The infrared conductivity of Na$_x$CoO$_2$ evidence of gapped states

EXPERIMENTAL INVESTIGATION AND MODELING OFTHE INFLUENCE OF MICROSTRUCTURE ON THERESISTIVE CONDUCTIVITY OF A Cu±Ag±Nb IN SITUCOMPOSITED.MATTISSEN1,D.RAABE{1{and F.HERINGHAUS21Institut fu r Metallkunde und Metallphysik,RWTH Aachen,52056Aachen,Germany and2Degussa AG,Edelmetall Forschung und Entwicklung,63457Hanau,Germany(Received18May1998;accepted21December1998)AbstractÐA Cu±8.2wt%Ag±4wt%Nb in situ metal matrix composite was manufactured by inductive melting,casting,swaging,and wire drawing.The®nal wire( ln A0a A 10X5,A:wire cross section) had a strength of1840MPa and46%of the conductivity of pure Cu.The electrical resistivity of the com-posite wires was experimentally investigated as a function of wire strain and temperature.The microstruc-ture was examined by means of optical and electron microscopy.The observed decrease in conductivity with increasing wire strain is interpreted in terms of inelastic electron scattering at internal phase bound-aries.The experimental data are in very good accord with the predictions of an analytical size-e ect model which takes into account the development of the®lament spacing as a function of wire strain and the mean free path of the conduction electrons as a function of temperature.The experimentally obtained and calculated resistivity data are compared to those of the pure constituents.#1999Acta Metallurgica Inc. Published by Elsevier Science Ltd.All rights reserved.1.INTRODUCTIONDue to their combination of high strength and good electrical conductivity,in situ processed Cu-based metal matrix composites(MMCs)are con-sidered as candidate materials for the production of highly mechanically stressed electrical devices. Applications in the®elds of steady state and long-pulse high-®eld resistive magnet design[1±7]and industrial robotics[8]are of particular interest in this context.Most studies in the past concentrated on the in-vestigation of binary Cu±Nb[9±20]and Cu±Ag composites[21±26].Copper and niobium form a quasi monotectic system and have no mutual solu-bility by practical means[27,28].During casting the Nb solidi®es dendritically and forms into thin elongated curled®laments during wire drawing. Alloys consisting of Cu and20wt%Nb have an ul-timate tensile strength(UTS)of up to 2.2GPa (Z 12)[12,13,16,17].Copper and silver form a simple eutectic system with limited substitutional solubility[29].Alloys containing more than6wt%Ag usually reveal two phases,a Cu-rich solid solution and a Cu±Ag eutec-tic.During deformation the eutectic and the Cu-rich matrix form into lamellar®laments.An inter-mediate heat treatment leads to Ag precipitations. These can be used to increase the matrix strain and to form additional®bers during further drawing. After large wire strains Cu±Ag MMCs reveal an UTS of up to s=1.5GPa(Z 10)[22,23].In continuation of these studies on binary alloys recent work focused on the development of a new generation of ternary in situ Cu±Ag±Nb composites with the aim to combine the hardening e ects of both Nb and Ag[30±34].While the processing and the mechanical proper-ties of these ternary compounds have been the sub-ject of previous publications[30±34],their electromagnetic properties have not yet been stu-died.The electrical conductivity of heavily deformed Cu-or Ag-based composites is typically smaller than expected from the linear rule of mix-tures(ROM).This e ect is commonly referred to as size e ect.It is due to inelastic scattering of the conduction electrons at the internal phase boundaries[9,20,26,35,36].This study presents an experimental investigation of the evolution of the resistive electrical conduc-tivity of a heavily wire drawn ternary Cu±8.2wt% Ag±4wt%Nb in situ processed MMC as a function of wire strain and temperature and its dependence on the microstructure.The experimental obser-vations are quantitatively compared to predictions of an analytical size-e ect model which takes into account the development of the®lament spacing as a function of the wire strain.Acta mater.Vol.47,No.5,pp.1627±1634,1999#1999Acta Metallurgica Inc.Published by Elsevier Science Ltd.All rights reservedPrinted in Great Britain1359-6454/99$20.00+0.00PII:S1359-6454(99)00026-9{Present address:Luchweg10,14621Scho nwalde,Germany.{To whom all correspondence should be addressed.16272.SAMPLE PREPARATIONA Cu±8.2wt%Ag±4wt%Nb alloy was prepared by inductive melting using a frequency of 10kHz and a power of 50kW [33].All constituents had an initial purity of at least 99.995%.Ingots of 18mm diameter were cast under an argon atmosphere at a pressure of 0.6Â105Pa.A crucible and a mould of high purity graphite were used.The mould was pre-heated to about 6008C to ensure good ¯uidity and ®lling.From the cast cylindrical ingots wires were produced by rotary swaging and drawing through hard metal drawing bench dies.A maximum true wire strain above Z 10(Z ln A 0a A ,A :wire cross section)was attained without intermediate annealing.Further processing details are reported elsewhere [33,37].3.EXPERIMENTAL PROCEDURE3.1.Experimental investigation of the microstructure Optical and scanning electron microscopy (SEM)were used to determine the morphology and top-ology both of the Cu matrix and of the Ag and Nb ®laments.Due to insu cient contrast,an unam-biguous optical identi®cation of the various phases was sometimes not possible.The samples were thus additionally analyzed using energy-disperse X-rayspectrometry (EDX).The morphology of the iso-lated Nb ®bers was also investigated by use of a selective etching technique,where the Cu and Ag were dissolved by dilute nitric acid.Details about the experimental procedure were reported previously [32].3.2.Experimental investigation of the resistive elec-trical conductivitySystematic measurements of the resistive conduc-tivity at 298and 77K as a function of the wire strain were carried out for Cu±8.2wt%Ag±4wt%Nb by means of the direct current (d.c.)four-probe technique using a sample current of 100mA.For a number of Cu±8.2wt%Ag±4wt%Nb,pure Cu,pure Ag,and pure Nb wires of identical total wire strain;the in¯uence of the temperature on the resis-tive conductivity was studied within the temperature range 3±350K.4.EXPERIMENTAL RESULTS4.1.Microstructure evolution as a function of wire strainFigure 1shows the development of the diameters of the Cu matrix phase (d Cu ),the Nb ®laments (d Nb ),and the Ag ®laments (d Ag )in thecompositeFig.1.Development of the diameters of the Nb ®laments,the Ag ®laments,and the Cu matrix phasein the Cu±8.2wt%Ag±4wt%Nb composite as investigated by quantitative SEM.MATTISSEN et al.:Cu±Ag±Nb IN SITU COMPOSITE1628as a function of the true wire strain Z .At low strains the Ag ®laments were thicker and shorter than the Nb ®laments.With increasing strain their average thickness became more similar to that of the Nb ®laments.At a wire strain of Z 3X 6the average Ag ®lament diameter amounted to d Ag I 676nm and at Z 6to d Ag I 260nm.At a wire strain of Z 2X 6the average Nb ®lament diameter amounted to d Nb I 529nm and at Z 9X 5to d Nb I 66nm.For including the evolution of the ®lament morphology in an analytical size-e ect model the average phase diameters were exponentially ®tted from the metallographic data according to d Cu =31767nm Âexp(À0.6415Z ),d Ag =2630nm Âexp(À0.3861Z ),and d Nb =1386.6nm Âexp(À0.413Z ).4.2.Resistive conductivity as a function of wire strain and temperatureFigure 2shows the dependence of the electrical resistivity of Cu±8.2wt%Ag±4wt%Nb on the strain at 298and 77K.At true wire strains above Z 8X 5the conductivity decreases drastically.The increase in the resistivity with increasing strain is more pronounced at 77K (from H 10n O m at Z 3X 5to H 20n O m at Z I 10)than at 298K (from H 27n O m at Z 3X 5to H 38n O m at Z I 10).Consequently,the resistivity ratio of Cu±8.2wt%Ag±4wt%Nb,r 298K a r 77K ,drops as a func-tion of the true wire strain (Fig.3).At temperatures below the transition temperature of pure Nb the wire drawn Cu±8.2wt%Ag±4wt%Fig.2.Electrical resistivity of the ternary Cu±8.2wt%Ag±4wt%Nb composite as a function of thetrue (logarithmic)wire strain Z (Z ln A 0a A ,A :wire cross section)at T 298and 77K.Fig.3.Electrical resistivity ratio r 298K a r 77K of the ternary Cu±8.2wt%Ag±4wt%Nb compositeas a function of the true (logarithmic)wire strain Z (Z ln A 0a A ,A :wire cross section).MATTISSEN et al.:Cu±Ag±Nb IN SITU COMPOSITE 1629Nb reveals superconducting properties.Figure 4shows for the composite the transition to the super-conducting state as a function of strain.The data reveal that an increasing wire strain leads to a shift of the transition temperature to lower values.A detailed analysis of the superconducting properties of the ternary composite is given in Ref.[38]based on Ginzburg±Landau theory.The electrical resistivity of pure Cu wires and pure Ag wires was practically independent of the degree of deformation and was always lower than for the composite (Fig.5).The e ect of defor-mation on the resistivity temperature coe cient of pure Cu,pure Ag,pure Nb,and Cu±8.2wt%Ag±4wt%Nb is given in Fig.6.While the temperature coe cient of the pure wires is practically indepen-dent on wire strain,that of the composite drops with increasing wire strain.5.MODELING OF THE ELECTRICAL RESISTIVITYOF THE Cu±Ag±Nb COMPOSITE5.1.Fundamentals of the modelAny analytical calculation of absolute values ofthe electrical resistivity of MMCs requires very detailed data both on the impurity content and dis-tribution and on the density and distribution of the lattice defects (e.g.dislocation density,grain size,etc.).Since these data are usually not known with su cient reliablility,analytical models of the resis-tivity of composites are commonly exclusively based on the size e ect,which typically provides by far the most dominant contribution to inelastic internalscattering of the conduction electrons in such materials [9,20,26,35,36].The predictions of such models can then be compared to the relative changes observed experimentally.Analytical predictions of the electrical resistivity of composites on the basis of the size e ect require the volume fractions and the topologies of each phase in the composite and some intrinsic con-stants.The model starts with the calculation of the elec-trical resistivity of each phase according to the phe-nomenological expression for surface and phase boundary scattering given by Sondheimer [39]r d r 0 1 34 1Àpl 0 Td1 where r (d )is the resistivity as a function of the ®la-ment thickness,r 0the resistivity for a sample with-out scattering at phase boundaries (in®nite sampleor phase size),p the scattering factor,l 0the mean free path of the conduction electrons in that par-ticular phase and d the thickness of the ®lament.According to Dingle [35]the scattering factor p rep-resents the probability of elastic scattering and (1Àp )that of inelastic scattering at the phase boundary.The mean free