Absence of the Effects of Vortices in the Gauge Glass

合集下载

油气田燃料天然气组分特征对实测碳排放因子的影响

油气田燃料天然气组分特征对实测碳排放因子的影响廉军豹付玥张鑫袁良庆刘宏彬李世熙谭小红（大庆油田设计院有限公司）摘要：通过实测碳排放因子计算公式理论分析及油气田典型燃料天然气实例分析，探索燃料天然气组分特征对实测碳排放因子的影响。

结果表明：各生产系统使用的油气田燃料天然气含碳原子数量较多的组分含量越多，实测含碳量碳排放因子及实测低位发热量碳排放因子越大，含碳原子数量较少的组分或H 2、O 2、N 2、He 不含碳的组分含量越多，实测含碳量碳排放因子及实测低位发热量碳排放因子越小；除实测方法系统性差异外，一定含量的CO 2，是导致油气田燃料天然气实测低位发热量碳排放因子与实测含碳量碳排放因子之间存在显著差异的重要原因；各类燃料天然气碳排放因子存在普遍性差异，干气的实测碳排放因子明显比湿气的小。

上述结论将为油气田燃料天然气碳排放核算提供技术支持。

关键词：油气田；燃料天然气；碳排放因子；组分特征；实测DOI :10.3969/j.issn.2095-1493.2023.11.016The influences of fuel natural gas composition characteristics on measured carbon emission factors in oil and gas fieldLIAN Junbao，FU Yue，ZHANG Xin，YUAN Liangqing，LIU Hongbin，LI Shixi，TAN Xiaohong Daqing Oilfield Design Institute Co ．，Ltd ．Abstract：The influences of fuel natural gas composition characteristics on measured carbon emission factors are explored through the theory analysis of measured carbon emission factors formula and the cas-es analysis of typical fuel natural gas in oil and gas field．The results show that the higher the content of components with more carbon atoms in the natural gas used as fuel of each production system in oil and gas fields，the greater the carbon emission factor from measured carbon content and that from measured low calorific value．The higher the content of components with less carbon atoms or components with-out carbon such as H 2，O 2，N 2，He in natural gas used as fuel in oil and gas fields，the smaller the car-bon emission factor from measured carbon content and that from measured low calorific value．What's more，in addition to systematic differences between measurement methods，a certain amount of CO 2is an important reason for the significant difference between the carbon emission factor from measured carbon content and that from measured low calorific value of natural gas used in oil and gas fields．In addition，there are universal differences in various carbon emission factors of fuel natural gases in oil and gas fields，and the measured carbon emission factors of dry gas are significantly smaller than those of wet gas．Most importantly，the above conclusions will be provided technical support for the carbon emis-sion accounting for fuel natural gas in oil and gas fields ．Keywords：oil and gas field；fuel natural gas；carbon emission factor；composition characteristics；measurement第一作者简介：廉军豹，高级工程师，硕士研究生，2010年毕业于中国地质大学（武汉）（应用化学专业），从事油气田碳资产研发技术研（碳控楼），163712。

中考英语经典科学实验与科学理论深度剖析阅读理解20题

中考英语经典科学实验与科学理论深度剖析阅读理解20题1<背景文章>Isaac Newton is one of the most famous scientists in history. He is known for his discovery of the law of universal gravitation. Newton was sitting under an apple tree when an apple fell on his head. This event led him to think about why objects fall to the ground. He began to wonder if there was a force that acted on all objects.Newton spent many years studying and thinking about this problem. He realized that the force that causes apples to fall to the ground is the same force that keeps the moon in orbit around the earth. He called this force gravity.The discovery of the law of universal gravitation had a huge impact on science. It helped explain many phenomena that had previously been mysteries. For example, it explained why planets orbit the sun and why objects fall to the ground.1. Newton was sitting under a(n) ___ tree when he had the idea of gravity.A. orangeB. appleC. pearD. banana答案：B。

钙离子对零价铁胶体稳定性的影响

technology (Elliott and Zhang, 2001; Henn and Waddill, 2006), nevertheless, a high reactivity alone is not sufﬁcient to make NZVI a good in-situ remediation agent. NZVI particles must also be readily dispersible in water such that they can migrate through water saturated porous media to the contaminated zone. Bare NZVI, however, aggregates rapidly in water, making subsurface delivery difﬁcult (Phenrat et al., 2007). Thus, for the purpose of in-situ environmental remediation, the surface of NZVI can be modiﬁed using organic
w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 2 4 8 9 e2 4 9 6
Available online at
journal homepage: /locate/watres
Inﬂuence of calcium ions on the colloidal stability of surface-modiﬁed nano zero-valent iron in the absence or presence of humic acid

Monopoles contra vortices in SU(2) lattice gauge theory

a rXiv:h e p-la t/97312v118Mar1997UNITU-THEP-01/97February 4,1997Monopoles contra vortices in SU(2)lattice gauge theory?∗Kurt Langfeld and Hugo Reinhardt Institut f¨u r Theoretische Physik,Universit¨a t T¨u bingen D–72076T¨u bingen,Germany.We show that the scenario of vortex induced conﬁnement of center–projected SU(2)lattice gauge theory is not necessarily in conﬂict with the ﬁndings in the positive plaquette model.Recently [1],it was reported that the vortices of center projected SU(2)lattice gauge theory reproduce the full string tension,whereas the lattice conﬁgurations fail to yield a non-zero string tension,if the vortices are suppressed.The authors argue that these vortices are the relevant degrees of freedom to conﬁne quarks in the fundamental representation.In order to be more precise,center–projection was deﬁned in [1]on top of Abelianprojection.The maximal Abelian gauge [2]makes a link variable U µ(x )as diagonal as possible,and Abelian projection replaces a link variableU µ(x )=α0(x )+i α(x )ˆn (x ) τ,α20+ α2=1(1)by the Abelian link variableA=α0(x)+iα3(x)τ3α20+α23=cosθ(x)+i sinθ(x)τ3.(2)Center–projection is then deﬁned by assigning to each link variable a value±1 according the rule A(x)→sign(cosθ(x)).A plaquette is deﬁned to be part of the vortex,if the product of the center–projected links is−1.This result of ref.[1]seems to be in conﬂict with theﬁndings of ref.[3,4],where lattice calculations have been performed in the positive plaquette model(PPM)in the maximal Abelian gauge.In the PPM,conﬁgurations giving rise to plaquettes with negative trace are rejected.Nevertheless,this model reproduces the linear rising conﬁnement potential.From this observation,the authors of ref.[4]concluded that vortices are not responsible for the string tension in contradiction to theﬁndings of[1].Here we show that the results of the vortex-approach[1]and the results of the PPM[4]are not necessarily in conﬂict.For this purpose,let us assume that Abelian projection has been performed and consider a particular plaquette conﬁguration P=U1U2U3U4,which is generated by the Abelian link variablesU k=cosφk+i sinφkτ3,k=1...4.(3)The plaquette can be written asP=cos 4 k=1φk +i sin 4 k=1φk τ3.(4) It is easy to choose a set of link variables such thatφ1∈[0,π2,π[,4k=1φk∈[0,πthe value+1and to the links U k=2...4the value−1implying that the conﬁguration represents a vortex,since the product of the center–projected links yields−1.Our example shows that the vortex conﬁgurations discussed in[1]are not excluded in the PPM.This result is obviously not restricted to Abelian projected links.In order to further clarify the role of the vortices occurring in the center–projected lattice theory,we suggest to study the center-projection of the positive plaquette model.。

Bose-Einstein condensates with vortices in rotating traps

a r X i v :c o n d -m a t /9906144v211J un1999Bose-Einstein condensates with vortices in rotating trapsY.Castin 1and R.Dum 1,21Laboratoire Kastler Brossel ∗,´Ecole normale sup´e rieure,24rue Lhomond,F-75231Paris Cedex 05,France2Institut d’optique,BP 147,F-91403Orsay Cedex,France (16March 1999)We investigate minimal energy solutions with vortices for an interacting Bose-Einstein condensate in a rotating trap.The atoms are strongly conﬁned along the axis of rotation z ,leading to an eﬀective 2D situation in the x −y plane.We ﬁrst use a simple numerical algorithm converging to local minima of energy.Inspired by the numerical results we present a variational Ansatz in the regime where the interaction energy per particle is stronger than the quantum of vibration in the harmonic trap in the x −y plane,the so-called Thomas-Fermi regime.This Ansatz allows an easy calculation of the energy of the vortices as function of the rotation frequency of the trap;it gives a physical understanding of the stabilisation of vortices by rotation of the trap and of the spatial arrangement of vortex cores.We also present analytical results concerning the possibility of detecting vortices by a time-of-ﬂight measurement or by interference eﬀects.In the ﬁnal section we give numerical results for a 3D conﬁguration.I.INTRODUCTION After the achievement of Bose-Einstein condensates in trapped atomic gases [1]many properties of these systems have been studied experimentally and theoretically [2].However a striking feature of superﬂuid helium,quantized vortices [3],[4],has not yet been observed in trapped atomic gases.There is an abundant literature on vortices in helium II,an overview is given in [4].The atomic gases have interesting properties which justify eﬀorts to generate vortices in these systems:the core size of the vortices is adjustable,as in contrast to helium the strength of the interaction can be adjusted through the density;the number of vortices in atomic gases can be in principle well controlled;for a small number of particles in the gas metastability of the vortices can be studied,that is one can watch spontaneous transitions between conﬁgurations with diﬀerent number of vortices.Several ways to create vortices in atomic gases have been suggested.A method inspired from liquid helium consists in rotating the trap conﬁning the atoms [5];at a large enough rotation frequency it becomes energetically favorable at low temperatures to produce vortices;two diﬀerent paths could be in principle followed:(1)producing ﬁrst a condensate then rotating the trap,or (2)cooling the gas directly in a rotating trap.It has been recently proposed in [6]to use quantum topological eﬀects to obtain a vortex.Other methods that do not rely on thermal equilibrium have been suggested [7],[8].Here we study theoretically the minimal energy conﬁgurations of vortices in a rotating trap [9].The model is deﬁned in section II;in sections III to VI we assume a strong conﬁnement of the atoms along the rotation axis z so that we face an eﬀective 2D problem in the transverse plane x −y .We present numerical results for solutions with vortices that are local minima of the Gross-Pitaevskii energy functional (section III).These solutions contain only vortices with a charge ±1,the vortices with a charge larger than or equal to 2are thermodynamically unstable (section IV).We discuss possibilities to get experimental evidence of vortices in atomic gases in section V.Finally,we concentrate on the regime where the interaction energy is much larger than the trap frequenciesωx,y ,the so-called Thomas-Fermi limit [2].This is complementary to the work of [10].We obtain inthis “strong interacting”regime analytical predictions based on a variational Ansatz that reproducesatisfactorily the numerical results (section VI).In section VII we present results for vortices in 3D,that is in a trap with a weak conﬁnement along the rotation axis.II.MODEL CONSIDERED IN THIS PAPERThe atoms are trapped in a potential rotating at angular velocity Ω.In the laboratory frame theHamiltonian of the gas is therefore time dependent.To eliminate this time dependence we introducea rotating frame at the angular velocity Ωso that the trapping potential becomes time independent;this change of frame is achieved by the single-atom unitary transform:U(t)=e i Ω· Lt/¯h(1) where L is the angular momentum operator of a single atom.As the unitary transform is timedependent the Hamiltonian in the rotating frame contains an extra inertial term,given for eachatom byi¯h U†(t)dφ|φ +1φ|φ 2.(3)In this energy functional H0contains the kinetic energy and the trapping potential energy of theparticles:H0=−¯h22mω2αr2α.(5)Furthermore in all but in section VII we will assume that the trapping potential is much strongeralong the z axis than along the x,y axis,with an oscillation frequency much larger than the typicalinteraction energy Ng3D|φ|2per particle.This situation,although not realized experimentally yet,is not out of reach,in particular when one uses optical traps rather than magnetic traps[11].Inthis strong conﬁning regime the motion of the particles along z is frozen in the ground state of thestrong harmonic potential:φ(x,y,z)≃ψ(x,y) mωz2¯hωz:E[ψ,ψ∗]= d2 rψ∗( r)[H⊥−ΩL z]ψ( r)2Ng|ψ|42m ∆x,y+12π¯h 1/2.(9)Most of the results of the paper are dealing with the2D energy functional;a numerical result for a local minimum of the full3D energy functional will be given in the section VII.We concentrate on the so-called Thomas-Fermi regime,where the interaction energy per particle is much larger than ¯hωx,y.The opposite regime has already been studied in[10].III.LOCAL MINIMA OF ENERGY WITH VORTICES In this section we brieﬂy discuss the general problem of minimizing energy functionals of the type Eq.(7).We present the numerical algorithm that we have used and we give numerical results for the2D problem.A.A numerical algorithm toﬁnd local minimaThe algorithm in our numerical calculations is commonly used in the literature to minize energy functionals E[ψ,ψ∗]of the form Eq.(7).The intuitive idea is to start from a randomψand move it opposite to the local gradient of E[ψ,ψ∗]that is along the local downhill slope of the energy. Numerically this is implemented by an evolution ofψparametrized by aﬁctitious timeτ:−dδψ∗[ψ,ψ∗].(10)Assuming aψnormalized to unity we get the following equation of motion forψ:−ddτE[ψ,ψ∗]=−2 d2 r δE2mΩ2r2cannot exceed the trapping potential.Therefore E has to convergeto aﬁnite value forτ→∞.Asymptotically dE/dτ=0andψsatisﬁesδEωx=ω/(1+ǫ)(14)ωy=ω(1+ǫ).(15) In Fig.1we show diﬀerent local minima conﬁgurations obtained forǫ=0.3and a rotation frequencyΩ=0.2ω;each conﬁguration has been obtained for diﬀerent random initialψ’s.The holes observedin the spatial density correspond to the vortex cores.We have always found that the phase ofψchanges by2πaround a vortex core;we have not found vortices with a charge±q,where the integerq is strictly larger than one;this fact will be explained in the next section.Furthermore the senseof circulation is the same for all vortices.To quantify the eﬀect of the non-axisymmetry of the trap we have plotted in Fig.2the dependenceof energy of diﬀerent vortex conﬁgurations onωx/ωy for aﬁxedω;we measure the energies fromE iso,the energy of the zero-vortex solution in the axisymmetric caseǫ=0.The zero-vortex solutionexhibits a signiﬁcant variation of energy withǫ;for a non-zeroǫthe wavefunctionψdevelops a phase proportional toΩfor weakΩ’s,which accounts for the energy change as explained in section VI B.The solutions with vortices experience quasi the same energy shift as function ofǫ.As only theenergy diﬀerence between the various local minima matters we will from now on only consider the axisymmetric caseǫ=0to identify the solution with the absolute minimal energy.Note that the solutionsψwith several vortices obtained in the limiting caseǫ=0are not eigen-vectors of L z;this reﬂects a general property of non-linear equations such as the Gross-Pitaevskiiequations to have symmetry broken solutions;it is explained in[10]how to reconcile this symmetrybreaking with the fact that eigenvectors of the full N-atom Hamiltonian are of well deﬁned angular momentum.IV.STABILITY PROPERTIES OF VORTICESIn this section we recall that a(normalized)wavefunctionψsuch that E[ψ,ψ∗]has a local min-imum inψ,describes a condensate having all the desired properties of stability,that is dynamicaland thermodynamical stability.We then show that a vortex centered at r= 0with an angular mo-mentum strictly larger than¯h is not a local minimum of energy and is therefore thermodynamicallyunstable.A.Stability properties of local minimaLet us express the fact thatψcorresponds to a local minimum of the energy.Aﬁrst condition isthat the energy functional is stationary forψ,that isψsolves the Gross-Pitaevskii equation Eq.(13).To get the second condition,we consider a small variation ofψ,ψ→ψ+δψ(16) preserving the normalization of the condensate wavefunction to unity:||ψ+δψ||2−||ψ||2=0= ψ|δψ + δψ|ψ + δψ|δψ .(17) We expand the energy functional E[ψ,ψ∗]in powers ofδψ,neglecting terms of orderδψ3or higher.Using Eq.(17)and Eq.(13)weﬁnd that terms linear inδψvanish so that1δE=1.Dynamical stabilityConsiderﬁrst the problem of so-called“dynamical stability”:to be a physically acceptable con-densate wavefunction,ψhas to be a stable solution of the time dependent Gross-Pitaevskii equationi¯h∂tψ=H GPψ(21) otherwise any small perturbation ofψ,e.g.the eﬀect of quantumﬂuctuations or experimental noise,may lead to an evolution ofψfar from its initial value.To determine the evolution of a smalldeviationδψas in Eq.(16)we linearize Eq.(21):i¯h∂t |δψ |δψ∗ =L |δψ |δψ∗ (22) where the operator L is related to L c byL c= 100−1 L.(23)Asψis time independent,so is L and dynamical stability is equivalent to the requirement that theeigenvalues of L have all a negative or vanishing imaginary part.As we now show the positivity ofL c leads to a purely real spectrum for L.Consider an eigenvector(u,v)of L with the eigenvalueε.Contracting Eq.(23)between the ket(|u ,|v )and the bra( u|, v|)we getε[ u|u − v|v ]=( u|, v|)L c |u |v .(24)Note that the matrix element of L c is real positive as L c is a positive hermitian operator.We nowface two possible cases for the real quantity u|u − v|v :• u|u − v|v =0.In this case L c has a vanishing expectation value in(|u ,|v );as L c is positive(|u ,|v )has to be an eigenvector of L c with the eigenvalue zero;from Eq.(23)and the fact that 100−1 is invertible weﬁnd that(|u ,|v ) is also an eigenvalue of L with the eigenvalue0,so thatε=0is a real number.• u|u − v|v >0:we getεas the ratio of two real numbers,so thatεis real.2.Thermodynamical stabilityA second criterion of stability is the so-called“thermodynamical”stability.For zero temperature,this condition can be formulated in the Bogoliubov approach[2],where the particles out of thecondensate,which always exist because of the interactions,are described by a set of uncoupledharmonic oscillators with frequenciesεsign[ u|u − v|v ]/¯h,where(u,v)is an eigenvector of L withthe eigenvalueε.In order for a thermal equilibrium to exist for these oscillators,their frequenciesshould be strictly positive,which is the case here in virtue of Eq.(24)[13].If a mode with a negativefrequency were present thermalization by collisions would transfer particles from the condensateψto this mode,leading to a possible evolution of the system far from the initial stateψ[14].What happens for solutionsψof the Gross-Pitaevskii equations that are not local minima of energy?The operator L c has at least an eigenvector with a strictly negative eigenvalue.In thiscase one cannot have thermodynamical stability,that is one cannot haveε[ u|u − v|v ]>0forall modes[13].From the non-positivity of L c one cannot however distinguish between a simplethermodynamically instability or a more dramatic dynamical instability.B.Why not a vortex of angular momentum larger than¯h?For simplicity we consider only a single vortex in the center of an axi-symmetric trap.We show that vortices with a change of phase of2qπare not local minima of energy,that is are(at leastthermodynamically)unstable.We have found numerically a solution of the Gross-Pitaevskii equationEq.(13)by an evolution in complex time,starting from a wavefunctionψwith an angular momentumq¯h along z,as already done in[15];our solution of the Gross-Pitaevskii equation with imposedsymmetry is a local mimimum of energy in the subspace of functions with angular momentum q¯halong z,but not necessarily a local minimum in the whole functional space,as we will see for|q|>1.In the Thomas-Fermi regimeµ≫¯hωweﬁnd that the solutions can be well reproduced bya variational Ansatz of the formψ(x,y)=e iqθ[tanhκq r]|q| ˜µ−1Ng 1/2(25) whereθis the polar angle in the x−y plane and where˜µ,the chemical potential in the lab frame˜µ=µ+q¯hΩ(26) does not depend onΩ.In this Ansatz the vortex core is accounted for by tanh|q|,a function thatvanishes as r|q|in zero as it should,and the condensate density outside the core coincides withthe Thomas-Fermi approximation commonly used for the zero-vortex solution[2].We calculate themean energy Eq.(7)of the variational Ansatz and we minimize it with respect to the variationalparameterκq;we getκq= ˜µmq2 +∞0du u tanh2|q|(u)−1 2(28) is a number(c1=0.7687,c2=0.5349,...).In order for the vortex of charge q to be a local minimum of energy,the operator L c of Eq.(19)has to be positive.This implies that the operator on theﬁrst line,ﬁrst column of L c,the so-calledHartree-Fock Hamiltonian,be positive:H HF=H⊥+2Ng|ψ|2−˜µ+q¯hΩ−ΩL z≥0.(29) To show that this is not the case it is suﬃcient toﬁnd a wavefunction f(x,y)leading to a negative expectation value for H HF.As the potential appearing in H HF has a dip at r=0we have taken fof a form localized around r=0:1f(x,y)=¯h2 1/2r (30) whereγis adjusted to minimize the expectation value.For e.g.q=2we takeγ=1leading tof|H HF|fsection the trap is axi-symmetry with a time dependent frequencyω(t).We consider the evolutionin the laboratory frame,as the detection is performed in this frame:i¯h∂tψlab= −¯h22mω2(t)r2+Ng|ψlab|2 ψlab.(32)As shown in[19,20]the eﬀect of the time dependence ofω(t)can be absorbed by a scaling and gaugetransform of the wavefunction:1ψlab( r,t)=−ω2(t)λ(34)λ3with initial conditionsλ(0)=1,˙λ(0)=0;if the trap in the x−y plane is abruptly switched oﬀatt=0+the scaling parameter is given byλ(t)==dτ(36)λ2(t)weﬁnd that˜ψsolves the same equation asψlab with a constant trap frequency equal toω(0):i¯h∂τ˜ψ= −¯h22mω2(0)r2+Ng|˜ψ|2 ˜ψ.(37)Asψlab rotates in the trap at the frequencyΩin the lab frame,so does˜ψin terms of the renormalizedtimeτ.In the limit of t→∞,τtends to aﬁnite valueτmax,so that˜ψis rotated by aﬁnite angleduring the ballistic expansion:Ωτmax=Ω ∞0dt2ΩVI.INTUITIVE V ARIATIONAL CALCULATIONTo get a better understanding of the numerical results we now proceed to an intuitive Ansatzfor the wavefunction with several vortices.It coincides very well with the numerical results andallows an easy construction of the minimal energy conﬁgurations with vortices.It gives a physical understanding of the stability conditions and of the structure of the solutions:a set of n vortices isequivalent to a gas of interacting particles in presence of an external potential adjusted by the rota-tion frequency of the trap.We restrict to the case of an axi-symmetric trap,a good approximationfor weak(<10%)non-axisymmetries(see section III B).A.Ansatz for the densityTo construct the Ansatz we splitψin a modulus and a phase:ψ(x,y)=|ψ|e iS.(40) In the Thomas-Fermi regime,the modulus in presence of n vortices appears as a slowly varyingenvelope given by the Thomas-Fermi approximation used in the0-vortex case:ψslow= µ−1Ng 1/2(41)with narrow holes digged by the vortices with charge q=±1,represented by tanh functions ofadjustable widths and with zeros at adjustable positions:|ψ|=ψslow×nk=1tanh[κk| r− αk R|].(42)The positions of the vortex cores αk are expressed in units of the Thomas-Fermi radius R of the condensate:R= mω2.(43)From section IV B we expect as typical values for the inverse width of the vortex coresκk≃(mµ/¯h2)1/2.The chemical potential is not an independent variable but is expressed as a functionof the other parameters from the normalization condition ψ|ψ =1;neglecting overlap integralsbetween the holes we getµ=µ0 1+2n k=1(1−α2k)ln2(κR)4) (44)where1/(κR)4∼(¯hω/µ)4≪1and whereµ0is the Thomas-Fermi approximation for the condensatechemical potential without vortices:µ0= mω2Ngcentered on the vortex core and S 0is the single-valued part of the phase.The function S 0can in principle be determined from the modulus of ψfrom the continuity equation:div[|ψ|2 v ]=0.(47)The local velocity ﬁeld v is related to the phase S byv =¯h ¯h [x∂y −y∂x ]|ψ|2=0.(49)This can be turned into an equation for the single-valued part S 0of the phase;because the density |ψ|2in a trap vanishes at the border of the condensate S 0is uniquely determined (up to a constant)by the resulting equation (see Appendix);this is to be contrasted to the case of superﬂuid helium in a container,where the ﬂux,not the density,vanishes at the border,which requires a boundary condition on the gradient of the phase.Eq.(49)can be solved for a non-axisymmetric trap in the absence of vortices.The solution is given byS (x,y )=−m Ωω2x +ω2yxy (50)which leads to a change in the energy per particleδE =−1(ω2x +ω2y )ω2x ω2y(51)where µT F is the Thomas-Fermi approximation for the chemical potential for Ω=0,µT F =(mωx ωy Ng/π)1/2[23].As can be seen in Fig.2this prediction is in good agreement with our numerical results.In presence of vortices the equation for S is more diﬃcult to solve analytically.From now on we consider the case of an axi-symmetric trap,as the energy ordering of the vortices solutions is not aﬀected for weak (<10%)non-axisymmetries (see section III B).For a single vortex at the center of the trap one can see that S 0=0solves Eq.(49).From the spatial dependence of the phase obtained numerically (section III B)for a displaced vortex or several vortices we have identiﬁed the following heuristic Ansatz,obtained in setting ωx =ωy =ωin Eq.(50):S 0(x,y )≡0(52)that we will use in the remaining part of the section.C.Further approximations for the mean energyIn the calculation of the mean energy,we make some further approximations in the spirit of the Ansatz Eq.(42).The reader not interested by these more technical considerations can proceed to the next subsection.The kinetic energy involves an integral of the gradient squared of the wavefunction:| ∇ψ|2=|ψ|2 ( ∇ln |ψ|)2+( ∇S )2 .(53)For the gradient of the modulus of ψwe neglect the variation of the slow envelope ψslow :∇ln |ψ|≃nk =1κktanh ′of ψinvolves holes with a density varying as 1−tanh 2=sech 2.In the following we keep the sech 2for the vortex k only if it is multiplied by ( ∇θk )2,a quantity diverging in the center of the core;the other terms lead toconverging integrals smaller by a factor (µ/¯h ω)2,which is the inverse surface of a vortex core ( d 3 r |ψslow |2sech 2κr ∝1/(κR )2).This ﬁnally leads toE kin ≃¯h 22mω2r 2+13µ0+nk =1W ( αk ,κk )+1µ012ln(1−α2)−q ¯h Ω (1−α2)2 +µ0(κR )2(60)where C =0.495063.The lines inEq.(60)correspond successively to E kin ,E rot and E pot .This can be seen as an eﬀective potential for the vortices.One can check that the part of W independent of Ωexpells the vortex core from the trap center,whereas the part proportional to Ωprovides a conﬁnement of the vortex core (see the following subsection).The vortex interaction potential is given by12m q αq β d 2 r |ψslow |2 ∇θ αR · ∇θ βR .(61)This interaction term is equivalent to the one found in the homogeneous case and describes a repulsive interaction for vortices turning in the same direction (q αq β>0)and is attractive for vortices with opposite charges [9].An attractive interaction will lead to the coalescence and consequently annihilation of vortices with opposite charges.Therefore we ﬁnd in stationary systems always vortices with equal charges.As the interaction potential V ( α, β)does not depend on the parameters κwe can optimize sepa-rately the self-energy part with respect to κand ﬁnd(κR)2=ξ2(1−α2) µ03(4ln2−1) 1/2≃1.08707.By rewriting the above equation as¯h2κ22ξ2 µ−1µ0 13+lnνµ0¯hω2(1−α2) (64) whereν=0.49312.E.Case of a single vortex:critical frequenciesIn Fig.4we have plotted the self-energy of a vortex as a function of the displacement of the corefrom the trap center,for diﬀerent values of the rotation frequencyΩ.The analytical predictioncoincides very well with the numerical value[24].ForΩ=0the position of the vortex at the trap center gives an energy maximum.ForΩ>0therotation of the trap provides an eﬀective conﬁnement of the vortex core at the center of the trap forpositive charges q(see the term proportional toΩin Eq.(64));from now one we therefore take allthe charges q k to be equal to+1.For a large enoughΩwe reach a situation where a vortex at thetrap center corresponds to a local energy minimum,by further increasingΩthe vortex state at thetrap center becomes a global minimum with energy less than the condensate without vortex.The above suggests that we have to distinguish two critical rotation frequencies:Theﬁrst onedeﬁnes the frequencyΩstab above which the vortex is a local minimum of energy.Above the frequencyΩc the single vortex solution has an energy lower than the condensate without vortex.We calculateΩstab from the condition d2W/dα2=0atα=0andΩc from the condition W=0atα=0:Ωc=¯hω2¯hω (65)Ωstab=¯hω2¯hω (66)where C′=e(2ln2+1)/3+1/2ν≃1.8011.As we are in the regimeµ0≫¯hωΩc is approximately twice Ωstab[25].Our prediction forΩc scale as(logµ0)/µ0as in[15],with a coeﬃcient C′leading to better agreement with the numerics.F.Case of several vorticesBy integrating Eq.(61)we get an explicit form for the vortex interaction potential for vortices with equal charges:V( α, β)=(¯hω)2(1− α· β)+1| α− β|4 (67)At short distances between the two vortex cores the logarithmic term in the above expression dominates,leading to a repulsive potential∼−2(1− α· β)log| α− β|(¯hω)2/µ0.In Fig.5we plot the interaction energy between a vortex at the center of the trap and one of equal charge displaced by αR;the interaction is purely repulsive.A conclusion which essentially holds as well for arbitrary vortex positions.In Fig.6we show the total(interaction+self-energy)for two vortices symmetrically displaced from the trap center,as function of the displacement;the analytical prediction coincides again very well with the numerical results[24].To obtain the equilibrium distance between the two vortex cores one minimizes the total energy overαin Fig.6.To get the minimal energy conﬁgurations as function of the rotation frequency of the trap,we minimize our analytical prediction for the energy over the positions of the n=1,2,...vortex cores.The result is shown in Fig.7.Each curve corresponds to aﬁxed value of n;it starts atΩ=Ωstab(n)(forΩ<Ωstab(n)there is no local minima of energy with n vortices);it becomes the global energyminimum forΩ=Ωc(n).We have plotted these two critical frequencies as function of n in Fig.8.We have also given numerical results(circles)in Fig.7.Even if there is good agreement between analytical and numerical results,we still need a numerical calculation to check the stability of thesolutions;our simple analytical Ansatz is indeed not suﬃcient to predict the destabilization of agiven vortex conﬁguration at highΩ,a phenomenon studied with a numerical calculation of theBogoliubov spectrum for a single vortex in[26].For aﬁxed value of the number of vortices n there may exist local minima of energy,in addition to the global minimum plotted in Fig.7,a situation known from superﬂuid helium[4].E.g.for n=6(see Fig.9)the global minimum of energy is given by a conﬁguration with six vortex cores on acircle;there exists also a local minimum of energy with one vortex core at the center of the trap andﬁve vortex cores on a circle.The energy diﬀerence per particle between the two conﬁgurations isvery small,δE≃0.002¯hωfor the parameters of theﬁgure and probably beyond the accuracy of ourvariational Ansatz.For relatively large rotation frequenciesΩone canﬁnd local minima of energyconﬁgurations with many vortices(see[4]for superﬂuid helium);we plot two conﬁgurations with18vortices in Fig.10,with an energy diﬀerenceδE=0.0034¯hω.In estimating the physical relevance of these energy diﬀerences one should keep in mind that NδE matters,rather thanδE,where N is the number of particles in the condensate: e.g.at aﬁnite temperature T the ground energy conﬁguration is statistically favored as compared to themetastable one when NδE≫k B T.VII.VORTICES IN A3D CONFIGURATIONWe have extended the numerical calculation to the case of a3D cigar-shaped trap,that is witha conﬁnement weaker along the rotation axis than in the x−y plane.Even in this case rotationof the trap can stabilize the vortex.We show in Fig.11density cuts of a solution with5vortices;the vortex cores are almost straight lines in the considered Thomas-Fermi regime,except at vicinityof the borders of the condensate.As in section VI the core diameter is determined by the localchemical potential in the gas.This suggests that our2D Ansatz(section VI)can be generalized to3D situations,with αk and κk depending on z.VIII.CONCLUSION AND PERSPECTIVESWe have presented in this paper an eﬃcient numerical algorithm and a heuristic variational Ansatz to determine the local minima energy conﬁgurations for a Bose-Einstein condensate stronglyconﬁned along z and subject to a rotating harmonic trap in the x−y plane.Our results can be used as aﬁrst step towardsﬁnite temperature calculations.Interesting prob-lems are e.g.the critical temperature for the vortex formation and the Magnus forces induced bythe non-condensed particles on the vortex core[27].Acknowledgement:We acknowledge useful discussions with Sandro Stringari and Dan Rokhsar.We thank J.Dalibard for useful comments on the manuscript.We thank the ITP at Santa Barbarafor its hospitality and the NSF for support under grant No.PHY94-07194.This work was partiallysupported by the TMR Network“Coherent Matter Wave Interactions”,FMRX-CT96-0002.∗L.K.B.is an unit´e de recherche de l’Ecole Normale Sup´e rieure et de l’Universit´e Pierre et Marie Curie,associ´e e au CNRS.APPENDIX A:UNIQUENESS OF THE PHASE FROM THE CONTINUITY EQUATION IN A TRAPConsider two solutions S1and S2of the continuity equation:mΩdiv[|ψ|2 ∇S]=。

