Forced vibrations of wave equations with non-monotone nonlinearities

1/4波片quarter-wave plateCG矢量耦合系数Clebsch-Gordan vector coupling coefficient; 简称“CG[矢耦]系数”。

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Wave-equation Migration Velocity Analysis Biondo Biondi and Paul Sava∗,Stanford UniversitySUMMARYWe introduce a new wave-equation method of Migration VelocityAnal-ysis.The method is based on the linear relation that can be established between a perturbation in the migrated image and the generating per-turbation in the slowness function.Our method iteratively updates the slowness function to account for improvements in the focusing quality of the migrated image.As a wave-equation method,our MV A is robust and generates smooth slowness functions without model regularization. We also show that our method has the potential to exploit the power of residual prestack migration.INTRODUCTIONSeismic imaging is a two-step process:velocity estimation and migra-tion.As the velocity function becomes more complex,the two steps become more and more dependent on each other.In complex depth imaging problems,velocity estimation and migration are applied itera-tively in a loop.To assure that this iterative imaging process converges to a satisfactory model,it is crucial that the migration and the velocity estimation are consistent with each other.Kirchhoff migration often fails in complex areas,such as sub-salt, because the wavefield is severely distorted by lateral velocity varia-tions and thus complex multipathing occurs.As the shortcomings of Kirchhoff migration have become apparent(O’Brien and Etgen,1998), there has been a renewal of interest in wave-equation migration and the development of computationally efficient3-D prestack depth mi-gration methods based on the wave equation(Biondi and Palacharla, 1996;Biondi,1997;Mosher et al.,1997).However,there has been no corresponding progress in the development of Migration Velocity Analysis(MV A)methods that can be used in conjunction with wave-equation migration.We present a method that aims atfilling this gap and that,at least in principle,can be used in conjunction with any downward-continuation migration method.In particular,we have been applying our new methodology to downward continuation based on the Double Square Root equation in2-D(Yilmaz,1979;Claerbout,1985; Popovici,1996)and on common-azimuth continuation in3-D(Biondi and Palacharla,1996).As for migration,wave-equation MV A is intrinsically more robust than ray-based MV A because it avoids the well-known problems that rays encounter when the velocity model is complex and has sharp bound-aries.The transmission component offinite-frequency wave propaga-tion is mostly sensitive to the smooth variations in the velocity model. Consequently,wave-equation MV A produces smooth velocity updates and is thus stable.In most cases,no smoothing constraints are needed to assure stability in the inversion.On the contrary,ray-based methods require strong smoothing constraints to avoid quick divergence.Our method is closer to conventional MV A than other wave-equation methods that have been proposed to estimate the background velocity model(Noble et al.,1991;Bunks et al.,1995;Fogues et al.,1998)be-cause it tries to maximize the quality of the migrated image instead of trying to match the recorded data.In this respect,our method is related to Differential Semblance Optimization(Symes and Carazzone,1991) and Multiple Migration Fitting(Chavent and Jacewitz,1995).How-ever,with respect to these two methods,our method has the advantage of exploiting the power of residual prestack migration to speed up the convergence.ESTIMATION ALGORITHMWe estimate velocity by iteratively migrating the prestack data and looping over the following steps:1.Downward continuation with current velocity2.Extraction of Common-Image Gathers from prestack wave-field(Prucha et al.,1999)3.Residual prestack migration of Common-Image Gathers4.Estimation of image perturbation from residual prestack mi-gration results5.Estimation of velocity perturbation from image perturbations The core technical element of the method is the estimation of velocity perturbations from image perturbations.The next section presents the linear theory that enables us to achieve this goal.LINEAR THEORYIn migration by downward continuation(Figure1),data measured at the surface(D)is recursively pushed down in depth to generate the complete wavefield(U).Downward continuation requires us to make an assumption of the slownessfield(S).Once the wavefield is known, we can apply the imaging condition which gives us the wavefield at time zero,or in the other words,the image or reflectivity map at the moment the reflectors explode(R).In the presence of the background wavefield(U),a perturbation in slowness( S)will generate a scattered wavefield( W),which can, by the same method as the backgroundfield,be downward continued ( U)and imaged( R)(Figure1).We can now take the perturbation in image( R)and apply the adjoint operation.This will lead to an adjoint perturbation in wavefield( U∗), an adjoint scatteredfield( W∗),and eventually to an adjoint pertur-bation in slowness( S∗)(Figure1).Considering afirst order Born relation between the perturbation in slowness and the scattered wave-field,we can establish a direct linear relation between the perturbation in image( R)and the perturbation in slowness( S).It follows that if we can obtain a better focused image,we can iteratively invert for the perturbation in slowness that generates the better focusing.This is the foundation of our wave-equation MV A method.In the following sections we will briefly present the mathematical re-lations on which our method is based.Backgroundfield:Forward operatorMigration by downward continuation,in post-stack or pre-stack,is done in two steps:thefirst step is to downward continue the data (D)measured at the surface,and the second is to apply the imaging condition,that is to extract the wavefield at time t=0,or the image (R),at the moment the reflectors explode(Claerbout,1985).1.Downward continuationThefirst step of migration consists of downward continuationof the wavefield measured at the surface(a.k.a.the data),which is done by the recursive application of the equation:u z+1=T z u z0(1) initialized by the wavefield at the surface:u10=f·d(2) where:Figure1:Processing chart.•u z(ω)is the wavefield u0(ω)at depth z.•u1(ω)is the wavefield u0(ω)at the surface.•T z(ω,s0)is the downward continuation operator at depth z.•d(ω)is the data,i.e.the wavefield at the surface.•f(ω)is a frequency dependent scale factor for the data.2.ImagingThe second step of the migration by downward continuation is imaging.In the exploding reflector concept,the image is found by selecting the wavefield at time t=0,or equivalently,by summing over the frequencies(ω):r z0=Nω1u z0(ω)(3)where:•r z0is the image(reflectivity)corresponding to a givendepth level(z).Perturbationfield:Forward OperatorIf we perturb the velocity model we introduce a perturbation in the wavefield.In other words,the perturbation in slowness has generateda secondary scattered wavefield.1.Scattering and Downward ContinuationIf we consider the perturbation in wavefield at the surface,wecan recursively downward continue it,adding at every depthstep the scattered wavefield:u z+1=T z u z+ v z+1(4) where• u z(ω)is the perturbation in the wavefield generated by the perturbation in velocity,and downward contin-ued from the surface.• v z+1(ω)represents the scattered wavefield caused at depth level z+1by the perturbation in velocity fromthe depth level z.Thefirst order Born approximation of the scattered wavefieldcan be written as:v z+1=T z G z u z0 s z(5) where:•G z(ω,s0)is the scattering operator at depth z.• s z(ω)is the perturbation in slowness at depth z.