paths of the conduction electrons in the various phases (as a function of temperature)were determined from the temperature dependent resistivities of the bulk phases usings T l 0 T e 2N el "h V 3p 2N elVÀ1a 32Fig.4.Transition of the electrical resistivity of the ternary Cu±8.2wt%Ag±4wt%Nb composite from the normal resistive state to the superconducting state as a function of temperature for two di erent degrees of the true (logarithmic)wire strain (Z 8,Z 5X 96)(Z ln A 0a A ,A :wire cross section).MATTISSEN et al.:Cu±Ag±Nb IN SITU COMPOSITE1630where s (T )is the conductivity and N el /V the elec-tron density.The right-hand side of equation (2)was calculated using a value of N el a V 5X 57Â1029a m 3under the assumption of mono-valence for Ag and Cu and a value of N el a V 5X 325Â1029a m 3for Nb.Finally,the individual resistivities r i of the phases were topologically combined to give the overall res-istivity of the composite r MMC .The model treats all phases as resistors that are arranged parallelr MMCni 1f i r iÀ13where the f i are the volume fractions of the phases i 1,F F F ,n ,and r i the electrical resistivities of the phases i 1,F F F ,n .5.2.Application of the modelThe prediction of the electrical resistivity of the Cu±8.2wt%Ag±4wt%Nb composite on the basis of equations (1)±(3)requires some topologicalcon-Fig.5.Electrical resistivity of pure Cu and pure Ag as a function oftemperature.Fig.6.Temperature coe cient of the electrical resistivity of Cu,Ag,Nb,and the ternary Cu±8.2wt%Ag±4wt%Nb composite between 273and 373K as a function of the true (logarithmic)wire strain Z(Z ln A 0a A ,A :wire cross section).MATTISSEN et al.:Cu±Ag±Nb IN SITU COMPOSITE 1631siderations about the incorporation of the topology of the Ag®laments.In the as-cast sample the Ag had a lamellar shape and formed a Ag±Cu eutectic whilst the Nb was precipitated in the form of iso-lated Wul polyhedra and dendrites[32,33]. Therefore,the composite was treated as a material consisting of two primary phases,namely, 95.82vol.%Cu±Ag and4.18vol.%Nb,in which the former consists of two sub-phases,namely, 91.92vol.%Cu and8.08vol.%Ag.The weight fractions of the primary phases and of the sub-phases were calculated from the weight composition of Cu±8.2wt%Ag±4wt%Nb as(90.66wt%Cu±9.34wt%Ag)±4wt%Nb and the volume fractions correspondingly as(91.92vol.%Cu±8.08vol.% Ag)±4.18vol.%Nb.Equation(3)was®rst applied to the two sub-phases Cu and Ag which then in turn were combined parallel with Nb to form the overall composite.Values for the interface scattering factors p as-sociated with the Cu±Ag interfaces were taken from previous investigations and simulations on this binary system[27].These were for Cu±Ag:p 0X81 at T 298K and p 0X84at T 77K.The size-e ect approach as outlined in equation(1)can be derived from the Boltzmann transport equation for cases where d b l0.This condition holds for the Cu (d Cu a l0Cu I3),the Ag(d Ag a l0Ag I3),and the Nb phase(d Nb a l0Nb I20)corresponding to the current data for Z 10and T 293K.5.3.Predictions of the modelThe predictions of the size-e ect model for the composite,Cu±8.2wt%Ag±4wt%Nb,and for the various phases,Cu,Ag,Cu±Ag,and Nb,are given in Fig.7as a function of the wire strain at T 77K[Fig.7(a)and(b)]and at T 298K[Fig.7(c) and(d)].A strong e ect can be found in the Cu and Ag phases and thus also in Cu±Ag,whereas Nb reveals only weak changes with deformation. Figure7(b)(T 77K)and(d)(T 298K)show that a very good agreement between the model and the experimental data is found at low and elevated strains,particularly for T 298K,while the model slightly underpredicts the resistivity at intermediate strains between Z 6and8.6.DISCUSSIONThe resistivity of Cu±8.2wt%Ag±4wt%Nb increases considerably with the degree of defor-mation.The strong dependence may be chie¯y attributed to the scattering of conduction electrons at the various internal phase boundaries.This e ect becomes particularly pronounced when the average ®lament spacing is,after heavy deformation,of the same order of magnitude as the mean free path of the conduction electrons in the Cu and the Ag phase(Figs2and7)[9,36].Since the mean free electron path linearly decreases as a function of temperature in the regime above the Debye tem-perature,due to the increase of phonon scattering, the contribution of interface scattering to the over-all resistivity is more pronounced at low tempera-tures[Fig.7(b),increase by H100%]than at elevated temperatures[Fig.7(d),increase by H40%].Since the Cu±Ag interfaces have a low,and the Cu±Nb and Ag±Nb interfaces a very high e ect on inelastic scattering,the latter are assumed to be primarily responsible for the observed increase in resistivity.The density of deformation induced lattice dislo-cations is of minor importance for the dependence of the resistivity on wire strain since only their cores add to the electrical resistivity,but contribute only a very small resistivity change per unit length of a dislocation[36,40,41].Here the applied d.c. four-probe technique is not accurate enough to exactly account for such a change.The composite(Cu±8.08vol.%Ag)±4.18vol.% Nb can be described as consisting of two®rst-order phases,95.82vol.%Cu±Ag and4.18vol.%Nb,the former of which consists of two second-order phases,91.8vol.%Cu and8.08vol.%Ag(see Fig.7).Using this approach enables one to make an analytical topological prediction of the size e ect due to interface scattering.A determination of the absolute values of the electrical resistivity is not feasible due to the e ects of impurities and mutual solution.The latter,although of particular import-ance in the Cu±Ag phase,cannot be incorporated owing to the unavailability of appropriate exper-imental data.In this context the slight discrepancy found at in-termediate degrees of deformation between model and experiment[see Fig.7(b)and(d)]may be quali-tatively attributed to deformation-induced changes in the solubility or in the state of precipitation. While changes in the solubility can be explained in terms of the Gibbs±Thomson equation,which relates solubility to interface curvature,changes in the precipitation state can only be attributed to fric-tional heating of the sample during wire drawing. However,both e ects may either not be as domi-nant anymore at high degrees of deformation[i.e. at strain above Z 8,see Fig.7(b)and(d)]due to the dominance of strong interface scattering,or be reverted owing to the presence of a high density of internal interfaces.The latter argument,however,is not covered by experimental evidence and thus is of speculative character.Regarding the e ect of the microstructure of the individual phases on inelastic scattering[Fig.7(a) and(c)],it may be concluded that the size e ects in the Cu phase and in the Ag phase are chie¯y re-sponsible for the observed increase in the electrical resistivity of the Cu±Ag phase and thus ultimately of the ternary composite.In comparison to the Cu phase and the Cu±Ag phase,the size e ect in Ag, particularly at large strains,is much stronger atMATTISSEN et al.:Cu±Ag±Nb IN SITU COMPOSITE 1632F i g .7.M o d e l e d a n d e x p e r i m e n t a l l y o b s e r v e d r e l a t i v e c h a n g e s o f t h e e l e c t r i c a l r e s i s t i v i t y o f C u ,N b ,A g ,a n d t h e t e r n a r y C u ±8.2w t %A g ±4w t %N b c o m p o s i t e a t T 298a n d 77K a s a f u n c t i o n o f t h e t r u e (l o g a r i t h m i c )w i r e s t r a i n Z (Z l n A 0a A ,A :w i r e c r o s s s e c t i o n ).(a )T 77K ,s i z e e e c t m o d e l f o r t h e v a r i o u s p h a s e s a n d f o r t h e c o m p o -s i t e .(b )T 77K ,c o m p a r i s o n b e t w e e n s i z e -e e c t m o d e l a n d e x p e r i m e n t a l d a t a .(c )T 298K ,s i z e -e e c t m o d e l f o r t h e v a r i o u s p h a s e s a n d f o r t h e c o m p o s i t e .(d )T 298K ,c o m p a r i s o n b e t w e e n s i z e -e e c t m o d e l a n d e x p e r i m e n t a l d a t a .MATTISSEN et al.:Cu±Ag±Nb IN SITU COMPOSITE1633T 298K[Fig.7(a)]than at T 77K[Fig.7(c)]. This e ect is due to the stronger temperature-dependence of the mean free electron path in Cu as compared to Ag.7.CONCLUSIONSA ternary in situ Cu±8.2wt%Ag±4wt%Nb MMC was manufactured by melting,casting,swa-ging,and wire drawing.The microstructure was investigated using electron microscopy and EDX. The resistive conductiving properties were examined using four-probe d.c.tests at various temperatures. The main results are:.The ternary MMC was very ductile.A maximum wire strain of Z 10X5was reached without inter-mediate annealing..Wires of the ternary MMC of maximum strain (Z max 10X5)had an UTS of1840MPa and46% of the conductivity of pure Cu(IACS)..The electrical resistivity of the ternary MMC at large strains drastically increased with increasing strain.This was attributed to the size e ect,i.e. to the inelastic scattering of the conduction elec-trons at the internal interfaces..The in¯uence of the size e ect on the course of the electrical resistivity of the ternary MMC was modeled using an analytical solution of the Boltzmann transport equation.At low and very large strains the model was in very good accord with the experimental data.At intermediate strains between Z 6and8the model underpre-dicted the resistivity.This deviation was inter-preted in terms of changes in the solubility and probably in the precipitation state.AcknowledgementsÐThe authors are indebted to G. Gottstein,H.-J.Scheider-Muntau,and J.D.Embury for helpful discussions.One of the authors(D.R.)gratefully acknowledges the®nancial support by the Deutsche Forschungsgemeinschaft through the Heisenberg program and by the National High Magnetic Field Laboratory in Tallahassee,Florida.REFERENCES1.Foner,S.and Bobrov,E.,I.E.E.E.Magn.,1987,24,1059.2.Asano,T.,Sakai,Y.,Inoue,K.,Oshikiri,M.andMaeda,H.,I.E.E.E.Magn.,1992,28,888.3.Heringhaus,F.,Eyssa,Y.M.,Pernambuco-Wise,P.,Bird,M.D.,Gottstein,G.and Schneider-Muntau,H.-J.,Metall.,1996,50,272.4.Embury,J.D.,Hill,M.A.,Spitzig,W.A.and Sakai,Y.,MRS Bull.,1993,8,57.5.Heringhaus, F.,Le ers,R.,Gottstein,G.andSchneider-Muntau,H.-J.,Processing,Properties,and Application of Cast Metal Matrix Composites,TMS Fall Meeting,Vol.1,1996,p.127.6.Schneider-Muntau,H.-J.,I.E.E.E.Trans.Magn.,1982,18,32.7.Wood,J.T.,Embury,J.D.and Ashby,M.F.,Actamater.,1997,45,1099.8.Raabe,D.,Matissen,K.,Miyake,K.,Takahara,H.and Heringhans,F.,in Proc.Int.Conf.``Dialogues at Lake Louise''1997,CompositesÐDesign for Performance,ed.P.S.Nicholson.Eagle Press, Burington,Ontario,Canada,pp.146±154.9.Bevk,J.,Harbison,J.P.and Bell,J.L.,J.appl.Phys.,1978,49,6031.10.Karasek,K.R.and Bevk,J.,J.appl.Phys.,1981,52,1370.11.Funkenbusch,P. 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Material Sciences 材料科学, 2021, 11(4), 453-461Published Online April 2021 in Hans. /journal/mshttps:///10.12677/ms.2021.114053二元层状钴掺杂锰氧化物的制备及电催化性能研究龙霞中南大学材料科学与工程学院，湖南长沙收稿日期：2021年3月26日；录用日期：2021年4月21日；发布日期：2021年4月28日摘要锰在地球上的储量丰富、毒性低，且其层状结构具有强可调性，具备巨大的应用潜力。

