reference system takes the Earth centre as the origin of coordinate . IAU provides the metric and methods for computing proper time.Rotating geocentric reference system is supposed as rotated with the Earth together, its X3 axis is the rotation axis of the Earth, and it is taken as International Terrestrial Reference System (ITRS) by IAU. For the rotation direction is not considered, the time in non-rotating geocentric reference system and rotating geocentric reference system is the same.Barycentric Celestial Reference System (BCRS) is recommended by IAU, its origin is the mass centre of the solar system,its third axis is approximately the rotation axis of the Earth.International Celestial Reference System is a centroid coordinate, it is made up of circle of right ascension and circle of declination of approximate 600 quasars, the coordinates are provided by International Earth Rotation and Reference Systems Service (IERS) Most general coordinates are introduced by the mathematical textbooks, so they are omitted here.4. 4.2 Measure UNITThe frame of time measure unit is as follows:Measure of timeUnits of measureTime intervalDynamical time intervalDuration fixed time intervalTime interval with the duration fixedby an ephemerisIntegral time scaleDynamical time scale is referred to as measured values of time parameters by physical quantities in a physical system. Basically, a proper time interval is a dynamical time scale.The main units of dynamical time scales in the ontology are concerned with ephemeris time units. A second in ephemeris time is defined as the fraction 1/31,556,925.9747 of the tropical year in Julian calendar for 1900 January 0 at 12 hours ephemeris time by International Committee for Weights and Measures (CIPM), from this unit, Julian century, year, week and day can be worked out.An integral time scale is accumulated value copied from a contracted time start point, for example, atomic time scale. So it may be proper time or coordinate time.V. T IME MEASURE AND COMPUTATION MODELSComponent ②is the set of the measure and computation models, which are from two resources: one is from the institutions put forward by some organizations such as IAU stipulating how to measure and computation, another resource is from the exact solutions of the (3) or (4).The models are programmed in Mathematica as the Application Programming Interface (API) so that a users’ programs can call these API.EXAMPLE 1[41]: a model (group) to compute a coordinated universal timeUTC (t) – TAI(t) = ns (5)UTC (t) –UT 1(t)=<0.9s; (6) Here, UTC(t) is a time expressed in coordinated universal time’ institution unit, TAI(t) means a time of Atomic Time International, n is natural number; s is the second, UT 1(t) is a time expressed in UT 1.© 2013 ACADEMY PUBLISHEREXAMPLE 2 is calling from a user’s application for the interface of a model, which is drawn from reference [42] and re-wrote by the author, to get an exact solution of Einstein’s field equation given Roberson-Walker Metric:1 /*An application from users in pseudo-code callingthe model-interface. See the tree in the attachment*/2 e num Space-Time in non- inertial system3 {4 B ianchi I Space-Time,5……6R obertson-WalkerSpace-Time7 /*Here, all the 16 Space-Time in non- inertialsystem in the tree enumerated */8 } Metric[16];9 for(i=0;i<16;i++){10 switch(Metric [i])11 case Robertson-Walker Space-Time:12 input and assign vector:13 v = {t, r, e, phi};141516 M = {-1, R[t]^2/(1 - K (r^2), (r^2) (R [t]^2), (r^2) (Sin[e]^2) (R [t]^2)};Call Einstein [M, v]}“Einstein.m”1 E instein [g_, v_] := Block[2 {invsg, dg1, dg2, dg3, Christf2, dChristf2, Ruv1,Ruv2, Ruv3, Ruv4, RicciTensor, R, EMTensor} 3 EMTensor = {}; (*Save return value.*)(*Calculate the inverse metric of g.*)4 g=DiagonalMatrix[M];5 invsg = Inverse[g];(*Calculate the affine connection.*)6 dg1 = Outer[D, g, v];7 dg2 = Transpose[dg1, {1, 3, 2}];8 dg3 = Transpose[dg1, {2, 3, 1}];9 Christf2 = (1/2) invsg.(dg1 + dg2 - dg3);(*Calculate the Ricci tensor.