•u z(ω)is the background wavefield at depth z.If we introduce the equation(5)in(4)we obtain that:u z+1=T z u z+G z u z0 s z (6)2.ImagingAs for the background image,the perturbation in image( r z),caused by the perturbation in slowness,is obtained by a sum-mation over all the frequencies(ω):r z=Nω1u z(ω)(7)The equations(6)and(7)establish a linear relation between the per-turbation in slowness( s z)and the perturbation in image( r z).We can use this linear relation in an iterative algorithm to invert for the perturbation in slowness from the perturbation in image. Perturbationfield:Adjoint OperatorIn the adjoint operation,we begin by upward propagating the pertur-bation in wavefield at depth:u z=T z∗ u z+1+ r z(8) where•T z∗is the upward continuation operator at depth z.We can then obtain the perturbation in slowness from the perturbation in wavefield by applying the adjoint of the scattering operator:s z=u z0∗G z∗ T z∗ u z+1− u z (9)The equations(6)and(7)for the forward operator,and the equations (8)and(9)for the adjoint operator,express the linear relation estab-lished between the perturbation in slowness( S)and the perturbation in image( R).Figure2:Originalimage.Figure3:Better focused image after residual migration.EXAMPLEIn thefirst part of our example we will concentrate on improving the focusing of the image.To achieve an enhanced focusing,we used Stolt residual migration in the prestack domain(Stolt,1996;Sava, 1999).Another alternative to obtain a better focusing would be to use velocity continuation(Fomel,1997).The dataset is part of a gas-hydrate study,and was recorded at the Blake Outer Ridge,offshore Florida and Georgia(Ecker,1998).Figure(2)shows the image obtained with a starting velocity model, while Figure(3)shows an image obtained by applying residual migra-tion to the original.The second image is clearly better focused than the original,and therefore appears more energetic.We can take the difference between the two images,(2)and(3),to be the perturbation in image( R),and use it to invert for the slowness model that generates the better focus.For the second part of our example,we have constructed a model in-spired by the sections in Figures(2)and(3).The goal is to convert the differences in focusing between the two images(perturbation in image) into a better slowness model(i.e.tofind the perturbation in slowness). Figure(4)represents the background slowness model(S).We will use this model to generate the background wavefield(U),and the back-ground image(R)from the synthetic data at the surface(D).Figure(5)contains the perturbation in slowness( S).We will use this model to generate the scattered wavefield( W),the perturbation wavefield( U),and the perturbation in image( R).We will start the inversion by assuming zero perturbation in slowness.Figure(6)represents the perturbation in slowness obtained at thefirst iteration.For now,only a small perturbation in slowness is obtained, though it is not totally concentrated at the right location.Part of the energy of the section is spread,for example at about midpoint2.2−2.4km and at depth1.3−1.4km.This artifact is the result of the still imperfect definition of the slowness anomaly,and possibly it is also due to the proximity of the edge.By the20th iteration(Figure7),the perturbation in slowness is much better shaped,and the artifact at depth is much weaker.Also,the absolute magnitude of the anomaly is getting very close to the correct value:s max=0.088s/km for the original,and s max=0.084s/km for the inversion at iteration20.CONCLUSIONWe have presented a recursive wave-equation Migration Velocity Anal-ysis method operating in the image domain.Our method is based on the linearization of the downward continuation operator that relates perturbations in slowness to perturbations in image.The fundamental idea is to improve the quality of the slowness function by optimizing the focusing of the migrated image.The iterative method is very stable and accurate when applied to a synthetic dataset.It also converges to the solution without the need for any regularization of the slowness model.We are currently in the process of applying the method to the real seismic dataset used as an example in this expanded abstract.REFERENCESBiondi, B.,and Palacharla,G.,1996,3-D prestack migration of common-azimuth data:Geophysics,61,1822–1832.Biondi,B.,1997,Azimuth moveout+coomon-azimuth migration: Cost-effective prestack depth imaging of marine data:67th Annual Internat.Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,1375–1378.Bunks,C.,Saleck,F.M.,Zaleski,S.,and Chavent,G.,1995,Multiscale seismic waveform inversion:Geophysics,60,no.5,1457–1473.Chavent,G.,and Jacewitz,C.A.,1995,Determination of background velocities by multiple migrationfitting:Geophysics,60,no.2,476–490.Claerbout,J.F.,1985,Imaging the Earth’s Interior:Blackwell Scien-tific Publications.Ecker,C.,1998,Seismic characterization of gas hydrates structures: Ph.D.thesis,Stanford University.Fogues,E.,Scala,E.,and Pratt,R.G.,1998,High resolution velocity estimation from refraction and reflection data:68th Annual Internat. Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,1211–1214. Fomel,S.,1997,Velocity continuation and the anatomy of residual prestack migration:67th Ann.Internat.Meeting,Soc.Expl.Geo-phys.,1762–1765.Mosher,C.C.,Foster,D.J.,and Hassanzadeh,S.,1997,Common angle imaging with offset plane waves:67th Annual Internat.Mtg.,Soc. Expl.Geophys.,Expanded Abstracts,1379–1382.Noble,M.,Lindgren,J.,and Tarantola,A.,1991,Large-sized,nonlinear inversion of a marine data set:Retrieving the source,the background velocity and the impedance contrasts:61th Annual Internat.Mtg., Soc.Expl.Geophys.,Expanded Abstracts,893–896.O’Brien,M.J.,and Etgen,J.T.,1998,Wavefield imaging of com-plex structures with sparse point-receiver data:68thAnnual Internat. Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,1365–1368. Popovici,A.M.,1996,Short note-prestack migration by split-step DSR:Geophysics,61,no.05,1412–1416.Prucha,M.,Biondi,B.,and Symes,W.,1999,Angle-domain common image gathers by wave-equation migration:69th Annual Internat. Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,submitted. Sava,P.,1999,Short note-On Stolt prestack residual migration:SEP-Report,100.Stolt,R.H.,1996,Short note-a prestack residual time migration operator:Geophysics,61,no.02,605–607.Symes,W.W.,and Carazzone,J.J.,1991,Velocity inversion by differ-ential semblance optimization:Geophysics,56,no.5,654–663. Yilmaz,O.,1979,Prestack partial migration:Ph.D.thesis,StanfordUniversity.Figure4:Background slowness(S).Figure5:Perturbation in slowness( S). Figure6:Recovered perturbation at iteration1. Figure7:Recovered perturbation at iteration20.。

a r X i v :a s t r o -p h /0607328v 1 14 J u l 2006Mon.Not.R.Astron.Soc.000,1–34(2006)Printed 5February 2008(MN L A T E X style file v2.2)Global structures in a composite system of twoscale-free discs with a coplanar magnetic fieldYu-Qing Lou 1,2,3⋆and Xue-Ning Bai 11Physics Department and Tsinghua Centre for Astrophysics (THCA),Tsinghua University,Beijing 100084,China;2Departmentof Astronomy and Astrophysics,The University of Chicago,5640South Ellis Avenue,Chicago,IL 60637,USA;3National Astronomical Observatories,Chinese Academy of Science,A20,Datun Road,Beijing 100012,China.Accepted .Received ;in original formABSTRACTWe investigate a theoretical magnetohydrodynamic (MHD)disc problem involv-ing a composite disc system of gravitationally coupled stellar and gaseous discs with acoplanar magnetic field in the presence of an axisymmetric dark matter halo.The two discs are expediently approximated as razor-thin,with a barotropic equation of state,a power-law surface mass density,a ring-like magnetic field,and a power-law rota-tion curve in radius r .By imposing the scale-free condition,we construct analytically stationary global MHD perturbation configurations for both aligned and logarithmic spiral patterns using our composite MHD disc model.MHD perturbation configura-tions in a composite system of partial discs in the presence of an axisymmetric dark matter halo are also considered.Our study generalizes the previous analyses of Lou &Shen and Shen &Lou on the unmagnetized composite system of two gravitation-ally coupled isothermal and scale-free discs,of Lou and Shen et al.on the cases of a single coplanarly magnetized isothermal and scale-free disc,and of Lou &Zou on magnetized two coupled singular isothermal discs.We derive analytically the station-ary MHD dispersion relations for both aligned and unaligned perturbation structures and analyze the corresponding phase relationships between surface mass densities and the magnetic fipared with earlier results,we obtain three solution branches corresponding to super fast MHD density waves (sFMDWs),fast MHD density waves (FMDWs)and slow MHD density waves (SMDWs),respectively.We examine the m =0cases for both aligned and unaligned MHD perturbations.By evaluating the unaligned m =0case,we determine the marginal stability curves where the two unstable regimes corresponding to Jeans collapse instability and ring fragmentation instability are identified.We find that the aligned m =0case is simply the limit of the unaligned m =0case with the radial wavenumber ξ→0(i.e.,the breath-ing mode)which does not merely represent a rescaling of the equilibrium state.We further show that a composite system of partial discs behaves much differently from a composite system of full discs in certain aspects.We provide numerical examples by varying dimensionless parameters β(rotation velocity index),η(ratio of effective sound speed of the two discs),δ(ratio of surface mass density of the two discs),q (a measure of coplanar magnetic field strength),F (gravity potential ratio),ξ(radial wavenumber).Our formalism provides a useful theoretical framework in the study of stationary global perturbation configurations for MHD disc galaxies with bars,spirals and barred spirals.Key words:MHD waves—ISM:magnetic fields —galaxies:kinematics and dynam-ics —galaxies:spiral —star:formation —galaxies:structure.