然而不恰当的电子结构和较低的导带水平阻碍了其在电催化水裂解中的应用，缺陷工程是提高MnO2电子电导率和电化学性能的重要策略。

本文以层状二氧化锰为基体，通过固相烧结掺杂不同比例钴元素制备了一系列二元锰钴氧化物，作为非贵金属OER催化剂。

其中Na-Mn0.5Co0.5O2二元层状锰钴氧化物材料在10 mA∙cm−2处表现出最佳性能，过电势降低至380 mV，Tafel斜率低至55 mV∙dec−1，优于锰钴单金属氧化物催化剂以及其他二元层状锰钴氧化物。

外源元素掺杂提高了本征电子电导率，增加氧化还原活性中心浓度，加速离子扩散和电荷存储转移，从而达到降低过电位的目的。

关键词二元锰钴氧化物层状材料，纳米片，电催化，OERPreparation and ElectrocatalyticPerformance of Binary LayeredCobalt-Doped ManganeseOxideXia LongSchool of Materials Science and Engineering, Central South University, Changsha HunanReceived: Mar. 26th, 2021; accepted: Apr. 21st, 2021; published: Apr. 28th, 2021龙霞Abstract Manganese is abundant on the earth, because of its low toxicity and strong adjustable layer struc-ture; it has huge application potential. However, improper electronic structure and low conduc-tion band level hinder its application in electrocatalytic water splitting. Defect engineering is an important strategy to improve the electronic conductivity and electrochemical performance of MnO 2. In this paper, a series of binary manganese cobalt oxides were prepared by solid-phase sin-tering doped with different proportion of cobalt on layered manganese dioxide as non-noble metal OER catalyst. The Na-Mn 0.5Co 0.5O 2 binary layered manganese cobalt oxide material shows the best performance at 10 mA ∙cm −2, with overpotential reduced to 380 mV and Tafel slope as low as 55 mV ∙dec −1, which is better than the single metal oxide catalyst and other binary layered oxides. Ex-ogenous element doping improves the intrinsic electronic conductivity, increases the concentra-tion of redox active centers, accelerates ion diffusion and charge transfer, and thus achieves low overpotential. KeywordsBinary Manganese Cobalt Oxide Layered Material, Nanosheet, Electrocatalysis, OERCopyright © 2021 by author(s) and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). /licenses/by/4.0/1. 引言随着石油危机的爆发，能源问题引起了广泛关注。

a rXiv:c ond-ma t/97390v11Mar1997The crossover between Aslamazov-Larkin and short wavelength fluctuation regimes in HTS conductivity experiments M.R.Cimberle,C.Ferdeghini,E.Giannini,D.Marr´e ,M.Putti,A.Siri INFM /CNR,Dipartimento di Fisica,Universit`a di Genova,via Dodecaneso 33,Genova 16146,Italy F.Federici,A.Varlamov Laboratorio “Forum”dell’INFM,Dipartimento di Fisica Universit`a di Firenze,Largo E.Fermi 2,50125Firenze,Italy (February 1,2008)We present paraconductivity (AL)measurements in three different high temperature supercon-ductors:a melt textured Y Ba 2Cu 3O 7sample,a Bi 2Sr 2CaCu 2O 8epitaxial thin film and a highly textured Bi 2Sr 2Ca 2Cu 3O 10tape.The crossovers between different temperature regimes in excess conductivity have been analysed.The Lawrence-Doniach (LD)crossover,which separates the 2D and 3D regimes,shifts from lower to higher temperatures as the compound anisotropy decreases.Once the LD crossover is overcome,the fluctuation conductivity of the three compounds shows the same universal behaviour:for ǫ=ln T /T c >0.23all the curves bend down according to the 1/ǫ3law.This asymptotic behaviour was theoretically predicted previously for the high temperature region where the short wavelength fluctuations (SWF)become important.PACS:74.25.-q;74.25.Fy;74.40.+k It is well known that,owing to strong anisotropy,high critical temperature and low charge carrier concentration,thermodynamic fluctuations play an important role in the explanation of the normal state properties of high tempera-ture superconductors (HTS).Just after the realization of high quality epitaxial single crystal samples,the in-plane fluc-tuation conductivity was investigated in detail and the Lawrence-Doniach (LD)crossover between three-dimensional (3D)and two-dimensional (2D)regimes (or at least a tendency to it)was observed in the vicinity of T c in the majority of HTS compounds.Analogous phenomena were observed in magnetic susceptibility,thermoconductivity 1and other properties of HTS.Let us recall that LD crossover takes place in the temperature dependence of in-plane conductivity and it is related to the fact that fluctuative Cooper pairs motions change from 2D to 3D rotations.It takes place at the temperature T LD which is defined by the condition ξc (T LD )≈s ,where ξc is the coherence length and s is the interlayer distance.Nevertheless,the LD crossover in the temperature dependencies of different characteristics does not exhaust all possibilities:additional crossovers can be observed in HTS compounds.For instance,another kind of crossover (0D →3D)can take place in c -axis paraconductivity temperature dependence,at the same temperature T LD .It is due to the fact that the pair propagation along c-axis has a zero-dimensional character relatively far from T c and it changes into a three-dimensional rotation in the immediate vicinity of the transition.This effect was predicted 2and observed 3in fully oxygenated YBCO samples while in BSCCO samples it is masked by the increase of resistivity due to fluctution density of states renormalization.Below we will remind the reader of the possible kinds of crossover phenomena taking place in layered superconductors and finally we will present the experimental evidences of the crossover related to the breakdown of Ginzburg Landau (GL)approximation,due to the importance of short wavelength fluctuations.How the LD crossover appears in the framework of the GL theory can be shown explicitly considering the model of an open electron Fermi surface which,for instance,can be chosen in the form of a “corrugated cylinder”4.In this case the energy spectrum has the formξ(p )=ǫ0(p )+J cos(p ⊥s )−E F ,(1)where ǫ0(p )=p 2/(2m ),p ≡(p ,p ⊥),p ≡(p x ,p y )is a two-dimensional,intralayer wavevector,and J is an effective hopping energy.The Fermi surface is defined by the condition ξ(p F )=0and E F is the Fermi energy.This spectrum is the most appropriate for strongly anisotropic layered materials where J/E F≪1.In the framework of the Ginzburg-Landau theory for an isotropic spectrum,the fluctuation contribution to the free energy of a superconductor above the critical temperature can be presented as the sum over long wavelength fluctuations 5:F =−T qln πTsome dimensional coefficient)and in the case of anisotropic spectrum(1)must be substituted by the more sofisticated expression including the additional dependence on q⊥:(v·q)2 = [ξ(p)−ξ(q−p)]2 =1f(ǫ).(4)16¯h sIn the GL region of temperature,whereǫ≪1,f(ǫ)=1/ǫand the result coincides with the well known AL one.In the opposite caseǫ≫1,for clean2D superconductors,f(ǫ)∼1/ǫ3=1/ln3(T/T c)was carried out.In the theoretical consideration it was natural to assume formally the very rigid restrictionǫ≫1for the validity of the latter asymptotic behaviour.Nevertheless,as it will be seen below,in experiments the crossover to this asymptotic behaviour takes place universally for all the samples investigated atǫ∼0.23and this can be attributed to some particularly fast convergence of the integrals in the expression of f(ǫ).The long tails in the in-planefluctuation conductivity of HTS materials have been observed frequently.One of the efforts tofit the high temperature paraconductivity with the extended AL theory results was undertaken in13where the deviation of the excess conductivity from AL behaviour was analysed for three Bi2Sr2CaCu2O8epitaxialfilms. Very goodfit with the formula(4)was found in the region of temperatures0.02<∼ǫ<∼0.14.We show here that the careful analysis of the higher temperature region(just above the edge of the region investigated in13)allows to observe the surprisingly early approaching to the SWF asymptotic regime(at the reduced teperatureǫ∗∼ln(T∗/T c)∼0.23). We have performed resistivity measurement of three different HTS compounds:a melt textured YBa2Cu3O7sample (Y123),a Bi2Sr2CaCu2O8(Bi2212)thickfilm and a highly textured Bi2Sr2Ca2Cu3O10(Bi2223)tape.The Y123was obtained by melting14;the sample was cut in a nearly regular parallelepipedal shape with a cross section of about 4mm2and a length of7mm.The resistivity measurements were performed from85to330K.The critical temperature,defined as the point where the temperature derivative is maximal,is92K;ρN(100K)=120µΩcm, whereρN is the resistivity in the normal state extrapolated from the high temperature region whereρis linear.The Bi2212film was prepared by a liquid phase epitaxy technique15.Thefilm has a thickness of about1µm.The resistivity measurements were performed from80to170K.The critical temperature was estimated to be84.2K andρN(100K)=150µΩcm.The Bi2223tape was obtained by means of the power in tube procedure,as described elsewhere16.The thickness of the oxidefilament inside the tape was about30µm;thefilament turned out to bestrongly textured(rocking angle≈8◦)with the c-axis oriented perpendicular to the tape plane.The resistivity measurements were performed in the range from100to250K,after removing the silver sheathing chemically.The critical temperature was estimated to be108K andρN(100K)=300µΩcm.We ascribe this high value ofρN to different causes:first,the grain boundaries may determine a resistance in series with the grain resistance;second,the chemical treatment may have damaged the surface of the sample and the effective cross section of the superconductor can be decreased.The excess conductivity was estimated by subtracting the background of the normal state conductivityσN= 1/ρN.The evaluation ofρN was made with particular accuracy;in fact,starting the interpolation at a certain temperature corresponds to forcingσfl to vanish artificially at such temperature.Therefore,we need to estimateρN at a temperature as large as possible and to verify thatρN does not depend on the temperature range where the interpolation is performed.In the case of Y123sample the resistivity shows a linear behavior from160to330K.In this range we have verified thatρN does not change by shifting the interpolation temperature region. Therefore,for the Y123sample,the upper limit ofǫat which the excess conductivity may be analysed isǫup≈ln(160/92)=0.55.In an analogous way we obtainǫup≈0.46and0.51for Bi2212and Bi2223,respectively.In Fig.1,in a log-log scale,we plotσfl 16hsǫ.The interlayer distance s is considered as a free parameterand it has been adjusted so that the experimental data can follow the1/ǫbehaviour in theǫregion where the AL behavior is expected.We can see that all the curves exhibit the same general behaviour.The region where the2D1/ǫbehaviour is followed,has different extension for each compound,depending on its anisotropy,and atǫ≈0.23all the curves bend downward and follow the same asymptotic1/ǫ3behaviour.We discuss now some features in detail:1)The interlayer distance values wefind are the following:for Y123we obtain s≈13˚A which must be comparedwith the YBCO interlayer distance that is about12˚A;for Bi2212we obtain s≈11˚A to be compared with 15˚A,and for Bi2223we obtain s≈25˚A to be compared with18˚A.The differences in the interlayer distance evaluation are all compatible with the uncertainty on the geometrical factors.We point out that the smallest error is for Y123(about10%)that is a bulk sample with a well defined rger errors are found for the Bi2212thickfilm(about30%),for which the evaluation of the thickness is rough,and for the Bi2223tape (about40%)for which an overestimation of the cross section of the tape is possible,as we mentioned above.We conclude that the AL behaviour is well followed.2)On the lowǫvalue side(ǫ<0.2)the three compounds show different behaviours due to the different extensionof the AL region.The least anisotropic compound,Y123,forǫ<0.1bends going asymptotically to the3D behaviour(1/ǫ0.5)showing the LD crossover atǫ≈0.09;the Bi2223sample starts to bend forǫ<0.03while the most anisotropic Bi2212in the overallǫrange considered shows the2D behaviour.3)On the highǫvalue side,starting from the AL behaviour,the curves show a crossover at aboutǫ=0.23and thenbend downward following the asymptotic1/ǫ3behaviour.At the valueǫ≈0.45all the curves drop indicating the end of the observablefluctuation regime.This value is lower than the above reportedǫup values,at which thefluctuation conductivity comes out to be zero.To conclude:we have observed in three different HTS compounds the universal high temperature behaviour of the in-plane conductivity that manifests itself in the2D regime,once the LD crossover is passed.Beyond the AL regime all the curves reach soon the SWF1/ǫ3regime.For all the compounds the crossover occurs at the same point ǫ≈0.23,which corresponds to T≈1.3T c and,therefore,is experimentally well observable.The universality of the paraconductivity behaviour is much more surprising if we consider that it has been observed in three compounds with different crystallografic structure and anisotropy,and moreover prepared by means of very different techniques.We gratefully acknowledge the fruitful discussions with Giuseppe Balestrino.4In principle it is possible to start from ellipsoidal Fermi surface,but the crossover in this case can be observed when the increase of anisotropy results in the intersection of the Fermi surface with the Brillouin zone boundary only.This fact implies actually the return to the open Fermi surface.5A.A.Abrikosov,The Fundamentals of the Theory of Metals,North-Holland,Amsterdam,(1988).6A.Varlamov,L.Reggiani,Phys.Rev.B45,1060(1992).7K.Maki,“Gapless Superconductivity”in Superconductivity vol.2edited by R.Parks,N.Y.(1969).8H.Schmidt,Ann.Phys.Lpz216,336(1968).9L.Aslamazov,A.Varlamov,Jour.of Low Temp.Phys.38,223(1980).10F.Federici,A.Varlamov,JETP Letters,64,497-501(1996).11A.Varlamov and L.Yu,Phys.Rev.B44,7078(1991).12L.Reggiani,R.Vaglio,A.Varlamov,Phys.Rev.B44,9541(1991).13G.Balestrino,M.Marineli,ani,L.Reggiani,R.Vaglio,A.Varlamov,Phys.Rev.B46,14919(1992).14M.Marella,G.Dinelli,B.Burtet Fabris,B.Molinas J.Alloy and Compounds189,L23(1992).15G.Balestrino,M.Marinelli,ani,A.Paoletti and P.Paroli J.Appl.Phys.68,361(1990).16B.Hensen,G.Grasso and R.Fl¨u kiger,Phys.Rev.B51,15456(1995).FIG.1.σfl 16hsǫ。