*)10 dChristf2 = Outer[D, Christf2, v];11 Ruv1 = Table[Sum[dChristf2[[k, i, k, j]], {k, 4}],{i, 4}, {j, 4}];12 Ruv2 = Table[Sum[dChristf2[[k, i, j, k]], {k, 4}],{i, 4}, {j, 4}];13 R uv3 = Table[Sum[Christf2[[k, i, j]] Christf2[[h,k, h]], {k, 4}, {h, 4}], {i, 4}, {j, 4}];14 Ruv4 = Table[ Sum[Christf2[[k, i, h]] Christf2[[h,j, k]], {k, 4}, {h, 4}], {i, 4}, {j, 4}];15 RicciTensor = Ruv1 - Ruv2 - Ruv3 + Ruv4;(*Calculate the Curvature Scalar.*)16R = Sum[invsg[[i, i]] RicciTensor[[i, i]], {i, 4}];(*Calculate the field equation left part.*)17EMTensor = RicciTensor - (1/2) g R ;18return [EMTensor]19]20End[]21EndPackage[]This program is divided into two parts: the first part is user’s input for computation, which is space-time dimensions v in a spherical coordinator, in which, t is the cosmological time (see 4. 2 Time Type), M is Roberson-Walker Metric. Users can input similar metrics for calling the function Einstein[ ],which is saved in the second part, a document Einstein.m, starting from the sentence BeginPackage["Einstein`"]. mathlink.h in VC++ enables to run Mathematica programs in VC++ environment The section Block[] is a function of local variables for calling.Outer[] is to give the partial derivative ∂f/∂x.Transpose[dg1, {1, 3, 2}] is to transposes dg1 so that the k th level in dg1 is the n k th level in the result.D [] is to get partial differential.Table [] is to generate a list of the expression Sum[].Sum[] is to get sum.The line 19 is the computation result of left part of (3), yet the cosmological constant is omitted. The right part of (3) is considered as zero.VI. M ECHANISM AND R UNNING OF T HE A RCHITECTURETOboMTT is designed to be a tree not only for satisfying the structure and classification of knowledge of time, but also for developing the knowledge in Web Ontology Language (OWL), which is based on Resource Description Framework (RDF) in a tree. Thus we can divide TOboMTT into some sub-trees and further expressed them in OWL or RDF. Figure 2 is a sample of Class—SubClass relation in RDF. As a result, navigation of knowledge of time, based on TOboMTT, become navigation of resources and serves, based on eXtensible Markup Language (XML) compatible with both OWL and RDF.A query for a sub-class or property value will give the corresponding answer by rational calculus on a XML scheme. For the example in Figure 2, “Space-Time Type includes Euclid Space-Time ” will be the answer for the query “What kind does the Space-Time Type include?” Therefore, query and answer is the first and direct results of navigation of knowledge of time by TOboMTT.<?xml version="1.0"?>© 2013 ACADEMY PUBLISHER。
CFD基础教程-1-introcfd
SPRING 2005
1.1 What is Computational Fluid Dynamics? “Computational fluid dynamics” is simply the use of computers and numerical techniques to solve problems involving fluid flow. Computational fluid dynamics (CFD) has been successfully applied in many areas, including those that are the natural arena of civil engineers (highlighted below). Examples include: • aerodynamics of aircraft and automobiles; • hydrodynamics of ships; • engine flows – IC engines and jet engines; • turbomachinery – pumps and turbines; • heat transfer – heating and cooling systems; • combustion; • process engineering – mixing and reacting chemicals; • windpower; • wind loading – forces and dynamic response of structures; • building ventilation; • fire and explosion hazards; • environmental engineering – transport of pollutants and effluent; • coastal and offshore engineering – loading on coastal and marine structures; • hydraulics – pipe networks, reservoirs, channels, weirs, spillways; • sediment transport – sediment load, scour and bed morphology; • hydrology – flow in rivers and aquifers; • oceanography – tidal flows, ocean currents; • meteorology – numerical weather forecasting; • high-energy physics – plasma flows; • biomedical engineering – blood flow in heart, veins and arteries; • electronics – cooling of circuitry. This range of applications is very broad and encompasses many different fluid phenomena. Accordingly, many of the techniques used for high-speed aerodynamics (where compressibility is a dominant feature and viscosity comparatively unimportant) are different from those used to solve low-speed, frictional and gravity-driven flows typical of hydraulic and environmental engineering. Although many of the techniques learnt will be general, this course will focus primarily on viscous, incompressible flow by the finite-volume technique. CFD 1-1 David Apsley