⋆E-mail:xiaobai2Y.-Q.Lou,X.N.Baivarious complementary aspects.Lin&Shu(1964,1966)and their co-workers pioneered the classic density wave theory and achieved a great success in understanding the dynami-cal nature of spiral galaxies(Lin1987;Binney&Tremaine 1987;Bertin&Lin1996).The basic idea of analyzing such a large-scale density wave problem is to treat coplanar perturbations in a background axisymmetric rotating disc; this procedure has been proven to be powerful in prob-ing the galactic dynamics to various extents.In such a model development,perturbations(either linear or non-linear)are introduced onto a background equilibrium to form local or large-scale structures and to perform stabil-ity analysis under various situations.Broadly speaking,ax-isymmetric and non-axisymmetric perturbations may lead to aligned configurations while non-axisymmetric perturba-tions can naturally produce spiral wave patterns.Theoreti-cally,a disc system may be treated as razor-thin for simplic-ity(Syer&Tremaine1996;Shen&Lou2004b;Lou&Zou 2004;Shen et al.2005),with a mass densityρ=Σ(r,θ)δ(z) under the situation where the thickness of a galactic disc is sufficiently small compared with its radial size scale;in this manner,the model problem reduces to a two-dimensional one.In theoretical model investigations,two classes of disc models are frequently encountered.One class is the so-called singular isothermal discs(SIDs),which bears aflat rotation curve and a constant‘temperature’with a diverg-ing surface mass density towards the centre[e.g.,Shu et al. (2000)].Since the early study by Mestel(1963)more than four decades ago,this idealized theoretical SID model has attracted considerable interest among astrophysicists in various contexts of disc dynamics[e.g.,Zang(1976); Toomre(1977);Lemos et al.(1991);Goodman&Evans (1999);Shu et al.(2000);Lou(2002);Lou&Fan(2002); Lou&Shen(2003);Lou&Zou(2004);Lou&Wu(2005); Lou&Zou(2006)].The other class is the so called scale-free discs[e.g.Syer&Tremaine(1996);Shen&Lou(2004b); Shen et al.(2005);Wu&Lou(2006)]and is the main focus of this paper.Being of a more general form for differentially rotating discs,a scale-free disc has a rotation curve in the form of v∝r−β(the case ofβ=0corresponds to aflat rotation curve)and a barotropic equation of state in the form ofΠ=KΣn whereΠis the vertically integrated two-dimensional pressure.There is no characteristic spatial scale and all quantities in the disc system vary as powers of ra-dius r.In our analysis,the rotation velocity indexβsatisfies −1/4<β<1/2for warm discs.Furthermore,it is possible to construct stationary(i.e.ω=0)density wave patterns in scale-free discs(Syer&Tremaine1996;Shen&Lou2004b; Shen et al.2005;Wu&Lou2006),clearly indicating that the pattern speed of a density wave is in the opposite sense of the disc rotation speed.Because of the self-gravity,one important technical as-pect in dealing with thin disc galaxies involves the Poisson integral,relating the mass density distribution and grav-itational potential.In the early development of the den-sity wave theory,this Poisson integral is evaluated by an asymptotic analysis valid in the large wavenumber regime of the Wentzel-Kramers-Brillouin-Jeffreys(WKBJ)approx-imation.Based on this,the pursuit of analytical solu-tions leads to a further exploration of the problem.Sev-eral potential-density pairs are generalized in Chapter2of Binney&Tremaine(1987).One special utility is the logarithmic spiral potential-density pairfirst derived by Kalnajs(1971).This is a powerful tool in analyzing non-axisymmetric perturbations in an axisymmetric background disc.Furthermore,Qian(1992)made use of the techniques of Lynden-Bell(1989)and found a larger family of potential-density pairs in terms of the generalized hypergeometric ing these results for scale-free discs under our consideration,the Poisson integral is solved analytically for both aligned and spiral perturbations(Shen&Lou2004b; Shen et al.2005;Wu&Lou2006).Magneticfield is an important ingredient in various as-trophysical disc systems.In the interstellar medium(ISM), the partially or fully ionized gases make the cosmic space an ideal place for applying the magnetohydrodynamics(MHD) equations.In many astrophysical situations involving large-scale dynamics,the magneticfield can be effectively con-sidered as completely frozen into the gas.While in some cases the magnetic force is relatively weak and has lit-tle impact on the dynamical process.There do exist cer-tain situations when the magneticfield plays a crucial role in both dynamics and diagnostics,such as in spi-ral galaxies and accretion processes[e.g.Balbus&Hawley (1998);Balbus(2003);Fan&Lou(1996,1997);Shu et al. (2000);Lou&Fan(1998a);Lou(2002);Lou&Fan(2003); Lou&Zou(2004,2006);Shen et al.(2005);Lou&Wu (2005)].In terms of MHD model development,we need to prescribe the magneticfield geometry.Shu&Li(1997)in-troduced a model in which a disc is‘isopedically’magnetized such that the mass-to-flux ratio remains spatially uniform and the effect of magneticfield is subsumed into two pa-rameters(Shu&Li1997;Shu et al.2000;Lou&Wu2005; Wu&Lou2006).In fact,Lou&Wu(2005)have shown ex-plicitly that a constant mass-to-flux ratio is a natural conse-quence of the frozen-in condition from the ideal MHD equa-tions.In parallel,the coplanar magneticfield also serves as an interesting model(Lou2002;Lou&Zou2004;Shen et al. 2005)with the magneticfield being azimuthally embedded into the disc system.In particular,with the inclusion of an azimuthal magneticfield,one can construct the so-called fast and slow MHD density waves(FMDWs and SMDWs) (Fan&Lou1996,1997;Lou&Fan1998a;Lou2002)and the interlaced optical and magnetic spiral arms in the nearby spiral galaxy NGC6946are sensibly explained along this line.The stability of such MHD discs is yet another lively debated issue.In the WKBJ or tight-winding regime,the well-known Q parameter criterion(Safronov1960;Toomre 1964)was suggested to determine the galactic local ax-isymmetric stability in the absence of magneticfield. Meanwhile,there have been numerous studies concern-ing the global stability of the disc problem[e.g.,Zang (1976);Toomre(1977);Lemos et al.(1991);Evans&Read (1998a,b);Goodman&Evans(1999);Shu et al.(2000)].For example,stationary perturbations of the zero-frequency neu-tral modes are emphasized as the marginal instability modes in scale-free discs.In this context,Syer&Tremaine(1996) made a breakthrough in obtaining semi-analytic solutions for stationary perturbation configurations in a class of scale-free discs.Shu et al.