摘要新型可再生能源如风能、太阳能、潮汐能等都具有间歇性和随机性的特点，往往不能满足实时、有效、稳定的能量供给需求，因此，发展高效便捷的储能技术已经成为各个国家的研究热点。

目前，锂离子电池占据了便携式移动电子设备的主要市场，而且在电动汽车、电力储能系统方面也有重要的应用。

随着锂离子电池的大规模应用，锂元素的需求量会越来越多，而地球上有限的锂资源无法满足我们日益增长的需求。

钠和锂位于同一主族，具有相似的物理和化学性质，而且钠元素在地壳中的储量丰富，提炼简单（海洋中含有大量的钠），因此，钠离子电池在未来化学电源应用中具有极大的优势。

本论文以Na3V2(PO4)3和Na2.4Fe1.8(SO4)3两种钠离子电池正极材料为研究对象，采用固相法制备了以壳聚糖为碳源包覆的Na3V2(PO4)3/C正极材料，并对其电化学性能进行了研究。

结果表明壳聚糖碳源能够在活性材料中形成一种导电网络，大大增加了Na3V2(PO4)3/C的导电性。

其中，理论碳源添加量30%的样品具有相对优越的电化学性能。

在1 C电流密度下，首圈放电比容量115.01 mAh g-1，循环200圈后，比容量仍有107.21 mAh g-1，容量保持率为93.2%；2 C电流密度下，首圈放电比容量92.74 mAh g-1，循环200圈后，比容量为79.02 mAh g-1，容量保持率为85.2%，循环性能稳定。

采用固相法合成了Na2.4Fe1.8(SO4)3正极材料，并利用导电聚合物PEDOT与Na2.4Fe1.8(SO4)3复合，合成了Na2.4Fe1.8(SO4)3/PEDOT复合材料，探索了导电聚合物(PEDOT)添加量对Na2.4Fe1.8(SO4)3/PEDOT电化学性能的影响。

结果表明：导电聚合物添加量40%的Na2.4Fe1.8(SO4)3/PEDOT正极材料，在0.05 C电流密度下放电比容量最高，达到118.1 mAh g-1。

大学英语六级模拟试卷555(题后含答案及解析)题型有：1. Writing 2. Reading Comprehension (Skimming and Scanning) 3. Listening Comprehension 4. Reading Comprehension (Reading in Depth) 5. Cloze 8. TranslationPart I Writing (30 minutes)1．For this part, you are allowed 30 minutes to write a short essay entitled Should We Abandon Nuclear Power? You should write at least 150 words according to the outline given below.1．有人认为应该放弃核能2．有人则认为应该坚持发展核能3．我的看法Should We Abandon Nuclear Power?正确答案：Should We Abandon Nuclear Power? (1) There is an ongoing debate about whether nuclear power should be abandoned. (2) Proponents believe that nuclear power poses many threats to people and the environment, (3) such as the problem of storage of radioactive nuclear waste, as well as health risks and environmental damage from uranium mining. (2) They also contend that there have been serious nuclear accidents, (3) e.g. Japan’s 2011 nuclear disaster. (4) Opponents, however, claim that nuclear power is a sustainable energy source that reduces carbon emissions and increases energy security by (5) decreasing dependence on imported energy sources. (4) They argue that problems like the risks of storing waste are small and can be further reduced by using the latest technology in newer reactors. (4) Besides, the operational safety record of nuclear power plants has been excellent compared to the other major kinds of power plants. (6) In my opinion, nuclear power remains a perfect alternative of fossil fuel and shouldn’t be abandoned due to some minor problems. After all, nuclear power has caused far fewer accidental deaths. Energy production from coal, natural gas, and hydropower has caused far more deaths due to accidents.解析：(1)开篇点题(2)说明支持放弃核能者的两个理由(3)举例更有说服力(4)说明反对放弃核能者的三个理由，有针对性(5)亮点表达：“减少对进口能源的依赖”(6)给出自己的看法。