On the Effect of the Internal Friction of Fluids on the Motion of Pendulums

ON THE EFFECT OF THE INTERNAL FRICTION OF FLUIDS ON THE MOTION OF PENDULUMSSir George Gabriel Stokes[Read December 9, 1850.][From the Transactions of the Cambridge Philosophical Society, Vol. IX. p. [8]Reprinted in Mathematical and Physical Papers, Sir George Gabriel Stokes and Sir J. Larmor, Vol. 3, 1880-1905]T HE great importance of the results obtained by means of the pendulum has induced philosophers to devote so much attention to the subject, and to perform the experiments with such a scrupulous regard to accuracy in every particular, that pendulum observations may justly be ranked among those most distinguished by modern exactness. It is unnecessary here to enumerate the different methods which have been employed, and the several corrections which must be made, in order to deduce from the actual observations the result which would correspond to the ideal case of a simple pendulum performing indefinitely small oscillations in vacuum. There is only one of these corrections which bears on the subject of the present paper, namely, the correction usually termed the reduction to a vacuum. On account of the inconvenience and expense attending experiments in a vacuum apparatus, the observations are usually made in air, and it then becomes necessary to apply a small correction, in order to reduce the observed result to what would have been observed had the pendulum been swung in a vacuum. The most obvious effect of the air consists in a diminution of the moving force, and consequent increase in the time of vibration, arising from the buoyancy of the fluid. The correction for buoyancy is easily calculated from the first principles of hydrostatics, and formed for a considerable time the only correction which it was thought necessary to make for reduction to a vacuum. But in the year 1828 Bessel, in a very important memoir in which he determined by a new method the length of the seconds' pendulum, pointed out from theoretical considerations the necessity of taking account of the inertia of the air as well as of its buoyancy. The numerical calculation of the effect of the inertia forms a problem of hydrodynamics which Bessel did not attack; but he concluded from general principles that a fluid, or at any rate a fluid of small density, has no other effect on the time of very small vibrations of a pendulum than that it diminishes its gravity and increases its moment of inertia. In the case of a body of which the dimensions are small compared with the length of the suspending wire, Bessel represented the increase of inertia by that of a mass equal to k times the mass of the fluid displaced, which must be supposed to be added to the inertia of the body itself. This factor k be determined experimentally for a sphere a little more than two inches in diameter, swung in air and in water. The result for air, obtained in a rather indirect way, was k = 0.9459, which value Bessel in a subsequent paper increased to 0.956. A brass sphere of the above size having been swung in water with two different lengths of wire in succession gave two values of k, differing a little from each other, and equal to only about two-thirds of the value obtained for air.The attention of the scientific world having been called to the subject by the publication of Bessel's memoir, fresh researches both theoretical and experimental soon appeared. In order to examine the effect of the air by a more direct method than that employed by Bessel, a large vacuum apparatus was erected at the expense of the Board of Longitude, and by means of this apparatus Captain (now Colonel) Sabine determined the effect of the air on the time of vibration of a particular invariable pendulum. The results of the experiments are contained in a memoir read before the Royal Society in March 1829, and printed in the Philosophical Transactions for that year. The mean of eight very consistent experiments gave 1.655 as the factor by which for that pendulum the old correction for buoyancy must be multiplied in order to give the whole correction on account of the air. A very remarkable fact was discovered in the course of these experiments. While the effects of air at the atmospheric pressure and under a pressure of about half an atmosphere were found to be as nearly as possible proportional to the densities, it was found that the effect of hydrogen at the atmospheric pressure was much greater, compared with the effect of air, than corresponded with its density. In fact, it appeared that the ratio of the effects of hydrogen and air on the times of vibration was about 1 to 5 1/4, while the ratio of the densities is only about 1 to 13. In speaking of this result Colonel Sabine remarks, "The difference of this ratio from that shewn by experiment is greater than can well be ascribed to accidental error in the experiment, particularly as repetition produced results almost identical. May it not indicate an inherent property in the elastic fluids, analogous to that of viscidity in liquids, of resistance to the motion of bodies passing through them, independently of their density ? a property, in such case,possessed by air and hydrogen gas in very different degrees; since it would appear from the experiments that the ratio of the resistance of hydrogen gas to that of air is more than double the ratio following from their densities. Should the existence of such a distinct property of resistance, varying in the different elastic fluids, be confirmed by experiments now in progress with other gases, an apparatus more suitable than the present to investigate the ratio in which it is possessed by them, could scarcely be devised: and the pendulum, in addition to its many important and useful purposes in general physics, may find an application for its very delicate, but, with due precaution, not more delicate than certain, determinations, in the domain of chemistry." Colonel Sabine has informed me that the experiments here alluded to were interrupted by a cause which need not now be mentioned, but that as far as they went they confirmed the result of the experiments with hydrogen, and pointed out the existence of a specific action in different gases, quite distinct from mere variations of density.Our knowledge on the subject of the effect of air on the time of vibration of pendulums has received a most valuable addition from the labours of the late Mr Baily, who erected a vacuum apparatus at his own house, with which he performed many hundreds of careful experiments on a great variety of pendulums. The experiments are described in a paper read before the Royal Society on the 31st of May 1832. The result for each pendulum is expressed by the value of n, the factor by which the old correction for buoyancy must be multiplied in order to give the whole effect of the air as deduced from observation. Four spheres, not quite 1 1/2 inch in diameter, gave as a mean n = 1.864, while three spheres, a little more than 2 inches in diameter, gave only 1.748. The latter were nearly of the same size as those with which Bessel, by a different method, had obtained k = 0.946 or 0.956, which corresponds to n = 1.946 or 1.956. Among the "Additional Experiments " in the latter part of Baily's paper, is a set in which the pendulums consisted of plain cylindrical rods. With these pendulums it was found that n regularly increased, though according to an unknown law, as the diameter of the rod decreased. While a brass tube 1 1/2 inch in diameter gave n equal to about 2.3, a thin rod or thick wire only 0.072 inch in diameter gave for n a value as great as 7.530.Mathematicians in the meanwhile were not idle, and several memoirs appeared about this time, of which the object was to determine from hydrodynamics the effect of a fluid on the motion of a pendulum. The first of these came from the pen of the celebrated Poisson. It was read before the French Academy on the 22nd of August 1831, and is printed in the 11th Volume of the Memoirs. In this paper, Poisson considers the case of a sphere suspended by a fine wire, and oscillating in the air, or in any gas. He employs the ordinary equations of motion of an elastic fluid, simplified by neglecting the terms which involve the square of the velocity; but in the end, in adapting his solution to practice, be neglects, as insensible, the terms by which alone the action of an elastic differs from that of an incompressible fluid, so that the result thus simplified is equally applicable to fluids of both classes. He finds that when insensible quantities are neglected n = 1.5, so that the mass which we must suppose added to that of the pendulum is equal to half the mass of the fluid displaced. This result does not greatly differ from the results obtained experimentally by Bessel in the case of spheres oscillating in water, but differs materially from the result he bad obtained for air. It agrees pretty closely with some experiments which bad been performed about fifty years before by Dubuat, who bad in fact anticipated Bessel in shewing that the time of vibration of a pendulum vibrating in a fluid would be affected by the inertia of the fluid as well as by its density. Dubuat's labours on this subject had been altogether overlooked by those who were engaged in pendulum experiments; probably because such persons were not likely to seek in a treatise on hydraulics for information connected with the subject of their researches. Dubuat had, in fact, rather applied the pendulum to hydrodynamics than hydrodynamics to the pendulum.In the Philosophical Magazine for September 1833, p. 185, is a short paper by Professor Challis, on the subject of the resistance to a ball pendulum, After referring to a former paper, in which he had shewn that no sensible error would be committed in a problem of this nature by neglecting the compressibility of the fluid even if it be elastic, Professor Challis, adopting a particular hypothesis respecting the motion, obtains 2 for the value of the factor n for such a pendulum. This mode of solution, which is adopted in several subsequent papers, has given rise to a controversy between Professor Challis and the Astronomer Royal, who maintains the justice of Poisson's result.In a paper read before the Royal Society of Edinburgh on the 16th of December 1833, and printed in the 13th Volume of the Society's Transactions, Green has determined from the common equations of fluid motion the resistance to an ellipsoid performing small oscillations without rotation. The result is expressed by a definite integral; but when two of the principal axes of the ellipsoid become equal, the integral admits of expression in finite terms, by means of circular or logarithmic functions. When the ellipsoid becomes a sphere, Green's result reduces itself to Poisson's.In a memoir read before the Royal Academy of Turin on the 18th of January 1835, and printed in the 37th Volume of the memoirs of the Academy, M. Plana has entered at great length into the theory of the resistance of fluids to pendulums. This memoir contains, however, rather a detailed examination of various points connected with the theory, than the determination of the resistance for any new form of pendulum. The author first treats the case of an incompressible fluid, and then shews that the result would be sensibly the same in the case of an elastic fluid. In the case of a ball pendulum, the only one in which a complete solution of the problem is effected, M. Plana's result agrees with Poisson's.In a paper read before the Cambridge Philosophical Society on the 29th of May 1843, and printed in the 8th Volume of the Transactions, p. 105*, 1 have determined the resistance to a ball pendulum oscillating within a concentric spherical envelope, and have pointed out the source of an error into which Poisson had fallen, in concluding that such an envelope would have no effect . When the radius of the envelope becomes infinite, the solution agrees with that which Poisson had obtained for the case of an unlimited mass of fluid. I have also investigated the increase of resistance due to the confinement of the fluid by a distant rigid plane. The same paper contains likewise the calculation of the resistance to a long cylinder oscillating in a mass of fluid either unlimited, or confined by a cylindrical envelope, having the same axis as the cylinder in its position of equilibrium. In the case of an unconfined mass of fluid, it appeared that the effect of inertia was the same as if a mass equal to that of the fluid displaced were distributed along the axis of the cylinder, so that n = 2 in the case of a pendulum consisting of a long cylindrical rod. This nearly agrees with Baily's result for the long 1 ½-inch tube ; but, on comparing it with the results obtained with the cylindrical rods, we observe the same sort of discrepancy between theory and observation as was noticed in the case of spheres. The discrepancy is, however, far more striking in the present case, as might naturally have been expected, after what had been observed with spheres, on account of the far smaller diameter of the solids employed.* [Ante, Vol. 1. p. 179.]A few years ago Professor Thomson communicated to me a very beautiful and powerful method which he had applied to the theory of electricity, which depended on the consideration of what he called electrical images. The same method, I found, applied, with a certain modification, to some interesting problems relating to ball pendulums. It enabled me to calculate the resistance to a sphere oscillating in presence of a fixed sphere, or within a spherical envelope, or the resistance to a pair of spheres either in contact, or connected by a narrow rod, the direction of oscillation being, in all these cases, that of the line joining the centres of the spheres. The effect of a rigid plane perpendicular to the direction of motion is of course included as a particular case. The method even applies, as Professor Thomson pointed out to me, to the uncouth solid bounded by the exterior segments of two intersecting spheres, provided the exterior angle of intersection be a submultiple of two right angles. A set of corresponding problems, in which the spheres are replaced by long cylinders, may be solved in a similar manner. These results were mentioned at the meeting of the British Association at Oxford in 1847, and are noticed in the volume of reports for that year, but they have not yet been published in detail.The preceding are all the investigations that have fallen under my notice, of which the object was to calculate from hydrodynamics the resistance to a body of given form oscillating as a pendulum. They all proceed on the ordinary equations of the motion of fluids. They all fail to account for one leading feature of the experimental results, namely, the increase of the factor n with a decrease in the dimensions of the body. They recognize no distinction between the action of different fluids, except what arises from their difference of density.In a conversation with Dr Robinson about seven or eight years ago on the subject of the application of theory to pendulums, he noticed the discrepancy which existed between the results of theory and experiment relating to a ball pendulum, and expressed to me his conviction that the discrepancy in question arose from the adoption of the ordinary theory of fluid motion, in which the pressure is supposed to be equal in all directions. He also described to me a remarkable experiment of Sir James South's which be had witnessed. This experiment has not been published, but Sir James South has kindly allowed me to mention it. When a pendulum is in motion, one would naturally have supposed that the air near the moving body glided past the surface, or the surface past it, which comes to the same thing if the relative motion only be considered, with a velocity comparable with the absolute velocity of the surface itself. But on attaching a piece of gold leaf to the bottom of a pendulum, so as to stick out in a direction perpendicular to the surface, and then setting the pendulum in motion, Sir James South found that the gold leaf retained its perpendicular position just as if the pendulum had been at rest ; and it was not till the gold leaf carried by the pendulum had been removed to some distance from the surface, that it began to lag behind. Thisexperiment shews clearly the existence of a tangential action between the pendulum and the air, and between one layer of air and another. The existence of a similar action in water is clearly exhibited in some experiments of Coulomb's which will be mentioned in the second part of this paper, and indeed might be concluded from several very ordinary phenomena, Moreover Dubuat, in discussing the results of his experiments on the oscillations of spheres in water, notices a slight increase in the effect of the water corresponding to an increase in the time of vibration, and expressly attributes it to the viscosity of the fluid.Having afterwards occupied myself with the theory of the friction of fluids, and arrived at general equations of motion, the same in essential points as those which had been previously obtained in a totally different manner by others, of which, however, I was not at the time aware, I was desirous of applying, if possible, these equations to the calculation of the motion of some kind of pendulum. The difficulty of the problem is of course materially increased by the introduction of internal friction, but as I felt great confidence in the essential parts of the theory, I thought that labour would not be ill-bestowed on the subject. I first tried a long cylinder, because the solution of the problem appeared likely to be simpler than in the case of a sphere. But after having proceeded a good way towards the result, I was stopped by a difficulty relating to the determination of the arbitrary constants, which appeared as the coefficients of certain infinite series by which the integral of a certain differential equation was expressed. Having failed in the case of a cylinder, I tried a sphere, and presently found that the corresponding differential equation admitted of integration in finite terms, so that the solution of the problem could be completely effected. The result, I found, agreed very well with Baily's experiments, when the numerical value of a certain constant was properly assumed ; but the subject was laid aside for some time. Having afterwards attacked a definite integral to which Mr Airy bad been led in considering the theory of the illumination in the neighbourhood of a caustic, I found that the method which I had employed in the case of this integral* would apply to the problem of the resistance to a cylinder, and it enabled me to get over the difficulty with which I bad before been baffled. I immediately completed the numerical calculation, so far as was requisite to compare the formulae with Baily's experiments on cylindrical rods, and found a remarkably close agreement between theory and observation. These results were mentioned at the meeting of the British Association at Swansea in 1848, and are briefly described in the volume of reports for that year.The present paper is chiefly devoted to the solution of the problem in the two cases of a sphere and of a long cylinder, and to a comparison of the results with the experiments of Baily and others. Expressions are deduced for the effect of a fluid both on the time and on the arc of vibration of a pendulum consisting either of a sphere, or of a cylindrical rod, or of a combination of a sphere and a rod. These expressions contain only one disposable constant, which has a very simple physical meaning, and which I propose to call the index of friction of the fluid. This constant we may conceive determined by one observation, giving the effect of the fluid either on the time or on the arc of vibration of any one pendulum of one of the above forms, and then the theory ought to predict the effect both on the time and on the arc of vibration of all such pendulums. The agreement of theory with the experiments of Baily on the time of vibration is remarkably close. Even the rate of decrease of the are of vibration, which it formed no part of Baily's object to observe, except so far as was necessary for making the small correction for reduction to indefinitely small vibrations, agrees with the result calculated from theory as nearly a& could reasonably be expected under the circumstances.* [Ante, Vol. II. p. 328.]It follows from theory that with a given sphere or cylindrical rod the factor n increases with the time of vibration. This accounts in a good measure for the circumstance that Bessel obtained so large a value of k for air, as is shewn at length in the present paper; though it unquestionably arose in a great degree from the increase of resistance due to the close proximity of a rigid plane to the swinging ball.I have deduced the value of the index of friction of water from some experiments of Coulomb's on the decrement of the are of oscillation of disks, oscillating in water in their own plane by the torsion of a wire. When the numerical value thus obtained is substituted in the expression for the time of vibration of a sphere, the result agrees almost exactly with Bessel's experiments with a sphere swung in water.The present paper contains one or two applications of the theory of internal friction to problems which are of some interest, but which do not relate to pendulums. The resistance to a sphere moving uniformly in a fluid may be obtained as a limiting case of the resistance to a ball pendulum, provided the circumstances be such that the square of the velocity may be neglected. The resistance thus determined proves to be proportional, for a given fluid and a given velocity, not to the surface, but to the radius of the sphere; and therefore the accelerating force of theresistance increases much more rapidly, as the radius of the sphere decreases, than if the resistance varied as the surface, as would follow from the common theory. Accordingly, the resistance to a minute globule of water falling through the air with its terminal velocity depends almost wholly on the internal friction of air. Since the index of friction of air is known from pendulum experiments, we may easily calculate the terminal velocity of a globule of given size, neglecting the part of the resistance which depends upon the square of the velocity. The terminal velocity thus obtained is so small in the case of small globules such as those of which we may conceive a cloud to be composed, that the apparent suspension of the clouds does not seem to present any difficulty. Had the resistance been determined from the common theory, it would have been necessary to suppose the globules much more minute, in order to account in this way for the phenomenon. Since in the case of minute globules falling with their terminal velocity the part of the resistance depending upon the square of the velocity, as determined by the common theory, is quite insignificant compared with the part which depends on the internal friction of the air, it follows that were the pressure equal in all directions in air in the state of motion, the quantity of water which would remain suspended in the state of cloud would be enormously diminished. The pendulum thus, in addition to its other uses, affords us some interesting information relating to the department of meteorology.The fifth section of the first part of the present paper contains an investigation of the effect of the internal friction of water in causing a series of oscillatory waves to subside. It appears from the result that in the case of the long swells of the ocean the effect of friction is insignificant, while in the case of the ripples raised by the wind on a small pool, the motion subsides very rapidly when the disturbing force ceases to act.PART I.ANALYTICAL INVESTIGATION.SECTION I.Adaptation of the general equations to the case of the fluid surrounding a body which oscillates as a pendulum. General laws which follow from the form of the equations. Solution of the equations in the case of an oscillating plane.1. IN a paper "On the Theories of the Internal Friction of Fluids in Motion, &c.*,'' which the society did me the honour to publish in the 8th Volume of their Transactions, I have arrived at the following equations for calculating the motion of a fluid when the internal friction of the fluid itself is taken into account, and consequently the pressure not supposed equal in all directions: with two more equations which may be written down from symmetry. In these equations u, v, w, are the components of the velocity along the rectangular axes of x, y, z; X, Y, Z are the components of the accelerating force ; p is the pressure, t the time, ρ the density, and µ a certain constant depending on the nature of the fluid.The three equations of which (1) is the type are not the general equations of motion which apply to a heterogeneous fluid when internal friction is taken into account, which are those numbered 10 in my former paper, but are applicable to a homogeneous incompressible fluid, or to a homogeneous elastic fluid subject to small variations of density, such as those which accompany sonorous vibrations. It must be understood to be included in the term homogeneous that the temperature is uniform throughout the mass, except so far as it may be raised or lowered by sudden condensation or rarefaction in the case of an elastic fluid. The general equations contain the differential coefficients of the quantity µwith respect to x, y, and z; but the equations of the form (1) are in their present shape even more general than is required for the purposes of the present paper.* [Ante. Vol. I. p. 75.]These equations agree in the main with those which had been previously obtained, on different principles, by Navier, by Poisson, and by M. de Saint-Venant, as I have elsewhere observed*. The differences depend only on the coefficient of the last term, and this term vanishes in the case of an incompressible fluid, to which Navier bad confined his investigations.The equations such as (1) in their present shape are rather complicated, but in applying them to the case of a pendulum they may be a good deal simplified without the neglect of any quantities which it would be important to retain. In the first place the motion is supposed very small, on which account it will be allowable to neglect the terms which involve the square of the velocity. In the second place, the nature of the motion that we have got to deal with is such that the compressibility of the fluid has very little influence on the result, so that we may treat the fluid as incompressible, and consequently omit the last terms in the equations. Lastly, the forces X, Y, Z are in the present case the components of the force of gravity, and if we writeFor p, we may omit the terms X, Y, Z.If z' be measured vertically downwards from a horizontal plane drawn in the neighbourhood of the pendulum, and if g be the force of gravity, ∫ (Xdx + Ydy + Zdz) = gx', the arbitrary constant, or arbitrary function of the time if it should be found necessary to suppose it to be such, being included in Π. The part of the whole force acting on the pendulum which depends on the terms Π+ gρ z'is simply a force equal to the weight of the fluid displaced, and acting vertically upwards through the centre of gravity of the volume.* Report on recent researches in Hydrodynamics. Report of the British Association for 1846, p. 16. [Ante, Vol. I.p. 182.]When simplified in the manner just explained, the equations such as (1) becomewhich, with the equation of continuity,are the only equations which have to be satisfied at all points of the fluid, and at all instants of time.In applying equations (2) to a particular pendulum experiment, we may suppose µconstant ; but in order to compare experiments made in summer with experiments made in winter, or experiments made under a high barometer with experiments made under a low, it will be requisite to regard µ as a quantity which may vary with the temperature and pressure of the fluid. As far as the result of a single experiment*, which has been already mentioned, performed with a single elastic fluid, namely air, justifies us in drawing such a general conclusion, we may assert that for a given fluid at a given temperature µ varies as ρ +.2. For the formation of the equations such as (1), 1 must refer to my former paper; but it will be possible, in a few words, to enable the reader to form a clear idea of the meaning of the constant µ.Conceive the fluid to move in planes parallel to the plane of xy, the motion taking place in a direction parallel to the axis of y. The motion will evidently consist of a sort of continuous sliding, and the differential coefficient。