(2000)analyzed the stability of isope-dically magnetized SIDs and derived stationary perturba-tion solutions.They interpreted these aligned and unalignedCoupled Magnetized Scale-Free Discs3configurations as onsets of bar-like instabilities.Lou(2002) performed a coplanar MHD perturbation analysis on az-imuthally magnetized SIDs from a perspective of stationary FMDWs and SMDWs.Our analysis on two-dimensional coplanar MHD pertur-bations has avoided at least two major issues.If perturbation velocity and magneticfield components perpendicular to the disc plane are allowed,it is then possible to describe Alfv´e nic fluctuations and model disc warping process.If one further takes into account of vertical variations across the disc(i.e., the disc thickness is not negligible),magneto-rotational in-stabilities can develop(e.g.,Balbus2003).These two as-pects are important and should bear physical consequences in modelling disc galaxies.In a typical disc galaxy system,the basic component involves stars,gases,dusts,cosmic rays,and a massive dark matter halo(Lou&Fan1998a,2003).In terms of theoreti-cal analysis,it would be a great challenge to include all these factors into one single model consideration.While limited in certain aspects,it remains sufficiently challenging and inter-esting to consider a composite system consisting of a copla-narly magnetized gas disc,a stellar disc as well as an axisym-metric background of a massive dark matter halo.A seminal analysis concerning a composite disc system dates back to Lin&Shu(1966,1968)who combined a stellar distribution function and a gasfluid description to derive a local disper-sion relation for galactic spiral density waves in the WKBJ approximation.Since then,there have been extensive the-oretical studies on perturbation configurations and stabil-ity problems of the composite disc system.Jog&Solomon (1984a,b)investigated the growth of local axisymmetric per-turbations in a composite stellar and gaseous disc system. Bertin&Romeo(1988)considered the spiral modes con-taining gas in a two-fluid model.Vandervoort(1991a,b) studied the effect of interstellar gas on oscillations and the stability of spheroidal galaxies.Romeo(1992)considered the stability of two-componentfluid discs withfinite thickness. Two-fluid approach was adopted into modal analysis mor-phologies of spiral galaxies by Lowe et al.(1994),support-ing the notion that spiral structures are long-lasting and slowly evolving.Elmegreen(1995)and Jog(1996)suggested an effective Q ef f(or Q s−g)parameter criterion(Safronov 1960;Toomre1964)for local axisymmetric two-fluid insta-bilities of a disc galaxy.Lou&Fan(1998b)explored basic properties of open and tight spiral density-waves modes in a two-fluid model to describe a composite system of coupled stellar and gaseous discs.Recently,Lou&Shen(2003)stud-ied a composite SID system to derive stationary global per-turbation configurations and further explored the axisym-metric instability properties(Shen&Lou2003)where they proposed a fairly straightforward D criterion for the ax-isymmetric instability problem for a composite SID system. Shen&Lou(2004b)extended these analysis to a compos-ite system of two scale-free discs and carried out analytical analysis on both aligned and logarithmic spiral perturba-tion configurations.By adding a coplanar magneticfield to the background composite SIDs,Lou&Zou(2004)obtained MHD perturbation configurations and further studied the axisymmetric instability problem(Lou&Zou2006).The main objective of this paper is to construct global scale-free stationary configurations in a two-fluid gaseous and stellar disc system with an embedded coplanar mag-neticfield in the gas disc.Meanwhile,an axisymmetric in-stability analysis is also performed.There are several new features compared with previous works(Lou&Zou2004; Shen&Lou2004b;Shen et al.2005)that may provide cer-tain new clues to understand large-scale structures of disc galaxies.This paper is structured as follows.In Section2,we present the theoretical formalism of the problem;both the stationary equilibrium state and the linearized MHD pertur-bation equations are summarized.In Section3,we perform numerical calculations for the aligned perturbation configu-rations.Both the dispersion relation and phase relationship between density and the magneticfield perturbations are deduced and evaluated.In Section4,we apply the same procedure to the analysis of global logarithmic spiral con-figurations.The m=0marginal stability is also discussed. Finally,we summarize and discuss our results in Section5. Several technical details are included in Appendices A,B, and C.2FLUID-MAGNETOFLUID DISCSWe adopt thefluid-magnetofluid formalism in this paper to construct large-scale stationary aligned and unaligned copla-nar MHD disturbances in a background MHD rotational equilibrium of axisymmetry[Lou&Shen(2003);Lou&Zou (2004);Shen&Lou(2004b);Lou&Wu(2005);Lou&Zou (2006);Wu&Lou(2006)].All the background physical quantities are assumed to be axisymmetric and to scale as power laws in radius r.Specifically,the rotation curves bear an index of−β(viz.,v∝r−β)and the vertically integrated mass density has the formΣ0∝r−αwith−αbeing another index.Physically,the magnetofluid formalism is directly ap-plicable to the magnetized gas disc,while thefluid formal-ism is only an approximation when applied to the stellar disc,where a distribution function approach would give a more comprehensive description.For our purpose of mod-elling large-scale stationary MHD perturbation structures and for mathematical simplicity,as well as the similarity between the two sorts of descriptions(Shen&Lou2004b), it suffices to work with thefluid-magnetofluid formalism.In this section,we present basic MHD equations of the fluid-magnetofluid description for a composite system con-sisting of a scale-free stellar disc and a coplanarly magne-tized gas disc.In our approach,the two gravitationally cou-pled discs are treated using the razor-thin approximation (i.e.,we use vertically integratedfluid-magnetofluid equa-tions and neglect vertical derivatives of physical variables along z)and the two-dimensional barotropic equation of state to construct global MHD perturbation structures.A coplanar magneticfield is involved in the dynamics of the thin gas disc following the basic MHD equations.The back-ground state of axisymmetric rotational equilibrium isfirst derived.We then superpose coplanar MHD perturbations onto the equilibrium state and obtain linearized equations for MHD perturbations in the composite disc system.2.1Ideal Nonlinear MHD EquationsBy our conventions,we use either subscript or superscript‘s’and‘g’to denote physical variables in association with the stellar disc and the magnetized gas disc,respectively.For4Y.-Q.Lou,X.N.Bailarge-scale MHD perturbations of our interest at this stage, all diffusive effects such as viscosity,resistivity,thermal con-duction,and radiative losses etc.are ignored for simplicity. In cylindrical coordinates(r,θ,z)and coincident with the z=0plane,we readily write down the basic nonlinear ideal MHD equations for the composite disc system,namely∂Σgr ∂r2∂∂t +u g∂u gr2∂u gr3=−1∂r−∂φΣg d zBθ∂r−∂B r∂t +u g∂j gr2∂j gΣg∂Πg∂θ+14π ∂(rBθ)∂θ(3)for the magnetized gas disc,and∂Σsr ∂r2∂∂t +u s∂u sr2∂u sr3=−1∂r−∂φ∂t +u s∂j sr2∂j sΣs∂Πs∂θ(6)for the stellar disc in the‘fluid’approximation,respectively. Here,Σdenotes the surface mass density,u is the radial component of the bulkflow velocity,j≡rv is the spe-cific angular momentum in the vertical z-direction and v is the azimuthal bulkflow velocity,Πis the vertically inte-grated two-dimensional pressure,B r and Bθare the radial and azimuthal components of the coplanar magneticfield B≡(B r,Bθ,0),andφis the total gravitational potential. Thisφcan be expressed in terms of the Poisson integral Fφ(r,θ)= dϕ ∞0−GΣ(r′,ϕ,t)r′d r′∂r +∂Bθ∂t=1∂θ(u g Bθ−v g B r),(9)∂Bθ∂r(u g Bθ−v g B r).(10)Among(8)−(10),only two of them are independent.Thebarotropic equation of state for the scale-free discs isΠi=K iΣn i,(11)where K i>0is a constant proportional coefficient andn i>0is the barotropic index with subscript i denotingeither g or s for the two discs(we use this convention forsimplicity).An isothermal equation of state has n i=1.Forthe stellar disc and the magnetized gas disc,K i are allowedto be different,but we need to require n g=n s=n in orderto meet the scale-free requirement(see the next subsection).It follows that the sound speed a i(in the stellar disc the ve-locity dispersion mimics the sound speed)for either disc isreadily defined bya2i≡dΠi04πΣg0 B20dz(14)varying with r in general,andv s02=−αa2s+rdφ0/dr(15)in the stellar disc.Poisson integral(7)yieldsFφ0=−2πGrΣ0P0(α),(16)where the numerical factor P0(α)is explicitly defined byP0(α)≡Γ(−α/2+1)Γ(α/2−1/2)Coupled Magnetized Scale-Free Discs5with Γ(···)being the standard gamma function.Expression (17)can alsobeincludedin a more general form of P m (β)defined later in equation (55).Inordertosatisfy the scale-free condition,radial force balances (13)and (15)should hold for all radii,leading to the following simple relation among the four indices 2β=α(n −1)=2γ−α=α−1.