上海市各高中名校2019届高三英语题型分类专题汇编--阅读理解C篇学校:___________姓名：___________班级：___________考号：___________一、阅读选择Public distrust of scientists stems in part from the blurring of boundaries between science and technology, between discovery and manufacture. Most governments, perhaps all governments, justify public expenditure on scientific research in terms of the economic benefits the scientific enterprise has brought in the past and will bring in the future. Politicians remind their voters of the splendid machin es “our scientists” have invented, the new drugs to relieve old disorders, and the new surgical equipment and techniques by which previously unmanageable conditions may now be treated and lives saved. At the same time, the politicians demand of scientists that they tailor their research to “economics needs”, and that they award a higher priority to research proposals that are “near the market” and can be translated into the greatest return on investment in the shortest time. Dependent, as they are, on politicians for much of their funding, scientists have little choice but to comply. Like the rest of us, they are members of a society that rates the creation of wealth as the greatest possible good. Many have reservations, but keep them to themselves in what they perceive as a climate hostile to the pursuit of understanding for its own sake and the idea of an inquiring, creative spirit.In such circumstances no one should be too hard on people who are suspicious of conflicts of interest. When we learn that the distinguished professor assuring us of the safety of a particular product holds a consultancy with the company making it, we cannot be blamed for wondering whether his fee might conceivably cloud his professional judgment. Even if the professor holds no consultancy with any firm, some people may still distrust him because of his association with those who do, or at least wonder about the source of some of his research funding.This attitude can have damaging effects. It questions the integrity of individuals working in a profession that prizes intellectual honesty as the supreme virtue, and plays into the hands of those who would like to discredit scientists by representing them as corruptible. This makes it easier to dismiss all scientific pronouncements, but especially those made by the scientists who present themselves as “experts”. The scientist most likely to understand the safety of a nuclear reactor, for example, is a nuclear engineer, and a nuclear engineer is most likely to be employedby the nuclear industry. If a nuclear engineer declares that a reactor is unsafe, we believe him, because clearly it is not to his advantage to lie about it. If he tells us it is safe, on the other hand, we distrust him, because he may well be protecting the employer who pays his salary. 1．What is the chief concern of most governments when it comes to scientific research? A．The reduction of public expenditure. B．Quick economic returns.C．The budget for a research project. D．Support from the voters.2．Why won’t scientists complain about the government’s policy concerning scientific research?A．They know it takes patience to win support from the public.B．They realize they work in an environment hostile to the free pursuit of knowledge. C．They think compliance with government policy is in the interests of the public. D．They are accustomed to keeping their opinions to themselves.3．According to the author, people are suspicious of the professional judgment of scientists because ______.A．some of them do not give priority to intellectual honestyB．sometimes they hide the source of their research fundingC．they could be influenced by their association with the project concernedD．their pronouncements often turn out to be wrong4．Why does the author say that public distrust of scientists can have damaging effects? A．Scientists themselves may doubt the value of their research findings.B．People will not believe scientists even when they tell the truth.C．It makes things difficult for scientists to seek research funds.D．It may wear out the enthusiasm of scientists for independent research.What is the single most effective way to reduce greenhouse-gas emissions? Go vegetarian? Replant the Amazon? Cycle to work? None of the above. The answer is: makeair-conditioners radically better. On one calculation, replacing refrigerants(制冷剂) that damage the atmosphere would reduce total greenhouse gases by the equivalent of 90bn tonnes of CO2 by 2050. Making the units more energy-efficient could double that.Air-conditioning is one of the world’s great overlooked industries. Automobiles andair-conditioners were invented at roughly the same time, and both have had a huge impact on where people live and work. Unlike cars, though, air-conditioners have drawn little criticismfor their social impact, emissions or energy efficiency. Most hot countries do not have rules to govern their energy use.Yet air-conditioning has done quite a lot things to benefit humankind. It has transformed productivity in the tropics and helped turn southern China into the workshop of the world. In Europe, its spread has pushed down heat-related deaths ten times less than what it was in 2003, when 70,000 people, most of them elderly, died in a heatwave. For children, air-conditioned classrooms and dormitories are associated with better grades at school.Environmentalists who call air-conditioning “a luxury we cannot afford” have half a point, however. In the next ten years, as many air-conditioners will be installed around the world as were put in between 1902 (when air-conditioning was invented) and 2005. Until energy can be produced without carbon emissions, these extra machines will warm the world. At the moment, therefore, air-conditioners create a vicious cycle. The more the earth warms, the more people need them. But the more there are, the warmer the world will be.Cutting the impact of cooling requires three things (beyond turning up the thermostat(温度调节器) to make rooms less Arctic). First, air-conditioners must become much more efficient. The most energy-efficient models on the market today consume only about one-third as much electricity as average ones. Minimum energy-performance standards need to be raised, or introduced in countries that lack them altogether, to push the average unit’s performance closer to the standard of the best.Next, manufacturers should stop using damaging refrigerants. One category of these, hydrofluorocarbons, is over 1,000 times worse than carbon dioxide when it comes to trapping heat in the atmosphere. An international deal to phase out these pollutants, called the Kigali amendment, will come into force in 2019. Foot-draggers should approve and implement it; America is one country that has not done so.Last, more could be done to design offices, malls and even cities so they do not need as many air-conditioners in the first place. More buildings should be built with overhanging roofs or balconies for shade, or with natural air-circulation. Simply painting roofs white can help keep temperatures down.Better machines are necessary. But cooling as an overall system needs to be improved if air-conditioning is to fulfil its promise to make people healthier, wealthier and wiser, without too high an environmental cost. Providing indoor sanctuaries of air-conditioned comfort need not come at the expense of an overheating world.5．Why does the author think air-conditioning is an overlooked industry？A．Because many hot countries haven’t put the energy-controlling rules into force. B．Because it has caused the same impact on people’s life and work a s automobiles have. C．Because it has brought great economic, physical, and educational benefits to humans. D．Because it doesn’t get the due criticism for its environmental impact as automobiles do. 6．What can we learn from Paragraph 4?A．The price of air-conditioning will go up due to the large demand for it.B．A high environmental cost will come along with the air-conditioning service. C．Environmentalists are expecting extra machines which can warm the world. D．Governments partially agree that air-conditioning is a luxury we cannot afford.7．With regard to the measures to cut the impact of cooling, which of the following statements is TRUE?A．Manufacturers should only stop using hydrofluorocarbons.B．People should avoid turning up the air-conditioners to have cool rooms on hot days. C．People should adopt more environmentally-friendly materials when designing buildings. D．Governments should give a green light to the agreement on eliminating the pollutants. 8．The author writes this passage to _______.A．arouse people’s attention to the global warming.B．appeal for the global joint efforts to combat global warming.C．give credit to air-conditioning for its great contributions to humansD．offer a new perspective on how to reduce greenhouse gasses emissionsD iscoveries in science and technology are thought by “untaught minds” to come in blinding flashes or as the result of dramatic accidents. Sir Alexander Fleming did not, as legend would have it, look at the mold (霉) on a piece of cheese and get the idea for penicillin there and then. He experimented with antibacterial substances for nine years before he made his discovery. Inventions and innovations almost always come out of tough trial and error. Innovation is like soccer; even the best players miss the goal and have their shots blocked much more frequently than they score.The point is that the players who score most are the ones who take most shots at the goal—and so it goes with innovation in any field of activity. The prime difference between innovation and others is one of approach. Everybody gets ideas, but innovators workconsciously on theirs, and they follow them through until they prove practicable or otherwise. What ordinary people see as fanciful abstractions, professional innovators see as solid possibilities.“Creative thinking may mean simply the realization that there’s no particular goodness in doing things the way they have always been done.” Wrote Rudolph Flesch, a language authority. This accounts for our reaction to seemingly simple innovations like plastic garbage bags and suitcases on wheels that make life more convenient: “How come nobody thought of that before?”The creative approach begins with the proposal that nothing be as it appears. Innovators will not accept that there is only one way to do anything. Faced with getting from A to B, the average person will automatically set out on the best-known and apparently simplest route. The innovator will search for alternate courses, which may prove easier in the long run and are sure to be more interesting and challenging even if they lead to dead ends. Highly creative individuals really do march to a different drummer.9．What does the author probably mean by “untaught mind” in the first paragraph?A．An individual who often comes up with new ideas by accident.B．A person who has had no education.C．A citizen of a society that restricts personal creativity.D．A person ignorant of the hard work involved in experimentation.10．According to the author, what differs innovators from non-innovators?A．The way they present their findings. B．The way they deal with problems. C．The intelligence they possess. D．The variety of ideas they have. 11．The phrase “march to a different drummer” (the last line of the passage) suggests that highly creative individuals are ________.A．unwilling to follow common ways of doing thingsB．diligent in pursuing their goalsC．concerned about the advance of societyD．devoted to the progress of science12．The most suitable title for this passage might be ________.A．The Relation Between Creation and DiligenceB．To Be a Creative Expert in the Study of Human CreativityC．What Are So Special about Creative IndividualsD．Discoveries and InnovationTo be really happy and really safe, one ought to have at least two or three hobbies, and they must all be real. It is no use starting late in life to say “I will take an interest in this or that.” Such an attempt only aggravates the strain of mental effort. A man may acquire great knowledge of topics unconnected with his daily work, and yet hardly get any benefit or relief. It is no use doing what you like; you have got to like what you do.Broadly speaking, human beings may be divided into three classes: those who are toiled to death, those who are worried to death and those who are bored to death. It is no use offering the manual labourer, tired out with a hard week’s sweat and effort, the chance of playing a game of football or baseball on Saturday afternoon. It is no use inviting the politician or the professional or business man, who has been working or worrying about serious things for six days, to work or worry about trifling things at the weekend. As for the unfortunate people who can command everything they want, who can gratify every caprice and lay their hands on almost every object of desire — for them a new pleasure, a new excitement is only an additional satiation. In vain they rush frantically round from place to place, trying to escape from the avenging boredom by mere clatter and motion. For them discipline in one form or another is the most hopeful path.It may also be said that rational, industrious, useful human beings are divided into two classes: first, those whose work is work and whose pleasure is pleasure; and secondly, those whose work and pleasure are one. Of these the former are the majority. They have their compensations. The long hours in the office or the factory bring with them as their reward, not only the means of sustenance, but a keen appetite for pleasure even in its simplest and most modest forms. But Fortune’s favoured children belong to the second class. Their life is a natural harmony. For them the working hours are never long enough. Each day is a holiday, and ordinary holidays when they come are grudged as enforced interruptions in an absorbing vocation. Yet to both classes the need of an alternative outlook, of a change of atmosphere, of a diversion of effort, is essential. Indeed, it may well be that those whose work is their pleasure are those who most need the means of banishing it at intervals from their mind.13．What does “are toiled” in the 2nd paragraph mean?A．have hobbies B．feel pleasedC．work very hard D．are busy14．Which is NOT true based on the first two paragraphs?A．Being late in life to attempt to cultivate hobbies adds to mental stress.B．Great knowledge irrelevant to the daily work can’t guarantee benefit.C．Those tired out for a week’s labour are reluctant to play football on weekends. D．Unfortunate people need discipline to help them build up hope.15．For those whose work is work and whose pleasure is pleasure, they ______.A．are very willing to work long hours in the office or the factoryB．earn a large amount of money due to their hard work for a long timeC．are keen to enjoy the pleasure when they are off dutyD．usually enjoy themselves in the simplest and most modest forms16．Which statement will the author agree with according to the 3rd paragraph?A．The first class are lazy and the second class are bound to succeed.B．The second class never need holidays because their life is harmonious.C．The minority are more favoured by fortune because they never stop working.D．One really needs alternation for a change in order to work better.Ladies and gentlemen,I feel that this award was not made to me as a man, but to my work - a life's work in the agony（痛苦）and sweat of the human spirit. But I would like to use this moment as a climax from which I might be listened to by the young men and women already dedicated to the same agony and sweat, among whom is already that one who will someday stand here where I am standing.Our tragedy today is a general and universal physical fear so long sustained by now that we can even bear it. Because of this, the young man or woman writing today has forgotten the problems of the human heart in conflict with itself which alone can make good writing because only that is worth writing about, worth the agony and the sweat.He, the writer, must learn them again. He must teach himself that the worst of all things is to be afraid; and, teaching himself that, forget it forever, leaving no room in his workshop for anything but the old truths of the heart, the old universal truths lacking which any story is short-lived and doomed - love and honor and pity and pride and sympathy and sacrifice. Until he does so, he labors under a curse（诅咒）. He writes not of love but of desire, of defeats in which nobody loses anything of value, of victories without hope and, worst of all, without pity or sympathy. His griefs grieve on no universal bones, leaving no scars. He writes not of theheart but of the glands（腺体）.Until he relearns these things, he will write as though he stood among and watched the end of man. I decline to accept the end of man. It is easy enough to say that man is immortal simply because he will endure. I refuse to accept this. I believe that man will not merely endure: he will prevail. He is immortal, not because he alone among creatures has an inexhaustible voice, but because he has a soul, a spirit capable of sympathy and sacrifice and endurance. The poet's, the writer's, duty is to write about these things. It is his privilege to help man endure by lifting his heart, by reminding him of the courage and honor and hope and pride and sympathy and pity and sacrifice which have been the glory of his past. The poet's voice need not merely be the record of man, it can be one of the pillars to help him endure and prevail.17．The word “that” in the 2nd paragraph probably means ______.A．the agony and sweat of the human spiritB．the general and universal physical fearC．the sustenance and endurance for a long timeD．the human heart in conflict with itself18．According to the speaker, the old truths of the heart are so important that ______. A．they are love, honor, pity, pride, sympathy and sacrificeB．they prolong a writer’s life and protect him from cursesC．they are the soul of a real and powerful piece of writingD．they can effectively stop the trend towards the end of man19．How can poets / writers help man endure and prevail?A．By inspiring man with his past glories through words.B．By helping man endure the end through endless voices.C．By recording sympathy, sacrifice and endurance in his soul.D．By building spiritual pillars through immortal hearts.20．The speaker may probably agree that ______.A．the award was not fair because his life was too painfulB．young writers now are too fearful to bear the agony and sweatC．the biggest obstacle to good writing is the writer’s fearD．writing about man’s soul signals his final prevalenceBy now you’ve probably heard about the “you’re not special” speech, when Englishteacher David McCullough told graduating seniors at Wellesley High School: “Do not get the idea you’re anything special, because you’re not.” Mothers and fathers present at the ceremony — and a whole lot of other parents across the Internet —took issue with McCullough’sego-puncturing words. But lost in the uproar was something we really should be taking to heart: our young people actually hav e no idea whether they’re particularly talented or accomplished or not. In our eagerness to elevate their self-esteem, we forgot to teach them how to realistically assess their own abilities, a crucial requirement for getting better at anything from math to music to sports. In fact, it’s not just privileged high-school students: we all tend to view ourselves as above average.Such inflated self-judgments have been found in study after study, and it’s often exactly when we’re least competent at a given task that we rate our performance most generously. In a 2006 study published in the journal Medical Education, for example, medical students who scored the lowest on an essay test were the most charitable in their self-evaluations, while high-scoring students judged themselves much more stringently. Poor students, the authors note, “lack insight” into their own inadequacy. Why should this be? Another study, led by Cornell University psychologist David Dunning, offers an enlightening explanation. People who are i ncompetent, he writes with coauthor Justin Kruger, suffer from a “dual burden”: they’re not good at what they do, and their very ineptness prevents them from recognizing how bad they are.In Dunning and Kruger’s study, subjects scoring at the bottom of the heap on tests of logic, grammar and humor “extremely overestimated” their talents. Although their test scores put them in the 12th percentile, they guessed they were in the 62nd. What these individuals lacked (in addition to clear logic, proper grammar an d a sense of humor) was “metacognitive skill”: the capacity to monitor how well they’re performing. In the absence of that capacity, the subjects arrived at an overly hopeful view of their own abilities. There’s a paradox here, the authors note: “The skill s that engender competence in a particular domain are often the very same skills necessary to evaluate competence in that domain.” In other words, to get better at judging how well we’re doing at an activity, we have to get better at the activity itself.There are a couple of ways out of this double bind. First, we can learn to make honest comparisons with others. Train yourself to recognize excellence, even when you yourself don’t possess it, and compare what you can do against what truly excellent individuals are able to accomplish. Second, seek out feedback that is frequent, accurate and specific. Find a critic whowill tell you not only how poorly you’re doing, but just what it is that you’re doing wrong. As Dunning and Kruger note, success indicates to us that everything went right, but failure is more ambiguous: any number of things could have gone wrong. Use this external feedback to figure out exactly where and when you screwed up.If we adopt these strategies — and most importantly, teach them to our children — they won’t need parents, or a commencement（毕业典礼）speaker, to tell them that they’re special. They’ll already know that they are, or have a plan to get that way.21．Which can be the best title of this passage?A．Special or Not? Teach Kids To Figure It OutB．Let's Admit That We Are Not That SpecialC．Tips On Making Ourselves More SpecialD．Tell The Truth: Kids Overestimate their Talents22．The author thinks the real problem is that ______.A．we don't know whether our young people are talented or notB．young people don't know how to assess their abilities realisticallyC．no requirement is set up for young people to get betterD．we always tend to consider ourselves to be privileged23．Which is NOT mentioned about poor students according to the passage?A．They usually give themselves high scores in self-evaluations.B．They tend to be unable to know exactly how bad they are.C．They are intelligently inadequate in tests and exams.D．They lack the capacity to monitor how well they are performing.24．We can infer from the passage that those high-scoring students ______.A．know how to cultivate clear logic and proper grammarB．don't know how well they perform due to their stringent self-judgementC．don't view themselves as competent because they know their limitsD．tend to be very competent in their high-scoring fields.25．The strategies of becoming special suggest that ______.A．we need internal honesty with ourselves and external honesty from othersB．the best way to get better is to carefully study past success and failureC．through comparison with others, one will know where and when he failsD．neither parents nor a commencement speaker can tell whether one is specialTraditional surgical procedures require surgeons to make large incisions(伤口) in a p atient’s body in order to gain access to the internal organs. It was once common for heart surgeons, who perform highly specialized and complex procedures, to make long incisions in a patient’s chest and then split the breastbone to reach the heart. Patien ts who undergo surgery are often at the risk of infection, as bacteria can infect the cut in the skin. In addition, there is often a lengthy recovery period.A surgical technique known as “keyhole surgery” has become more common in recent years. In general, the surgeon will make a couple of small incisions around the area where the operation is going to be performed. Tubes are pushed into the holes, and a tiny camera, which is called an endoscope, is put into the body. The camera is attached to a large monitor screen that is positioned so that the doctor can see it while he performs the operation. In addition to the camera, doctors also push their tiny surgical instruments through the tubes. The awkward part of keyhole surgery is that it is counterintuitive; that is to say, if a surgeon wants to move the tool to the left, he or she must push it to the right.Other advancements in technology are also being used today in the OR (operation room).A new machine called the “da Vinci Surgical System” has been teste d in hospitals in the U.S.. Unlike keyhole surgery, the da Vinci’s robot’s moving parts are designed to imitate the natural hand and wrist movement of a surgeon, thus providing better control and sensitivity. The system is controlled by a surgeon from a console(控制台). Sitting at a console a few feet from the patient, the surgeon can perform an operation by holding and moving highly sensitive pads that enable him or her to control the instruments. The area of the body on which the surgeon is working is enlarged on a screen, which is attached to the console. This gives surgeons a realistic three-dimensional view of the area — similar to what they would see during a traditional surgical procedure.Although the da Vinci Surgical System is undergoing some trials for some procedures, it has been welcomed as revolutionary by many surgeons. Patients with serious illnesses must still undergo major surgery, but the smaller incisions and less invasive procedures typically mean that a shorter recovery time is needed. In s ome cases, the patient’s stay in the hospital has been cut in half when the da Vinci Surgical System was used. On the downside, some operations have taken up to fifty minutes longer because surgeons are inexperienced at using the new technology. As surgeons become more familiar with the machines, the time needed forsurgical procedures is likely to decrease.26．What can be learned about the traditional surgery according to the passage?A．The cost of the traditional surgery is very high.B．It often leaves a large wound in a person’s body.C．Long incisions are made in a patient’s chest.D．The incision is often infected after the operation.27．Which of the following is one DISADV ANTAGE of keyhole surgery?A．It requires the use of long, thin tools and a tiny camera.B．The doctor can not view the inside of the patient’s body clearly.C．The direction in which a doctor moves the surgical tools is reversed.D．An endoscope has to be inserted into the patient’s body in advance.28．The da Vinci Surgical System differs from keyhole surgery in that _______. A．requires that a surgeon make more small incisions on a patientB．reduces the amount of time it takes to perform a surgical procedureC．allows the surgeon to use the surgical instruments more sensitivelyD．eliminates the need for surgeons to make large incisions on patients29．The passage mainly tells the reader ________.A．the challenges brought about by new technologyB．the benefits and drawbacks of the da Vinci Surgical SystemC．the reflections on the development in medical scienceD．the application of new technologies in modern surgeryThe study of psychology is facing a crisis. The Research Excellence Framework(the Ref) has led to a research culture which is holding back attempts to stabilize psychology in particular, and science in general. The Ref encourages universities to push for groundbreaking, novel, and exciting research in the form of 4* papers, but it does not reward the efforts of those who replicate(复制) studies.The point of replicating a study is to test whether a statistically significant result will appear again if the experiment is repeated. Of course, a similar result may not appear – casting into question the validity(有效性) of the results from the first experiment.Last year, the Open Science Collaboration attempted to replicate 100 studies from highly ranked psychological journals. While 97% of the original studies had a statistically significant。