填空题翻译

Exercise 11. 起初，我被她严肃的样子吓到了；但是当我更深入的了解她之后，我发觉她是非常（搞笑的）。

【如果不是为了做题，我认为可译为“她的笑点很低”】2. 新生婴儿既不是一个被动形体，也不是主动形体，而是一个可以被称作主动（接受）的形体，热切注意着外界的情景和声音。

3. 武器运输（停顿）带来的喘息之机给作战各方一个机会去重新评估自己的处境。

4. 重组DNA实验的倡议者决定（支持）联邦政府监管他们的工作，他们希望通过这样的妥协，能够预先阻止拟定中的来自州政府和地方政府的可能更为严格的控制。

5. 即使那些不同意卡门观点的人也很少因为她把观点表达出来而诟病她，因为她的观点不仅是有争议的，而且是（经过缜密思考的）。

6. 在目前变暖的趋势超出了正常气候的波动范围之前，科学家将会对于大气中二氧化碳含量的增加导致长期气温上升效应的可能性存在相当程度的（不确定性）。

【until单独出现与before意思一样。

】7. 目前数据表明，尽管在恐惧和攻击之间存在（过渡）状态，但恐惧和攻击无论在生理上还是心理上都是截然不同的。

8. 尽管伊冯·雷娜1974年的电影有女权主义的内涵，但这部电影要（早于）电影的制作人参与到女权政治运动中。

【feminist: adj. Of or relating to feminism [AHD]】9. 他们的忠诚对象的（次序），首先是对自己，其次是亲属，然后是本部落成员，最后是全体同胞。

10. 根除污染不仅仅是一个（美学）问题，尽管大自然宏伟的美确实是一个很重要的考虑因素。

Exercise 21. 该公司只期待其销售额在明年有一个（适度的）增长，尽管为恢复其零售业务，已做出了为期一年的努力。

2. 托马斯·佩恩，他的政治著作通常很华丽，在私生活方面，他却惊人的（简朴）：住着租来的房子，吃得很少，穿着朴素的衣服。

3. 暴露在低强度的伽马射线下可以减缓食物中腐败微生物的生长速率，与此作用方式大致相同的是，巴氏消毒法中的低热（抑制了）牛奶中微生物的腐败作用。

机械工程学专业词汇英语翻译(A)1

机械工程学专业词汇英语翻译(A)1abandon 抛弃abaxial 离轴的ablation 烧蚀abnormal liquid 异常液体abrasion 磨耗abrasion hardness 耐磨硬度abrasion test 磨损试验abrasion tester 磨损试验机abrasives 研磨材料abrupt perturbation 突然扰动abscissa 横坐标absence of collision 无碰撞absence of gravity 失重absence of stress 无应力absence of vortices 无旋涡absolute 绝对的absolute acceleration 绝对加速度absolute angular momentum 绝对角动量absolute ceiling 绝对升限absolute coordinates 绝对坐标absolute deviation 绝对偏差absolute elastic body 完全弹性体absolute equilibrium 绝对平衡absolute extremum 绝对极值absolute flying height 绝对飞行高度absolute frequency 绝对频率absolute geopotential 绝对位势absolute humidity 绝对湿度absolute instability 绝对不稳定性absolute motion 绝对运动absolute path 绝对路径absolute perturbation 绝对扰动absolute pressure 绝对压力absolute rest 绝对静止absolute rotation 绝对旋转absolute similarity 完全相似性absolute stability margin 绝对稳定性限度absolute temperature 绝对温度absolute thermometer 绝对温度表absolute velocity 绝对速度absolute viscosity 绝对粘度absolute vorticity 绝对涡度absolute weight 绝对重量absolute zero 绝对零度absolute zero point 绝对零度absorbability 吸收性absorbing agent 吸收剂absorbing medium 吸收媒质absorbing resistance 吸收阻抗absorptiometer 吸收率计absorption 吸收；缓冲absorption curve 吸收曲线absorption dynamometer 吸收功率计absorption heat 吸收热absorption loss 吸收损失absorption model 吸收模型absorption potential 吸收势absorption tube 吸收管absorption wave meter 吸收式波长计absorptive 吸收的absorptive power 吸收本领absorptivity 吸收率accelerated creep 加速蠕变accelerated motion 加速运动accelerating ability 加速能力accelerating field 加速场accelerating gradient 加速梯度accelerating impact 加速撞击accelerating period 加速周期accelerating tube 加速管accelerating unit 加速装置acceleration 加速度acceleration diagram 加速度图acceleration energy 加速度能量acceleration field 加速度场acceleration meter 加速度计acceleration nozzle 加速喷嘴acceleration of creep 蠕变加速度acceleration of gravity 重力加速度acceleration of moving space 牵连加速度acceleration potential 加速势acceleration pressure 加速压acceleration time graph 加速度时间图acceleration vector 加速度矢量acceleration wave 加速波acceleration work 加速功accelerationless 无加速的accelerograph 加速度记录仪accelerometer 加速度计accessibility 可达性accessible point 可达点accidental 偶然的accidental coincidence 偶然符合accidental error 随机误差accidental resonance 偶然共振accommodation 适应accommodation coefficient 适应系数accumulated error 累积误差accumulator 蓄压器储压器accuracy 准确度accuracy of measurement 测量准确度accuracy of readings 读数准确度accurate adjustment 精确蝶accurate measurement 精确测量accurate model 准确模型accurate similarity 准确相似accurate simulation 准确模拟acicular structure 针状组织acoustic 声的acoustic absorption 声吸收acoustic absorptionsound absorption 声吸收acoustic absorptivity 声吸收率acoustic admittance 声导纳acoustic analysis 声学分析acoustic baffle 隔音板acoustic conductivity 声导率acoustic dispersion 声弥散acoustic disturbance 声音干扰acoustic efficiency 声效率acoustic energy 声能acoustic field 声场acoustic filter 滤声器acoustic frequency 音频acoustic impedance 声阻抗acoustic load 声负载acoustic material 隔声材料acoustic mechanical efficiency 声机械效率acoustic power 声功率acoustic pressure 声压acoustic radiation pressure 声辐射压acoustic reactance 声抗acoustic resistance 声阻acoustic resonance 共鸣acoustic velocity 声速acoustical 声的acoustical wave 声波acting force 织力action at distance 超距酌action center 活动中心action integral 酌积分action of deflagration 爆燃酌action of force 力的酌action principle 酌原理action sphere 酌区action turbine 冲唤涡轮action variable 酌变量action wave 酌波activation 活化active earth pressure 织土压active flight 织飞行active force 织力active gas 活性气体active load reaction 有功负载反酌active pressure 织压力activity of force 力功率actual load 实际载荷actual stress 实际应力actual value 实际值actuator 执行器acyclic 非循环的adaptability 适应性adapter 转接器adaptometer 适应计addition 附加additional drag 附加阻力additional load 附加载荷additional mass 附加质量additional pressure 附加压力adhere 粘着adherence 附着adhesion 附着adhesion coefficient 粘着系数adhesive force 粘附力adhesive tension 粘附张力adiabat 绝热线adiabatic 绝热的adiabatic approximation 绝热近似adiabatic atmosphere 绝热大气adiabatic calorimeter 绝热式量热器adiabatic change 绝热变化adiabatic change of state 态的绝热变化adiabatic compression 绝热压缩adiabatic cooling 绝热冷却adiabatic curve 绝热线adiabatic efficiency 绝热效率adiabatic ellipse 绝热椭圆adiabatic equilibrium 绝热平衡adiabatic expansion 绝热膨胀adiabatic factor 绝热因子adiabatic heating 绝热加热adiabatic hypothesis 绝热假设adiabatic invariant 绝热不变量adiabatic invariant of eddy 涡旋的绝热不变量adiabatic invariant of vortex 涡旋的绝热不变量adiabatic perturbation 绝热扰动adiabatic principle 绝热原理adiabatic process 绝热过程adiabatic pulsations 绝热脉动adjoint operator 伴算子adjustable guide vane 可导叶adjusting device 蝶装置adjusting spring 蝶弹簧adjusting valve 蝶阀adjusting wedge 蝶楔块adjustment 蝶adjustment mark 照准标志admissible concentration 容许浓度admissible crror 容许误差admissible load 容许荷载admissible pressure 容许压力admissible stress 容许应力admissible value 容许值admission 进气admission pipe 进气管admission pressure 进气压力admixture 混合物adsorb 吸附adsorbent 吸附剂adsorption 吸附adsorption force 吸附力adsorption layer 吸附层advancing rate 超前速率advancing wave 前进波advection 平流advection fog 平另advective 平聊aeration 充气aerator 通风机aerial 空气的aerial ropeway 架空死aeroballistics 航空弹道学aerodonetics 滑翔学aerodromics 滑翔力学aerodromometry 空气速度测量法aerodynamic action 空气动力酌aerodynamic analogy 空气动力比拟aerodynamic angle of attack 气动迎角aerodynamic angle of incidence 气动迎角aerodynamic balance 风洞天平aerodynamic center 气动中心aerodynamic coefficient 气动力系数aerodynamic derivative 空气动力导数aerodynamic drag 气动阻力aerodynamic force 气动力aerodynamic heating 气动力加热aerodynamic lift 气动升力aerodynamic resistance 气动阻力aerodynamic stability 空气动力稳定性aerodynamical 空气动力学的aerodynamical moment 气动力矩aerodynamics 空气动力学aerodyne 重航空器aeroelasticity 气动弹性aeroelastics 气动弹性力学aeroengine 飞机发动机aerohydrodynamics 空气铃动力学aerology 高空气象学aeromechanics 航空力学aerometer 气体比重计aeromotor 飞机发动机aeronautical 航空的aeronautics 航空学aeroplane 飞机aeropulse engine 脉动式喷气发动机aerosol 气溶胶aerospace engineering 航空航天技术aerostat 轻航空器aerostatics 气体静力学aerothermodynamics 气动热力学aerothermoelasticity 空气热弹性学；气动热弹性aerotonometry 气体张力测量法affine transformation 仿射变换affinity 亲合力after effect 后效after effect function 后效函数afterbody 后部afterburner 加力燃烧室aftershock wave 余震波age hardening 时效硬化ageing 应变时效ageing test 老化试验agglomeration 凝聚aileron 副翼air amount 空气量air brake 空气制动器air bubble 气泡air buffer 空气缓冲器air burst 空中爆炸air cap 空气冠air circulation 空气环流air column 空气柱air compressor 空气压缩机air condenser 空气电容器air conveying 气龄送air coolant 空气冷却剂air cooling 空气冷却air coordinates 空间坐标air current 气流air cushion 气垫air cylinder 压气缸air damper 空气阻尼器air damping 空气阻尼air density 空气密度air drag 空气阻力air duct 风道air eddy 空气涡旋air flow 气流空气量air flow meter 气疗air friction 空气摩擦air gap 空隙air gas 风煤气air hammer 空气锤air hardening 空气淬火air hoist 风动起重滑车air humidity 空气湿度air inflating 充气air injection diesel engine 空气喷射柴油发动机air inrush 空气侵入air intake valve 进气阀air jet 空气喷射air pipe 气管air plasma 空气等离子体air pressure gage 空气压力计air pressure head 空气压头air pressure reducer 空气减压器air proof 气密的air pump 空气泵air register 空气活门air relief cock 放气塞air reservoir 储气筒air resistance 空气阻力air shock wave 空气激波air speed 空气速率air speed indicator 空气速率指示器air streamline 空气吝air tank 空气箱air temperature 气温air tight 气密的air to air missile 空对空导弹air trajectory 空气轨迹air wave 空气波air wedge 空气楔aircraft dynamics 飞机动力学airfoil 机翼airfoil profile 翼型airfoil section 翼剖面airfoil theory 机翼理论airless injection 无气喷射airline 飞行航线airlock 气锁airmechanics 空气力学airplane 飞机airscrew 空气螺旋桨。

Vortices in Schwinger-Boson Mean-Field Theory of Two-Dimensional Quantum Antiferromagnets

a rXiv:c ond-ma t/95471v119Apr1995Vortices in Schwinger-Boson Mean-Field Theory of Two-Dimensional Quantum Antiferromagnets Tai-Kai Ng department of Physics,Hong Kong University of Science and Technology,Clear Water Bay Road,Kowloon,Hong Kong (February 6,2008)Abstract In this paper we study the properties of vortices in two dimensional quantum antiferromagnets with spin magmitude S on a square lattice within the frame-work of Schwinger-boson mean-ﬁeld theory.Based on a continuum descrip-tion,we show that vortices are stable topological excitations in the disordered state of quantum antiferromagnets.Furthermore,we argue that vortices can be divided into two kinds:the ﬁrst kind always carries zero angular momen-tum and are bosons,whereas the second kind carries angular momentum S under favourable conditions and are fermions if S is half-integer.A plausible consequence of our results relating to the RVB theories of High-T c supercon-ductors is pointed out.PACS Nos,75.10.Jm,75.30.Ds,79.60.-iTypeset using REVT E XI.INTRODUCTIONIn the past few years there has been a lot of interests in the study of quantum anti-ferromagnets in two dimension on a square lattice,stimulated by the discovery of High-T c superconductors[1,2].Among others,one approximated approach to the quantum antiferro-magnet problems is the Schwinger-Boson Mean-ﬁeld Theory(SBMFT).[2].In this approach, the quantum spins are represented as Schwinger bosons and an approximated ground state is constructed by bose condensation of spin-singlet pairs.The mean-ﬁeld theory can also be formulated in a large-N expansion as the saddle point solution to a generalized SU(N) quantum spin model[2,3].In the limit N→∞,the mean-ﬁeld theory becomes exact. SBMFT predicts that in one dimension,Heisenberg antiferromagnet is always disordered, with a non-zero spin gap in the excitation spectrum.The theory is found to give an adequate description for integer spin chains,while it fails to describe the massless state of half-integer spin chains.This is because the topological Berry phase term which plays crucial role in the latter case is not taken into account correctly in SBMFT.[4]However,in two dimension topological term does not exist and SBMFT is more reliable.In particular,the theory pre-dicts that the disordered(spin gap)phase exists only when the spin magnitude S is small enough,when S<S c∼0.19.It turns out that SBMFT oﬀers a fairly accurate description for the magnetic properties of the High-T c compounds in the low doping regime[5].However, at large doping levels,the generalization of SBMFT which includes holes as fermions[6], does not seem to describe the High-T c compounds correctly.For example,photo-emission experiments[7]indicate that the compounds have”large”Fermi-surfaces which satisfy Lut-tinger theorem,whereas the generalization of SBMFT to include holes predicts a”small”Fermi surface with area proportional to concentration of holes.In the large doping regime, it turns out that the slave-boson mean-ﬁeld theory[8]which treats the spins as fermions and holes as bosons produces a lot of properties of High-T c compounds correctly[9]and the SBMFT is only superier in describing the low-doping,antiferromagnetic state.Thus a natural question is:what is the relation between the two theories?Can one understand thetwo theories within a single framework?How does nature crossover from one description tothe other as concentration of holes increases?In SBMFT,the spin operator S i on site i is expressed in terms of Schwinger bosons S=¯Z i σZ i,where σis the Pauli matrix,Z i(¯Z i)are two component spinors¯Z i=(¯Z i↑,¯Z i↓), ietc.Notice that in order to represent a spin with magnitude S,there should be2S bosonsper site[2].The Hamiltonian can then be represented in terms of Schwinger bosons,and amean-ﬁeld theory can be formulated by introducing order parameters∆i,i+η=<Z i↑Z i+η↓−Z i↓Z i+η↑>(η=±ˆx,±ˆy)[2].Alternatively,SBMFT can also be formulated in a large-N expansion as the saddle point solution to a generalized SU(N)quantum spin model.To derive the large-N theory,we divide the square lattice into A and B sublattices and consider the following transformation for the Schwinger bosons on B-sublattice,Z B j↑(¯Z B j↑)→−Z B j↓(¯Z B j↓),Z B j↓(¯Z B j↓)→Z B j↑(¯Z B j↑),for all sites j on the B sublattice.The Schwinger bosons on the A sublattice remainsunchanged in the above transformation.The Lagrangian of the Heisenberg model can thenbe represented in the transformed boson coordinates as[3]L= iσ[¯Z A iσ(d dτ+iλj)Z B jσ−i2Sλj]+J i,η=±ˆx,±ˆy|∆i,i+η|2−J iσ,η=±ˆx,±ˆy[∆∗i,i+ηZ A iσZ B i+ησ+H.C.](1) whereλi’s are Lagrange multiplierﬁelds enforcing the constraint that there are2S bosons per site,∆i,i+η’s are Hubbard-Stratonovichﬁelds introduced in decoupling of H.σis the spin index.A SU(N)spin theory can be formulated with the above Lagrangian if the usual SU(2)spins↑and↓are extented to the SU(N)case where N-spin species are introduced. SBMFT can be considered as the saddle point solution of the path integral over L which becomes exact in the limit N→∞[3].For inﬁnite system with no defects,the saddle point solution has position independent∆i,i+η’s andλ’s and the solution is formally verysimilar to the BCS solution for superconductors,except that in present case the pairing objects are Schwinger bosons but not electrons.Another important diﬀerence is that in the present case,the pairing bosons are always located on diﬀerent sublattices,whereas no such distinction is found in the case of superconductors.The similarity between SBMFT and BCS theory leads us to ask the natural question of whether vortex-like solutions can be found in SBMFT as in the case of superconductors. More precisely,one may ask the question of whether one can construct a stable solution in SBMFT where∆i,i+ηhas a phase structure∆i,i+η∼|∆i,i+η|e iθ(i+η/2),whereθ( x)is a smooth function of x and has a singular point at x′∼0such that for distance| x|>>0,θ( x)→θ( x)+2πif one moves vector x around a close loop C which enclosed the point x′=0.As in the case of superconductors,the simplest way to address this question is to construct a continuum description for SBMFT(analogous to Ginsburg-Landau theory for superconductors)and study the possibility of having vortex solution in the continuum approximation.In the following we shall perform such a study in the disordered state in SBMFT where the Schwinger bosons are not bose-condensed and spin is a good quantum number.In realistic High-T c cuprates long range antiferromagnetic order is destroyed by introduction of charge carriers(holes).We shall not consider complications introduced by holes here and shall assume simply a disordered magnetic state with realistic spin magnitudes which can be described by the spin gap phase of SBMFT.We shall examine the properties of vortices within the continuum description.In section II we shall derive the continuum theory.Based on the continuum equations,we shallﬁrst study the properties of a single,non-magnetic impurity in the disordered state of SBMFT,where we shall point out the important diﬀerence between perturbations which are symmetric to the A and B sublattices,and perturbations which distinguish the two sublattices.In section III,we shall study static vortex excitations in our model.Based on the continuum theory,we shall argue that vortices are stable topological excitations in the disordered state of2D quantumantiferromagnets.We shall then show that there exists two kind of vortices in the continuum theory,corresponding to vortices centered on the mid-point of a plaquette,and vortices centered on a lattice point.We shall show that the properties of these two kinds of vortices are very diﬀerent,because of the diﬀerent symmetry with respect to the two sublattices.The ﬁrst kind of vortex which is symmetric to the two sublattices can carry only zero angular momentum and is a boson,whereas the second kind of vortex distinguishes between the two sublattices can carry angular momentum S under favourble conditions and is a fermion if S is half-integer.In section IV we shall concentrate ourselves at the case S=1/2which is the physical case of interests and shall examine properties of a”liquid”of fermionic vortices. Based on simple symmetry arguments,we shall argue that the eﬀective theory of a liquid of fermionic vortices has precisely the same form as the slave-boson mean-ﬁeld theory for spins in the undoped limit.The case withﬁnite concentration of holes will also be discussed.The ﬁndings in this paper will be summarized in section V,where we shall discuss a plausible scenerio of how the system crossover from a state described by SBMFT to a state described by slave-boson meanﬁeld theory upon doping.II.CONTINUUM DESCRIPTION FOR SBMFTTo derive the continuum theory we following Read and Sachdev[3]and consider the representation where our system has two sites per unit cell and introduce the’uniform’and ’staggered’components in the∆andλﬁelds,where∆i,i±η=12)+q±η(i±η2)+A±η(i±η2[λA( k)+λB( k)],(2b) Aτ( k)=1Theφ( x)ﬁeld describes uniform antiferromagnetic correlations whereas q( x)ﬁeld de-scribes spin dimerization(spin-Peierls)eﬀects[3].θ( x)and Aη( x)areﬁelds describing the corresponding uniform and staggered phaseﬂuctuations,respectively.Allﬁelds are slowly varying on the scale of a unit cell.Notice that the reason why four independent(real)ﬁelds are needed to describeﬂuctuations in one unit cell is precisely because we have divided the system into A and B sublattices.In the case of usual superconductors such a distinction is not present and only two realﬁelds(or one complex scalarﬁeld)enters into the Ginsburg-Landau equation.Notice that Vµ( x)=∂µθ( x)and Aµ( x)can be considered as U(1)gauge ﬁelds coupling to the Schwinger boson Z’s.The’uniform’gaugeﬁeld Vµ( x)couples to the bosons on the two sublattices with same gauge charge,whereas the gauge charges for the ’staggered’gaugeﬁeld Aµ( x)are opposite on the two sublattices.A single vortex solution centered at x′=0corresponds to a solution of SBMFT with boundary conditionVµ( x)dxµ=2nπ,or in terms of the gaugeﬁeld,there is a’uniform’gaugeﬂux of n/2ﬂux quantum passing through the origin,similar to the case of superconductors.Notice that in SBMFT where<∆i,i+η>=0,the gauge symmetry associated with the’uniform’gaugeﬁeld Vµ( x) (Z A→Z A e iΓ,Z B→Z B e iΓ,Vµ→Vµ−2∂µΓ)is broken,whereas the’staggered’gauge symmetry(Z A→Z A e iΓ,Z B→Z B e−iΓ,Aµ→Aµ−∂µΓ)remains intact in SBMFT.The existence of vortex solution is tied with the broken symmetry gaugeﬁeld Vµ( x)as in usual superconductors.At distance much larger than lattice spacing,ﬂuctuations associated with the’uniform’variablesφandθτare unimportant.Thus we shall neglect the∇φ(x)and∇θτ(x)terms in the following and derive a continuum theory for the rest of the variables.Notice that the Vµvariable is kept in our continuum theory since the term is essential for studying of vortices. In the continuum limit,the Lagrangian L becomesL→dτd 2x σ{¯Z A σ(x )∂∂τZ B σ(x )−µ=ˆx ,ˆy φ(x )(1−12φ(x )(D µ¯Z A σ(x ))(D ∗µ¯Z B σ(x ))+12 µ[φ(x )2+q µ(x )2]−4Sθτ(x ) ,(3)where D µ=∂µ+iA µand D ∗µ=∂µ−iA µ.The continuum Lagrangian Eq.(3)can befurther simpliﬁed by introducing new boson ﬁeldsψσ=12(Z A σ−¯Z B σ).The πσﬁeld can be integrated out safely at large distance and low energy [3],leaving eﬀective Lagrangian for ψσﬁeld,L =σ dτd 2x φ(x ) |D ∗µψσ|2+m (x )2|ψσ|2 +(φ1(x ))−1(D τ−q µD µ)ψ+σ(D ∗τ+q µD ∗µ)ψσ+18(V µ(x )V µ(x )))+m (x )2 (4)where φ( x )m ( x )2=2θτ( x )−4[1−(1/8)(V µ( x )V µ( x )]φ( x )and and φ1( x )=(1/2){θτ( x )+2[1−(1/8)(V µ( x )V µ( x )]φ( x )}.In the limit q µ=0and A µ=0,and neglecting gradient terms ∇φ,∇θτ,the above Lagrangian can be easily diagonalized resulting in an eﬀective Lagrangian L eﬀin terms of the φ( x )and V µ( x )ﬁelds.The dynamical eﬀect of the remaining terms can be obtained by looking at Gaussian ﬂuctuations of the ﬁelds around the saddle point solution A µ,q µ=0.[3]In particular,in the small m ( x )∼m →0limit,we obtain (see Appendix)L eﬀ=dτ d2x (a−4(2S+1))φ+φ2+(1φ)qµqµ+(2S+1)φF2µν+icFµτqµ+O(m2) ,(5) 2e2where e2∼m,a(<4(2S+1)),b and c are constants of order O(1).The precise values of a,b,c depend on the underlying lattice structure and cannot be obtained in a continuum theory.We have consider the realistic case N=2in deriving the above expression.Notice that similar eﬀective Lagrangian has been obtained by Read and Sachdev previously in studying eﬀect of instantons[3].The only diﬀerence here is that the VµVµterm which was not considered by Read and Sachdev is now retained.Recall that Vµis the’uniform’U(1) gaugeﬁeld coupling to the bosons and the VµVµterm in Eq.(5)just represents the Meissner eﬀect associated with nonzero order parameter∆in SBMFT.Notice that as in case of usual superconductors,we have choosen the London gauge∇. V=0in our derivation.The term can also be written in a gauge invariant way by replacing Vµby the gauge invariant object Vµ−2∂µΓin Eq.(5).This term does not contribute to the instanton eﬀect discussed by Read and Sachdev[3]but is crucial to the study of vortices.To understand more bout the continuum theory weﬁrst consider the properties of a singlenon-magnetic impurity in the disordered state of SBMFT.[10]We shall assume that a non-magnetic impurity simply replaces a spin at site i by a non-magnetic object.The simplestway to model this in our formalism is to is replace the constraint equation¯ZZ=2S onsite i by¯ZZ=2S(1−n i)=0,where n i is the number of non-magnetic impurity on site i.It is than easy to see that the eﬀect of nonzero n i in our eﬀective Lagrangian Eq.(5)is tointroduce in the Coulomb gauge an extra term−(2Sn i e i)Aτ,where e i=±1,depending onwhether the impurity is located on the A-or B-sublattices,[10]i.e.,non-magnetic impuritiesappear as eﬀective(staggered)gauge charges of magnitude2Se localized at the impuritysites.A corresponding electrostatic potential V(r)∼(2Se i)ln(r/ξ)(whereξ∼m−1)will beinduced around the impurity.To lower the electrostatic energy,2S bosons will be nucleatedout from the vacuum to screen the electricﬁeld,resulting in formation of local magneticmoment of magnitude S around a non-magnetic impurity[10].Notice that this eﬀect hasbeen observed experimentally in the High-T c compounds in the underdoped region upon substitution of Cu by Zn in the conducting planes[11].This result can also be understood in an alternative way by observing that the same physical eﬀect should have occurred if instead of replacing a spin on site i by an non-magnetic impurity,we let the Heisenberg coupling J i to go to zero for those bonds joining to site i. In this case the’impurity’site i behaves as an non-magnetic impurity as far as the rest of the system is concerned.The only diﬀerence is that a free spin of magnitude S now remains on site i.However,the eﬀect of this approach on our eﬀective Lagrangian Eq.(5)looks rather diﬀerent compared with our previous approach.Instead of introducing a’staggered’electric charge of magnitude2Se on site i,a boundary condition∆i,i+η=0(η=±ˆx,±ˆy)is now imposed on our ing Eq.(2a),the corresponding boundary condition in the continuum theory becomesqˆn(x i)=±ˆnφ(x i)where i→x i in the continuum limit.ˆn is a unit vector.±depends on whether site i is on A-or B-sublattices.The properties of the system around the non-magnetic impurity is obtained by minimizing the free energy Eq.(5)under this boundary condition.Performing the calculation,weﬁndﬁrst of all thatφ(x i)=0and correspondingly q(x i)= 0.The reason for this behaviour can be understood easily from Eq.(5)by noticing that the coeﬃcient in front of the qµqµterm becomes negative asφbecomes smaller than2b, implying that spontaneously dimerization will occur whenφbecomes small enough.Because of stability requirement,it can be shown that dimmerization| q|cannot have value largerthan q o=(√2)φ(see Appendix).Anyway bothφ(xi)and q(x i)∼ q o should be nonzeroin the continuum solution.The reason why q should be nonzero can also be understood from symmetry consideration.Notice that theφ(x)ﬁeld is symmetric under exchange of A-and B-sublattices whereas qµ(x)ﬁeld is antisymmetric.Thus a solution with qµ(x)ﬁeld identically zero would not distinguish between the two sublattices.However,the single non-magnetic impurity problem certainly distinguishes the two sublattices since the impuritycan only be placed on either one of the two sublattices.Thus we expect qµ(x)to be nonzero around a single impurity.Minimizing the free energy with respect to the qµﬁeld weﬁnd also that E(x)∼ q(x),where Eµ=iFµτis the’staggered’electricﬁeld in the system.With the boundary condition q∼(±ˆn)φaround the impurity weﬁnd that electricﬁeld radiating out (or in)from the impurity is obtained in our solution,i.e.,depending on whether the impurity is located on the A-or B-sublattices,it behaves as source or sink for the electricﬁeld,in exact agreement with our previous approach which predicts that non-magnetic impurity behaves as a single staggered gauge charge added to the system.One may also extend our approach to discuss the case when the Heisenberg coupling J′joining to the site i is small but nonzero,so that the spin at site i still couples weakly with the surrounding environment.The previous discussions still apply,except that the spin at site i appears now as a localized spinon state occupied by2S spinons in the system (notice that at two dimension,an arbitrary small attractive interaction is enough to generate a bound state[12]).The spinon state again behaves as a(staggered)gauge charge(with magnitude2S),and will bind2S other spinons with opposite gauge charge(or localized on opposite sublattice)next to itself as in the case with J′=0.However for nonzero J′the localized spinons on the two sublattices will interact antiferromagnetically because of the underlying antiferromagnetic correlation in the system,[13]forming at the end a localized spin singlet around site i.It is only in the limit J′→0that the two spinons are decoupled and free local magnetic moments appear.Our discussion can also be extended to study other forms of local defects.For example, one may study the situation when the Heisenberg coupling J i,i+ˆx between sites i and i+ˆx is set to zero,i.e.,a single bond is being removed from the system.Notice that the perturbation is symmetric with respect to interchange of A-and B-sublattices.It is straightforward to generalize our previous discussion to this case where weﬁnd that the perturbation now appears as an eﬀective electric dipole moment in L eﬀ.No local moment is expected to form around the impurity bond in this case because of the follow reason:because of the symmetry between A-and B-sublattices bosons(spinons)can be nucleated out from vaccuum only inpairs,with one localized on the A sublattice and one on the B sublattice.The interaction between the nucleated spinon pairs will again be antiferromagnetic and has a magnitude ∼Je−x/ξ,where x is the distance between the two spinons andξ∼m−1is the’size’of the spinon wavefunction.For the single bond defect,the distance x between the two spinons is of order of lattice spacing<<ξ.Thus the eﬀective interaction between the two spinons is of order J,i.e.,they will form a strong local spin singlet and no isolated magnetic moment will appear.Experimentally,the Cu ion in the conducting plane of high-T c cupartes can be substituted by Zn(non-magnetic impurity)[11]and magnitude of Heisenberg exchange J can be modiﬁed locally by introducing impurities out of conduction planes or substitution of O ions.It is observed that while substitution of Cu by Zn in the conducting plane introduces local magnetic moments in the underdoped(spin gap)phases of High-T c cuprates[11],no such eﬀect is observed in other ways of introducing defects.Our theoretical investigation on disordered state of quantum antiferromagnets based on continuum description of SBMFT is in satisfying agreement with experimental results.[10]III.STATIC VORTICES IN DISORDERED STATE OF SBMFTIn the continuum theory,a unit vortex centered as x=0corresponds to a solution ofδL eﬀ=0,withθ(r,Ω)=Ω,where r andΩare the distance and angle in the(2D) polar co-ordinate.The nonzero vorticity introduces a diverging kinetic energy through the VµVµ∼(∇θ)2term in L eﬀ,which supresses the magnitude ofφaround the vortex core r→0,as in the case of usual superconductors.Minimizing the free energy with respect√2)φ,weﬁnd thatφ=| q|=0for toφ,and keeping in mind that for smallφ,| q|∼(r<r o∼[(8(2S+1)+4b−2a)/(2S+1)]1/2,but not going to zero smoothly as r→0, as in the case of usual superconductors.This result is an artifact of our continuum theory where the(∇φ)2term is not included in L eﬀ.Nevertheless,the qualitative eﬀect whereφis being suppressed around the vortex core is clear.For large r,φ(r)→φo=(4(2S+1)−a)/2and q→0,indicating that vortices are stable topological excitations in SBMFT.The behaviour of vortices in SBMFT is very similar to vortices in usual superconductors at large r.However,the small r behaviours are very diﬀerent.The suppression ofφand qﬁelds around vortex core reﬂects the fact that around the center of vortex,the bond amplitude ∆i,i+µ’s are being suppressed.As has been discussed in the previous section,suppression of local bond amplitudes may lead to generation of localized magnetic moments,depending on the detailed bond conﬁguration.To understand the properties of a vortex,it is thus important to understand the underlying bond structure at the vortex core.Before studying the bond structure at vortex core,let us explainﬁrst how local magnetic moment binding to vortex core modiﬁes the properties of a vortex.For a unit vortex the magneticﬂux seen by a Schwinger boson is halfﬂux quantum.(recall that Vµis an’uniform’gaugeﬁeld which has same gauge charge for bosons on both sublattices)Therefore the orbital angular momentum of a Schwinger boson around a unit vortex is1the VµVµterm.Following similar analysis as in previous section weﬁnd that the sup-pressed bonds introduce in the continuum theory an eﬀective electric quadrapole structure surrounding the vortex center.Notice that as in the case of single broken bond the structure is symmetric with respect to the A-and B-sublattices.Thus we expect that localized spinon pairs may form around the center of vortex but isolated magnetic moments cannot occur. Thus this kind of vortex carries zero angular momentum and is a boson.The second kind of vortex is centered at a lattice point and as a result,it is expected that the four bonds joining to the vortex center(see Fig.1b)will be largely suppressed. This situation is very similar to the case of single non-magnetic impurity discussed in the last section.First of all,2S spinons will be found localized at the vortex center because of the suppressed bonds.The spinons behaves as a’staggered’gauge charge with magnitide 2S and2S other spinons with opposite gauge charge will be nucleated from the vacuum to screen the’staggered’electricﬁeld generated by the spinons localized at the vortex cen-ter.The spinons on opposite sublattices interact antiferromagnetically through an eﬀective Heisenberg exchange of order J′∼J|∆c|2,where∆c is the bond amplitude of the four bonds joining to the vortex center.As a result,a spin singlet will be formed.The vortex carries zero angular momentum and is again a boson.Notice that this is true even in the limit J′→0since integer number of bosons=4S are found binding to the vortex.The situation is however quite diﬀerent if we consider aﬁnite density of the second kind of vortices.We shall show that when density of vortices is large enough,it may become energetically unfavourable to nucleate spinons from vacuum to screen the staggered gauge ﬁeld and as a result,only2S spinons will be found binding to vortex center resulting in fermionic vortices when S is half-integer(odd number of bound bosons).For simplicity we shallﬁrst consider two vortices seperated by distance l,with one vortex on each sublattice. First let us consider the energy when spinons are nucleated from the vacuum to screen the staggered gauge charge on each vortex.The total energy will be sum of three terms:(i) the electrostatic energy which is of order2(2Se)2ln(l o/ξ),where l o∼ξis the’size’of the nucleated spinon wavefunction,(ii)The exchange energy between the spinons localized asvortex center and nucleated spinons,which is of order−2S(S+1)J′e−l o/ξ∼−2S(S+1)J′, and(iii)The energy needed to nucleate the spinons from the vacuum,which is of order 4Sm.The sum of the three terms is of order2S(2m−(S+1)J′).The energy for the second case when no spinons are nucleated from vacuum consists of two terms:(i)the electrostatics energy which is of order(2Se)2ln(l/ξ)and(ii)the exchange energy between spinons located at the center of the two vortices which is or order−S(S+1)J′e−l/ξ.In2D,e2∼m and the electrostatic energy is of order4S2m.ln(l/ξ).For l>>ξ,it is certainly energtically more favourable to nucleate bosons from vacuum to screen the vortex gauge charge.However, when l≤ξ,the energy cost of the second case is of order−S(S+1)J′,and is energetically more favourable if S(S+1)J′<4Sm.Notice that J′∼J|∆c|2is expected to be very small because of suppresion eﬀect around vortex core.Thus the condition can be satisﬁed easily even with a relatively small m.Forﬁnite density of vorticesδ,l∼δ1which are rather easy to acheive.We cannot,however,be absolutely sure whether’fermionic’vortices exist because of the natural limitation of a continuum theory which gives only or-der of magnitude estimates.Notice also one important distinction between the vortices we study in this paper and usual vortices in superﬂuids.In the present case,vortices cannot be distingished by sign of vorticity since vortices carrying1/2(orπ)and−1/2ﬂux quanta should be considered as identical.On a lattice where the order parameterﬁeld∆i,i+µis a link-variable,πand−πvortices can be related by a pure gauge transformation.The usual singularity encountered in the gauge transformation in continous space does not arise here because of the discretized lattice structure.It is important to clarify the diﬀerent roles played by the’uniform’and’staggered’gaugeﬁelds in deciding the properties of vortices.The gaugeﬁelds arise fromﬂuctuation in phases of the order parameter∆i,i+µ’s.The uniform gaugeﬁeld couples to bosons on the two sublattices with same gauge charge,and the corresponding gauge symmetry is broken in SBMFT.Vortices are stable because of this broken gauge symmetry,and corresponds to solutions with”uniform”magneticﬂux penetrating center of vortices.The’staggered’gaugeﬁeld couples to bosons on opposite sublattices with opposite gauge charge.It plays no role in generating a stable vortex solution,but has strong eﬀects in determining the precise properties of the vortex core.Without the’staggered’gaugeﬁeld,spinons need not be nucleated from vacuum to screen the’staggered’charges generated at,for example,the center of the second kind of vortex.In this case,for half-integer spin systems,the second kind of vortices will always be fermions independent of density,since only odd number of bosons are found binding to center of each vortex(corresponding to the spin S at center of vortex).Similarly,local magnetic moments will not be generated by non-magnetic impurities if’staggered’gaugeﬁeld does not exist.It is also interesting to point out that similar vortex excitations have been considered by Read and Chakraborty[15]in a short-ranged RVB wavefunction for S=1/2quantum antiferromagnets.They considered also the two kinds of vortices we discussed here.The statistics of the vortices were examined by direct Berry phase computations where similar。