(18)This in turn immediately gives the explicit expressions ofindices α,γand n in terms of β,namely α=1+2β,γ=(1+4β)(1+2β).(19)Since n >0for warm discs,we have β>−1/4.Further-more,Poisson integral (7)converges when 1<α<2which corresponds to 0<β<1/2.In addition,for a finite total gravitational force a larger β-range of −1/2<β<1/2is allowed.Therefore,the physical range for βis constrained by −1/4<β<1/2(Syer &Tremaine 1996;Shen &Lou 2004b;Lou &Zou 2004;Shen et al.2005).For simplicity,we introduce the following parameters A i ,D i ,and q defined by a 2i=A 2ir β,C 2A≡q 2a 2g=q 2A 2gr=A i D ird (r 2Ωi )4β+2q2=A 2s (D 2s +1)=2πG 2βP 0Σ0r 1+2β/F .(22)We now introduce two dimensionless parameters to com-pare the properties of the two scale-free discs.The first oneis simply the surface mass density ratio δ≡Σg 0/Σs0,and the second one is the square of the ratio of effective sound speedsη≡a 2g /a 2s =A 2g /A 2s .For disc galaxies,the ratio δcan be either greater (i.e.,younger disc galaxies)or less (i.e.,older disc galaxies)than 1,depending on the type and evolution stage of a disc galaxy.Meanwhile,the ratio ηcan be gen-erally taken as less than 1because the sound speed in themagnetized gas disc is typically less than the stellar velocity dispersion (regarded as an effective sound speed).With these notations,we now have from condition (22)Σg 0=F A 2g [D 2g +1+(4β−1)q 2/(4β+2)]δ2πG (2βP 0)(1+δ)r (1+2β).(23)Note that expressions (22)and (23)reduce to expression (14)of Shen &Lou (2004b)when the magnetic field van-ishes (i.e.,q =0)and are also in accordance with Shen et al.(2005)when a single magnetized scale-free gas disc is con-sidered.Since the magnetic field effect is represented by the q parameter multiplied by a factor (1−γ)or (4β−1)[see eq.(13)or eq.(22)],we know that in the special case of β=1/4,the Lorentz force vanishes due to the cancella-tion between the magnetic pressure and tension forces in the background equilibrium (Shen et al.2005).Moreover,when −1/4<β<1/4,the net Lorentz force arising from the azimuthal magnetic field points radially inward,while for 1/4<β<1/2,the net Lorentz force points radially outward (Shen et al.2005).Another point should also be noted here.From equa-tion (22),there exists another physical requirement for the rotational Mach number D g ,i.e.,it should be large enoughto warrant a positive D 2s .This requirement for D 2g is simplyD 2s=ηD 2g +1+4β−1∂t+1∂r(r Σg 0u g1)+Ωg∂Σg 1r 2∂j g1∂t+Ωg∂u g 1r=−∂Σg 0+φ1+(1−4β)C 2A Σg 1Σg 0d zb θ∂r −14πr∂(rb θ)∂θ,(26)6Y.-Q.Lou,X.N.Bai∂j g12Ωg u g1+Ωg∂j g1∂θ a2gΣg1Σg0 d zb r∂r(27)in the magnetized gas disc and∂Σs1r ∂∂θ+Σs0∂θ=0,∂u s1∂θ−2Ωsj s1∂r a2sΣs1∂t +rκ2s∂θ=−∂Σs0+φ1(28)in the stellar disc,respectively.All dependent variables are taken to thefirst-order smallness with nonlinear terms ig-nored.The perturbed Poisson integral appears asφ1= dϕ ∞0−G(Σg1+Σs1)r′d r′∂r +∂bθ∂t =1∂θ(u g1B0−rΩg b r),∂bθ∂r (u g1B0−rΩg b r)(30)from the divergence-free condition and the magnetic induc-tion equation.2.3.1Non-Axisymmetric Cases of m 1As the background equilibrium state is stationary and ax-isymmetric,these perturbed physical variables can be de-composed in terms of Fourier harmonics with the periodic dependence exp(iωt−i mθ)whereωis the angular frequency and m is an integer to characterize azimuthal variations. More specifically,we writeΣi1=S i(r)exp(iωt−i mθ),u i1=U i(r)exp(iωt−i mθ), j i1=J i(r)exp(iωt−i mθ),φ1=V(r)exp(iωt−i mθ),b r=R(r)exp(iωt−i mθ),bθ=Z(r)exp(iωt−i mθ),(31) where we use the italic superscript i to indicate associations with the two discs and the roman i for the imaginary unit. We also define V i(i=s,g)for the corresponding gravi-tational potentials associated with the stellar and gaseous discs such that V(r)≡V s(r)+V g(r).By substituting ex-pressions(31)into equations(25)−(30),we readily attaini(ω−mΩg)S g+1dr(rΣg0U g)−i mΣg0J gr=−dΨg2Σg0r−14πr d(rZ)Σg0d zZ dr,(33)i(ω−mΩg)J g+rκ2gΣg0 d zR dr(34)for the magnetized gas disc,andi(ω−mΩs)S s+1dr(rΣs0U s)−i mΣs0J sr=−dΨs2ΩsU s=i mΨs(35)for the stellar disc,respectively,where we defineΨi≡a2i S i/Σi0+V.(36)The perturbed Poisson integral now becomesV(r)= dϕ ∞0−G(S g+S s)cos(mϕ)r′dr′dr−i mZ=0,i(ω−mΩg)R+i mB0dr(rΩg R−B0U g).(38)A combination of equations(32)−(35)and(37)−(38)consti-tutes a complete description of coplanar MHD perturbationsin a composite disc system.From equation(38),we obtainZ=−idr,R=−mB0U gr=−dΨg2Σg0r−C2A d22r d r2 i U g2ΩgU g=i mΨg−mC2A(1−4β)U gCoupled Magnetized Scale-Free Discs7 with a coplanar magneticfield.For m 1,we setω=0inMHD perturbation equations to deducemΩg S g+1dr(rΣg0i U g)+mΣg0J gr=dΨg2Σg0r−C2Adr2+1−12βdr+2β(1+4β)−m2Ωg,(43)mΩg J g+rκ2g2ri U gdr B0i U g rΩg,(45) for the magneticfield perturbation.For coplanar perturba-tions in the stellar disc,we derivemΩs S s+1dr(rΣs0i U s)+mΣs0J sr=dΨs2Ωsi U s=−mΨs.(46)As part of the derivation,we deduce from the last two equa-tions of(46)for the expressions of U s and J s asU s=−i mΩsr+dr =−1r+κ2sdr Ψs.(47)A substitution of equation(47)into equation(46)gives a single equation relating S s andΨs for coplanar perturba-tions in the stellar disc,namelymΩs S s+1dr mΩs rΣs0r+d m2Ω2s−κ2s m2Ωs2rΩs dr dr =−ωdΨg2Σg0r−C2A d22r d r2 i U g,(50)ωJ g=rκ2gdr(B0i U g)(52) for the magnetized gas disc.For coplanar perturbations in the stellar disc,we have in parallelωS s=1dr(rΣs0i U s),ωi U s−2ΩsJ sdr,ωJ s=rκ2s8Y.-Q.Lou,X.N.Bairespectively.The numerical factor P m (β)is defined explic-itly by P m (β)≡Γ(m/2−β+1/2)Γ(m/2+β)ri U g+m Σg 02m Ωg r 2i U g+2Ωg2r Σg 0S g+4πGβP m S s,(57)m Ωg J g +(1−β)r Ωg −C 2A (1−4β)r Σg 0S g +2πGmr P m S s ,(58)Z =−1m Ωg r,R =B 0U g(m 2+4β−4β2)−a 2s +2πGr Σs 0P mS s+2πGr Σs 0P m Sg =0(60)for the stellar disc.Notethat equations (56)−(59)arethe same as equation (43)of Shen et al.(2005)for a sin-gle magnetized scale-free disc by setting S s =0and equa-tion (60)is exactly the same as the first one of equation (35)in Shen &Lou (2004b).A combination of equations (56)−(58)and (60)then gives a complete solution for the stationary dispersion relation in the gravitational coupled MHD discs that are scale free.Because these equations are linear and homogeneous,to obtain non-trivial solutions for (S g ,S s ,U g ,J g ),the determinant of the coefficients of equa-tions (56)−(58)and (60)should vanish.This actually gives rise to the stationary MHD dispersion relation.Meanwhile,in order to get a physical sense of the dispersion relation,we solve the above MHD equations directly.A combination of equations (56)and (58)produces re-lations of i U g and J g in terms of S g and S s ,namely i U g =m Ωg rΣg 0{[−1+3β(ΘA +ΞA )]S g+3βΘA S s},(61)where for notational simplicity,we define ΘA ≡(2πGr P m Σg 0)/∆A ,ΞA ≡(−a 2g +Ω2g r 2)/∆A ,∆A ≡(1+2β)Ω2g r 2+(2β−1/2)C 2A .(62)Here,we use the subscript A to indicate the ‘aligned case’.In particular,ΘA and ΞA are two dimensionless constant parameters.A substitution of equation (61)into equation (57)and a further combination with equation (60)lead to[K A (ΘA +ΞA )+L A −2πG Σg 0r (2βP m )]Sg+[K A ΘA −2πG Σg 0r (2βP m )]S s=0,2πG Σs 0r P m Sg+[M A +2πG Σs 0r P m ]Ss=0,(63)where for notational simplicity we defineK A ≡(m 2+6β)Ω2g r 2−[m 2−(1−4β)2/2]C 2A ,L A ≡(1/2−2β)C 2A −2Ω2g r 2+2βa 2g ,M A ≡(m 2+2β−2)Ω2s r 2/(m 2+4β−4β2)−a 2s .(64)We now obtain the stationary MHD dispersion relation bycalculating the coefficient determinant of equation (63).Af-ter a proper rearrangement,we obtain ∆AK A,(65)where the left-hand side consists of two factors.One can show that the left bracket is exactly the dispersion relation for a single coplanar magnetized scale-free disc discussed by Shen et al.(2005)and the second parentheses denotes the dispersion relation for a single hydrodynamic scale-free disc.The right-hand side denotes the effect of gravitational coupling between perturbations in the two scale-free discs.By setting β=0for an isothermal composite disc system,equation (65)then reduces to dispersion relation (62)of Lou &Zou (2004)where MHD perturbations in isothermal fluid-magnetofluid discs are investigated.These calculations are straightforward but tedious and we turn to the following subsections for further analyses.3.2The Aligned m =0CaseAs already discussed earlier,the m =0case is special andshould be treated in the procedure of setting m =0and then taking the limit of ω→0.By letting ω→0in equa-tions (49)−(53),we find U =0and R =0similar to the earlier work [e.g.,Shu et al.(2000);Lou &Shen (2003);Shen &Lou (2004b);Lou &Zou (2004);Shen et al.(2005)].By further requiring the scale-free condition,other physical quantities should be in the forms of Z ∝r −γand J ∝r 1−βwhich are exactly the same as those of the background equi-librium.Since these perturbations are axisymmetric,it turns out that such perturbations simply represent a sort of rescal-ing of the axisymmetric background equilibrium.Neverthe-less,by carefully taking limits in calculations,we can also find a stationary ‘dispersion relation’.We leave this anal-ysis to Appendix A for a further discussion and focus our attention on m 1cases in the next subsection.。