气科院大气物理面试英语专业词汇[1]
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大气科学系微机应用基础Primer of microcomputer applicationFORTRAN77程序设计FORTRAN77 Program Design大气科学概论An Introduction to Atmospheric Science大气探测学基础Atmospheric Sounding流体力学Fluid Dynamics天气学Synoptic Meteorology天气分析预报实验Forecast and Synoptic analysis生产实习Daily weather forecasting现代气候学基础An introduction to modern climatology卫星气象学Satellite meteorologyC语言程序设计 C Programming大气探测实验Experiment on Atmospheric Detective Technique云雾物理学Physics of Clouds and fogs动力气象学Dynamic Meteorology计算方法Calculation Method诊断分析Diagnostic Analysis中尺度气象学Meso-Microscale Synoptic Meteorology边界层气象学Boundary Layer Meteorology雷达气象学Radar Meteorology数值天气预报Numerical Weather Prediction气象统计预报Meteorological Statical Prediction大气科学中的数学方法Mathematical Methods in Atmospheric Sciences专题讲座Seminar专业英语English for Meteorological Field of Study计算机图形基础Basic of computer graphics气象业务自动化Automatic Weather Service空气污染预测与防治Prediction and Control for Air Pollution现代大气探测Advanced Atmospheric Sounding数字电子技术基础Basic of Digital Electronic Techniqul大气遥感Remote Sensing of Atmosphere模拟电子技术基础Analog Electron Technical Base大气化学Atmospheric Chemistry航空气象学Areameteorology计算机程序设计Computer Program Design数值预报模式与数值模拟Numerical Model and Numerical Simulation接口技术在大气科学中的应用Technology of Interface in Atmosphere Sciences Application海洋气象学Oceanic Meteorology现代实时天气预报技术（MICAPS系统）Advanced Short-range Weather Forecasting Technique(MICAPS system)1) atmospheric precipitation大气降水2) atmosphere science大气科学3) atmosphere大气1.The monitoring and study of atmosphere characteristics in near space as an environment forspace weapon equipments and system have been regarded more important for battle support.随着临近空间飞行器的不断发展和运用,作为武器装备和系统环境的临近空间大气特性成为作战保障的重要条件。
1汉英力学名词(1993)
BZ反应||Belousov-Zhabotinski reaction, BZ reactionFPU问题||Fermi-Pasta-Ulam problem, FPU problemKBM方法||KBM method, Krylov-Bogoliubov-Mitropolskii method KS[动态]熵||Kolmogorov-Sinai entropy, KS entropyKdV 方程||KdV equationU形管||U-tubeWKB方法||WKB method, Wentzel-Kramers-Brillouin method[彻]体力||body force[单]元||element[第二类]拉格朗日方程||Lagrange equation [of the second kind] [叠栅]云纹||moiré fringe; 物理学称“叠栅条纹”。
[叠栅]云纹法||moiré method[抗]剪切角||angle of shear resistance[可]变形体||deformable body[钱]币状裂纹||penny-shape crack[映]象||image[圆]筒||cylinder[圆]柱壳||cylindrical shell[转]轴||shaft[转动]瞬心||instantaneous center [of rotation][转动]瞬轴||instantaneous axis [of rotation][状]态变量||state variable[状]态空间||state space[自]适应网格||[self-]adaptive meshＣ0连续问题||C0-continuous problemＣ1连续问题||C1-continuous problemＣＦＬ条件||Courant-Friedrichs-Lewy condition, CFL condition ＨＲＲ场||Hutchinson-Rice-Rosengren fieldＪ积分||J-integralＪ阻力曲线||J-resistance curveＫＡＭ定理||Kolgomorov-Arnol'd-Moser theorem, KAM theoremＫＡＭ环面||KAM torusｈ收敛||h-convergenceｐ收敛||p-convergenceπ定理||Buckingham theorem, pi theorem阿尔曼西应变||Almansis strain阿尔文波||Alfven wave阿基米德原理||Archimedes principle阿诺德舌[头]||Arnol'd tongue阿佩尔方程||Appel equation阿特伍德机||Atwood machine埃克曼边界层||Ekman boundary layer埃克曼流||Ekman flow埃克曼数||Ekman number埃克特数||Eckert number埃农吸引子||Henon attractor艾里应力函数||Airy stress function鞍点||saddle [point]鞍结分岔||saddle-node bifurcation安定[性]理论||shake-down theory安全寿命||safe life安全系数||safety factor安全裕度||safety margin暗条纹||dark fringe奥尔-索末菲方程||Orr-Sommerfeld equation奥辛流||Oseen flow奥伊洛特模型||Oldroyd model八面体剪应变||octohedral shear strain八面体剪应力||octohedral shear stress八面体剪应力理论||octohedral shear stress theory巴塞特力||Basset force白光散斑法||white-light speckle method摆||pendulum摆振||shimmy板||plate板块法||panel method板元||plate element半导体应变计||semiconductor strain gage半峰宽度||half-peak width半解析法||semi-analytical method半逆解法||semi-inverse method半频进动||half frequency precession半向同性张量||hemitropic tensor半隐格式||semi-implicit scheme薄壁杆||thin-walled bar薄壁梁||thin-walled beam薄壁筒||thin-walled cylinder薄膜比拟||membrane analogy薄翼理论||thin-airfoil theory保单调差分格式||monotonicity preserving difference scheme 保守力||conservative force保守系||conservative system爆发||blow up爆高||height of burst爆轰||detonation; 又称“爆震”。