机电英语词汇

机电英语词汇abandon 抛弃abaxial 离轴的ablation 烧蚀abnormal liquid 异常液体abrasion 磨耗abrasion hardness 耐磨硬度abrasion test 磨损试验abrasion tester 磨损试验机abrasives 研磨材料abrupt perturbation 突然扰动abscissa 横坐标absence of collision 无碰撞absence of gravity 失重absence of stress 无应力absence of vortices 无旋涡absolute 绝对的absolute acceleration 绝对加速度absolute angular momentum 绝对角动量back flow 回流逆流back mixing 反混back pressure 背压力back reaction 逆反应back substitution 回代backpressure 反向压力；反压力backscattering technique 逆散射法back streaming 逆流backward difference 后向差分backward motion 逆向运动backward precession 逆旋进backward thrust 逆推力backward wave 逆向行波backwash 后涡流backwater 回水backwater curve 回水曲线backwater distance 回水距离backwater function 回水函数backwater surface 回水面cable stayed bridge 斜拉桥cad 计算机辅助设计calculator 计算机calculus of approximation 近似计算calculus of finite differences 差分演算calibration 校准calibrator 校准器calorific capacity 热容量calorimetric measurement 量热测量camber changing flap 改变机翼弯度的襟翼canal 管道canal vortex 沟渠涡旋canal wave 沟渠波canard 鸭翼canonical coordinate 正则坐标Dalton law 道尔顿定律dam 堤dam break 溃坝dam crest 坝顶dam with lifting gates 具有提升式闸门的坝damage curve 损坏曲线damage line 损坏曲线damage mechanics 损伤力学damage of composite materials 复合材料损伤damage of rock 岩石损伤damped 阻尼的eagre 涌潮earth 土earth atmosphere 地面大气earth attraction 地球引力earth axis 地轴earth gravity 地球重力earth lateral pressure 土的侧压力earth orbit 地球轨道earth pressure 土压力earth pressure at rest 静土压力earth revolution 地球公转earth rotation 地球自转earth tides 地球潮汐earthquake force 地震烈度earthquake intensity 地震烈face ring flux 正面通量face ring leakage flux 正面漏泄通量factor 因子fading memory 衰退记忆fading period 衰落周期failing stress 破坏应力failure 破坏failure condition 断裂条件faired curve 光滑曲线fairing 吝体fairway 航道fall 落下fall velocity 沉降速度falling ball method 落球法gage length 标距长度gage pressure 表压力gage transformation 规范变换gain loss 增益损失gal 伽Galilean frame of reference 伽利略参考系Galilean principle of relativity 伽利略相对性原理Galilean transformation 伽利略变换Galileo law of inertia 伽利略惯性定律Gallitzin pendulum 伽利津摆gallon 加仑h function h 函数h theorem h 定理hail storm 雹暴hair crack 毛细裂纹half amplitude 半振幅half circulation 半环流half elliptic spring 半椭圆形弹簧half frequency 半频half moment theory 半矩理论half period 半周期i beam 工字梁i section 工字形断面icing 结冰ideal aerodynamics 理想空气动力学ideal condition 理想条件ideal constraint 理想约束ideal drag 理想铃中的阻力ideal elasticity 理想弹性ideal fluid 理想铃ideal gas 理想气体ideal gas law 理想气体定律ideal gas state equation 理想气体状态方程ideal liquid 理想液体ideal non uniformity 理想非均j integral j 积分jato 起飞用火箭助推器jeans viscosity equation 金斯粘度方程k equation model k 方程模型keplerian cllipse 轨道椭圆labile 不稳定的labile equilibrium 不稳平衡lability 不稳定性lacing 栅格桁架lag 延迟lag angle 滞后角mach angle 马蒜角mach cone 马蒜锥；马赫锥mach criterion 马赫判据mach disk 马赫盘mach fringe 马赫条纹mach line 马赫线mach net 马赫网mach number 马赫数mach pendulum 马赫摆mach principle 马赫原理mach quadrangle 马赫四角形mach reflection 马赫反射mach scale law 马赫相似律n body problem n 体问题nacelle 发动机短舱naive model 简单模型naked hull 裸船体narrow band frequency 窄带频率narrow band frequency modulation 窄带档narrow band noise 窄带噪声natural ageing 自然时效natural angle of repose 静止角natural angular frequency 固有角频率natural circulation 自然循环natural convection 自然对流objective function 目标函数oblique 斜的oblique angle 斜角oblique angled 斜角的oblique beam 斜梁oblique bending 倾斜弯曲oblique coordinates 斜角坐标系oblique cylinder 斜柱oblique flow 斜流oblique illumination 侧面照明oblique impact 斜冲击paddle 桨叶pair force 偶力pair interaction 偶相互酌pair of element 运动副pair potential 对势pancaking 平坠panel point 格点parabolic creep 抛物线型蠕变parabolic curve 抛物曲线parabolic flow 抛物线型流parabolic orbit 抛物线轨道parabolic potential 抛物线型势quadratic displacement field 二次位移场quadratic effect 二次效应quadratic form 二次形式quadric of stress 应力二次曲面quadric of stretching 拉伸二次曲面quadric of the tensor 张量二次曲面quantity of flow 量quantity of motion 动量quantity of state 状态量quantum fluid 量子铃quantum mechanical 量子力学的quantum mechanical resonance 量子力学共振quantum mechanics 量子力学quantum potential 量子势radial 径向的radial acceleration 径向加速度radial component 径向分量radial cross section 径向截面radial distribution function 径向分布函数radial expansion 径向膨胀radial extent 径向伸长safe load 安全载荷safe seismic distance 安全震距safe stress 安全应力safety coefficient 安全系数safety element 安全元件safety explosive 安全炸药safety factor 安全因数safety limit 安全限值safety valve 安全阀sag 下弯saltation 跃移t beam t 型梁t type tail t 型尾翼tab 补翼tachometer 转速表tachymeter 视距仪tackle block 滑车组tactile sensor 接触式传感器触觉感受器tail 尾部tail area 尾部面积tail band 拖尾带u tube manometer u 形管压力计ultimate bearing capacity 极限承载力ultimate elongation 极限伸长ultimate load 临界载荷ultimate modulus 极限模量ultimate pressure 极限压力ultimate strength 强度极限ultimate stress 极限应力ultimate tensile strength 抗张强度ultimate vacuum 极度真空ultra high speed 超高速ultracentrifuge 超速离心机vacancy 空位vacant site 空位vacuum 真空vacuum apparatus 真空装置vacuum chamber 真空室vacuum diagram 真空图vacuum diffusion 真空扩散vacuum effect 真空效应vacuum pump 真空泵vacuum state 真空态vacuum tank 真空罐vacuum tight 真空密闭的vacuum value of velocity 真空速度vacuum valve 真空阀wafer 薄片Wagner beam 瓦格纳梁Wagner effect 瓦格纳效应wake 尾流伴流wake of boundary layer 边界层尾流wake region 尾柳wake space 死水区wake vortex 尾列wake wave 尾哩wall boundary layer 壁边界层wall effect 壁效应wall friction 壁面摩擦wall pressure 壁压x ray analysis x 射线分析x ray crystal analysis x 射线晶体分析x ray method x 射线法x rays x 射线y connection y 形接法y deflection y 偏转yaw 偏航yield 屈服yield condition 屈服条件yield limit 屈服极限yield load 屈服载荷yield point 屈服点yield strength 屈服强度yield stress 屈服应力yield surface 屈服曲面yielding model 屈服模型yielding support 弹性支承young modulus 杨氏模量young's modulus 弹性横量zero balance 零点平衡zero element 零元素zero energy level 零能级zero gravity 失重zero incidence wing 零攻角机翼。

纹理物体缺陷的视觉检测算法研究--优秀毕业论文

摘要
在竞争激烈的工业自动化生产过程中，机器视觉对产品质量的把关起着举足轻重的作用，机器视觉在缺陷检测技术方面的应用也逐渐普遍起来。与常规的检测技术相比，自动化的视觉检测系统更加经济、快捷、高效与安全。纹理物体在工业生产中广泛存在，像用于半导体装配和封装底板和发光二极管，现代化电子系统中的印制电路板，以及纺织行业中的布匹和织物等都可认为是含有纹理特征的物体。本论文主要致力于纹理物体的缺陷检测技术研究，为纹理物体的自动化检测提供高效而可靠的检测算法。纹理是描述图像内容的重要特征，纹理分析也已经被成功的应用与纹理分割和纹理分类当中。本研究提出了一种基于纹理分析技术和参考比较方式的缺陷检测算法。这种算法能容忍物体变形引起的图像配准误差，对纹理的影响也具有鲁棒性。本算法旨在为检测出的缺陷区域提供丰富而重要的物理意义，如缺陷区域的大小、形状、亮度对比度及空间分布等。同时，在参考图像可行的情况下，本算法可用于同质纹理物体和非同质纹理物体的检测，对非纹理物体的检测也可取得不错的效果。在整个检测过程中，我们采用了可调控金字塔的纹理分析和重构技术。与传统的小波纹理分析技术不同，我们在小波域中加入处理物体变形和纹理影响的容忍度控制算法，来实现容忍物体变形和对纹理影响鲁棒的目的。最后可调控金字塔的重构保证了缺陷区域物理意义恢复的准确性。实验阶段，我们检测了一系列具有实际应用价值的图像。实验结果表明本文提出的纹理物体缺陷检测算法具有高效性和易于实现性。关键字: 缺陷检测；纹理；物体变形；可调控金字塔；重构
Keywords: defect detection, texture, object distortion, steerable pyramid, reconstruction
II