the electrical conductivity wasconductedThe electrical conductivity is a fundamental property that describes how well a material conducts electricity. It is a crucial parameter in various applications, ranging from power transmission to electronic devices. Therefore, it is essential to measure the electrical conductivity accurately.The measurement of electrical conductivity is typically done using a conductivity meter. This instrument applies a constant voltage across two electrodes immersed in the material being tested. The current that flows through the material is then measured, and the electrical conductivity is calculated based on the applied voltage and the measured current.The accuracy of the measurement depends on several factors. Firstly, the electrodes must be clean and free from corrosion or deposits. Any fouling on the electrodes can lead to measurement errors. Therefore, it is essential to clean the electrodes regularly or to use disposable electrodes for each measurement.Secondly, the temperature of the material being tested can affect the electrical conductivity. Many materials have their electrical conductivity optimum at certain temperatures. Therefore, it is essential to control the temperature of the material during the measurement. This can be achieved using temperature-controlled chambers or by immersing the electrodes in a temperature-controlled bath.Thirdly, the calibration of the conductivity meter is crucial for accurate measurements. Regular calibration using standards of known conductivity can ensure that the instrument is accurate and reliable. It is recommended to perform calibration at least once a year or after any significant instrument repair or modification.In conclusion, the measurement of electrical conductivity is crucial for various applications. It requires clean electrodes, controlled temperatures, and regularcalibration of the conductivity meter to ensure accurate and reliable measurements.。