2015年北京师范大学考博英语真题(总分68, 做题时间90分钟)1. Reading ComprehensionThe human ear contains the organ for hearing and the organ for balance. Both organs involve fluid-filled channels containing hair cells that produce electrochemical impulses when the hairs are stimulated by moving fluid. The ear can be divided into three regions: outer, middle, and inner. The outer ear collects sound waves and directs them to the eardrum separating the outer ear from the middle ear. The middle ear conducts sound vibrations through three small bones to the inner ear. The inner ear is a network of channels containing fluid that moves in response to sound or movement. To perform the function of hearing, the ear converts the energy of pressure waves moving through the air into nerve impulses that me brain perceives as sound. Vibrating objects, such as the vocal cords of a speaking person, create waves in me surrounding air. These waves cause the eardrum to vibrate with the same frequency. The three bones of the middle ear amplify and transmit the vibrations to the oval window, a membrane on the surface of the cochlea, the organ of hearing. Vibrations of me oval window produce pressure waves in the fluid inside me cochlea. Hair cells in the cochlea convert the energy of the vibrating fluid into impulses that travel along the auditory nerve to the brain. The organ for balance is also located in the inner ear. Sensations related to body position are generated much like sensations of sound. Hair cells in the inner ear respond to changes in head position with respect to gravity and movement. Gravity is always pulling down on the hairs, sending a constant series of impulses to the brain. When the position of the head changes—as when the head bends forward—the force on the hair cells changes its output of nerve impulses. The brain then interprets these changes to determine the head's new position.1.What can be inferred about the organs for hearing and balance?A Both organs evolved in humans at the same time.B Both organs send nerve impulses to the brain.C Both organs contain the same amount of fluid.D Both organs are located in me ear's middle region.2.Hearing involves all of the following EXCEPT______.A motion of the vocal cords so that they vibrateB stimulation of hair cells in fluid-filled channelsC amplification of sound vibrationsD conversion of wave energy into nerve impulses3.It can be inferred from Paragraphs 2 and 3 that the cochlea is a part of______.A the outer earB me eardrumC the middle earD the inner ear4.What can be inferred from Paragraph 4 about gravity?A Gravity has an essential role in the sense of balance.B The ear converts gravity into sound waves in the air.C Gravity is a force that originates in the human ear.D The organ for hearing is not subject to gravity.5.In this passage, the author mainly explains______.A the organs of the human earB the function of the hearingC the three regions of the earD how the ear organ performs the hearing and balanceThe geology of the Earth's surface is dominated by the particular properties of water. Present on Earth in solid, liquid, and gaseous states, water is exceptionally reactive. It dissolves, transports, and precipitates many chemical compounds andis constantly modifying the face of the Earth. Evaporated from the oceans, water vapor forms clouds, some of which are transported by wind over the continents. Condensation from the clouds provides the essential agent of continental erosion: rain. Precipitated onto the ground, the water trickles down to form brooks, streams, and rivers, constituting what is called the hydrographic network. This immense polarized network channels the water toward a single receptacle: an ocean. Gravity dominates this entire step in the cycle because water tends to minimize its potential energy by running from high altitudes toward the reference point that is sea level. The rate at which a molecule of water passes through the cycle is not random butis a measure of the relative size of the various reservoirs. If we define residence time as the average time for a water molecule to pass through one of the three reservoirs—atmosphere, continent, and ocean—we see that the times are very different. A water molecule stays, on an average, eleven days in the atmosphere, one hundred years on a continent and forty thousand years in the ocean. This last figure shows the importance of the ocean as the principal reservoir of the hydrosphere but also the rapidity of water transport on the continents. A vast chemical separation process takes places during the flow of water over the continents. Soluble ions such as calcium, sodium, potassium, and some magnesium are dissolved and transported. Insoluble ions such as aluminum, iron, and silicon stay where they are and form the thin, fertile skin of soil on which vegetation can grow. Sometimessoils are destroyed and transported mechanically during flooding. The erosion of the continents thus results from two closely linked and interdependent processes, chemical erosion and mechanical erosion. Their respective interactions and efficiency depend on different factors.6.According to the passage, clouds are primarily formed by water______.A precipitating onto the groundB changing from a solid to a liquid stateC evaporating from the oceansD being carried by wind7.The passage suggests that the purpose of the "hydrographic network" is to______.A determine the size of molecules of waterB prevent soil erosion caused by floodingC move water from the Earth's surface to the oceansD regulate the rate of water flow from streams and rivers8.What determines the rate at which a molecule of water moves through the cycle, as discussed in the third paragraph?A The potential energy contained in water.B The effects of atmospheric pressure on chemical compounds.C The amounts of rainfall that fall on the continents.D The relative size of the water storage areas.9.All of the following are examples of soluble ions EXCEPT______.A magnesiumB ironC potassiumD calcium10.The word "efficiency" in line 21 is closest in meaning to______.A relationshipB growthC influenceD effectivenessScientists have long understood that supermassive black holes weighing millions or billions of suns can tear apart stars that come too close. The black hotels gravity pulls harder on the nearest part of the star, an imbalance that pulls the star apart over a period of minutes or hours, once it gets close enough. Scientists say this uneven pulling is not the only hazard facing the star. The strain of these unbalanced forces can also trigger a nuclear explosion powerful enough to destroy the star from within. Matthieu Brassart and Jean-Pierre Luminet of the Observatoire de Paris in Meudon, France, carried out computer simulations of the final moments of such anunfortunate star's life, as it veered towards a supermassive black hole. When the star gets close enough, the uneven forces flatten it into a pancake shape. Some previous studies had suggested this flattening would increase the density and temperature inside the star enough to trigger intense nuclear reactions that would tear it apart. But other studies had suggested that the picture would be complicated by shock waves generated during the flattening process and that no nuclear explosion should occur. The new simulations investigated the effects of shock waves in detail, and found that even when their effects are included, the conditions favor a nuclear explosion. " There will be an explosion of the star — it will be