交通流

Network impacts of a road capacity reduction:Empirical analysisand model predictionsDavid Watling a ,⇑,David Milne a ,Stephen Clark baInstitute for Transport Studies,University of Leeds,Woodhouse Lane,Leeds LS29JT,UK b Leeds City Council,Leonardo Building,2Rossington Street,Leeds LS28HD,UKa r t i c l e i n f o Article history:Received 24May 2010Received in revised form 15July 2011Accepted 7September 2011Keywords:Trafﬁc assignment Network models Equilibrium Route choice Day-to-day variabilitya b s t r a c tIn spite of their widespread use in policy design and evaluation,relatively little evidencehas been reported on how well trafﬁc equilibrium models predict real network impacts.Here we present what we believe to be the ﬁrst paper that together analyses the explicitimpacts on observed route choice of an actual network intervention and compares thiswith the before-and-after predictions of a network equilibrium model.The analysis isbased on the ﬁndings of an empirical study of the travel time and route choice impactsof a road capacity reduction.Time-stamped,partial licence plates were recorded across aseries of locations,over a period of days both with and without the capacity reduction,and the data were ‘matched’between locations using special-purpose statistical methods.Hypothesis tests were used to identify statistically signiﬁcant changes in travel times androute choice,between the periods of days with and without the capacity reduction.A trafﬁcnetwork equilibrium model was then independently applied to the same scenarios,and itspredictions compared with the empirical ﬁndings.From a comparison of route choice pat-terns,a particularly inﬂuential spatial effect was revealed of the parameter specifying therelative values of distance and travel time assumed in the generalised cost equations.When this parameter was ‘ﬁtted’to the data without the capacity reduction,the networkmodel broadly predicted the route choice impacts of the capacity reduction,but with othervalues it was seen to perform poorly.The paper concludes by discussing the wider practicaland research implications of the study’s ﬁndings.Ó2011Elsevier Ltd.All rights reserved.1.IntroductionIt is well known that altering the localised characteristics of a road network,such as a planned change in road capacity,will tend to have both direct and indirect effects.The direct effects are imparted on the road itself,in terms of how it can deal with a given demand ﬂow entering the link,with an impact on travel times to traverse the link at a given demand ﬂow level.The indirect effects arise due to drivers changing their travel decisions,such as choice of route,in response to the altered travel times.There are many practical circumstances in which it is desirable to forecast these direct and indirect impacts in the context of a systematic change in road capacity.For example,in the case of proposed road widening or junction improvements,there is typically a need to justify econom-ically the required investment in terms of the beneﬁts that will likely accrue.There are also several examples in which it is relevant to examine the impacts of road capacity reduction .For example,if one proposes to reallocate road space between alternative modes,such as increased bus and cycle lane provision or a pedestrianisation scheme,then typically a range of alternative designs exist which may differ in their ability to accommodate efﬁciently the new trafﬁc and routing patterns.0965-8564/$-see front matter Ó2011Elsevier Ltd.All rights reserved.doi:10.1016/j.tra.2011.09.010⇑Corresponding author.Tel.:+441133436612;fax:+441133435334.E-mail address:d.p.watling@ (D.Watling).168 D.Watling et al./Transportation Research Part A46(2012)167–189Through mathematical modelling,the alternative designs may be tested in a simulated environment and the most efﬁcient selected for implementation.Even after a particular design is selected,mathematical models may be used to adjust signal timings to optimise the use of the transport system.Road capacity may also be affected periodically by maintenance to essential services(e.g.water,electricity)or to the road itself,and often this can lead to restricted access over a period of days and weeks.In such cases,planning authorities may use modelling to devise suitable diversionary advice for drivers,and to plan any temporary changes to trafﬁc signals or priorities.Berdica(2002)and Taylor et al.(2006)suggest more of a pro-ac-tive approach,proposing that models should be used to test networks for potential vulnerability,before any reduction mate-rialises,identifying links which if reduced in capacity over an extended period1would have a substantial impact on system performance.There are therefore practical requirements for a suitable network model of travel time and route choice impacts of capac-ity changes.The dominant method that has emerged for this purpose over the last decades is clearly the network equilibrium approach,as proposed by Beckmann et al.(1956)and developed in several directions since.The basis of using this approach is the proposition of what are believed to be‘rational’models of behaviour and other system components(e.g.link perfor-mance functions),with site-speciﬁc data used to tailor such models to particular case studies.Cross-sectional forecasts of network performance at speciﬁc road capacity states may then be made,such that at the time of any‘snapshot’forecast, drivers’route choices are in some kind of individually-optimum state.In this state,drivers cannot improve their route selec-tion by a unilateral change of route,at the snapshot travel time levels.The accepted practice is to‘validate’such models on a case-by-case basis,by ensuring that the model—when supplied with a particular set of parameters,input network data and input origin–destination demand data—reproduces current mea-sured mean link trafﬁcﬂows and mean journey times,on a sample of links,to some degree of accuracy(see for example,the practical guidelines in TMIP(1997)and Highways Agency(2002)).This kind of aggregate level,cross-sectional validation to existing conditions persists across a range of network modelling paradigms,ranging from static and dynamic equilibrium (Florian and Nguyen,1976;Leonard and Tough,1979;Stephenson and Teply,1984;Matzoros et al.,1987;Janson et al., 1986;Janson,1991)to micro-simulation approaches(Laird et al.,1999;Ben-Akiva et al.,2000;Keenan,2005).While such an approach is plausible,it leaves many questions unanswered,and we would particularly highlight two: 1.The process of calibration and validation of a network equilibrium model may typically occur in a cycle.That is to say,having initially calibrated a model using the base data sources,if the subsequent validation reveals substantial discrep-ancies in some part of the network,it is then natural to adjust the model parameters(including perhaps even the OD matrix elements)until the model outputs better reﬂect the validation data.2In this process,then,we allow the adjustment of potentially a large number of network parameters and input data in order to replicate the validation data,yet these data themselves are highly aggregate,existing only at the link level.To be clear here,we are talking about a level of coarseness even greater than that in aggregate choice models,since we cannot even infer from link-level data the aggregate shares on alternative routes or OD movements.The question that arises is then:how many different combinations of parameters and input data values might lead to a similar link-level validation,and even if we knew the answer to this question,how might we choose between these alternative combinations?In practice,this issue is typically neglected,meaning that the‘valida-tion’is a rather weak test of the model.2.Since the data are cross-sectional in time(i.e.the aim is to reproduce current base conditions in equilibrium),then in spiteof the large efforts required in data collection,no empirical evidence is routinely collected regarding the model’s main purpose,namely its ability to predict changes in behaviour and network performance under changes to the network/ demand.This issue is exacerbated by the aggregation concerns in point1:the‘ambiguity’in choosing appropriate param-eter values to satisfy the aggregate,link-level,base validation strengthens the need to independently verify that,with the selected parameter values,the model responds reliably to changes.Although such problems–ofﬁtting equilibrium models to cross-sectional data–have long been recognised by practitioners and academics(see,e.g.,Goodwin,1998), the approach described above remains the state-of-practice.Having identiﬁed these two problems,how might we go about addressing them?One approach to theﬁrst problem would be to return to the underlying formulation of the network model,and instead require a model deﬁnition that permits analysis by statistical inference techniques(see for example,Nakayama et al.,2009).In this way,we may potentially exploit more information in the variability of the link-level data,with well-deﬁned notions(such as maximum likelihood)allowing a systematic basis for selection between alternative parameter value combinations.However,this approach is still using rather limited data and it is natural not just to question the model but also the data that we use to calibrate and validate it.Yet this is not altogether straightforward to resolve.As Mahmassani and Jou(2000) remarked:‘A major difﬁculty...is obtaining observations of actual trip-maker behaviour,at the desired level of richness, simultaneously with measurements of prevailing conditions’.For this reason,several authors have turned to simulated gaming environments and/or stated preference techniques to elicit information on drivers’route choice behaviour(e.g. 1Clearly,more sporadic and less predictable reductions in capacity may also occur,such as in the case of breakdowns and accidents,and environmental factors such as severe weather,ﬂoods or landslides(see for example,Iida,1999),but the responses to such cases are outside the scope of the present paper. 2Some authors have suggested more systematic,bi-level type optimization processes for thisﬁtting process(e.g.Xu et al.,2004),but this has no material effect on the essential points above.D.Watling et al./Transportation Research Part A46(2012)167–189169 Mahmassani and Herman,1990;Iida et al.,1992;Khattak et al.,1993;Vaughn et al.,1995;Wardman et al.,1997;Jou,2001; Chen et al.,2001).This provides potentially rich information for calibrating complex behavioural models,but has the obvious limitation that it is based on imagined rather than real route choice situations.Aside from its common focus on hypothetical decision situations,this latter body of work also signiﬁes a subtle change of emphasis in the treatment of the overall network calibration problem.Rather than viewing the network equilibrium calibra-tion process as a whole,the focus is on particular components of the model;in the cases above,the focus is on that compo-nent concerned with how drivers make route decisions.If we are prepared to make such a component-wise analysis,then certainly there exists abundant empirical evidence in the literature,with a history across a number of decades of research into issues such as the factors affecting drivers’route choice(e.g.Wachs,1967;Huchingson et al.,1977;Abu-Eisheh and Mannering,1987;Duffell and Kalombaris,1988;Antonisse et al.,1989;Bekhor et al.,2002;Liu et al.,2004),the nature of travel time variability(e.g.Smeed and Jeffcoate,1971;Montgomery and May,1987;May et al.,1989;McLeod et al., 1993),and the factors affecting trafﬁcﬂow variability(Bonsall et al.,1984;Huff and Hanson,1986;Ribeiro,1994;Rakha and Van Aerde,1995;Fox et al.,1998).While these works provide useful evidence for the network equilibrium calibration problem,they do not provide a frame-work in which we can judge the overall‘ﬁt’of a particular network model in the light of uncertainty,ambient variation and systematic changes in network attributes,be they related to the OD demand,the route choice process,travel times or the network data.Moreover,such data does nothing to address the second point made above,namely the question of how to validate the model forecasts under systematic changes to its inputs.The studies of Mannering et al.(1994)and Emmerink et al.(1996)are distinctive in this context in that they address some of the empirical concerns expressed in the context of travel information impacts,but their work stops at the stage of the empirical analysis,without a link being made to net-work prediction models.The focus of the present paper therefore is both to present theﬁndings of an empirical study and to link this empirical evidence to network forecasting models.More recently,Zhu et al.(2010)analysed several sources of data for evidence of the trafﬁc and behavioural impacts of the I-35W bridge collapse in Minneapolis.Most pertinent to the present paper is their location-speciﬁc analysis of linkﬂows at 24locations;by computing the root mean square difference inﬂows between successive weeks,and comparing the trend for 2006with that for2007(the latter with the bridge collapse),they observed an apparent transient impact of the bridge col-lapse.They also showed there was no statistically-signiﬁcant evidence of a difference in the pattern ofﬂows in the period September–November2007(a period starting6weeks after the bridge collapse),when compared with the corresponding period in2006.They suggested that this was indicative of the length of a‘re-equilibration process’in a conceptual sense, though did not explicitly compare their empiricalﬁndings with those of a network equilibrium model.The structure of the remainder of the paper is as follows.In Section2we describe the process of selecting the real-life problem to analyse,together with the details and rationale behind the survey design.Following this,Section3describes the statistical techniques used to extract information on travel times and routing patterns from the survey data.Statistical inference is then considered in Section4,with the aim of detecting statistically signiﬁcant explanatory factors.In Section5 comparisons are made between the observed network data and those predicted by a network equilibrium model.Finally,in Section6the conclusions of the study are highlighted,and recommendations made for both practice and future research.2.Experimental designThe ultimate objective of the study was to compare actual data with the output of a trafﬁc network equilibrium model, speciﬁcally in terms of how well the equilibrium model was able to correctly forecast the impact of a systematic change ap-plied to the network.While a wealth of surveillance data on linkﬂows and travel times is routinely collected by many local and national agencies,we did not believe that such data would be sufﬁciently informative for our purposes.The reason is that while such data can often be disaggregated down to small time step resolutions,the data remains aggregate in terms of what it informs about driver response,since it does not provide the opportunity to explicitly trace vehicles(even in aggre-gate form)across more than one location.This has the effect that observed differences in linkﬂows might be attributed to many potential causes:it is especially difﬁcult to separate out,say,ambient daily variation in the trip demand matrix from systematic changes in route choice,since both may give rise to similar impacts on observed linkﬂow patterns across re-corded sites.While methods do exist for reconstructing OD and network route patterns from observed link data(e.g.Yang et al.,1994),these are typically based on the premise of a valid network equilibrium model:in this case then,the data would not be able to give independent information on the validity of the network equilibrium approach.For these reasons it was decided to design and implement a purpose-built survey.However,it would not be efﬁcient to extensively monitor a network in order to wait for something to happen,and therefore we required advance notiﬁcation of some planned intervention.For this reason we chose to study the impact of urban maintenance work affecting the roads,which UK local government authorities organise on an annual basis as part of their‘Local Transport Plan’.The city council of York,a historic city in the north of England,agreed to inform us of their plans and to assist in the subsequent data collection exercise.Based on the interventions planned by York CC,the list of candidate studies was narrowed by considering factors such as its propensity to induce signiﬁcant re-routing and its impact on the peak periods.Effectively the motivation here was to identify interventions that were likely to have a large impact on delays,since route choice impacts would then likely be more signiﬁcant and more easily distinguished from ambient variability.This was notably at odds with the objectives of York CC,170 D.Watling et al./Transportation Research Part A46(2012)167–189in that they wished to minimise disruption,and so where possible York CC planned interventions to take place at times of day and of the year where impacts were minimised;therefore our own requirement greatly reduced the candidate set of studies to monitor.A further consideration in study selection was its timing in the year for scheduling before/after surveys so to avoid confounding effects of known signiﬁcant‘seasonal’demand changes,e.g.the impact of the change between school semesters and holidays.A further consideration was York’s role as a major tourist attraction,which is also known to have a seasonal trend.However,the impact on car trafﬁc is relatively small due to the strong promotion of public trans-port and restrictions on car travel and parking in the historic centre.We felt that we further mitigated such impacts by sub-sequently choosing to survey in the morning peak,at a time before most tourist attractions are open.Aside from the question of which intervention to survey was the issue of what data to collect.Within the resources of the project,we considered several options.We rejected stated preference survey methods as,although they provide a link to personal/socio-economic drivers,we wanted to compare actual behaviour with a network model;if the stated preference data conﬂicted with the network model,it would not be clear which we should question most.For revealed preference data, options considered included(i)self-completion diaries(Mahmassani and Jou,2000),(ii)automatic tracking through GPS(Jan et al.,2000;Quiroga et al.,2000;Taylor et al.,2000),and(iii)licence plate surveys(Schaefer,1988).Regarding self-comple-tion surveys,from our own interview experiments with self-completion questionnaires it was evident that travellersﬁnd it relatively difﬁcult to recall and describe complex choice options such as a route through an urban network,giving the po-tential for signiﬁcant errors to be introduced.The automatic tracking option was believed to be the most attractive in this respect,in its potential to accurately map a given individual’s journey,but the negative side would be the potential sample size,as we would need to purchase/hire and distribute the devices;even with a large budget,it is not straightforward to identify in advance the target users,nor to guarantee their cooperation.Licence plate surveys,it was believed,offered the potential for compromise between sample size and data resolution: while we could not track routes to the same resolution as GPS,by judicious location of surveyors we had the opportunity to track vehicles across more than one location,thus providing route-like information.With time-stamped licence plates, the matched data would also provide journey time information.The negative side of this approach is the well-known poten-tial for signiﬁcant recording errors if large sample rates are required.Our aim was to avoid this by recording only partial licence plates,and employing statistical methods to remove the impact of‘spurious matches’,i.e.where two different vehi-cles with the same partial licence plate occur at different locations.Moreover,extensive simulation experiments(Watling,1994)had previously shown that these latter statistical methods were effective in recovering the underlying movements and travel times,even if only a relatively small part of the licence plate were recorded,in spite of giving a large potential for spurious matching.We believed that such an approach reduced the opportunity for recorder error to such a level to suggest that a100%sample rate of vehicles passing may be feasible.This was tested in a pilot study conducted by the project team,with dictaphones used to record a100%sample of time-stamped, partial licence plates.Independent,duplicate observers were employed at the same location to compare error rates;the same study was also conducted with full licence plates.The study indicated that100%surveys with dictaphones would be feasible in moderate trafﬁcﬂow,but only if partial licence plate data were used in order to control observation errors; for higherﬂow rates or to obtain full number plate data,video surveys should be considered.Other important practical les-sons learned from the pilot included the need for clarity in terms of vehicle types to survey(e.g.whether to include motor-cycles and taxis),and of the phonetic alphabet used by surveyors to avoid transcription ambiguities.Based on the twin considerations above of planned interventions and survey approach,several candidate studies were identiﬁed.For a candidate study,detailed design issues involved identifying:likely affected movements and alternative routes(using local knowledge of York CC,together with an existing network model of the city),in order to determine the number and location of survey sites;feasible viewpoints,based on site visits;the timing of surveys,e.g.visibility issues in the dark,winter evening peak period;the peak duration from automatic trafﬁcﬂow data;and speciﬁc survey days,in view of public/school holidays.Our budget led us to survey the majority of licence plate sites manually(partial plates by audio-tape or,in lowﬂows,pen and paper),with video surveys limited to a small number of high-ﬂow sites.From this combination of techniques,100%sampling rate was feasible at each site.Surveys took place in the morning peak due both to visibility considerations and to minimise conﬂicts with tourist/special event trafﬁc.From automatic trafﬁc count data it was decided to survey the period7:45–9:15as the main morning peak period.This design process led to the identiﬁcation of two studies:2.1.Lendal Bridge study(Fig.1)Lendal Bridge,a critical part of York’s inner ring road,was scheduled to be closed for maintenance from September2000 for a duration of several weeks.To avoid school holidays,the‘before’surveys were scheduled for June and early September.It was decided to focus on investigating a signiﬁcant southwest-to-northeast movement of trafﬁc,the river providing a natural barrier which suggested surveying the six river crossing points(C,J,H,K,L,M in Fig.1).In total,13locations were identiﬁed for survey,in an attempt to capture trafﬁc on both sides of the river as well as a crossing.2.2.Fishergate study(Fig.2)The partial closure(capacity reduction)of the street known as Fishergate,again part of York’s inner ring road,was scheduled for July2001to allow repairs to a collapsed sewer.Survey locations were chosen in order to intercept clockwiseFig.1.Intervention and survey locations for Lendal Bridge study.around the inner ring road,this being the direction of the partial closure.A particular aim wasFulford Road(site E in Fig.2),the main radial affected,with F and K monitoring local diversion I,J to capture wider-area diversion.studies,the plan was to survey the selected locations in the morning peak over a period of approximately covering the three periods before,during and after the intervention,with the days selected so holidays or special events.Fig.2.Intervention and survey locations for Fishergate study.In the Lendal Bridge study,while the‘before’surveys proceeded as planned,the bridge’s actualﬁrst day of closure on Sep-tember11th2000also marked the beginning of the UK fuel protests(BBC,2000a;Lyons and Chaterjee,2002).Trafﬁcﬂows were considerably affected by the scarcity of fuel,with congestion extremely low in theﬁrst week of closure,to the extent that any changes could not be attributed to the bridge closure;neither had our design anticipated how to survey the impacts of the fuel shortages.We thus re-arranged our surveys to monitor more closely the planned re-opening of the bridge.Unfor-tunately these surveys were hampered by a second unanticipated event,namely the wettest autumn in the UK for270years and the highest level ofﬂooding in York since records began(BBC,2000b).Theﬂooding closed much of the centre of York to road trafﬁc,including our study area,as the roads were impassable,and therefore we abandoned the planned‘after’surveys. As a result of these events,the useable data we had(not affected by the fuel protests orﬂooding)consisted ofﬁve‘before’days and one‘during’day.In the Fishergate study,fortunately no extreme events occurred,allowing six‘before’and seven‘during’days to be sur-veyed,together with one additional day in the‘during’period when the works were temporarily removed.However,the works over-ran into the long summer school holidays,when it is well-known that there is a substantial seasonal effect of much lowerﬂows and congestion levels.We did not believe it possible to meaningfully isolate the impact of the link fully re-opening while controlling for such an effect,and so our plans for‘after re-opening’surveys were abandoned.3.Estimation of vehicle movements and travel timesThe data resulting from the surveys described in Section2is in the form of(for each day and each study)a set of time-stamped,partial licence plates,observed at a number of locations across the network.Since the data include only partial plates,they cannot simply be matched across observation points to yield reliable estimates of vehicle movements,since there is ambiguity in whether the same partial plate observed at different locations was truly caused by the same vehicle. Indeed,since the observed system is‘open’—in the sense that not all points of entry,exit,generation and attraction are mon-itored—the question is not just which of several potential matches to accept,but also whether there is any match at all.That is to say,an apparent match between data at two observation points could be caused by two separate vehicles that passed no other observation point.Theﬁrst stage of analysis therefore applied a series of specially-designed statistical techniques to reconstruct the vehicle movements and point-to-point travel time distributions from the observed data,allowing for all such ambiguities in the data.Although the detailed derivations of each method are not given here,since they may be found in the references provided,it is necessary to understand some of the characteristics of each method in order to interpret the results subsequently provided.Furthermore,since some of the basic techniques required modiﬁcation relative to the published descriptions,then in order to explain these adaptations it is necessary to understand some of the theoretical basis.3.1.Graphical method for estimating point-to-point travel time distributionsThe preliminary technique applied to each data set was the graphical method described in Watling and Maher(1988).This method is derived for analysing partial registration plate data for unidirectional movement between a pair of observation stations(referred to as an‘origin’and a‘destination’).Thus in the data study here,it must be independently applied to given pairs of observation stations,without regard for the interdependencies between observation station pairs.On the other hand, it makes no assumption that the system is‘closed’;there may be vehicles that pass the origin that do not pass the destina-tion,and vice versa.While limited in considering only two-point surveys,the attraction of the graphical technique is that it is a non-parametric method,with no assumptions made about the arrival time distributions at the observation points(they may be non-uniform in particular),and no assumptions made about the journey time probability density.It is therefore very suitable as aﬁrst means of investigative analysis for such data.The method begins by forming all pairs of possible matches in the data,of which some will be genuine matches(the pair of observations were due to a single vehicle)and the remainder spurious matches.Thus, for example,if there are three origin observations and two destination observations of a particular partial registration num-ber,then six possible matches may be formed,of which clearly no more than two can be genuine(and possibly only one or zero are genuine).A scatter plot may then be drawn for each possible match of the observation time at the origin versus that at the destination.The characteristic pattern of such a plot is as that shown in Fig.4a,with a dense‘line’of points(which will primarily be the genuine matches)superimposed upon a scatter of points over the whole region(which will primarily be the spurious matches).If we were to assume uniform arrival rates at the observation stations,then the spurious matches would be uniformly distributed over this plot;however,we shall avoid making such a restrictive assumption.The method begins by making a coarse estimate of the total number of genuine matches across the whole of this plot.As part of this analysis we then assume knowledge of,for any randomly selected vehicle,the probabilities:h k¼Prðvehicle is of the k th type of partial registration plateÞðk¼1;2;...;mÞwhereX m k¼1h k¼1172 D.Watling et al./Transportation Research Part A46(2012)167–189。