Role of Heat Transfer and Thermal Conductivity in the Crystallization Behavior of Polypropylene-Containing Additives:A Phenomenological ModelS.Radhakrishnan,Pradip S.SonawanePolymer Science&Engineering,National Chemical Laboratory,Pune411008,IndiaReceived5June2002;accepted5November2002ABSTRACT:The thermal conductivity of afiller and the thermal conductivity of a composite made from thatfiller influence the heat-transfer process during melt processing. The heat-transfer process from the melt to the mold wall becomes an important factor in developing the skin–core morphology.These aspects were examined in this study. The thermal conductivity of polypropylene–filler compos-ites was estimated with a standard model for variousfillers such as calcium carbonate,talc,silica,wollastonite,mica, and carbonfibers.The rate of cooling under given condi-tions,including the melting temperature,mold wall temper-ature,mass of the composite,andfiller content,was esti-mated with standard heat-transfer equations.The time to attain the crystallization temperature for polypropylene was evaluated with a regression method with differential tem-perature steps.The crystallization curves were experimen-tally determined for the differentfillers,and from them,the induction period for the onset of crystallization was esti-mated.These observations were correlated with the ex-pected trends from the aforementioned formalism.The ex-cellentfit of the curves showed that in all these cases,the thermal conductivity of thefiller and composite played a dominant role in controlling the onset of the crystallization process.However,the nucleation effects became important in the later stages after the crystallization temperature was attained.©2003Wiley Periodicals,Inc.J Appl Polym Sci89: 2994–2999,2003Key words:poly(propylene)(PP);crystallization;thermal properties;fillers;additivesINTRODUCTIONPolymers are generally used with different types of additives,such as stabilizers,processing aids,coloring agents,andfillers.In the polymer processing industry, many types offillers are incorporated into resins for different reasons,including improvements in the me-chanical properties,color matching,surfacefinishing, gloss,and cost reduction.1–3Polypropylene(PP)has drawn considerable attention in recent years because it can be modified by additives andfillers to obtain properties that are comparable to those of engineering plastics.4,5These various additives are known to affect the crystallization behavior of the polymer.Studies have been reported by several groups,including our own,on the crystallization behavior of PPs containing calcium carbonate,calcium sulfate,talc,mica,and wollastonite.In most of these studies,the emphasis was placed on the nucleation,preferential growth,and so forth.6–10However,it is well known that the rate of cooling plays an important role in determining the crystallinity and/or morphology obtained in thefinal product made by melt processing.11Because the ther-mal conductivity of thefiller and that of the composite containing thatfiller are important factors governing the heat-transfer process,we felt that a systematic investigation into the role of thermal conductivity in the crystallization of PPs containing differentfillers would lead to a better understanding of these phe-nomena.However,until now,no work has been re-ported on developing the corelationships of the ther-mal conductivity,induction time,cooling time,crys-tallinity value,and so forth.Furthermore,because the crystal structure and the morphology are responsible for the properties of thefinal product,a knowledge and understanding of the crystallization process are important for designing the material for a given prod-uct.This article addresses these issues,and an attempt has been made to correlate the different parameters with the help of a phenomenological model described here.PHENOMENOLOGICAL MODEL Polymers are usually processed in industry by either injection molding or extrusion techniques.The crys-tallization of a polymer from the melt takes place while it cools in the mold or as it extrudes out in the cooling zone(usually a water trough).During this step,the heat from the melt has to be transferred to the surroundings.In the injection-molding and compres-Correspondence to:S.Radhakrishnnan(srr@che.ncl.res.in). Journal of Applied Polymer Science,Vol.89,2994–2999(2003)©2003Wiley Periodicals,Inc.sion-molding processes(considered for simplicity), the polymer is in contact with the mold,and the heat is conducted away from the melt by the mold walls. Because the polymer(melt or solid)has a quite low thermal conductivity(ca.0.01W/m),the heat transfer from the central portion of the melt is much slower than that at the surface.This leads to uneven crystal-lization rates through the polymer,giving rise to a skin–core morphology,as indicated in Figure1.Such morphological features have been reported previously by some authors,but they have not been correlated with the rate of heat transfer or the thermal conduc-tivity.12,13The addition offillers to the polymer leads to large changes in the thermal conductivity,giving rise to faster cooling.Therefore,this aspect isfirst considered in this formalism.The thermal conductivity(K)of polymers contain-ingfillers can be estimated by different models devel-oped for such composites,including the simple rule of mixtures,series/parallel models,the Hashin–Schtrik-man model,the Hamilton–Crosser model,and Niels-en’s model.14,15Among these,Nielsen’s model16is known to be most accurate in predicting the values of K.Therefore,it was used here.According to this model,the K value of a composite is given byK c K p ϭ͓1ϩ͑AϪ1͒B␾͔͑1Ϫ␺B␾͒(1)␺ϭ1ϩ͑1Ϫ␾max͒␾␾max2(2)Bϭ͑K f/K pϪ1͒͑K f/K pϩAϪ1͒(3)where␾is thefiller concentration(volume fraction);A and B are parameters;␾max is the maximumfiller packing for a given geometry;and the subscripts c,f, and p give the corresponding values for the composite,filler,and polymer,respectively.The coefficient A de-pends on the geometry and orientation of thefiller particles.Nielsen provided values of A for a wide range of commonfiller types.For sphericalfiller par-ticles,A is2.5.The values used for the parameters A and␾max in Nielsen’s equation are2.5and0.637,re-spectively.The values of K,the specific heat(C p),and ␾max for thefillers used are indicated in Table I.PP byitself has K and C p values of0.23W/mK and0.427 cal/g°C,respectively.17The K value for each of the compositions was estimated with these values in eqs.(1)–(3).These are indicated in Tables II and III.The rate of cooling of a molten composite can be estimated as follows.Initially,when the melt comes in contact with the external mold wall surface,the heat is transferred according to the Fourier equation for un-steady heat transfer in one dimension(x).A heat bal-ance for the object being cooled then gives the amount of heat transferred in the time interval(⌬t)as follows:⌬Q⌬tϭͫKA1⌬T⌬xͬ⌬Qϭ͑mC p⌬T͒(4)where⌬T is the temperature difference between the melt and the external medium,A1is the cross-section area,⌬x is the thickness of the sample,and m is the mass.It is assumed that the heat,once transferred to the wall,is rapidly conducted away(the metalbeingFigure1Schematic diagram of polymer melt cooling in themold with the formation of a skin layer.TABLE IReported Standard Values for K and C pfor Different Fillers21–24Filler typeK(W/mK)C p(cal/g.°C)⌽maxWollastonite0.8240.240.62Silica 1.490.190.70Glassfiber 1.170.1970.42Talc 2.090.2030.45Mica 2.50.2070.38Calcium carbonate 2.70.210.80Carbonfiber70.20.40TABLE IIDependence of the Induction Period on the K Values ofPP with Fillers at10wt%Composition(10wt%)K a(W/mK)Induction period b(s)Pure PP0.23263PPϩwollastonite0.263191PPϩglassfiber0.271183PPϩsilica0.277138PPϩtalc0.285135PPϩmica0.286140PPϩcalciumcarbonate0.286130PPϩcarbonfiber0.292108a Estimated from eqs.(1)–(3).b Samples isothermally crystallized at115°C from thestarting melt at200°C.HEAT TRANSFER AND THERMAL CONDUCTIVITY29951000times better as a conductor than the polymer). The cooling curve(the temperature at any given time) was generated with a⌬t value of1min.Equation(4) was used for estimating the temperature difference for the initial step,which gave the temperature attained by the melt after⌬t,which was then subsequently used for the next step and so on.The values of K and C p were those estimated for that type offiller and composition with the Nielsen model,which was de-scribed previously.To estimate the induction time for the onset of crys-tallization,we assumed that the melt had to reach the temperature at which maximum crystallization was observed for that polymer.Therefore,a line through this temperature was drawn parallel to the time axis on the cooling curve,and the common points gave the induction times for crystallization for that composi-tion.The nucleation effects were not taken into con-sideration,but they are discussed later in the article.EXPERIMENTALPP(Indothane,SM85N,MFI8-12,IPCL,India)was made into afine powder form by the precipitation of its solution followed by thorough washing with ace-tone and drying for24h in vacuo;this yielded the pure form of the PP powder.To study the crystallization behavior of PPfilled with different types offillers(e.g., wollastonite,silica,glassfiber,talc,calcium carbonate, mica,and carbonfiber),we mixed the additive,avail-able in a particulate form,in a desired quantity with PP powder in an agate pestle and mortar and thor-oughly ground the mixture for30min.The samples were subjected to isothermal melt crystallization on the hot stage of a polarizing microscope(melting tem-peratureϭ200°C,crystallization temperature ϭ115°C).The crystallization behavior was investi-gated by the continuous recording of the growth of spherulites and the intensity of transmitted light in the cross-polar mode of the optical polarizing microscope (Leitz,Germany)coupled to an image analyzer system (VIDPRO32,Leading Edge,Australia).The details of these experiments have been described else-where.18–20Care was taken to avoid any loss of time in the transfer of the sample from the hot plate to the microscope stage.From the isothermal crystallization curve,the induction period,crystallization half-time, growth rate,and so forth were evaluated.RESULTS AND DISCUSSIONThe cooling curves for PP melts containing different fillers(10%),for which K values were estimated with the aforementioned phenomenological model,are shown in Figure2.The melting temperature was as-sumed to be200°C,the mold wall temperature was 25°C,the specimen thickness was3mm,the cross-section area was1cm2,and⌬t was1min.The K and C p values in Table I were used in eq.(4)for the calculations with the same unit system.The density of PP was taken to be0.95g/cm3.The higher thermal conductivity of thefiller produced faster cooling,as expected from the model.The induction time,esti-mated with the method outlined earlier in this article, is shown in Figure3(10%filler concentration).The time required for the melt to attain the temperature for the onset of crystallization decreased with an increase in the thermal conductivity of thefiller present in the composite.Therefore,we expected that the induction period for the crystallization would also depend on the thermal properties of thefiller.The results of experiments on the isothermal crys-tallization kinetics,carried out at120°C,are depicted in Figure4for PPs containing different additives (10%).The onset of crystallization was found to de-pend on the type of additive.From these curves,the induction time was deduced from the time at which the onset of crystallization was observed,and it was compared with the expected value of the cooling time, which was determined for each composition with the aforementioned theory.Figure5compares these val-ues with those estimated from the melt cooling curves described earlier in this article.We have depicted the data in normalized scales with respect to the original PP to avoid any errors arising from sample-to-sample variations and PP grades,which may be different from those reported in the literature.Figure5shows that the overall trend for the experimentally observed data follows the same trend expected from the theory. There was some difference in the actual values:the experimentally noted induction time in some cases was lower than that expected from thermal conduc-tion.This might be due to nucleation effects,whichTABLE IIIVariation of K and Skin-Layer Thickness in PP with␾Composition (wt%)K a(W/mK)Skin-layer thickness b(mm)PP with5%TC0.2530.3810%TC0.2850.4120%TC0.3450.4430%TC0.4360.5440%TC0.5730.57PP with5%CC0.2570.4110%CC0.2860.4820%CC0.3540.5630%CC0.4540.5840%CC0.6120.64TCϭtalc;CCϭcalcium carbonate.a Estimated from Nielsen’s model with eqs.(1)–(3).b Data reported for injection-molded3-mm-thick samples(refs.12and13).2996RADHAKRISHNNAN AND SONAWANEFigure 2Effect of the thermal conductivity of the additive in the polymer melt on its cooling rate:(A)pure PP,(B)PP with wollastonite,(C)PP with silica,(D)PP with talc,(E)PP with mica,(F)PP with calcium carbonate,and (G)PP with carbon fiber.The filler concentration was 10wt %in allcases.Figure 3Variation of the induction time derived from the cooling curves with respect to the thermal conductivity of PPs filled with different fillers at 10wt %.HEAT TRANSFER AND THERMAL CONDUCTIVITY 2997depended on the filler–polymer interaction,the nucle-ating efficiency of the filler particle,and so forth.The rate of cooling of the melt has a profound effect on the morphology that develops in semicrystalline polymers during processing.For example,during the injection molding of PP,there is a faster cooling rate near the mold walls due to rapid heat transfer than in the central portion of the melt.This leads to uneven crystallization rates,and a skin–core morphology is known to present in final products,especiallythick-Figure 4Isothermal crystallization curves for PPs containing fillers (10wt %):(A)pure PP,(B)PP with silica,(C)PP with talc,(D)PP with calcium carbonate,(E)PP with mica,and (F)PP with carbonfiber.Figure 5Comparison of experimental data and theoretically estimated values for the induction time of crystallization with the thermal conductivity of the PP composite.The solid line has been drawn only as a guide.2998RADHAKRISHNNAN AND SONAWANEwalled items (see Fig.1).To determine the effect of a faster cooling rate on the crystallization process of PPs containing additives,we compiled data for the skin-layer thickness of injection-molded samples of PP with calcium carbonate and talc in Figure 6.The skin-layer thickness depended on the amount of the additive present in each PP sample.These data were redrawn in terms of the thermal conductivity of PP containing a filler,which was estimated with Nielsen’s model (see Table I).This graph clearly indicates the impor-tance of the thermal conductivity of a composite on its crystallization process and the morphology developed in the PP samples containing additives.This can be associated with the fact that a high thermal conduc-tivity filler content leads to better heat transfer and a faster cooling rate,which,in turn,produces greater skin-layer thickness than that of the original polymer.CONCLUSIONSThe crystallization behavior of polymers is dependent on the heat-transfer process from the melt to the sur-roundings (e.g.,quenched air and mold walls).A phe-nomenological model has been developed for estimat-ing the cooling rate for any given polymer with known K and C p values.The addition of fillers to the polymer leads to an increase in the thermal conduc-tivity of the composite,and so faster cooling is ex-pected for such systems.The role of the thermal con-ductivity of the filler/additive in the crystallization behavior of PP has clearly been presented in this arti-cle.The experimental results for PPs containing dif-ferent types of fillers clearly support the aforemen-tioned hypothesis.Also,the reported data on the skin-layer thickness for injection-molded PPs containing talc and calcium carbonate can be understood in terms of this model.References1.Deanin,R.D.;Schott,N.R.Fillers for Reinforcement for Plastics;American Chemical Society:Washington,DC,1974;pp 41and 114.2.Lutz,J.T.,Jr.Thermoplastic Polymer Additives:Theory and Practice;Marcel Dekker:New York,1989;p 255.3.Flick,E.W.Plastic Additives:An Industrial Guide;Noyes Data:Park Ridge,NJ,1993;p 140.4.Karger-Kocsis,J.Polypropylene;Kluwer Academic:Dordrecht,Netherlands,1999;pp 329,519,and 663.5.Van Der Ven,S.Polypropylene and Other Polyolefins;Elsevier:Amsterdam,1990;p 347.6.Vasile,C.;Seymour,R.B.Handbook of Polyolefins;Marcel Dekker:New York,1993;p 681.7.Pukanszky,B.;Tudos,F.;Kelen,T.In Polymer Composites:Proceedings of the Microsymposium on Macromolecules;Sed-lacek,B.,Ed.;de Gruyter:Berlin,1986;p 167.8.(a)Fujiyama,M.;Wakino,T.J Appl Polym Sci 1991,42,2739;(b)Fujiyama,M.;Wakino,T.J Appl Polym Sci 1991,42,2749.9.Khare,A.;Mitra,A.;Radhakrishnan,S.J Mater Sci 1996,31,5691.10.Radhakrishnan,S.;Saujanya,C.J Mater Sci 1998,33,1069.11.Saujanya,C.;Tangarilla,R.;Radhakrishnan,S.Macromol MaterEng 2002,287,272.12.Karger-Kocsis,J.Polypropylene Structure,Blends and Compos-ites;Chapman &Hall:London,1995;p 167.13.(a)Fujiyama,M.;Wakino,T.J Appl Polym Sci 1991,43,57;(b)Fujiyama,M.;Wakino,T.J Appl Polym Sci 1991,43,97.14.Bigg,D.M.Adv Polym Sci 1995,119,1.15.Torquado,S.Rev Chem Eng 1987,4,151.16.Nielsen,L.E.Ind Eng Chem Fundam 1974,13,17.17.Powell,T.;Klemens,H.Thermophysical Properties of Matter;Plenum Publishers:New York,1970;Vol.2,p 943.18.Radhakrishnan,S.;Saujanya,C.J Mater Sci 1998,33,1069.19.Radhakrishnan,S.;Saujanya,C.Polymer 2001,42,6723.20.Radhakrishnan,S.;Saujanya,C.Macromol Mater Eng 2001,286,1.21.Katz,H.S.;Milewski,J.V.Handbook of Fillers for Plastic;VanNostrand Reinhold:New York,1987;p 117.22.Plastic Additives and Modifiers Handbook;Edenbaum,J.,Ed.;Chapman &Hall:London,1996.23.Karian,H.G.Handbook of Polypropylene and PolypropyleneComposites;Marcel Dekker:New York,1999;p 237.24.Buyco,T.Thermophysical Properties of Matter;Plenum Pub-lishers:New York,1970;Vol.3.Figure 6Variation of the skin-layer thickness of injection-molded PPs containing different amounts of fillers:calcium carbonate (top)and talc (bottom).The data are plotted di-rectly in terms of the composite thermal conductivity esti-mated from Nielsen’s equation.HEAT TRANSFER AND THERMAL CONDUCTIVITY 2999。