completely destroyed," Brassart says. Although the explosion obliterates the star, it saves some of the star's matter from being devoured by the black hole. The explosion is powerful enough to hurl much of the star's matter out of the black hole's reach, he says. The devouring of stars by black holes may already have been observed, although at a much later stage. It is thought mat several months after the event that rips the star apart, its matter starts swirling into the hole itself. It heats up as it does so, releasing ultraviolet light and X-rays. If stars disrupted near black holes really do explode, then they could in principle allow these events to be detected at a much earlier stage, says Jules Hatpern of Columbia University in New York, US2. "It may make it possible to see the disruption of that star immediately if it gets hot enough," he says. Brassart agrees. "Perhaps it can be observed in the X-rays and gamma rays, but it's something that needs to be more studied," he says. Supernova researcher Chris Fryer of the Los Alamos National Laboratory in Los Alamos, New Mexico, US3, says the deaths of these stars are difficult to simulate, and he is not sure whether the researchers have proven their case that they explode in the process.11.Something destructive could happen to a star that gets too close to a black hole. Which of the following destructive statements is NOT mentioned in the passage?A The black hole could tear apart the star.B The black hole could trigger a nuclear explosion in the star.C The black hole could dwindle its size considerably.D The black hole could devour the star.12.According to the third paragraph, researchers differed from each other in the problem of ______.A whether nuclear reaction would occurB whether the stars would increase its density and temperatureC whether shock waves would occurD whether the uneven forces would flatten the stars13.According to the fourth paragraph, which of the following is NOT true?A No nuclear explosion would be triggered inside the star.B The star would be destroyed completely.C Much of the star's matter thrown by the explosion would be beyond the black hole's reach.D The black hole would completely devour the star.14.What will happen several months after the explosion of the star?A The star's matter will move further away from by the black hole.B The black hole's matter will heat up.C The torn star's matter will swirl into the black hole.D The black hole's matter will release ultraviolet light and X-rays.15.According to the context, the word "disruption" in Paragraph 6 means______.A confusionB tearing apartC interruptionD flatteningOur culture has caused most Americans to assume not only that our language is universal but that the gestures we use are understood by everyone. We do not realize that waving good-bye is the way to summon a person from the Philippines to one's side, or that in Italy and some Latin-American countries, curling the finger to oneself is a sign of farewell. Those private citizens who sent packages to our troops occupying Germany after World War II and marked them GIFT to escape duty payments did not bother to find out that " Gift" means poison in German. Moreover, we like to think of ourselves as friendly, yet we prefer to be at least 3 feet or an arm's length away from others. Latins and Middle Easterners like to come closer and touch, which makes Americans uncomfortable. Our linguistic and cultural blindness and the casualness with which we take notice of the developed tastes, gestures, customs and languages of other countries, are making us lose friends, business and respect in the world. Even here in the United States, we make few concessions to the needs of foreign visitors. There are no information signs in four languages on our public buildings or monuments; we do not have multilingual guided tours. Very few restaurant menus have translations, and multilingual waiters, bank clerks and policemen are rare. Our transportation systems have maps in English only and often we ourselves have difficulty understanding them. When we go abroad, we tend to cluster in hotels and restaurants where English is spoken. Then attitudes and information we pick up are conditioned by those natives—usually the richer —who speak English. Our business dealings, as well as the nation's diplomacy, are conducted through interpreters. For many years, America and Americans could get by with cultural blindness and linguistic ignorance. After all America is the most powerful country of the free world, the distributor needed funds and goods. But all that is past. American dollars no longer buy all good things, and we are slowly beginning to realize that our proper role in the world is changing. A 1979 Harris poll reported that 55 percent of Americans want this country to play a moresignificant role in world affairs; we want to have a hand in the important decisions of the next century, even though it may not always be the upper hand.16.It can be inferred that Americans being approached too closely by Middle Easterners would most probably______.A stand stillB jump asideC step forwardD draw back17.The author gives many examples to criticize Americans for their______.A cultural self-centerednessB casual mannersC indifference towards foreign visitorsD arrogance towards other countries18.In countries other than their own most Americans______.A are isolated by the local peopleB are not well informed due to the language barrierC tend to get along well with the nativesD need interpreters in hotels and restaurants19.According to the author, Americans' cultural blindness and linguistic ignorance will______.A affect their image in the new eraB cut themselves off from the outside worldC limit their role in world affairsD weaken the position of the US dollar20.The author's intention in writing this article is to make Americans realizethat______.A it is dangerous to ignore their foreign friendsB it is important to maintain their leading role in world affairsC it is necessary to use several languages in public placesD it is time to get acquainted with other culturesHistorians have only recently begun to note the increase in demand for luxury goods and services that took place in 18th-century England. McKendrick has explored the Wedgwood firm's remarkable success in marketing luxury pottery; Plumb has written about the proliferation of provincial theaters, musical festivals, and children's toys and books. While the fact of this consumer revolution is hardly in doubt, three key questions remain: Who were the consumers? What were their motives? And what were the effects of the new demand for luxuries? An answer to the first of these hasbeen difficult to obtain. Although it has been possible to infer from the goods and services actually produced what manufactures and servicing trades thought their customers wanted, only a study of relevant personal documents written by actual consumers will provide a precise picture of who wanted what. We still need to know how large this consumer market was and how far down the social scale the consumer demand for luxury goods penetrated. With regard to this last question, we might note in passing that Thompson, while rightly restoring laboring people to the stage of 18th-century English history, has probably exaggerated the opposition of these people to the inroads of capitalist consumerism in general; for example, laboring people in eighteenth-century England readily shifted from home-brewed beer to standardized beer produced by huge, heavily capitalized urban breweries. To answer the question of why consumers became so eager to buy, some historians have pointed to the ability of manufacturers to advertise in a relatively uncensored press. This, however, hardly seems a sufficient answer. McKendrick favors a Veblen model of conspicuous consumption stimulated by competition for status. The "middling sort" bought goods and services because they wanted to follow fashions set by the rich. Again, we may wonder whether this explanation is sufficient. Do not people enjoy buying things as a form of self-gratification? If so, consumerism could be seen as a product of the rise of new concepts of individualism and materialism(a preoccupation with or stress upon material rather than intellectual or spiritual things), but not necessarily of the frenzy for conspicuous