英文科技论文写作_北京理工大学中国大学mooc课后章节答案期末考试题库2023年

英文科技论文写作_北京理工大学中国大学mooc课后章节答案期末考试题库2023年1.If a real physical system shows a variation of both material properties acrossthe graded layer, the assumed linear variation may not give the bestapproximation.答案:may2.The idea of 'community' in terms of GRT lives is very strong and could beseen to correspond to some of the nostalgic constructs that non-GRT groups place on 'community'.答案:could be seen3.Is the research topic “How safe is nuclear power” effective?答案:正确4.Decide whether the following statement is true or false.c.Introductionincludes more detailed information than abstract.答案:正确5.Tertiary education may be ________ asthe period of study which is spent atuniversity.答案:defined6.Unbalanced Force ________ tothe sum total or net force exerted on an object.答案:refers7.This scatter can be attributed to the difficulties in measuring the dent depthdue to specimen processing.答案:can be attributed8.Choose a proper word from the choices to complete the following sentence.Arocket traveling away from Earth ____________ a speed greater than 11.186kilometers per second (6.95 miles per second) or 40,270 kilometers per hour (25,023 mph) will eventually escape Earth’s gravity.答案:at9.Choose a proper word from the choices to complete the following sentence.Inmechanical systems, power, the rate of doing work, can be computed____________ the product of force × velocity.答案:as10.Choose a proper word from the choices to complete the followingsentence.N ewton’s first law, the law of inertia, __________ that it takes a force to change the motion of an object.答案:states11.Choose a proper word from the choices to complete the followingsentence.Newton’s second law relates force, acceleration, and mass and it is often ___________ as the equation:f = ma答案:written12.Choose a proper word from the choices to complete the followingsentence.Because all types of energy can be expressed ___________ the sameunits, joules, this conversion can be expressed quantitatively in simplemodels.答案:in13.Choose a proper word from the choices to complete the followingsentence.So a key difference between a rocket and a jet plane is ____________ a rocket’s engine lifts it directly upward into the sky, whereas a jet’s engin es simply speed the plane forward so its wings can generate lift.答案:that14.Which of the following are the guidelines for writing formulas and equations?答案:Numbering all equations in sequence if referred to later._Centeringequations on their own separate lines._Using equations as grammatical units in sentences._Defining the symbols that are used.15.Acceleration relates to motion. It ________ a change in motion.答案:means16.Assertiveness is ________ asa skill of being able to stand up for your own orother people's rights in a calm and positive way, without being eitheraggressive, or passively accepting 'wrong'.答案:viewed17.The force that pushes a rocket upward is ________ thrust.答案:called18.Water ________ a liquid made up of molecules of hydrogen and oxygen in theratio of 2 to 1.答案:is19.The number of private cars increased ______60% from 2015 to 2016.答案:by20.Which can be the situations for writing a researchproposal?答案:Applying for an opportunity for a project_Applying for a bachelor’s, or master’s or doctor’s degree_Applying for some research funds or grants21.Who are usually the readers of the research proposals?答案:Specialists_Professors_Supervisors for the students_Professionals22.What are the elements to make the research proposal persuasive?答案:Reasonable budget_Clear Schedule_A Capable research team_Theimportance and necessity of the research question23.What are the language features of the research proposal?答案:Future tense_First person24.The purpose of writing a proposal is to ________________ the readers that theresearch plan is feasible and we are capable to do it.答案:persuade25.What types of information are generally supposed to be included in theintroduction section in the report?答案:Background_Summary of the results and conclusion_The purpose of the research26.Please decide whether the following statement is T(true) orF(false)according to the video.Discussion section analyzesand evaluates the research methods.答案:错误27.Please decide whether the following statement is T(true) orF(false)according to the video.Conclusion and recommendation sectionstates the significance of the findings and usually includes possible directions for further research.答案:正确28.These causes affected different regions differently in the 1990s, ______ Europehaving as much as 9.8% of degradation due to deforestation.答案:with29.Coal is predicted to increase steadily to 31q in 2030, whereas gas will remainstable ______ 25q.答案:at30.Manufacturing value added amounted ______12.3% of total U.S. grossdomestic product (GDP) in 2012, according to United Nations calculations.答案:to31.Chinese manufacturing value added accounted ______ 30.6% of its economy’stotal output in 2012, according to the UN.答案:for32.Japan ranked third ______ manufacturing value added at $1.1 trillion (seeFigure 1).答案:in33.About 4.2% of the 1,120 respondents were younger than 20 years, and 26.7%were ______ 21 and 30 years old.答案:between34.______ all the respondents, 67.1% were married and 32.9% were single.答案:of35.Decide whether the following statement is true or false.b.Both introductionand abstract include research findings.答案:错误36.Decide whether the following statement is true or false.a.It is possible to findtables or diagrams in introduction.答案:正确37.What are the possible contents of an introduction?答案:Reviewing the existing literature relevant to the presentstudy_Announcing the purpose/focus of the study_Identifying a gap in the existing literature_Explaining the significance or necessity of the research38.Choose the proper answers for the following questions.Ways to organize thereferences include:答案:a. Chronological order of publications_b. Researchmethods_c. Research theories_d. Research modes39.This indicates that there is a possibility of obtaining fluid density from soundspeed measurements and suggests that it is possible to measure soundabsorption with an ultrasonic cell to determine oil viscosity.In this sentence, the writer presents答案:Implication40.The measurements were shown to lead to an accurate determination of thebubble point of the oil.In this sentence, the writer presents答案:Results and achievement41.An ultrasonic cell was constructed to measure the speed of sound and testedin a crude oil sample. The speed of sound was measured at temperaturesbetween 260 and 411 K at pressures up to 75 MPs.In this sentence, thewriter presents答案:Methodology42.The aim of this study was to investigate the use of an ultrasonic cell todetermine crude oil properties, in particular oil density.In this sentence, the writer presents答案:Research aim43. A citation gives the s____ where the information or idea is from.答案:source44.An in-text citation usually includes information about the author and thep____ year.答案:publishing##%_YZPRLFH_%##publication45.To avoid plagiarism, using citations is the best way to give c____ to theoriginal author.答案:credit46.The publication details of the references listed at the end of the paper usuallyare put in a____ order.答案:alphabetical##%_YZPRLFH_%##alphabetic##%_YZPRLFH_%##alphab et47.The speed of sound in a fluid is determined by, and therefore an indicator of,the thermodynamic properties of that fluid.In this sentence, the writerpresents答案:Background factual information48.Citations are not necessary if the source is not clear.答案:错误49.Unintentional plagiarism can be excused.答案:错误50.Citing will make our writing less original.答案:错误51.Citing can effectively stress the originality of someone’s work.答案:正确52.As for the purposes of a literature review, which one is not included?答案:predicting the trend in relation to a central research question orhypothesis53. A literature review could be possibly presented as a/an ______.答案:all of the above54.The heading “Brief review of literature: drawing a timeline from 2005 to2017” shows the literature review is arranged in ______ order.答案:chronological55.About writing a literature review, which of the following statements is notcorrect?答案:To show respect to others’ work, our own interpretations should not be included.56.In terms of the writing feature, a research paper resembles a/an______.答案:argumentation57.Each citation can only have one particular citing purpose.答案:错误pared with in-text citations, the end-of-text references are more detailed.答案:正确59.In-text citations provide the abbreviation of an author’s given/first namerather than family/last name.答案:错误60.When the Chinese writers’ ideas are cited, the first names in Pinyin will begiven in in-text citations.答案:错误61.When a process is described, _____________ are usually used to show the orderof the stages or steps.答案:sequencers62.To help the reader better understand a complicated process, _____________ is(are) very often used.答案:visual aids63.What information is usually included when defining a process?答案:Equipment._Product_Material64.Decide whether the following statement is true or false.Researchers arerequired to use past tense when describing a process.答案:错误65.Decide whether the following statement is true or false.A definition of theprocess is very often given first when a process is described.答案:正确66.Escherichia coli, when found in conjunction with urethritis, often indicateinfection higher in the uro-genital tract.答案:正确67.The 'management' of danger is also not the sort of language to appear withinpolicy documents that refer to GRT children, which reflects systematicfailures in schools.错误68.Conceivably, different forms, changing at different rates and showingcontrasting combinations of characteristics, were present in different areas.答案:正确69.Viewing a movie in which alcohol is portrayed appears to lead to higher totalalcohol consumption of young people while watching the movie.答案:正确70.Furthermore, this proves that humans are wired to imitate.答案:错误71.One possibility is that generalized latent inhibition is likely to be weaker thanthat produced by pre-exposure to the CS itself and thus is more likely to be susceptible to the effect of the long interval.答案:正确72.It is unquestionable that our survey proved that the portrayal of alcohol anddrinking characters in movies directly leads to more alcohol consumption in young adult male viewers when alcohol is available within the situation.错误73.Implications of these findings may be that, if moderation of alcoholconsumption in certain groups is strived for, it may be sensible to cut down on the portrayal of alcohol in programmes aimed at these groups and thecommercials shown in between.答案:正确74.This effect might occur regardless of whether it concerns a real-lifeinteraction.答案:正确75.It definitely proves that a movie in which a lot of partying is involved triggersa social process between two participants that affects total drinking amounts.答案:错误76.It is believed that alcohol related health problems are on the rise.答案:believed77.Drinking to excess, or 'binge drinking' is often the cause of inappropriatebehaviour amongst teenagers.often78.It seems as though the experiment conducted simply confirms suspicionsheld by the academic and medical professions.答案:seems79.However, attrition was greatest among the heaviest drinking segment of thesample, suggesting under-estimation in the findings, and although the study provided associational, prospective evidence on alcohol advertising effects on youth drinking, it addressed limitations of other research, particularly the unreliability of exposure measures based on self-reporting (Synder andSlater, 2006).答案:suggesting80.These differences may be due to the fact participants reporting higherconsumption levels were primed to overrate their weekly drinking by the condition they were in.答案:may81.The crack tends to grow into the more brittle material and then stay in there,whether the initial crack tip lies in the graded material or in the more ductile material (and thereafter advances across the graded layer.答案:tends82.Decidewhether hedging language is used in thesentence below.Light smokingseems to have dramatic effects on cardiovascular disease.答案:正确83.Decidewhether hedging language is used in thesentence below.The impact ofthe UK’s ageing population will lead to increased welfare costs. Definitely,this will result in higher taxes and an increased retirement age for younger people.答案:错误84.Decidewhether hedging language is used in thesentence below.Althoughduration of smoking is also important when considering risk, it is highlycorrelated with age, which itself is a risk factor, so separating their effectscan be difficult.答案:正确85.Decidewhether hedging language is used in thesentence below.All these factstaken together point toward the likely presence of calcium carbonate in the soils that Phoenix has analyzed.答案:正确86.Decidewhether hedging language is used in thesentence below.Because thesefeatures are carved into the Tharsis Plateau, they must have an intermediate age.答案:错误87.Decidewhether hedging language is used in thesentence below.They appearto be covered with multiple layers of volcanic flows and sedimentary debris that originated in the south.答案:正确88.Decidewhether hedging language is used in thesentence below.Steven M.Clifford of the Lunar and Planetary Science Institute in Houston, amongothers, has conjectured that melting under a glacier or a thick layer ofpermafrost could also have recharged subterranean water sources.答案:正确89.Decidewhether hedging language is used in thesentence below.Earlier thisyear Philip Christensen of Arizona State University discovered gullies that clearly emerge from underneath a bank of snow and ice.答案:错误90.Put the following expressions in the proper place of the Discussion.A. Thesedata suggestB. In this study, we demonstrate C. it is critical to emphasizeD.additional research will be requiredE. we were unable todetermineDiscussionIndividuals who recover from certain viral infections typically develop virus-specific antibody responses that provide robustprotective immunity against re-exposure, but some viruses do not generate protective natural immunity, such as HIV-1. Human challenge studies for the common cold coronavirus 229E have suggested that there may be partialnatural immunity. However, there is currently no data whether humans who have recovered from SARS-CoV-2 infection are protected from re-exposure.This is a critical issue with profound implications for vaccine development, public health strategies, antibody-based therapeutics, and epidemiologicmodeling of herd immunity. _____1_______ that SARS-CoV-2 infection in rhesusmacaques provided protective efficacy against SARS-CoV-2 rechallenge.We developed a rhesus macaque model of SARS-CoV-2 infection thatrecapitulates many aspects of human SARS-CoV-2 infection, including high levels of viral replication in the upper and lower respiratory tract and clear pathologic evidence of viral pneumonia. Histopathology,immunohistochemistry, RNAscope, and CyCIF imaging demonstratedmultifocal clusters of virus infected cells in areas of acute inflammation, with evidence for virus infection of alveolar pneumocytes and ciliated bronchial epithelial cells. ______2_______ the utility of rhesus macaques as a model forSARS-CoV-2 infection for testing vaccines and therapeutics and for studying immunopathogenesis. However, neither nonhuman primate model led torespiratory failure or mortality, and thus further research will be required to develop a nonhuman primate model of severe COVID-19 disease.SARS-CoV-2 infection in rhesus macaques led to humoral and cellular immune responses and provided protection against rechallenge. Residual low levels ofsubgenomic mRNA in nasal swabs in a subset of animals and anamnesticimmune responses in all animals following SARS-CoV-2 rechallenge suggest that protection was mediated by immunologic control and likely was notsterilizing.Given the near-complete protection in all animals following SARS-CoV-2 rechallenge, ______3_______ immune correlates of protection in thisstudy. SARS-CoV-2 infection in rhesus monkeys resulted in the induction of neutralizing antibody titers of approximately 100 by both a pseudovirusneutralization assay and a live virus neutralization assay, but the relativeimportance of neutralizing antibodies, other functional antibodies, cellular immunity, and innate immunity to protective efficacy against SARS-CoV-2remains to be determined. Moreover, ______4_______ to define the durability of natural immunity.In summary, SARS-CoV-2 infection in rhesus macaquesinduced humoral and cellular immune responses and provided protectiveefficacy against SARS-CoV-2 rechallenge. These data raise the possibility that immunologic approaches to the prevention and treatment of SARS-CoV-2infection may in fact be possible. However,______5_______ that there areimportant differences between SARS-CoV-2 infection in macaques andhumans, with many parameters still yet to be defined in both species, andthus our data should be interpreted cautiously. Rigorous clinical studies will be required to determine whether SARS-CoV-2 infection effectively protects against SARS-CoV-2 re-exposure in humans.答案:BAEDC91.Rearrange the order of the following sentences to make a coherent andmeaningful abstract.1.These antibodies neutralized 10 representative SARS-CoV-2 strains, suggesting a possible broader neutralizing ability against otherstrains. Three immunizations using two different doses, 3 or 6 micrograms per dose, provided partial or complete protection in macaques against SARS-CoV-2 challenge, respectively, without observable antibody-dependentenhancement of infection.2.The coronavirus disease 2019 (COVID-19)pandemic caused by severe acute respiratory syndrome coronavirus 2(SARS-CoV-2) has resulted in an unprecedented public health crisis. Because of the novelty of the virus, there are currently no SARS-CoV-2–specifictreatments or vaccines available.3.Therefore, rapid development of effective vaccines against SARS-CoV-2 are urgently needed.4.Here, we developed apilot-scale production of PiCoVacc, a purified inactivated SARS-CoV-2 virus vaccine candidate, which induced SARS-CoV-2–specific neutralizingantibodies in mice, rats, and nonhuman primates.5.These data support the clinical development and testing of PiCoVacc for use in humans.答案:2341592.It seems likely that the details of the predictions depend on the assumedvariations of the toughness parameter and the yield stress.答案:It seems likely that93.The Relationships of Meteorological Factors and Nutrient Levels withPhytoplankton Biomass in a Shallow Eutrophic Lake Dominated byCyanobacteria, Lake Dianchi from 1991 to 2013A. The SHs, WS, and TPconcentrations controlled the bloom dynamics during the dry season, among which the TP concentration was the most important factors, whereas the TN and TP concentrations were the primary factors during the rainy season.B.Interannual analysis revealed that the phytoplankton biomass increased with increases in air temperature and TP concentration, with TP concentration as the main contributing factor.C. The results of our study demonstrated that both meteorological factors and nutrient levels had important roles incontrolling cyanobacterial bloom dynamics.D. All of these results suggest that both climate change regulation and eutrophication management should be considered in strategies aimed at controlling cyanobacterial blooms.E. Insummary, we analyzed the effects of meteorological factors and nutrientlevels on bloom dynamics in Lake Dianchi to represent the phytoplanktonbiomass.F. Further studies should assess the effects of climate change andeutrophication on cyanobacterial bloom dynamics based on data collected over a longer duration and more frequent and complete variables, andappropriate measures should be proposed to control these blooms.G.Decreasing nutrient levels, particularly the TP load should be initiallyconsidered during the entire period and during the dry season, anddecreasing both the TN and TP loads should be considered during the rainy season.H. However, the relative importance of these factors may changeaccording to precipitation patterns.1.2.B3.A4.G5.5. __________答案:F94.The Relationships of Meteorological Factors and Nutrient Levels withPhytoplankton Biomass in a Shallow Eutrophic Lake Dominated byCyanobacteria, Lake Dianchi from 1991 to 2013A. The SHs, WS, and TPconcentrations controlled the bloom dynamics during the dry season, among which the TP concentration was the most important factors, whereas the TN and TP concentrations were the primary factors during the rainy season.B.Interannual analysis revealed that the phytoplankton biomass increased with increases in air temperature and TP concentration, with TP concentration as the main contributing factor.C. The results of our study demonstrated that both meteorological factors and nutrient levels had important roles incontrolling cyanobacterial bloom dynamics.D. All of these results suggest that both climate change regulation and eutrophication management should be considered in strategies aimed at controlling cyanobacterial blooms.E. Insummary, we analyzed the effects of meteorological factors and nutrientlevels on bloom dynamics in Lake Dianchi to represent the phytoplanktonbiomass.F. Further studies should assess the effects of climate change andeutrophication on cyanobacterial bloom dynamics based on data collected over a longer duration and more frequent and complete variables, andappropriate measures should be proposed to control these blooms.G.Decreasing nutrient levels, particularly the TP load should be initiallyconsidered during the entire period and during the dry season, anddecreasing both the TN and TP loads should be considered during the rainy season.H. However, the relative importance of these factors may changeaccording to precipitation patterns.1.2.B3.A4.G5.4. __________答案:D95.The Relationships of Meteorological Factors and Nutrient Levels withPhytoplankton Biomass in a Shallow Eutrophic Lake Dominated byCyanobacteria, Lake Dianchi from 1991 to 2013A. The SHs, WS, and TPconcentrations controlled the bloom dynamics during the dry season, among which the TP concentration was the most important factors, whereas the TN and TP concentrations were the primary factors during the rainy season.B.Interannual analysis revealed that the phytoplankton biomass increased with increases in air temperature and TP concentration, with TP concentration as the main contributing factor.C. The results of our study demonstrated that both meteorological factors and nutrient levels had important roles incontrolling cyanobacterial bloom dynamics.D. All of these results suggest that both climate change regulation and eutrophication management should be considered in strategies aimed at controlling cyanobacterial blooms.E. Insummary, we analyzed the effects of meteorological factors and nutrientlevels on bloom dynamics in Lake Dianchi to represent the phytoplanktonbiomass.F. Further studies should assess the effects of climate change andeutrophication on cyanobacterial bloom dynamics based on data collected over a longer duration and more frequent and complete variables, andappropriate measures should be proposed to control these blooms.G.Decreasing nutrient levels, particularly the TP load should be initiallyconsidered during the entire period and during the dry season, anddecreasing both the TN and TP loads should be considered during the rainy season.H. However, the relative importance of these factors may changeaccording to precipitation patterns.1.2.B3.A4.G5.3. __________答案:H96.The Relationships of Meteorological Factors and Nutrient Levels withPhytoplankton Biomass in a Shallow Eutrophic Lake Dominated byCyanobacteria, Lake Dianchi from 1991 to 2013A. The SHs, WS, and TPconcentrations controlled the bloom dynamics during the dry season, among which the TP concentration was the most important factors, whereas the TN and TP concentrations were the primary factors during the rainy season.B.Interannual analysis revealed that the phytoplankton biomass increased with increases in air temperature and TP concentration, with TP concentration as the main contributing factor.C. The results of our study demonstrated that both meteorological factors and nutrient levels had important roles incontrolling cyanobacterial bloom dynamics.D. All of these results suggest that both climate change regulation and eutrophication management should be considered in strategies aimed at controlling cyanobacterial blooms.E. Insummary, we analyzed the effects of meteorological factors and nutrientlevels on bloom dynamics in Lake Dianchi to represent the phytoplanktonbiomass.F. Further studies should assess the effects of climate change andeutrophication on cyanobacterial bloom dynamics based on data collected over a longer duration and more frequent and complete variables, andappropriate measures should be proposed to control these blooms.G.Decreasing nutrient levels, particularly the TP load should be initiallyconsidered during the entire period and during the dry season, anddecreasing both the TN and TP loads should be considered during the rainy season.H. However, the relative importance of these factors may changeaccording to precipitation patterns.1.2.B3.A4.G5.2. __________答案:C97.The Relationships of Meteorological Factors and Nutrient Levels withPhytoplankton Biomass in a Shallow Eutrophic Lake Dominated byCyanobacteria, Lake Dianchi from 1991 to 2013A. The SHs, WS, and TPconcentrations controlled the bloom dynamics during the dry season, among which the TP concentration was the most important factors, whereas the TN and TP concentrations were the primary factors during the rainy season.B.Interannual analysis revealed that the phytoplankton biomass increased with increases in air temperature and TP concentration, with TP concentration as the main contributing factor.C. The results of our study demonstrated that both meteorological factors and nutrient levels had important roles incontrolling cyanobacterial bloom dynamics.D. All of these results suggest that both climate change regulation and eutrophication management should be considered in strategies aimed at controlling cyanobacterial blooms.E. Insummary, we analyzed the effects of meteorological factors and nutrientlevels on bloom dynamics in Lake Dianchi to represent the phytoplanktonbiomass.F. Further studies should assess the effects of climate change andeutrophication on cyanobacterial bloom dynamics based on data collected over a longer duration and more frequent and complete variables, andappropriate measures should be proposed to control these blooms.G.Decreasing nutrient levels, particularly the TP load should be initiallyconsidered during the entire period and during the dry season, anddecreasing both the TN and TP loads should be considered during the rainy season.H. However, the relative importance of these factors may changeaccording to precipitation patterns.1.2.B3.A4.G5.1. __________答案:E98.It is rare to offer recommendations forfuture researchin Conclusion section.。

高一科学探索英语阅读理解25题

高一科学探索英语阅读理解25题1<背景文章>The Big Bang Theory is one of the most important scientific theories in modern cosmology. It attempts to explain the origin and evolution of the universe. According to the Big Bang theory, the universe began as an extremely hot and dense singularity. Then, a tremendous explosion occurred, releasing an enormous amount of energy and matter. This event marked the beginning of time and space.In the early moments after the Big Bang, the universe was filled with a hot, dense plasma of subatomic particles. As the universe expanded and cooled, these particles began to combine and form atoms. The first atoms to form were hydrogen and helium. Over time, gravity caused these atoms to clump together to form stars and galaxies.The discovery of the cosmic microwave background radiation in 1964 provided strong evidence for the Big Bang theory. This radiation is thought to be the residual heat from the Big Bang and is uniformly distributed throughout the universe.The Big Bang theory has had a profound impact on modern science. It has helped us understand the origin and evolution of the universe, as well as the formation of stars and galaxies. It has also led to the development ofnew technologies, such as telescopes and satellites, that have allowed us to study the universe in greater detail.1. According to the Big Bang theory, the universe began as ___.A. a cold and empty spaceB. an extremely hot and dense singularityC. a collection of stars and galaxiesD. a large cloud of gas and dust答案：B。