Evolution of the Fine Structure Constant Driven by Dark Matter and the Cosmological Constan
Physics Department, McGill University, 3600 University St, Montreal,Quebec H3A 2T8, Canada
D´ epartement de Physique, Universit´ e du Qu´ ebec ` a Montr´ eal C.P. 8888, Succ. Centre-Ville, Montr´ eal, Qu´ ebec, Canada, H3C 3P8
1
Introduction
Speculations that fundamental constants may vary in time and/or space go back to the original idea of Dirac [1]. Despite the reputable origin, this idea has not received much attention during the last fifty years for the two following reasons. First, there exist various sensitive experimental checks that coupling constants do not change (See, e.g. [2]). Second, for a long time there has not been any credible theoretical framework which would predict such changes. Our theoretical mindset, however, has changed since the advent of the string theory. One of the most interesting low-energy features of string theory is the possible presence of a massless scalar particle, the dilaton, whose vacuum expectation value defines the size of the effective gauge coupling constants. A change in the dilaton v.e.v. induces a change in the fine structure constant as well as the other gauge and Yukawa couplings. The stabilization of the dilaton v.e.v., which usually renders the dilaton massive, represents one of the fundamental challenges to be addressed before string theory can aspire to describe the observable world. Besides the dilaton, string theory often predicts the presence of other massless or nearly massless moduli fields, whose existence may influence particle physics and cosmology and may also change the effective values of the coupling constants as well. Independent of the framework of string theory, Bekenstein [3] formulated a dynamical model of “changing α”. The model consists of a massless scalar field which has a linear −1 φFµν F µν , where M∗ is an associated coupling to the F 2 term of the U (1) gauge field, M∗ mass scale and thought to be of order the Planck scale. A change in the background value of φ, can be interpreted as a change of the effective coupling constant. Bekenstein noticed that F 2 has a non-vanishing matrix element over protons and neutrons, of order (10−3 − 10−2 )mN . This matrix element acts as a source in the φ equation of motion and naturally leads to the cosmological evolution of the φ field driven by the baryon energy density. Thus, the change in φ translates into a change in α on a characteristic time scale comparable to the lifetime of the Universe or larger. However, the presence of a massless scalar field φ in the theory leads to the existence of an additional attractive force which does not respect Einstein’s weak universality principle. The extremely accurate checks of the latter [4] lead to a firm lower limit on M∗ , M∗ /MPl > 103 that confines possible changes of α to the range ∆α < 10−10 − 10−9 for 0 < z < 5 [3, 5]. This range is five orders of magnitude tighter than the change ∆α/α ≃ 10−5 indicated in the observations of quasar absorption spectra at z = 0.5 − 3.5 and recently reported by Webb et al. [6]. Given the potential fundamental importance of such a result, one should remain cautious until this result is independently verified. Nevertheless, leaving aside the issue regarding the reliability of the conclusions reached by Webb et al. [6], it is interesting to explore the possibility of constructing a dynamical model, including 1
黎曼曲面讲义
3.5 Abel-Jacobi 定理 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
第四章 曲面与上同调
121
4.1 全纯线丛的定义 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
f 的实部和虚部分别为 u, v, 则 f 为全纯函数的充分必要条件是 u, v 满足如下的
Cauchy-Riemann 方程:
$ & ux “ vy,
% uy “ ´vx.
全纯函数的定义还有许多其他的等价形式.