competition. Finally, what were the consequences of this consumer demand for luxuries? McKendrick claims that it goes a long way toward explaining the coming of the Industrial Revolution. But does it? What, for example, does the production of high-quality pottery and toys have to do with the development of iron manufacture or textile mills? It is perfectly possible to have the psychology and reality of a consumer society without a heavy industrial sector. That future exploration of these key questions is undoubtedly necessary should not, however, diminish the force of the conclusion of recent studies: the insatiable demand in eighteenth-century England for frivolous as well as useful goods and services foreshadows our own world.21.In the first paragraph, the author mentions McKendrick and Plumb most probably in order to ______.A contrast their views on the subject of luxury consumerism in 18th-century EnglandB indicate the inadequacy of historiographical approaches to 18th-century English historyC give examples of historians who have helped to establish the fact of growing consumerism in 18th-century EnglandD support the contention that key questions about 18th-century consumerism remain to be answered22.Which of the following items, if preserved from 18th-century England, would provide an example of the kind of documents mentioned in lines 3-4, Paragraph 2?A A written agreement between a supplier of raw materials and a supplier of luxury goods.B A diary that mentions luxury goods and services purchased by its author.C A theater ticket stamped with the date and name of a particular play.D A payroll record from a company that produced luxury goods such as pottery.23.According to the text, Thompson attributes to laboring people in 18th-century England which of the following attitudes toward capitalist consumerism?A Enthusiasm.B Curiosity.C Ambivalence.D Hostility.24.In the third paragraph, the author is primarily concerned with______.A contrasting two theses and offering a compromiseB questioning two explanations and proposing a possible alternative to themC paraphrasing the work of two historians and questioning their assumptionsD examining two theories and endorsing one over the other25.According to the text, 18th-century England and the contemporary world of the text readers are______.A dissimilar in the extent to which luxury consumerism could be said to be widespread among the social classesB dissimilar in their definitions of luxury goods and servicesC dissimilar in the extent to which luxury goods could be said to be stimulant of industrial developmentD similar in their strong demand for a variety of goods and servicesPity those who aspire to put the initials PhD after their names. After 16 years of closely supervised education, prospective doctors of philosophy are left more or less alone to write the equivalent of a large book. Most social-science postgraduates have still not completed their theses by the time their grant runs out after three years. They must then get a job and finish in their spare time, which can often take a further three years. By then, most new doctors are sick to death of the narrowly defined subject which has blighted their holidays and ruined their evenings. The Economic and Social Research Council, which gives grants to postgraduate social scientists, wants to get better value for money by cutting short this agony. It would like to see faster completion rates; until recently, only about 25% of PhD candidates were finishing within four years. The ESRC's response has been to stop PhD grants to all institutions where the proportion taking less than four years is below 10% ; in the first year of this policy the national average shot up to 39%. The ESRC feels vindicated in its toughness, and will progressively raise the threshold to 40% in two years. Unless completion rates improve further, this would exclude 55 out of 73 universities and polytechnics — including Oxford University, the London Schoolof Economics and the London Business School. Predictably, howls of protest have come from the universities, who view the blacklisting of whole institutions as arbitrary and negative. They point out that many of the best students go quickly into jobs where they can apply their research skills, but consequently take longer to finis their theses. Polytechnics with as few as two PhD candidates complain that they are penalized by random fluctuations in student performance. The colleges say there is no hard evidence to prove that faster completion rates result from greater efficiency rather than lower standards or less ambitious doctoral topics. The ESRC thinks it might not be a bad thing if PhD students were more modest in their aims. It would prefer to see more systematic teaching of research skills and fewer unrealistic expectations placed on young men and women who are undertaking their first piece of serious research. So in future its grants will be given only where it is convinced that students are being trained as researchers, rather than carrying out purely knowledge-based studies. The ESRC can not dictate the standard of thesis required by external examiners, or force departments to give graduates more teaching time. The most it can do is to try to persuade universities to change their ways. Recalcitrant professors should note that students want more research training and a less elaborate style of thesis, too.26.By time new doctors get a job and try to finish their theses in spare time, ______.A most of them died of some sicknessB their holidays and evenings have been ruined by their jobsC most of them are completely tired of the narrowly defined subjectD most of their grants run out27.Oxford University would be excluded out of those universities that receive PhD grants from ESRC, because the completion rate of its PhD students' theses within four years is lower than ______.A 25%B 40%C 39%D 10%28.All the following statements are the arguments against ESRC's policy EXCEPT______.A all the institutions on the blacklist are arbitrary and negativeB there is no hard evidence to prove that faster completion rates result from greater efficiency rather than lower standards or less ambitious doctoral topicsC many of the best students go quickly into jobs where they can apply their research skills, but consequently take longer to finish their diesesD some polytechnics are penalized by random fluctuations in student performance29.The ESRC would prefer______.A that me students were carrying out purely knowledge-based studies rather than being trained as researchersB to see higher standards of PhD students' theses and more ambitious doctoral topicsC more systematic teaching of research skills to fewer unrealistic expectations placed on inexperienced young PhD studentsD that PhD students were less modest in their aims30.What the ESRC can do is to______.A force departments to give graduates more teaching timeB try to persuade universities to change their waysC dictate me standard of diesis required by external examinersD note mat students want more research training and less elaborate style of thesis2. English-Chinese Translation1.Washington Irving grasped this fact nearly a hundred years ago when he wrote: "The stranger who would form a correct opinion of English character must go forth into the country. He must sojourn in villages and hamlets; he must visit castles, villas, farmhouses, cottages; he must wander through parks and gardens, along hedges and green lanes; he must loiter about country churches, attend wakes and fairs and other rural festivals, and cope with me people in all their conditions and all their habits and humors. "2.The impact of decentralization trends, of course, extends well beyond cities. Sprawling development patterns are destabilizing many of the suburbs that surround America's cities. Older suburbs are experiencing the same challenges as cities: failing schools, persistent crime, and the loss of jobs and businesses to other, further out suburbs. Even suburban areas that are developing rapidly are finding that explosive growth has its drawbacks, especially in the form of overcrowded schools, but also in long commutes and the inability of local governments to pay for new roads, sewers, and other infrastructure.3. Chinese-English Translation1.发展中国家的人们若为移民问题操心，往往是想到硅谷或发达国家的医院和大学去创造自己最辉煌的未来。