机械词汇的英语翻译

A通用机枪AAT (Arme Automatique Transformable) 硬度降低 abating离轴的abaxial自动锅炉控制 abc活动]扳手abjustable spanner烧蚀冷却ablative cooling烧蚀材料ablative material异常液体 abnormal liquid超临界状态above critical state磨耗性 abradability磨损试验abrasion test磨损试验机abrasion tester磨料磨损abrasion wear砂带abrasive band砂带磨光abrasive belt grinding砂带磨床abrasive belt grinding machine砂布abrasive cloth砂轮切断机abrasive cut off machine切割砂轮abrasive cut off wheel磨料电解抛光abrasive ecp磨粒abrasive grain磨料喷射加工abrasive jet machining研磨加工abrasive machining砂纸abrasive paper研磨膏abrasive paste研磨粉abrasive powder研磨工具abrasive tool砂轮abrasive wheel砂线切割机床abrasive wire sawing machine研磨材料 abrasives突然扰动abrupt perturbation横坐标 abscissa无碰撞absence of collision失重absence of gravity无应力absence of stress无旋涡absence of vortices绝对的absolute绝对加速度absolute acceleration绝对角动量absolute angular momentum绝对汇编程序absolute assembler绝对升限absolute ceiling绝对坐标absolute coordinates 绝对偏差absolute deviation绝对数字控制absolute digital control绝对尺寸系数absolute dimensional factor 完全弹性体absolute elastic body绝对编码器absolute encoder绝对平衡absolute equilibrium绝对极值absolute extremum绝对飞行高度absolute flying height绝对频率absolute frequency绝对不稳定性absolute instability完全互换性absolute interchangeability绝对测量absolute measurement绝对运动absolute motion绝对路径absolute path绝对扰动absolute perturbation机械手的绝对位置 absolute position of manipulator机扑的绝对位置absolute position of robot 绝对静止absolute rest绝对旋转absolute rotation完全相似性absolute similarity绝对稳定性限度absolute stability margin 绝对单位制absolute system of units绝对温度表absolute thermometer绝对单位absolute unit绝对速度absolute velocity绝对涡度absolute vorticity绝对零度absolute zero吸收媒质absorbing medium吸收阻抗absorbing resistance吸收率计absorptiometer吸收计 absorptiometer?吸收功率计absorption dynamometer吸收式测功器absorption dynamometer?吸收热absorption heat吸收湿度计absorption hygrometer吸收损失absorption loss吸收模型absorption model吸收势absorption potential吸收泵；absorption pump吸收式冷冻机 absorption refrigerating machine吸收式制冷absorption refrigeration吸收管absorption tube吸收式波长计absorption wave meter吸收的absorptive吸收本领absorptive power交流交变电流ac交羚弧焊机ac arc welder交羚弧焊接ac arc welding适应控制电火花机床ac edm交立电机ac generator交羚动机ac motor加速蠕变accelerated creep加速运动accelerated motion加速能力accelerating ability加速场accelerating field加速梯度accelerating gradient加速撞击accelerating impact加速周期accelerating period加速泵accelerating pump加速管accelerating tube加速装置accelerating unit加速度分析acceleration analysis加速度图acceleration diagram加速度能量acceleration energy加速度场acceleration field加速喷嘴acceleration nozzle蠕变加速度acceleration of creep牵连加速度acceleration of moving space 加速度传感器acceleration pick up加速势acceleration potential加速压acceleration pressure加速度时间图acceleration time graph加速度矢量acceleration vector加速波acceleration wave加速功acceleration work无加速的 accelerationless加速栖杆accelerator lever加速皮板accelerator pedal加速泼accelerator pump加速度记录仪 accelerograph自记加速计accelerograph?容许噪声acceptable noise level验收证瞄acceptance certificate 验收试验acceptance test可达性 accessibility可达点accessible point附属品accessory?偶然的 accidental偶然符合accidental coincidence偶然共振accidental resonance适应系数accommodation coefficient 会计计算机accounting machine累积误差accumulated error同节累积误差accumulated pitch error 蓄压器储压器 accumulator蓄电池容量accumulator capacity蓄电池汽车accumulator car蓄电池极板accumulator plate精确度 accuracy精确控制accuracy control精度等级accuracy grade精确度寿命accuracy life对中精度accuracy of alignment仪表精度accuracy of instrument测量准确度accuracy of measurement 读数准确度accuracy of readings再现精度accuracy of reproduction尺寸精度accuracy to size准确化Accuralize精密蝶accurate adjustment精密磨削accurate grinding精确测量accurate measurement准确模型accurate model准确相似accurate similarity准确模拟accurate simulation醋酸纤维素acetylcellulose乙炔 acetylene乙炔燃烧器乙快焊炬acetylene burner 氧炔切割acetylene cutting氧炔切割机acetylene cutting machine 乙炔气acetylene gas乙炔发生器acetylene generator乙炔焊接acetylene welding消色差的 achromatic针状结构铸铁acicular cast iron针状组织acicular structure针状结构acicular structure?酸性转炉acid bessemer converter酸性转炉炼钢法acid bessemer process酸价acid number酸性平炉acid open hearth furnace酸性炼钢法acid process耐酸性的acid proof耐酸保护层acid proof coating酸雨acid rain抗酸合金acid resistant alloy酸性钢acid steel表面钢化acierage亚克米螺纹acme thread最佳适应控制 aco先进光学战斗瞄准具 ACOG (Advanced Combat Optical Gunsight)声的acoustic声吸收acoustic absorption声吸收率acoustic absorptivity声导纳acoustic admittance音响诊断acoustic diagnosis声弥散acoustic dispersion声音干扰acoustic disturbance声效率acoustic efficiency音频acoustic frequency声学气体分析器acoustic gas analyzer声阻抗 acoustic impedance音响检查acoustic inspection隔音 acoustic insulation隔声材料acoustic material声机械效率acoustic mechanical efficiency声振动acoustic oscillations声动印刷机acoustic printing machine声辐射压acoustic radiation pressure声抗acoustic reactance音响信号acoustic signal柯尔特自动手枪弹ACP (Automatic Colt Pistol)柯尔特自动手枪子弹. 由柯尔特公司设计, 一系列用于其生产的半自动手枪子弹名称. 有.25 ACP, .32 ACP, .380 ACP, .45ACP等. ACP: Automatic Colt Pistol,织力acting force酌action 超距酌action at distance活动中心action center酌积分action integral爆燃酌action of deflagration力的酌action of force战斗射击Action shooting酌区action sphere冲唤涡轮action turbine冲动式透平action turbine?酌变量action variable酌波action wave活性污泥泵activated sludge pump有功电流active current织土压active earth pressure累积瓦特计active energy meter织飞行active flight活性气体active gas有功负载反酌active load reaction织压力active pressure织式太阳能供暖active solar heating力功率activity of force实际啮合线actual line of action实际载荷 actual load实际值actual value控制电缆actuating cable执行器 actuator机扑的操　构actuator of robot非循环的 acyclic可以应用的adaptable适应性机扑adaptable robot转接器 adapter紧固套adapter sleeve适应控制adaptive control自适应控制机床 adaptive controlled machine机扑的适应控制adaptive robot control机扑的适应系统adaptive robot system适应性机扑综合技术 adaptive robot technical complex传感曝制自适应机扑 adaptive sensor guided robot适应计 adaptometer模拟数字转换器adc齿顶 addendum齿顶角addendum angletip angle齿顶圆addendum circle齿顶修正addendum modification齿顶修正系数addendum modification coefficient加法器 adder附加阻力additional drag附加质量additional mass附加压力additional pressure添加剂 additive粘着adhere粘附计 adherometer附着系数adhesion coefficient胶合磨损adhesion wear附着重量adhesion weight粘附力adhesive force附着接头adhesive joint粘着强度adhesive strength粘附张力adhesive tension粘附性adhesivity绝热的 adiabatic绝热近似adiabatic approximation绝热大气adiabatic atmosphere绝热式量热器adiabatic calorimeter绝热变化adiabatic change态的绝热变化adiabatic change of state绝热燃烧adiabatic combustion绝热效率adiabatic efficiency绝热椭圆adiabatic ellipse绝热因子adiabatic factor绝热假设adiabatic hypothesis绝热不变量adiabatic invariant涡旋的绝热不变量adiabatic invariant of eddy绝热扰动adiabatic perturbation绝热原理adiabatic principle绝热脉动adiabatic pulsations绝热温度adiabatic temperature伴算子adjoint operator可蝶的 adjustable可蝶轴承adjustable bearing可调隔膜泵；adjustable diaphragm pump齿轮比例泵；adjustable discharge gear pump 可导叶adjustable guide vane 可掂螺旋桨adjustable pitch propeller可第铰刀adjustable reamer可变电阻adjustable resistance可底管铰刀adjustable shell reamer可调式瞄准具Adjustable sight蒂电动机adjustable speed motor可悼锥adjustable tap可调式扳机Adjustable trigger蝶工adjuster可刀丝锥adjustible tap蝶螺栓adjusting bolt第套筒adjusting bush蝶凸轮adjusting cam蝶量规adjusting gauge蝶螺母adjusting nut蝶螺钉adjusting screw蝶弹簧adjusting spring蝶阀adjusting valve照准标志adjustment mark蝶范围adjustment range第式机扑adjustment robot总务部administration/general affairs dept船用黄铜admiralty brass容许的 admissible进气凸轮admission cam进气期间admission period进气管admission pipe吸气口admission port进气压力admission pressure进气冲程admission stroke导纳 admittance掺和物 admixture吸附力adsorption force吸附层adsorption layer吸附真空泵；adsorption vacuum pump提前点火advanced ignition提前进气advanced opening提前击发Advanced primer ignition急回系数advance-to return-time ratio超前速率advancing rate平流 advection平另advection fog平聊 advective通风机 aerator通气设备 aerator?空气的 aerial高架式输送机aerial conveyor高架铁路aerial railway航空弹道学aeroballistics滑翔学 aerodonetics滑翔力学 aerodromics空气速度测量法 aerodromometry气体动力的aerodynamic空气动力酌aerodynamic action空气动力比拟aerodynamic analogy气动迎角aerodynamic angle of attack 风洞天平aerodynamic balance空气动力轴承aerodynamic bearing空气动力制动装置aerodynamic brake 气动中心aerodynamic center气动力系数aerodynamic coefficient空气动力导数aerodynamic derivative 气动阻力aerodynamic drag气动力aerodynamic force气动力加热aerodynamic heating空气动力加热aerodynamic heating?气动升力aerodynamic lift空气动力升力 aerodynamic lift?空气动力力矩aerodynamic moment气动力相似aerodynamic similarity空气动力稳定性aerodynamic stability 空气动力学的 aerodynamical气体动力酌aerodynamical action空气动力天平aerodynamical balance 动力加热aerodynamical heating气动力矩aerodynamical moment空气动力学aerodynamics重航空器aerodyne气动弹性aeroelasticity气动弹性力学 aeroelastics飞机发动机aeroengine翼形剖面aerofoil profile风力发电机aerogenerator空气铃动力学 aerohydrodynamics高空气象学aerology 航空力学 aeromechanics气体比重计aerometer航空的 aeronautical航空学 aeronautics飞机 aeroplane脉动式喷气发动机aeropulse engine气溶胶aerosol悬浮微粒aerosol?航空航天技术 aerospace engineering轻航空器 aerostat空气静力轴承 aerostatic bearing气体静力学aerostatics空气静力学aerostatics?气动热力学aerothermodynamics空气热弹性学;气动热弹性 aerothermoelasticity气动热弹性aerothermoelasticity?气体张力测量法 aerotonometry飞行式无轨列车 aerotrain航空涡轮机aeroturbine仿射变换affine transformation尾发动机aft engine后效函数after effect function提供维修服务after sales service后部 afterbody加力燃烧室afterburner烧完 afterburning最终冷却器aftercooler余震波aftershock wave后处理aftertreatment应变时效ageing烧结机agglomerating plant腐蚀性气体aggressive gas腐蚀介质aggressive medium时效 aging搅拌器 agitator农用飞机agricultural aircraft农具 agricultural implements农业机器agricultural machine农业机械agricultural machines喷灌泵；agricultural spray pump农用喷药泵； agricultural spray pump for chemicals无人搬运车agv推进汽轮机ahead turbine副翼 aileron空气 air空气蓄压器air accumulator空气量 air amount空气轴承air bearing空气制动器air brake喷气发动机air breathing engine空气缓冲器air buffer空中爆炸air burst空气冠 air cap气垫车 air car旋风式发动机air cell engine气錾air chipper压缩空气式卡盘air chuck空气断路器air circuit breaker空气环流air circulation空气分级器air classifier空气滤清器air cleaner气旋塞 air cock空气柱air column空气电容器air condenser空气第器air conditioner空气消耗量air consumption空气污染air contamination气龄送 air conveying空气冷却剂air coolant气冷的 air cooled空气冷凝器air cooled condenser 气冷气缸air cooled cylinder气冷式发动机air cooled engine气冷式透平air cooled turbine气冷阀air cooled valve空气冷却片air cooling fin空间坐标air coordinates空气幕 air curtain气垫air cushion气垫船air cushion ship对地效应飞行器air cushion vehicle 压气缸air cylinder空气气缸air cylinder?空气阻尼器air damper 空气密度air density空气分配器air distributor风钻air drill风动振动机air driven vibrator空气涡旋air eddy空气喷射器air ejector空气分离器风选器air elutriator空气发动机air engine气轮胎air filled tyre气流空气量air flow气疗air flow meter空气摩擦air friction空气燃料混合物air fuel mixture空气燃料比air fuel ratio风煤气 air gas空气煤气air gas?气动测微仪air gauge风动凿岩机air hammer drill空气淬火air hardening空气硬化钢air hardening steel集气管 air header热风炉air heating furnace风动起重滑车air hoist气葫芦air hoist?风管air hose漏风air infiltration轮胎打气air inflating空气喷射柴油发动机 air injection diesel engine进气口air inlet空气侵入air inrush空气喷射air jet空气升液泵air lift?空气液化器air liquefier空气润滑air lubrication空气周路air main空气怜车air mobile vehicle气动发动机air motor风动机air operated machine压缩空气驱动泵；air operated pump气管air pipe空气等离子体air plasma空气压力计air pressure gage空气压头air pressure head空气减压器air pressure reducer空气压力试验air pressure test气密的 air proof空气泵air pump风动夯air rammer空气制冷机air refrigerating machine空气活门air register电器空气第器air register?放气塞air relief cock储气筒air reservoir空气分离air separation空气中凝固, 常温自硬自然硬化air set空气激波air shock wave空气速率air speed空气速率指示器air speed indicator空速指示器空速表示器air speed indicator? 空气弹簧air spring空气吝 air streamline气动悬架装置air suspension空气箱air tank航空集散站air terminal空气温度计air thermometer不透气的air tight气密接头air tight joint空对空导弹air to air missile空气轨迹air trajectory空气涡轮机air turbine气阀air valve净气器空气选净器air washer空气波air wave空气楔air wedge航空母舰aircraft carrier飞机动力学aircraft dynamics航空燃气涡轮机aircraft gas turbine航空工业aircraft industry航空仪表aircraft instrument飞机机械师aircraft mechanician飞机牵引车aircraft tractor气垫顶杆air-cushion eject-rod机翼 airfoil翼型airfoil profile翼剖面airfoil section 机翼理论airfoil theory无气喷射airless injection无气喷射柴油发动机airless injection diesel engine飞行航线 airline班机airliner气锁 airlock空气力学 airmechanics航空港 airport风动活塞泵；air-powered piston pump气动泥浆泵；air-pressure actuated slurry pump空气螺旋桨airscrew飞艇 airship软弹气枪 Airsoft跑道airstrip密闭式螺杆泵；airtight screw pump爱里应力函数airy stress function卡拉希尼可夫自动步枪AK (Avtomat Kalashnikov)警报 alarm闹钟alarm clock警告信号alarm signal告警系统alarm system醇alcohol乙醇计alcohol meter酒精温度计alcohol thermometer代数方程algebraic equation代数应力模型algebraic stress model算法 algorithm照准仪 alidade定向复合材料aligned composite material 定心 alignment对准,定位调整 Alignment定位销alignment pin导系统电源alignment system supply表面渗铝 alitizing硷性蓄电池alkaline battery碱土族金属alkaline earth metal龄咬alkaline etch碱蓄电池alkaline storage battery醇酸尸alkyd resin全青铜泵；all abronze pump铸铁泵；all iron pump万能的 all purpose全钢车身all steel body全天候飞机all weather aircraft全轮驱动all wheel drive方孔螺钉头用扳手allen wrench游标盘 allidade同素异形变化allotropic change容许间隙allowable clearance允许间隙allowable clearance?容许挠度allowable deflection容许偏差allowable deviation许用压力角allowable pressure angle许用应力allowable stress; permissible stress容许温度allowable temperature加工余量allowance for machining容许截面allowed cross section容许能带allowed energy band容许度 allowedness合金铸铁alloy cast iron切悉具合金alloy for cutting tools合金生铁alloy pig iron合金泵；alloy pump合金钢泵；alloy steel pump合金工具钢alloy tool steel合金成分alloying component合金元素alloying element字母数字码alphameric code反复浸没试验alternate immersion test交替负载alternate load交变弯曲alternating bending交变弯曲应力alternating bending stress交变弯曲试验alternating bending test交羚桥alternating current bridge交聋劣式电动机 alternating current commutator motor交僚服马达alternating current servomotor交替方向alternating direction交变滞后alternating hysteresis交变冲讳曲试验alternating impact bending test交变冲辉验alternating impact test交替载荷alternating load交变负载变形alternating load deformation 交变压力alternating pressure交替应力alternating stress交变 alternation负载交变alternation of load等高圈altitude circle高度差altitude difference高空锋面altitude front高度指示器altitude indicator铝黄铜合金aluminum brass铝青铜aluminum bronze铝铸件aluminum casting铝氧土aluminum oxide铝质活塞aluminum piston铝铆钉aluminum rivet双手通用 Ambidextrous周围的空气ambient air周围压力ambient pressure周围振动ambient vibration两极性扩散ambipolar diffusion救护车ambulance car阳极机械加工 amm安培计 ammeter阿芒拿 ammonal氨吸收冷冻机 ammonia absorption refrigerator氨气压缩冷冻机 ammonia compression refrigerator氨气压缩机ammonia compressor氨冷凝器ammonia condenser氨冷冻机ammonia refrigerator氨水ammonia water铵 ammonium水陆两用汽车ammphibious car阿米巴式运动amoeboid movement非晶质合金amorphous alloy无定形碳amorphous carbon无定形状态amorphous state能量amount of energy不平衡量amount of unbalance安培数amperage安匝ampere turn水陆飞机amphibian plane水陆两用机扑amphibian robot水陆两用飞机amphibious aircraft放大极限频率amplification limit frequency放大器 amplifier放大器盘amplifier panel脉冲幅度限幅amplitude clipping幅角余弦amplitude cosine振幅甄别器amplitude discriminator波幅畸变amplitude distortion幅频图amplitude frequency diagram振幅频率特性amplitude frequency response振幅函数amplitude function限幅器 amplitude limiter幅值轨迹 amplitude locus爹amplitude modulation振幅灯amplitude modulation?振幅共振amplitude resonance振幅响应amplitude response振幅选择器amplitude selector幅度变动amplitude swing上升锋面anabatic front上滑锋 anafront气压上升区anallobar模似计算机analog computer模拟控制analog control模拟数字计算机analog digital computer模拟数字计算机analog digital computer?模拟法analog method模拟伺服analog servomechanism模拟信号analog signal模拟计算机analogue computer相似法analogue method控制机扑的模拟信号 analogue signal for robot control磁场相似analogy of magnetic field分析学 analysis协方差分析analysis of covariance机构分析analysis of mechanism振荡分析analysis of the oscillation方差分析analysis of variance解析的 analytic解析变换analytic transformation分析化学analytical chemistry解析设计analytical design 分析力学analytical mechanics锚anchor锚链anchor chain起锚绞盘anchor windlass系泊 anchoring与电路and circuit滞弹性材料anelastic material风力自记曲线 anemogram风力记录仪anemograph风速表 anemometer风向仪 anemoscope　anergy无液测高计aneroid altimeter空盒气压表aneroid barometer空盒量热计aneroid calorimeter角度量具angle block角撑架angle bracket角旋塞angle cock斜角推土机angle dozer角传动angle drive角误差angle error量角规angle gauge角接 angle joint相角灯angle modulation超前角angle of advance到达角angle of arrival迎角angle of attack咬入角angle of bite毛细角angle of capillarity爬升角angle of climb切线角angle of contingence划孔角angle of countersinking交叉角angle of crossing偏斜角angle of declination起飞角angle of departure偏向角angle of deviation畸变角angle of distortion下洗角angle of downwash仰角angle of elevation出角angle of emergence射出角angle of emergence?襟翼偏转角angle of flap deflection 燎angle of flow点火提前角angle of ignition advance碰撞角angle of impact升角angle of lead偏光角angle of polarization螺纹截形角angle of screw thread侧滑角angle of sideslip失速角angle of stall螺面角angle of thread偏航角angle of yaw保角映射angle preserving mapping剪角铁机angle shears角离散angle straggling弯体式轴向活塞泵angle type axial piston pump角变量angle variable半贯流式轴流泵；弯管轴流泵；angle-type axial flow pump斜轴式轴向活塞泵；angle-type axial piston pump埃angstrom角加速度angular acceleration径向止推滚珠轴承angular ball bearing角皮带传动angular belt drive角系数angular coefficient角接触轴承angular contact bearing角接触向心轴承angular contact radial bearing角接触推力轴承angular contact thrust bearing角坐标angular coordinates角相关angular correlation角铣刀angular cutter角偏向损失angular derivation loss角微商angular derivative角偏差angular deviation角分散angular dispersion角位移angular displacement角距angular distance角分布angular distribution角分度angular division角频率angular frequency角冲量 angular impulse角动量angular momentum角动量守恒定律 angular momentum conservation law角动量算符angular momentum operator角动量张量angular momentum tensor 角动量定理angular momentum theorem 角运动angular motion角度分辨率angular resolution方向夹角angular separation角速度angular speed角单位angular unit角速比angular velocity ratio非低的anharmonic非谐振动anharmonic oscillation非谐振子anharmonic oscillator非低比anharmonic ratio苯胺 aniline动物油animal oil饲槽自动泵；家畜自动饮水泵；animal self-operated drinking water pump阴离子 anion非等熵怜anisentropic flow非等温渗透流anisothermal porous flow蛤异性体anisotropic body蛤异性液体anisotropic liquid蛤异性材料anisotropic material蛤异性岩石anisotropic rock蛤异性湍流anisotropic turbulence蛤异性常数anisotropy constant蛤异性比anisotropy ratio退火 annealing退火箱annealing box退火炉annealing furnace退火温度annealing temperature年用量annual consumption环壳泵；annular casing pump环形燃烧室annular combustion chamber 环状浮子annular float环流annular flow环形流annular flow?环形焦点 annular focus环形炉annular furnace环形槽annular groove环形磁铁annular magnet环形雾状流annular mist flow环形喷嘴annular nozzle环形间隙annular space弹簧环annular spring环状阀annular valve环状空间 annulus?正极 anode阳极被覆膜anode film阳极溅射anode sputtering阳极溶解anodic dissolution阳极保护anodic protection电解加工anodic removing阳性处理 Anodize异常吸收anomalous absorption反常扩散anomalous diffusion反常散射anomalous scattering反扩散anti diffusion防冰装置anti icer反时针方向旋转anticlockwise rotation反符合法anticoincidence method耐蚀薄膜anticorrosion film防腐蚀剂anticorrosive agent耐蚀合金anticorrosive alloy反气旋消散anticyclolysis反气旋涡度anticyclonic vorticity避眩灯antidazzle light防眩罩antidazzle visor防爆剂 antidetonant防泡剂 antifoamer防冻剂 antifreeze抗摩合金antifriction alloy滚动轴承antifriction bearing抗摩铸铁antifriction cast iron滚动导轨antifriction guide耐摩材料antifriction material减摩性anti-friction quality抗爆的 antiknock抗爆震燃料antiknock fuel抗爆汽油antiknock gasoline抗爆性antiknock quality反物资步枪，反设备步枪Anti-material rifle 锑铅 antimonial lead波腹antinode对映空间antipodal space反共振 antiresonance反共振频率antiresonance frequency减摇泵；anti-roll pump 防垢剂antiscale composition防滑链antiskid chain防滑轮胎antiskid tire反对称张量antisymmetric tensor反对称态antisymmetrical state反对称 antisymmetry减速风antitriptic wind抗磨添加剂antiwear additive测砧anvil砧座 anvil block砧面anvil face非周期的 aperiodic非周期衰减aperiodic damping非周期运动aperiodic motion非周期性速度波动 aperiodic speed fluctuation孔径比aperture ratio觇孔瞄准具Aperture sight远日点 aphelion齐酶镜 aplanat消球差的 aplanatic远心点 apocenter复消色差透镜 apochromat无极的 apolar远月点 apolune内切圆半径apothem表观吸收系数 apparent absorption coefficient表观粘力apparent cohesion表观扩散率apparent diffusivity表观能量apparent energy表观平衡apparent equilibrium表观膨胀apparent expansion视在膨胀apparent expansion?表观力apparent force表观弹性模量 apparent modulus of elasticity表面水分apparent moisture表观相角apparent phase angle表观功率 apparent power外表比重apparent specific gravity?表观粘度apparent viscosity表观功apparent work疲劳现象appearance of fatigue阿佩尔方程appell equation应用 application操作图, 应用图application drawing应用程序application program应用弹性学applied elasticity theory作用力applied force应用力学applied mechanics应用热力学applied thermodynamics驶近速度approach velocity核准/审核/承办 approved by / checked by / prepared by近似解析approximate analysis近似模型approximate model近似相似approximate similarity近似模拟approximate simulation近似解approximate solution近似 approximation近似计算approximation calculus拉格朗日函数近似approximation of lagrange function近似理论approximation theory近似值approximative value板式输送机apron conveyor任意单位arbitrary unit心轴 arbor电弧 arc电弧切割arc cutting电弧炉 arc furnace电弧刨削arc gouging弧光灯arc lamp电弧电压arc voltage电焊机arc welder电弧焊接arc welding电弧焊机扑arc welding robot拱形重力坝arch gravity dam拱形结构arch structure拱梁arched beam螺旋泵；Archimedean screw pump阿基米德原理archimedes principle阿基米德蜗杆archimedes' worm建筑术architecture机扑电脑结构architecture of robot computer 面积曲线area curve表面负载area load面积矩area moment接触面积area of contact面积比area ratio面加速度areal acceleration面积坐标areal coordinates面积速度areal velocity比量计 areometer氩激光器argon laser算术平均 arithmetic mean算术平均值arithmetic mean value算术级数arithmetic progression机扑运算处理装置 arithmetic robot processor运算装置 arithmetic unit边 arm力偶臂arm of couple轮辐arm of wheel电枢armature电枢铁芯armature core电枢绕组armature winding电枢绕线机armature winding machine阿姆克铁armco iron装甲板armor plate装甲钢板轧机armor plate mill装甲缆armored cable装甲车armored car络网玻璃armored glass钢丝包皮软管armored hose军用载人装甲车armored personnel carrier 军械士 Armorer穿甲弹armour piercing shell铠装泵；armoured pump芳香族石油aromatic base crude oil?轻型火绳枪Arquebus制动器 arrest阿雷尼厄斯方程arrhenius equation阿雷尼厄斯定律arrhenius law形发动机arrow engine w箭头 arrowhead艺术铸件art casting自廉头artesian head自廉压artesian pressure铰链的 articulated关节杆articulated arm副连杆articulated connecting rod活节联接器articulated coupling铰接机构articulated mechanism关节管articulated pipe多关节型机扑articulated robot铰接式无轨电车articulated trolleybus铰链滑片泵；articulated vane pump铰接式汽车articulated vehicle人造磨料artificial abrasive人工时效artificial aging人工脑artificial brain人造纤维汽车artificial fibre automobile人造纤维飞机artificial fibre plane人造燃料artificial fuel人造石墨artificial graphite人造重力artificial gravity人工水平仪artificial horizon人工智能artificial intelligence人工智能汽车artificial intelligence automobile 人造革artificial leather人造液体燃料artificial liquid fuel人工扰动artificial perturbation人造石油artificial petroleum合成尸artificial resin人工换气artificial ventilation人工视觉artificial vision铸态as cast condition石棉制动摩擦带asbestos brake band石棉纸板asbestos cardboard石棉垫圈 asbestos gasket石棉绒asbestos wool向上气流ascending air current上升运动ascending motion上行冲程ascending stroke上升冲程ascending stroke?灰 ash灰分组成ash composition灰分ash content吹灰器排灰器ash ejector放灰器排灰器ash ejector? 无灰分燃料ash free fuel起灰机 ash hoist灰槽ash pit灰渣泵；ash pump除灰ash removal展弦比aspect ratio吸气冲程aspirating stroke通风湿度计aspiration hygrometer吸引器 aspirator攻击性武器Assault weapon试金炉assay furnace汇编程序系统 assembler programming system. aps安装机;装配机械assembling machine装配机扑assembling robot装配自动化assembly automation装配条件assembly condition装配输送带assembly conveyor装配夹具assembly fixture装配用工业机扑assembly industrial robot 装配厂assembly plant装配过程assembly process装配架assembly stand装配站assembly station装配工艺assembly technology装配单位assembly unit结合累积associate cumulation缔合波associated wave相联只读存储器 associative read only memories. aroms杆组Assur group无定向蒂器astatic governor倒车轮机astern turbine天体力学 astromechanics宇宙航行学astronautics天文导航 astronavigation天体望远镜astronomical telescope天文单位astronomical unit非对称性分布asymmetrical distribution渐近线 asymptote渐近模型asymptotic model渐近稳定度asymptotic stability异步通信适配器asynchronouscommunication adapter. aca异步发电机asynchronous generator异步电机asynchronous machine感应电动机asynchronous motor机扑异步控制asynchronous robot control自动换刀装置 atc菸酒枪械管理局 ATF (Alcohol Tobacco and Firearms Bureau)冲压喷气发动机 athodyd汽化计 atmometer?大气边界层atmospheric boundary layer大气制动atmospheric braking大气式冷凝器atmospheric condenser大气式冷却器atmospheric cooler大气腐蚀atmospheric corrosion大气飞行atmospheric flight大气湿度atmospheric humidity大气层atmospheric layer大气扰动atmospheric perturbation气压图atmospheric pressure chart大气下沉atmospheric subsidence大气温度atmospheric temperature大气湍流atmospheric turbulence大气波atmospheric wave原子atom原子碰撞因子atom collision factor原子能电池atomic battery原子爆炸atomic blast原子龟裂atomic crack原子能atomic energy原子硬化atomic hardening原子核atomic nucleus原子序数atomic number原子动力atomic power原子飞机atomic powered aircraft核船atomic powered ship核动力推进atomic propulsion核潜艇atomic submarine原子量atomic weight喷雾化 atomization雾化压力atomization pressure自动带读出器 atr附属泵；attached pump 附属装置 attachment减温器过热降低器 attemperator维护规程attendance instruction衰减振动attenuation vibration衰减器 attenuator姿态控制attitude control吸引 attraction引力势attraction potential引力中心attractive center可听性 audibility可听音audible sound审计audit陆军通用步枪 AUG (Arme Universal Gewehr)回转式钻岩机 auger增加 augmentation加速室 augmenter角度偏差augular offset奥氏体 austenite奥氏体钢austenitic steel升车机auto hoist到装置auto levelizer车辆提升机auto lift汽车修理车间auto repair shop自乘谱auto spectrum汽车轮胎auto tire汽车外轮胎auto tyre高压釜 autoclave?自动准直仪autocollimator自动控制 autocontrol自相关autocorrelation自激 autoexcitation自应力加工autofrettage自点火autogeneous ignition自动陀螺仪autogiro旋翼飞机autogyro自动装载机autoloader自动装配automated assembly自动检验automated inspection自动化生产automated production自动仓库automated warehouse自动的 automatic自动弧焊机automatic arc welder。

流体特征描述、检测理论总结

流场特征描述、检测理论总结报告1.绪论特征定义为数据中不同成分间相关性的表现模式，具有两方面的含义：“（1）矢量场中有意义的形状、结构、变化和现象，如涡流、激波等；（2）从数据场中分离出来的用户感兴趣的区域。

” 。

目前流场特征的分析方法有多种，大致可以归结为三类：基于图像处理、基于拓扑分析（即基于矢量场分析）以及基于物理特征方法[1]，但主要是基于拓扑分析方法。

原因分析：流场特征结构概念的提出最原始就是基于拓扑分析方法，因此每个流场特征结构一般具有严格的数学定义，而不是像一般图像处理中的模式识别方法针对的目标对象，如人脸、指纹等不存在严格定义。

因此拓扑分析仍然是最有效的流场特征提取方法。

缺点：并不是所有的流场结构都有严格的数学定义，譬如涡旋结构，在2D 空间中，源点、汇点以及中心点等对应的流场周围都符合涡旋的特征。

2.基本概念为更好的描述矢量场，首先介绍如下基本概念[1]。

2.1 梯度三维空间中，标量p 有三个偏微分算子。

标量场的梯度这三个偏微分算子表示：{,,}p p p gradp p x y z∂∂∂=∇=∂∂∂ （1）向量场v 的梯度可以通过应用梯度算子在其分量{u,v,w}上而计算。

结果是一个3*3矩阵，称作Jacobian 矩阵，或者一阶算子。

u u u x y z v v v v x y z w w w x y z ⎡⎤∂∂∂ ⎢⎥∂∂∂⎢⎥⎢⎥∂∂∂∇= ⎢⎥∂∂∂⎢⎥⎢⎥∂∂∂ ⎢⎥∂∂∂⎣⎦ （2）该矩阵可用来计算一些导数场，譬如散度（divergence ），旋度(curl)，螺旋性(helicity)，加速(acceleration)，曲率(curvature)。