平均值公式:
若函数
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本书主要内容如下：第一章基本上是关于复变函数的简单复习，我们给出了 单值化定理的简单情形，即 Riemann 映照定理的证明。这一章也得到了调和函数 的梯度估计以及 Harnack 原理，这里采用的方法可以推广到一般的黎曼流形上。 第二章引入了抽象黎曼曲面的定义，并给出了单连通黎曼曲面的分类（单值化定 理），其中，黎曼环面作为一类重要的紧致黎曼曲面也加以了分类。证明单值化定 理的方法是通过调和函数（可能带有奇点）来构造特殊的全纯映射。而调和函数 的存在性是通过经典的 Perron 方法获得的。第三章是本书核心内容之一，我们给 出了 Riemann-Roch 公式的证明，并选择了若干有意思的应用加以介绍。我们选 择的 Riemann-Roch 公式的这个证明也是经典的，它也涉及某些给定奇性的亚纯 微分的存在性，这种亚纯微分的存在性是通过 Hodge 定理获得的，为了尽快的介 绍 Riemann-Roch 公式的应用，我们把重要的 Hodge 定理的证明放在本书第二个 附录中了。通过 Riemann-Roch 公式我们知道了紧致黎曼曲面上亚纯函数的丰富 性，我们也证明了亚纯函数域是一个一元代数函数域，并且它惟一地决定了黎曼曲 面本身。作为例子我们简单介绍了黎曼环面上的亚纯函数，它们就是经典的椭圆 函数。通过适当地挑选亚纯函数，我们把黎曼曲面全纯地嵌入到了复投影空间中， 因此可以从代数曲线的角度来研究它们。我们还介绍了计算总分歧数的 RiemannHurwitz 公式，并利用它简单研究了超椭圆型的黎曼曲面。接下来我们介绍了曲面 上的 Weierstrass 点，得到了 Weierstrass 点的个数估计。这些结果又被应用于曲面 的全纯自同构群，特别地，我们证明了亏格大于 1 的紧致黎曼曲面全纯自同构群 的阶的估计。作为第二章的结束，我们还介绍了重要的双线性关系、Jacobi 簇，证
罗达尼克效应
罗达尼克效应：引力波的探测之道引言罗达尼克效应（the Lense-Thirring effect）是由两位德国物理学家Josef Lense和Hans Thirring于1918年提出的一种预测，它描述了质量旋转物体产生的引力场对周围物体轨道运动的影响。
这一效应可以从相对论的角度解释，是广义相对论的重要应用之一。
在物理学家的不断努力下，罗达尼克效应的存在得到了验证，并且引力波的观测直接印证了这一效应的存在。
罗达尼克效应的原理罗达尼克效应是由质量旋转物体的旋转性质对周围狭义空间区域的影响而产生的。
根据广义相对论，质量可以扭曲周围的时空结构，形成引力场。
而对于静态物体，其引力场是球对称的。
然而，当物体具有旋转时，由于旋转对时空的影响，引力场呈现出一定的非球对称性。
以一个旋转的球体为例，球体的旋转使得在接近球面的区域，其周围的时空结构发生了变形。
这种变形导致了轨道物体所经历的时空之间的路径也发生了改变。
具体而言，物体的自转产生的旋转引力场会对周围物体轨道上的运动产生一定的“摩擦力”，使得轨道上的物体相对于球体自身的旋转发生偏移。
这个偏移效应就是罗达尼克效应。
罗达尼克效应的应用现代科学中的罗达尼克效应罗达尼克效应的研究对宇宙学、星际导航、引力波探测等领域有着重要的作用。
1.宇宙学：罗达尼克效应的研究在宇宙学中有重要的应用。
宇宙是一个巨大的物质系统，其中存在着大量的旋转天体，如恒星和星系。
罗达尼克效应的存在使得我们对宇宙中旋转物体的运动轨迹有了更深入的认识，帮助我们理解星系的演化、恒星的自转等现象。
2.星际导航：罗达尼克效应也在星际导航中起到关键作用。
对于飞船等轨道运动的物体来说，罗达尼克效应的存在意味着需要更精确地计算轨道和飞行路径，以避免不受控制的偏移。
在太阳系的星际航行中，精确计算罗达尼克效应可以帮助我们更准确地预测和规划太空探测任务。
3.引力波探测：罗达尼克效应的实验验证是引力波探测的重要突破之一。
Tube Model for Light-Front QCD
For instance, some of the zero modes that were otherwise constrained become dynamical. In light-front field theory, equations of motion are typically of the form ∂+(∂− + igV )φ = U(φ), where U(φ) is the potential term. When V = 0 it is clear why zero modes ∂−φ = 0 are not dynamical: they have no conjugate momentum. However, note that when V is nonzero, the associated kinetic term is small (since V is small) relative to the kinetic term of any non-zero mode. Thus, one may just as well treat these zero modes as non-dynamical (that is, as a solution of a constraint equation).
1 The gauge zero mode
Before we begin, we must discuss the “gauge zero mode,” V ≡ dx− A−. As has been noticed by several authors in the context of both light-front [5] and equal time [6] quantization, one cannot set V = 0 by choice of gauge because it is a genuine dynamical degree of freedom. Only the gauge choice ∂−A− = 0 is allowed.