速度场的旋度称作涡度（vorticity ）。

这些导数场暗示了流绕旋转轴旋转的强度。

这些数量已被用于不同的特征抽取技术方面，将在下面介绍。

2.2 本征分析(Eigenanalysis)另一种独立的数据技术是本征分析。

专八英语阅读

英语专业八级考试TEM-8阅读理解练习册（1）(英语专业2012级)UNIT 1Text AEvery minute of every day, what ecologist生态学家James Carlton calls a global ―conveyor belt‖, redistributes ocean organisms生物.It’s planetwide biological disruption生物的破坏that scientists have barely begun to understand.Dr. Carlton —an oceanographer at Williams College in Williamstown,Mass.—explains that, at any given moment, ―There are several thousand marine species traveling… in the ballast water of ships.‖ These creatures move from coastal waters where they fit into the local web of life to places where some of them could tear that web apart. This is the larger dimension of the infamous无耻的，邪恶的invasion of fish-destroying, pipe-clogging zebra mussels有斑马纹的贻贝.Such voracious贪婪的invaders at least make their presence known. What concerns Carlton and his fellow marine ecologists is the lack of knowledge about the hundreds of alien invaders that quietly enter coastal waters around the world every day. Many of them probably just die out. Some benignly亲切地，仁慈地—or even beneficially — join the local scene. But some will make trouble.In one sense, this is an old story. Organisms have ridden ships for centuries. They have clung to hulls and come along with cargo. What’s new is the scale and speed of the migrations made possible by the massive volume of ship-ballast water压载水— taken in to provide ship stability—continuously moving around the world…Ships load up with ballast water and its inhabitants in coastal waters of one port and dump the ballast in another port that may be thousands of kilometers away. A single load can run to hundreds of gallons. Some larger ships take on as much as 40 million gallons. The creatures that come along tend to be in their larva free-floating stage. When discharged排出in alien waters they can mature into crabs, jellyfish水母, slugs鼻涕虫，蛞蝓, and many other forms.Since the problem involves coastal species, simply banning ballast dumps in coastal waters would, in theory, solve it. Coastal organisms in ballast water that is flushed into midocean would not survive. Such a ban has worked for North American Inland Waterway. But it would be hard to enforce it worldwide. Heating ballast water or straining it should also halt the species spread. But before any such worldwide regulations were imposed, scientists would need a clearer view of what is going on.The continuous shuffling洗牌of marine organisms has changed the biology of the sea on a global scale. It can have devastating effects as in the case of the American comb jellyfish that recently invaded the Black Sea. It has destroyed that sea’s anchovy鳀鱼fishery by eating anchovy eggs. It may soon spread to western and northern European waters.The maritime nations that created the biological ―conveyor belt‖ should support a coordinated international effort to find out what is going on and what should be done about it. (456 words)1.According to Dr. Carlton, ocean organism‟s are_______.A.being moved to new environmentsB.destroying the planetC.succumbing to the zebra musselD.developing alien characteristics2.Oceanographers海洋学家are concerned because_________.A.their knowledge of this phenomenon is limitedB.they believe the oceans are dyingC.they fear an invasion from outer-spaceD.they have identified thousands of alien webs3.According to marine ecologists, transplanted marinespecies____________.A.may upset the ecosystems of coastal watersB.are all compatible with one anotherC.can only survive in their home watersD.sometimes disrupt shipping lanes4.The identified cause of the problem is_______.A.the rapidity with which larvae matureB. a common practice of the shipping industryC. a centuries old speciesD.the world wide movement of ocean currents5.The article suggests that a solution to the problem__________.A.is unlikely to be identifiedB.must precede further researchC.is hypothetically假设地，假想地easyD.will limit global shippingText BNew …Endangered‟ List Targets Many US RiversIt is hard to think of a major natural resource or pollution issue in North America today that does not affect rivers.Farm chemical runoff残渣, industrial waste, urban storm sewers, sewage treatment, mining, logging, grazing放牧,military bases, residential and business development, hydropower水力发电,loss of wetlands. The list goes on.Legislation like the Clean Water Act and Wild and Scenic Rivers Act have provided some protection, but threats continue.The Environmental Protection Agency (EPA) reported yesterday that an assessment of 642,000 miles of rivers and streams showed 34 percent in less than good condition. In a major study of the Clean Water Act, the Natural Resources Defense Council last fall reported that poison runoff impairs损害more than 125,000 miles of rivers.More recently, the NRDC and Izaak Walton League warned that pollution and loss of wetlands—made worse by last year’s flooding—is degrading恶化the Mississippi River ecosystem.On Tuesday, the conservation group保护组织American Rivers issued its annual list of 10 ―endangered‖ and 20 ―threatened‖ rivers in 32 states, the District of Colombia, and Canada.At the top of the list is the Clarks Fork of the Yellowstone River, whereCanadian mining firms plan to build a 74-acre英亩reservoir水库，蓄水池as part of a gold mine less than three miles from Yellowstone National Park. The reservoir would hold the runoff from the sulfuric acid 硫酸used to extract gold from crushed rock.―In the event this tailings pond failed, the impact to th e greater Yellowstone ecosystem would be cataclysmic大变动的，灾难性的and the damage irreversible不可逆转的.‖ Sen. Max Baucus of Montana, chairman of the Environment and Public Works Committee, wrote to Noranda Minerals Inc., an owner of the ― New World Mine‖.Last fall, an EPA official expressed concern about the mine and its potential impact, especially the plastic-lined storage reservoir. ― I am unaware of any studies evaluating how a tailings pond尾矿池，残渣池could be maintained to ensure its structural integrity forev er,‖ said Stephen Hoffman, chief of the EPA’s Mining Waste Section. ―It is my opinion that underwater disposal of tailings at New World may present a potentially significant threat to human health and the environment.‖The results of an environmental-impact statement, now being drafted by the Forest Service and Montana Department of State Lands, could determine the mine’s future…In its recent proposal to reauthorize the Clean Water Act, the Clinton administration noted ―dramatically improved water quality since 1972,‖ when the act was passed. But it also reported that 30 percent of riverscontinue to be degraded, mainly by silt泥沙and nutrients from farm and urban runoff, combined sewer overflows, and municipal sewage城市污水. Bottom sediments沉积物are contaminated污染in more than 1,000 waterways, the administration reported in releasing its proposal in January. Between 60 and 80 percent of riparian corridors (riverbank lands) have been degraded.As with endangered species and their habitats in forests and deserts, the complexity of ecosystems is seen in rivers and the effects of development----beyond the obvious threats of industrial pollution, municipal waste, and in-stream diversions改道to slake消除the thirst of new communities in dry regions like the Southwes t…While there are many political hurdles障碍ahead, reauthorization of the Clean Water Act this year holds promise for US rivers. Rep. Norm Mineta of California, who chairs the House Committee overseeing the bill, calls it ―probably the most important env ironmental legislation this Congress will enact.‖ (553 words)6.According to the passage, the Clean Water Act______.A.has been ineffectiveB.will definitely be renewedC.has never been evaluatedD.was enacted some 30 years ago7.“Endangered” rivers are _________.A.catalogued annuallyB.less polluted than ―threatened rivers‖C.caused by floodingD.adjacent to large cities8.The “cataclysmic” event referred to in paragraph eight would be__________.A. fortuitous偶然的，意外的B. adventitious外加的，偶然的C. catastrophicD. precarious不稳定的，危险的9. The owners of the New World Mine appear to be______.A. ecologically aware of the impact of miningB. determined to construct a safe tailings pondC. indifferent to the concerns voiced by the EPAD. willing to relocate operations10. The passage conveys the impression that_______.A. Canadians are disinterested in natural resourcesB. private and public environmental groups aboundC. river banks are erodingD. the majority of US rivers are in poor conditionText CA classic series of experiments to determine the effects ofoverpopulation on communities of rats was reported in February of 1962 in an article in Scientific American. The experiments were conducted by a psychologist, John B. Calhoun and his associates. In each of these experiments, an equal number of male and female adult rats were placed in an enclosure and given an adequate supply of food, water, and other necessities. The rat populations were allowed to increase. Calhoun knew from experience approximately how many rats could live in the enclosures without experiencing stress due to overcrowding. He allowed the population to increase to approximately twice this number. Then he stabilized the population by removing offspring that were not dependent on their mothers. He and his associates then carefully observed and recorded behavior in these overpopulated communities. At the end of their experiments, Calhoun and his associates were able to conclude that overcrowding causes a breakdown in the normal social relationships among rats, a kind of social disease. The rats in the experiments did not follow the same patterns of behavior as rats would in a community without overcrowding.The females in the rat population were the most seriously affected by the high population density: They showed deviant异常的maternal behavior; they did not behave as mother rats normally do. In fact, many of the pups幼兽，幼崽, as rat babies are called, died as a result of poor maternal care. For example, mothers sometimes abandoned their pups,and, without their mothers' care, the pups died. Under normal conditions, a mother rat would not leave her pups alone to die. However, the experiments verified that in overpopulated communities, mother rats do not behave normally. Their behavior may be considered pathologically 病理上，病理学地diseased.The dominant males in the rat population were the least affected by overpopulation. Each of these strong males claimed an area of the enclosure as his own. Therefore, these individuals did not experience the overcrowding in the same way as the other rats did. The fact that the dominant males had adequate space in which to live may explain why they were not as seriously affected by overpopulation as the other rats. However, dominant males did behave pathologically at times. Their antisocial behavior consisted of attacks on weaker male,female, and immature rats. This deviant behavior showed that even though the dominant males had enough living space, they too were affected by the general overcrowding in the enclosure.Non-dominant males in the experimental rat communities also exhibited deviant social behavior. Some withdrew completely; they moved very little and ate and drank at times when the other rats were sleeping in order to avoid contact with them. Other non-dominant males were hyperactive; they were much more active than is normal, chasing other rats and fighting each other. This segment of the rat population, likeall the other parts, was affected by the overpopulation.The behavior of the non-dominant males and of the other components of the rat population has parallels in human behavior. People in densely populated areas exhibit deviant behavior similar to that of the rats in Calhoun's experiments. In large urban areas such as New York City, London, Mexican City, and Cairo, there are abandoned children. There are cruel, powerful individuals, both men and women. There are also people who withdraw and people who become hyperactive. The quantity of other forms of social pathology such as murder, rape, and robbery also frequently occur in densely populated human communities. Is the principal cause of these disorders overpopulation? Calhoun’s experiments suggest that it might be. In any case, social scientists and city planners have been influenced by the results of this series of experiments.11. Paragraph l is organized according to__________.A. reasonsB. descriptionC. examplesD. definition12．Calhoun stabilized the rat population_________.A. when it was double the number that could live in the enclosure without stressB. by removing young ratsC. at a constant number of adult rats in the enclosureD. all of the above are correct13.W hich of the following inferences CANNOT be made from theinformation inPara. 1?A. Calhoun's experiment is still considered important today.B. Overpopulation causes pathological behavior in rat populations.C. Stress does not occur in rat communities unless there is overcrowding.D. Calhoun had experimented with rats before.14. Which of the following behavior didn‟t happen in this experiment?A. All the male rats exhibited pathological behavior.B. Mother rats abandoned their pups.C. Female rats showed deviant maternal behavior.D. Mother rats left their rat babies alone.15. The main idea of the paragraph three is that __________.A. dominant males had adequate living spaceB. dominant males were not as seriously affected by overcrowding as the otherratsC. dominant males attacked weaker ratsD. the strongest males are always able to adapt to bad conditionsText DThe first mention of slavery in the statutes法令，法规of the English colonies of North America does not occur until after 1660—some forty years after the importation of the first Black people. Lest we think that existed in fact before it did in law, Oscar and Mary Handlin assure us, that the status of B lack people down to the 1660’s was that of servants. A critique批判of the Handlins’ interpretation of why legal slavery did not appear until the 1660’s suggests that assumptions about the relation between slavery and racial prejudice should be reexamined, and that explanation for the different treatment of Black slaves in North and South America should be expanded.The Handlins explain the appearance of legal slavery by arguing that, during the 1660’s, the position of white servants was improving relative to that of black servants. Thus, the Handlins contend, Black and White servants, heretofore treated alike, each attained a different status. There are, however, important objections to this argument. First, the Handlins cannot adequately demonstrate that t he White servant’s position was improving, during and after the 1660’s; several acts of the Maryland and Virginia legislatures indicate otherwise. Another flaw in the Handlins’ interpretation is their assumption that prior to the establishment of legal slavery there was no discrimination against Black people. It is true that before the 1660’s Black people were rarely called slaves. But this shouldnot overshadow evidence from the 1630’s on that points to racial discrimination without using the term slavery. Such discrimination sometimes stopped short of lifetime servitude or inherited status—the two attributes of true slavery—yet in other cases it included both. The Handlins’ argument excludes the real possibility that Black people in the English colonies were never treated as the equals of White people.The possibility has important ramifications后果，影响.If from the outset Black people were discriminated against, then legal slavery should be viewed as a reflection and an extension of racial prejudice rather than, as many historians including the Handlins have argued, the cause of prejudice. In addition, the existence of discrimination before the advent of legal slavery offers a further explanation for the harsher treatment of Black slaves in North than in South America. Freyre and Tannenbaum have rightly argued that the lack of certain traditions in North America—such as a Roman conception of slavery and a Roman Catholic emphasis on equality— explains why the treatment of Black slaves was more severe there than in the Spanish and Portuguese colonies of South America. But this cannot be the whole explanation since it is merely negative, based only on a lack of something. A more compelling令人信服的explanation is that the early and sometimes extreme racial discrimination in the English colonies helped determine the particular nature of the slavery that followed. (462 words)16. Which of the following is the most logical inference to be drawn from the passage about the effects of “several acts of the Maryland and Virginia legislatures” (Para.2) passed during and after the 1660‟s?A. The acts negatively affected the pre-1660’s position of Black as wellas of White servants.B. The acts had the effect of impairing rather than improving theposition of White servants relative to what it had been before the 1660’s.C. The acts had a different effect on the position of white servants thandid many of the acts passed during this time by the legislatures of other colonies.D. The acts, at the very least, caused the position of White servants toremain no better than it had been before the 1660’s.17. With which of the following statements regarding the status ofBlack people in the English colonies of North America before the 1660‟s would the author be LEAST likely to agree?A. Although black people were not legally considered to be slaves,they were often called slaves.B. Although subject to some discrimination, black people had a higherlegal status than they did after the 1660’s.C. Although sometimes subject to lifetime servitude, black peoplewere not legally considered to be slaves.D. Although often not treated the same as White people, black people,like many white people, possessed the legal status of servants.18. According to the passage, the Handlins have argued which of thefollowing about the relationship between racial prejudice and the institution of legal slavery in the English colonies of North America?A. Racial prejudice and the institution of slavery arose simultaneously.B. Racial prejudice most often the form of the imposition of inheritedstatus, one of the attributes of slavery.C. The source of racial prejudice was the institution of slavery.D. Because of the influence of the Roman Catholic Church, racialprejudice sometimes did not result in slavery.19. The passage suggests that the existence of a Roman conception ofslavery in Spanish and Portuguese colonies had the effect of _________.A. extending rather than causing racial prejudice in these coloniesB. hastening the legalization of slavery in these colonies.C. mitigating some of the conditions of slavery for black people in these coloniesD. delaying the introduction of slavery into the English colonies20. The author considers the explanation put forward by Freyre andTannenbaum for the treatment accorded B lack slaves in the English colonies of North America to be _____________.A. ambitious but misguidedB. valid有根据的but limitedC. popular but suspectD. anachronistic过时的，时代错误的and controversialUNIT 2Text AThe sea lay like an unbroken mirror all around the pine-girt, lonely shores of Orr’s Island. Tall, kingly spruce s wore their regal王室的crowns of cones high in air, sparkling with diamonds of clear exuded gum流出的树胶; vast old hemlocks铁杉of primeval原始的growth stood darkling in their forest shadows, their branches hung with long hoary moss久远的青苔;while feathery larches羽毛般的落叶松,turned to brilliant gold by autumn frosts, lighted up the darker shadows of the evergreens. It was one of those hazy朦胧的, calm, dissolving days of Indian summer, when everything is so quiet that the fainest kiss of the wave on the beach can be heard, and white clouds seem to faint into the blue of the sky, and soft swathing一长条bands of violet vapor make all earth look dreamy, and give to the sharp, clear-cut outlines of the northern landscape all those mysteries of light and shade which impart such tenderness to Italian scenery.The funeral was over,--- the tread鞋底的花纹/ 踏of many feet, bearing the heavy burden of two broken lives, had been to the lonely graveyard, and had come back again,--- each footstep lighter and more unconstrained不受拘束的as each one went his way from the great old tragedy of Death to the common cheerful of Life.The solemn black clock stood swaying with its eternal ―tick-tock, tick-tock,‖ in the kitchen of the brown house on Orr’s Island. There was there that sense of a stillness that can be felt,---such as settles down on a dwelling住处when any of its inmates have passed through its doors for the last time, to go whence they shall not return. The best room was shut up and darkened, with only so much light as could fall through a little heart-shaped hole in the window-shutter,---for except on solemn visits, or prayer-meetings or weddings, or funerals, that room formed no part of the daily family scenery.The kitchen was clean and ample, hearth灶台, and oven on one side, and rows of old-fashioned splint-bottomed chairs against the wall. A table scoured to snowy whiteness, and a little work-stand whereon lay the Bible, the Missionary Herald, and the Weekly Christian Mirror, before named, formed the principal furniture. One feature, however, must not be forgotten, ---a great sea-chest水手用的储物箱,which had been the companion of Zephaniah through all the countries of the earth. Old, and battered破旧的，磨损的, and unsightly难看的it looked, yet report said that there was good store within which men for the most part respect more than anything else; and, indeed it proved often when a deed of grace was to be done--- when a woman was suddenly made a widow in a coast gale大风，狂风, or a fishing-smack小渔船was run down in the fogs off the banks, leaving in some neighboring cottage a family of orphans,---in all such cases, the opening of this sea-chest was an event of good omen 预兆to the bereaved丧亲者;for Zephaniah had a large heart and a large hand, and was apt有…的倾向to take it out full of silver dollars when once it went in. So the ark of the covenant约柜could not have been looked on with more reverence崇敬than the neighbours usually showed to Captain Pennel’s sea-chest.1. The author describes Orr‟s Island in a(n)______way.A.emotionally appealing, imaginativeB.rational, logically preciseC.factually detailed, objectiveD.vague, uncertain2.According to the passage, the “best room”_____.A.has its many windows boarded upB.has had the furniture removedC.is used only on formal and ceremonious occasionsD.is the busiest room in the house3.From the description of the kitchen we can infer that thehouse belongs to people who_____.A.never have guestsB.like modern appliancesC.are probably religiousD.dislike housework4.The passage implies that_______.A.few people attended the funeralB.fishing is a secure vocationC.the island is densely populatedD.the house belonged to the deceased5.From the description of Zephaniah we can see thathe_________.A.was physically a very big manB.preferred the lonely life of a sailorC.always stayed at homeD.was frugal and saved a lotText BBasic to any understanding of Canada in the 20 years after the Second World War is the country' s impressive population growth. For every three Canadians in 1945, there were over five in 1966. In September 1966 Canada's population passed the 20 million mark. Most of this surging growth came from natural increase. The depression of the 1930s and the war had held back marriages, and the catching-up process began after 1945. The baby boom continued through the decade of the 1950s, producing a population increase of nearly fifteen percent in the five years from 1951 to 1956. This rate of increase had been exceeded only once before in Canada's history, in the decade before 1911 when the prairies were being settled. Undoubtedly, the good economic conditions of the 1950s supported a growth in the population, but the expansion also derived from a trend toward earlier marriages and an increase in the average size of families; In 1957 the Canadian birth rate stood at 28 per thousand, one of the highest in the world. After the peak year of 1957, thebirth rate in Canada began to decline. It continued falling until in 1966 it stood at the lowest level in 25 years. Partly this decline reflected the low level of births during the depression and the war, but it was also caused by changes in Canadian society. Young people were staying at school longer, more women were working; young married couples were buying automobiles or houses before starting families; rising living standards were cutting down the size of families. It appeared that Canada was once more falling in step with the trend toward smaller families that had occurred all through theWestern world since the time of the Industrial Revolution. Although the growth in Canada’s population had slowed down by 1966 (the cent), another increase in the first half of the 1960s was only nine percent), another large population wave was coming over the horizon. It would be composed of the children of the children who were born during the period of the high birth rate prior to 1957.6. What does the passage mainly discuss?A. Educational changes in Canadian society.B. Canada during the Second World War.C. Population trends in postwar Canada.D. Standards of living in Canada.7. According to the passage, when did Canada's baby boom begin?A. In the decade after 1911.B. After 1945.C. During the depression of the 1930s.D. In 1966.8. The author suggests that in Canada during the 1950s____________.A. the urban population decreased rapidlyB. fewer people marriedC. economic conditions were poorD. the birth rate was very high9. When was the birth rate in Canada at its lowest postwar level?A. 1966.B. 1957.C. 1956.D. 1951.10. The author mentions all of the following as causes of declines inpopulation growth after 1957 EXCEPT_________________.A. people being better educatedB. people getting married earlierC. better standards of livingD. couples buying houses11.I t can be inferred from the passage that before the IndustrialRevolution_______________.A. families were largerB. population statistics were unreliableC. the population grew steadilyD. economic conditions were badText CI was just a boy when my father brought me to Harlem for the first time, almost 50 years ago. We stayed at the hotel Theresa, a grand brick structure at 125th Street and Seventh avenue. Once, in the hotel restaurant, my father pointed out Joe Louis. He even got Mr. Brown, the hotel manager, to introduce me to him, a bit punchy强力的but still champ焦急as fast as I was concerned.Much has changed since then. Business and real estate are booming. Some say a new renaissance is under way. Others decry责难what they see as outside forces running roughshod肆意践踏over the old Harlem. New York meant Harlem to me, and as a young man I visited it whenever I could. But many of my old haunts are gone. The Theresa shut down in 1966. National chains that once ignored Harlem now anticipate yuppie money and want pieces of this prime Manhattan real estate. So here I am on a hot August afternoon, sitting in a Starbucks that two years ago opened a block away from the Theresa, snatching抓取，攫取at memories between sips of high-priced coffee. I am about to open up a piece of the old Harlem---the New York Amsterdam News---when a tourist。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

a r X i v :c o n d -m a t /0207310v 1 [c o n d -m a t .d i s -n n ] 12 J u l 2002Absence of the Eﬀects of Vortices in the Gauge Glass Toshiyuki Hamasaki and Hidetoshi Nishimori Department of Physics,Tokyo Institute of Technology,Oh-okayama,Meguro-ku,Tokyo 152-8551,Japan 1Introduction The gauge glass,which is an extension of the XY model to the random spin system,attracts both theoretical and practical interest.This model provides good descriptions of some physical situations,for example,the XY magnet with random Dzyaloshinskii-Moriya interactions [1]and a granular supercon-ductivity and Josephson-junction arrays with positional disorder [2][3].Espe-cially,the two-dimensional gauge glass has been studied actively because of the interesting relation between the Kosterlitz-Thouless (KT)transition and the eﬀect of disorder.This relation was ﬁrst discussed by Rubinstein,Shraimanand Nelson [1].They have shown that for small amount of randomness,as the temperature is decreased,there appears ﬁrst the paramagnetic phase,then a KT-like phase,and ﬁnally again a paramagnetic phase.Thus a reentrant transition appears in the gauge glass.After their work,Natterman,Scheidl,Korshunov and Li [4]corrected their description of the reentrant transition to the one without reentrance.These latter authors pointed out an overesti-mation of vortex pair density in the previous work.Furthermore,Sheidl [5]found a new ordered phase in which single vortex excitations occur in thereentrant phase,and Maucourt and Grempel[6]suggested from Monte Carlo simulations that there is no indication of a low-temperature reentrant phase. Today,the two-dimensional gauge glass at low temperatures is generally be-lieved to have no reentrance[7],except for some researchers[8].Hence,the present major interest in the two-dimensional gauge glass is the structure of the KT phase,namely,the boundary between the freezing phase of the vortex-pair excitations and the non-freezing phase.The gauge glass has also been investigated in theﬁeld of the spin glass theory because the gauge glass is an extension of the Ising spin glass with continuous spin variables[9].Particularly,the method of gauge transformation,which was developed in the study of the spin glass,is a powerful technique for deriving analytical results for gauge glass.Ozeki and Nishimori[10]found the exact solution of the internal energy of the gauge glass under a special condition using the method of gauge transformation.This special condition relevant to the exact solution corresponds to a line in the phase diagram called the Nishi-mori line.Ozeki and Nishimori also showed that the phase boundary between the ordered and the disordered phases runs parallel to the temperature axis. Although they could obtain the exact solution on the Nishimori line,there exists a mysterious property associated with the line:For example,the exact solution of the internal energy on the Nishimori line has no singularity as a function of temperature although the the line runs across the phase boundary. From these facts in mind,we aim to clarify what occurs under the special condition of this line.In this paper,we calculate some gauge invariant quantities on the Nishimori line.First,we deﬁne the gauge glass and show that the exact solution of the internal energy can be calculated under the special condition in Section 2.Next,we introduce the gauge invariant correlation functions and calculate them using the spin wave approximation,gauge transformation and the Villain model in Section3.The gauge invariant distribution functions are introduced and calculated in Section4.From the results of Sections3and4,we discuss the physical properties of the Nishimori line in Section5.2General properties2.1Gauge glassThe gauge glass is deﬁned by the HamiltonianH=−J i,j cos(θi−θj−A ij),(1)where A ij is the quenched random phase shift and the coupling constant J is positive.The sum runs over all nearest-neighbor pairs on a lattice.Note that we do not specify the spatial dimensionality explicitly here.We assume that A ij is independently distributed at each bond as follows,P(A ij)=12πe K p cos A ij2πH e K i,j cos(θi−θj−A ij)2πe K i,j cos(θi−θj−A ij),(4)where the ranges of integration over A ij andθi are from0to2π.Here we apply the gauge transformation to eqn(4).Since the gauge transformation is just a change of running variables,the value of eqn(4)is independent of the choice of{φi}and therefore we may integrate eqn(4)over all gauge variables {φi},each from0to2π,and divide each integration ofφi by2π.Using the special condition K=K p,we obtain the exact internal energy asFig.1.The schematic phase diagram and the Nishimori line(dashed).The spin glass phase exists in three dimensions or over.E=−JN B I1(K p)Fig.2.Schematic diagram of the correlation function C p(r)and chirality.Leftﬁgure shows a path from site0to site r.The rightﬁgure shows two states with diﬀerent chiralities.3Gauge invariant correlation functions3.1DeﬁnitionsIn order to investigate the physical signiﬁcance of the result in the previous section,we introduce the gauge invariant correlation functions asC p= exp i(θ0−θr−r k=1A k−1,k) (6) C le= cos(θ0−θ1−A01)cos(θr−θr+1−A r,r+1) (7) C ch= sin(θ0−θ1−A01)sin(θr−θr+1−A r,r+1) .(8)Equation(6)is the gauge-invariant correlation function which measures the correlation along a path from site0to site r taking the phase twist of A ij into consideration.In Figure2,we sketch a schematic picture of a path of corre-lation function C p.Equation(7)means the local energy correlation function. The local energy correlation function is also gauge invariant.Equation(8)rep-resents the chirality correlation function.Chirality introduced by Villain[12] is an Ising-like degree of freedom.The chirality distinguishes the two states which are transformed to each other using the mirror transformation(Figure 2).The chirality correlation function is also gauge invariant.3.2Spin wave approximationLet us now consider the Hamiltonian introduced in eqn(1)in two dimensions. At suﬃciently low temperatures,the eﬀect of thermalﬂuctuations is small,so that the spins tend to align to each other with the twist A ij taken into account. Hence,we are able to expand the cosine term near(θi−θj−A ij)=0, H≃J2 1K G0r−σr2exp 1K G(−)0r−σ +1K p−1 2exp 1K G(−)0r−σ −1K p−1N k1−cos k·rN k(1−cos k1)(1±cos k·r)Now,applying the special condition K=K p,we can obtain these correlation functions as follows,C p=e−K−1p r/2,C le=e K−1p,C ch=0.(16) Surprisingly,the chirality correlation function vanishes under the condition K=K p.The chirality degrees of freedom behave perfectly independently from place to place.3.3Gauge transformationFrom comparison of the results of the spin wave approximation with the exact results,we can investigate the diﬀerence between the model with periodic-ity and the model without periodicity.In this section,we calculate the exact solutions of C p,C le and C ch for models with periodicity using gauge trans-formation under the special condition K=K p.After the derivations of the exact solutions of correlation functions,we study the asymptotic forms of the exact solutions at low temperatures and compare them with the solutions in the previous section using the spin wave approximation.The correlation functions which we introduced in Section3.1are invariant un-der the gauge transformation,and therefore the same calculation method as for the internal energy(5)in Section2can be applied to the calculation of the correlation functions.As a consequence,we obtain the following expression under the special condition K=K p,C p= I1(K)I0(K) 2,C ch=0.(17)When K=K p,the chirality correlation vanishes exactly and this solution is consistent with the result of spin wave approximation(16).At low tem-perature,the asymptotic behaviors of C p and C le in eqn(17)are written as follows,C p∼e−K−1p r/2,C le∼e−K−1p.(18) Equation(18)is also consistent with the solution of spin wave approxima-tion expressed in eqn(16).This comparison suggests that under the special condition K=K p,the system forms a characteristic structure which is not inﬂuenced by the vortices.The analysis of the Villain model in the following reinforces this picture.3.4Villain modelThe Hamiltonian of the spin wave approximation (9)neglects periodicity in-cluded in the cosine term (1).If we need to describe the system at low tem-peratures more accurately,it should be necessary to consider periodicity in the Hamiltonian.Accordingly,we consider the Villain model which adds the periodicity to the spin wave HamiltonianZ V =2π 0 i d θi 2 i,j (θi −θj −A ij −2m ij π)2.(19)where m ij is an integer between −∞and ∞.The random phase shift (10)also neglects the periodicity of modulo 2π.There-fore we also add 2m ij πinto the probability distribution of A ij (10).The con-ﬁgurational average is described as[···]=2π 0 i,j d A ij2πK −1p (···)∞ {m ij =−∞}e −K p2πe i(θ0−θr − k A k −1k )e −K p2(θi −θj −A ij −2m ij π)2=∞ −∞d A ij 2πK −1p e −K pSubstituting eqn(22)into eqn(21),we obtain the gauge-invariant correlation function asC p=e−K−1p r/2,(23) where we have used the relation K=K p.The result of this calculation agrees with the one of the spin wave approximation(16)and the asymptotic form of the exact solution(18)under the condition K=K p.The local energy correlation function and the chirality correlation function are derived by the same calculation as in the gauge invariant correlation.These results are written by simple formulas asC le=e−K−1p,C ch=0.(24) Those two correlation functions also agree with the results of the spin wave approximation(16)and asymptotic exact solution(18)under the condition K=K p.We may conclude from these results as follows.The spin wave approximation neglects periodicity,and the results of the spin wave approxi-mation do not include the eﬀects of vortices.The results for the Villain model in contrast include the eﬀects of vortices.Accordingly,the agreement of the results of spin wave approximation with those of the Villain model suggests the absence of the eﬀects of vortices on the correlation functions we calculated under the condition K=K p.Vortices are perfectly irrelevant to the gauge invariant correlation functions.4Distribution functionsIrrelevance of vortices in the gauge invariant correlation functions on the Nishi-mori line can be veriﬁed by using a distribution function with gauge invari-ance.This gauge invariant distribution function measures the distribution of the random phase twist between site i and j.The deﬁnition isP(x)= δ(x−(θi−θj−A ij)) .(25)Using the spin wave approximation and the Villain model,we obtain the comparable results as in the gauge invariant correlation functions when K= K p.The results using the spin wave approximation and the Villain model are, respectively,P sw(x)= 2πexp −K pK p2x2 ,(27)the latter being the exact solution.These two expressions are completely iden-tical.The distribution function of two bonds can also be calculated by the spin wave approximation and the Villain model.Weﬁrst show the deﬁnition of the two-bond distribution functionP(x,y)= δ(x−(θk−θl−A kl))·δ(y−(θm−θn−A mn)) .(28)Equation(28)is calculated by using the spin wave approximation and the Villain model for K=K p as,again the latter being the exact solution,P sw(x,y)=K p2(x2+y2) (29)P Villain(x,y)=K p2(x2+y2) .(30)Similarly to eqns(26)and(27),these results agree with each other.We there-fore see immediately that vortices have no eﬀects on the distribution function (28).It also follows that two-bond variables behave independently because eqns(29)/(30)are just products of eqns(26)/(27).It is instructive to consider another two-bond extension,P′(x,y)= δ(x−(θk−θl−A kl)) · δ(y−(θm−θn−A mn)) .(31)Although eqn(31)is gauge invariant,we can not calculate the exact solution even if we apply gauge transformation to eqn(31).Nevertheless,we can obtain the result by the spin wave approximation asP′sw (x,y)=K p1−A2exp −K pof the thermal averages of single-bond distribution function at two diﬀerent locations as in eqn(31),these are correlated:P′(x,y)=P(x)P(y).Physical signiﬁcance of this counter-intuitive results needs further clariﬁcation.5Summary and discussionsIn this paper,we have investigated the properties of the gauge glass on the Nishimori line through the gauge invariant quantities.Firstly we calculated the gauge invariant correlation functions using the spin wave approximation, gauge transformation and the Villain model.From these calculations,we found that the results of the spin wave approximation are identical to the results by the method taking periodicity into account.Thus,we expect that the peri-odicity or vortices has no inﬂuence on the system(gauge invariant quantities to be precise)under the condition K=K p.The eﬀect of vortices can be ne-glected on the Nishimori line.Next,we calculated the gauge invariant distribution functions using the spin wave approximation and the Villain model.We found the same results as for the gauge invariant correlation functions.Moreover,we showed that the dis-tribution function(28)is independently distributed at each bond.An variant of eqn(28)was also calculated by using the spin wave approximation.We may conclude from these results as follows.In the two-dimensional gauge glass,the eﬀect of vortices plays an important role because the phase transi-tion of the model is described by vortex-pair unbinding.Accordingly,the spin wave approximation which neglects the eﬀect of vortices is considered in gen-eral not to be able to describe the singularity related to the phase transition. However,our analysis based on the gauge invariant quantities predicts that under the condition K=K p,the singularity related to the phase transition vanishes for gauge invariant correlation functions even if we consider the eﬀect of vortices in the system.Thus,the renormalization group arguments[7][13], which analyze the eﬀects of vortices asymptotically,should be reconsidered seriously under the present perspective.Further investigation of the property of the Nishimori line is necessary.References[1]M.Rubinstein,B.Shraiman and D.R.Nelson,Phys.Rev.B27,1800(1983).[2] E.Granato and J.M.Kosterlitz,Phys.Rev.B33,6553(1986).[3]W.Y.Shih,C.Ebner and D.Stroud,Phys.Rev.B30,134(1984).[4]T.Nattermann,S.Scheidl,S.E.Korshunov and M.S.Li,J.Phys.(France)5,565(1995).[5]S.Sheidl,Phys.Rev.B55,457(1997).[6]J.Maucourt and D.R.Grempel,Phys.Rev.B56,2572(1997).[7] D.Carpentier and P.Doussal,Nucl.Phys.B588,565(1993).[8] C.Mudry and X-G.Wen,Nucl.Phys.B549,613(1999).[9]H.Nishimori,Prog.Theor.Phys.66,1169(1981).[10]Y.Ozeki and H.Nishimori,J.Phys.A26,3399(1993).[11]H.Nishimori,“Statistical Physics of Spin Glasses and Information Processing:An Introduction”Oxford University Press,(2001).[12]J.Villain,J.Phys.C10,4793(1977).[13]L-H.Tang,Phys.Rev.B54,3350-3366(1996).。