a rXiv:h ep-ph/57120v221J ul26HUTP-05/A0030UTAP-530RESCEU-10/05Dynamics of Gravity in a Higgs Phase Nima Arkani-Hamed a ,Hsin-Chia Cheng a ,b ,Markus A.Luty a ,c ,d ,Shinji Mukohyama a ,e ,Toby Wiseman a a Jefferson Laboratory of Physics,Harvard University Cambridge,Massachusetts 02138b Department of Physics,University of California Davis,California 95616c Physics Department,Boston University Boston,Massachusetts 02215d Physics Department,University of Maryland College Park,Maryland 20742∗e Department of Physics and Research Center for the Early Universe The University of Tokyo,Tokyo 113-0033,Japan Abstract We investigate the universal low-energy dynamics of the simplest Higgs phase for gravity,‘ghost condensation.’We show that the nonlinear dynam-ics of the ‘ghostone’field dominate for all interesting gravitational sources.Away from caustic singularities,the dynamics is equivalent to the irrota-tional flow of a perfect fluid with equation of state p ∝ρ2,where the fluid particles can have negative mass.We argue that this theory is free fromcatastrophic instabilities due to growing modes,even though the null energy condition is violated.Numerical simulations show that solutions generally have singularities in which negative energy regions shrink to zero size.We exhibit partial UV completions of the theory in which these singularities are smoothly resolved,so this does not signal any inconsistency in the effective theory.We also consider the bounds on the symmetry breaking scale M in this theory.We argue that the nonlinear dynamics cuts offthe Jeans instability of the linear theory,and allows M <∼100GeV.1IntroductionIs general relativity the correct description of gravity at long distances and times? Certainly,there are good reasons for thinking that this is the case.Experimentally, gravity has been probed at distance scales ranging from10−1mm(in short-range force experiments)to at least1014cm(the size of the solar system).Theoretically, general relativity is the unique Lorentz-invariant theory of massless spin2,and its conceptual elegance is beyond question.However,the situation is far less clear on cosmological distance and time scales.Structure formation,galaxy rotation curves and gravitational lensing,and the accelerating expansion of the universe cannot be explained by general relativity coupled to known matter.These anomalous effects are conventionally attributed to‘dark matter’and‘dark energy.’However,given the fact that the observed effects are purely gravitational,it makes sense to ask whether they may have a common origin in a modification of gravity in the infrared.These considerations have led to a revival of interest in consistent infrared modifications of gravity[1,2,3,4,5,6,7].In the present paper,we further investigate the model of Ref.[5],‘ghost conden-sation.’This can be viewed as the universal low-energy dynamics associated with the simplest Higgs phase for gravity,arising when Lorentz symmetry is broken sponta-neously.Breaking of Lorentz symmetry is of course ubiquitous.For example,time-dependentfields in cosmology define a preferred frame.However,these solutions are not the ground state of the theory:they carry energy density and dilute away as the universe expands.Any‘modification of gravity’induced by such solutions becomes relevant only at scales of order the horizon.We are instead interested in the situation where Lorentz symmetry is broken inflat spacetime,allowing nontrivial modification of gravity inside the horizon.This means that the symmetry breaking sector has peculiar properties;in particular,the stress-energy tensor must vanish in the ground state:Tµν =0.(1.1) Spontaneous breaking of Lorentz symmetry gives rise to a gapless scalar excitation analogous to the Nambu-Goldstone bosons that arise from spontaneous breaking of internal symmetries.‘Ghost condensation’gives rise to a single such mode,and is in this sense the minimal model of spontaneous breaking of Lorentz symmetry.We refer to the scalar mode as a‘ghostone boson.’In analogy with the Higgs phase for gauge theory,the ghostone mode mixes with the graviton,modifying gravity in a nontrivial manner.Ref.[5]studied this theory and analyzed the modification of gravity in the weak-field limit.The dynamics is governed by a consistent effective theory defined by the scale M where the symmetry is broken.It was shown that the ghostone mode gives a possible new origin for dark energy and dark matter.Ref.[8]showed that the ghostone mode may also be the inflaton,leading to interesting testable consequences.In the present paper,we further investigate the dynamics of this theory.We show that nonlinearities dominate the dynamics of the ghostone sector for all gravitational sources of interest.In particular,the time scale for the onset of nonlinear dynamics for afixed gravitational source is precisely the infall(or orbit)time associated with the source.Away from singularities,the nonlinear solutions are equivalent to the gradientflow of afluid with equation of stateρ2p=3,we discuss the nonlinear dynamics of the ghost condensate.We discuss the time scales and present thefluid picture.In section4,we show the numerical simulations of the nonlinear evolutions and discuss the resolution of caustic singularities.In section 5,we discuss the bounds of this theory.This includes mass and energy accretion in slow-moving objects,gravitational lensing and energy loss from moving objects. We do not claim to have a complete understanding of the dynamics,so this section is intended to be preliminary and provocative.In section6,we briefly discuss the possibility that ghost condensate may constitute the dark matter.We show that the initial growth of the density perturbations in the linear regime is identical to that of the standard cold dark matter.Whether it can form the correct structure depends on the details of the nonlinear evolution which is left for future investigations.Our conclusions are presented in section7.2Review of the Linear Theory2.1Effective TheoryWhat is a Higgs phase for gravity?It is easiest to answer this question in linearized general relativity,where we expand the metric aboutflat spacegµν=ηµν+hµν(2.1)and keep only terms quadratic in hµν.In this theory,thefields hµνare closely analo-gous to gaugefields with gauge transformation lawδhµν=−(∂µξν+∂νξµ),(2.2)whereξµare the generators of infinitesmal diffeomorphismsxµ→xµ+ξµ.(2.3) We want to consider the case where the time diffeomorphisms generated byξ0are spontaneously broken.This means that time diffeomorphisms are realized nonlinearly in the effective theory containing only the ghostonefield.The minimal model contains a single real ghostonefieldπthat shifts under time diffeomorphisms:δπ=−ξ0.(2.4)Note thatπnaturally has units of time.We now write the most general effective Lagrangian invariant under these symmetries.This contains the Einstein Lagrangian,and additional terms constructed from the invariantsΣ=˙π−1(˙h ij−∂i h0j−∂j h0i+2∂i∂jπ).(2.6)2The leading terms areL eff=L E+M4 12h00 2−α12M2K2+O(π3) .(2.7) (Note that we have built in the fact thatflat space is a solution by not writing any linear terms in the Lagrangian.)In the limit where we turn offgravity,we see that the ghostone mode has dispersion relationα k4ω2=A conventional effective Lagrangian for this theory isL=+1φ=0.This has solutions withφ=nµxµfor any constant 4-vector nµ.If nµis timelike,we can choose the time direction so that the solution isφ=ct.(2.11)This is a solution for any constant c.Atfirst sight it may appear that these are obviously not candidate ground states of the theory,but the situation is actually more subtle.Suppose we expand influctuations about this solutionφ=ct+π.(2.12)Note that under time diffeomorphisms,πtransforms asδπ=−ξ0/c,(2.13)just like the ghostone mode considered above.Expanding the Lagrangian to quadratic order inπ,onefinds that thefluctuations forπhave good time and space kinetic terms.This means that the solution is stable under localfluctuations for any value of c!The reason for this is that the theory has a conserved current associated with the shift symmetryJµ=∂µφ.(2.14)Solutions with c=0have a constant nonzero charge density.Local excitations cannot change the total charge,so configurations with lower energy cannot be reached. However,when we turn on gravity,solutions with c=0will cause the universe to expand,and the charge will dilute away.Lorentz invariance is therefore not broken spontaneously in this theory.Consider instead an effective Lagrangian of the formL eff=M4P(X),X=∂µφ∂µφ.(2.15) Note thatφhas dimensions of length(or time),so that X is dimensionless.This omits only terms with more than one derivative acting onφ,such as(We see that small perturbations are stable provided2c2P′′(c2)+P′(c2)>0,P′(c2)>0.(2.17) (Note that a conventional kinetic term P(X)=+12(X−1).(2.22)Stability in the linearized theory requires higher-derivative terms to give a nonzero spatial kinetic term,for example∆L eff=−αM2φ)2=−αM2αM2M2−,T J∼M2Pl M2ScreeningExponentially fallingPotentialFig.2.A schematic illustration of the screening effect for gauge theories in the Higgs phase.For M<∼10MeV,T J is longer than the lifetime of the universe and there is clearly no constraint from the Jeans instability.2.4Negative EnergyEven for time shorter than the Jeans time scale T J,stability is an issue because the ghostone energy can be negative.Recall that the ground state X=1is the boundary of the stability region.Expanding to higher orders inπ,wefind interaction terms such asL eff=M4 12˙π( ∇π)2+···−α˙π 1/2.(2.27) Quantum-mechanically,there arefluctuations at all length scales.Nonetheless,Ref.[5] showed that there is no quantum instability in the effective theory using a scaling ar-gument.If we scale energy by E→sE,the quadratic kinetic terms are left invariant−1Anti−ScreeningOscillating PotentialFig.3.A schematic illustration of the anti-screening effect for gravity in the Higgs phaseif we scalet→s−1t,(2.28)x→s−1/2 x,π→s1/4π.With this scaling the cubic operator˙π( ∇π)2in Eq.(2.26)scales as s1/4and is therefore (barely!)irrelevant.All other operators are even more irrelevant,showing that there is a regime of low energies where the expansion is under control.2.5Preview of Nonlinear EffectsThe arguments above show that the effects of the nonlinear terms are under control at low energies and smallfield amplitudes.However,in the presence of large classical gravitational sources the nonlinear terms can become important.In fact,the time scale for the ghostonefield near a classical source is just the gravitational infall time of the source.This can be understood from the form of the stress-energy tensor.In the approximation where the Lagrangian is L=P(X),the stress-energy tensor has the formTµν∝−P(X)gµν+2P′(X)uµuν.(2.29)whereuµ=∂µφ.(2.30) This has the form of a stress-energy tensor for a perfectfluid with4-velocity uµ.1 The fact that uµis a gradient means that theflow is irrotational:∂[µuν]=0implies ∇× u=0.The equations of motion for the ghostonefield follow from the conservation of the stress-energy tensor∇µTµν=0,which are intepreted as the conservation of energy and momentum in thefluid.In the presence of a classical gravitational source, afluid clearly responds on a time scale given by the infall time,and therefore so does the ghostone mode.As it will be shown in the next section,this is exactly the time scale where the nonlinear term becomes important.For smallfluctuations about the minimum X=1,P(X)can be approximated byP(X)≈12Σ2,(2.31)where an overall contribution to the cosmological constant has been removed.We can read offthe equation of state of thefluid from the energy-momentum tensor.It isp=ρ21The defining property of a perfectfluid is that at each point there is a frame in which the stress-energy tensor has the form Tµν=diag(−ρ,p,p,p).Such phenomena were also observed in some other scalarfield theories[11].Near these singularities,the higher-derivativeα( ∇2π)2term can no longer be neglected. This term contributes positive gradient energy,and wefind in numerical simulations that it generically smoothly resolves the caustic singularity,giving rise to a‘bounce’with outgoingπwaves and positive and negative regions ofΣnear the would-be caustic.The fact thatΣ(and henceρ)can be negative brings up again the question of the stability of the theory.As discussed above,regions withΣ<0modes with sufficiently long wavelengths are unstable.In numerical simulations,wefind that negative energy regions tend to shrink while the amplitude ofΣgrows inside the region.This can be understood from thefluid picture,since this is valid in the limit where we neglect the( ∇2π)2term,which is a good approximation away from caustic singularities.In this picture theΣ<0region consists offluid particles with negative mass.It is therefore clear that energy(mass)cannotflow across the boundary of theΣ<0region,since the boundary consists of particles with vanishing mass.The boundary can move however,and in theΣ<0region the positive pressure favors large gradients and causes theΣ<0region to shrink.Numerical simulations show that someΣ<0regions continue to shrink until they exit the regime of validity of the effective theory.These singularties need to be resolved in a more fundamental theory.Similar conclusion was also obtained in Ref.[12]which studied the two-dimensional case.However,we show that the total energy inside theΣ<0regions formed in astrophysical situations is very small,and does not lead to any observable consequences provided the singularities are regulated in a smooth way.We will discuss a partial UV completion to do this,and present numerical evidence that it works.The nonlinear dynamics affects the bounds on M derived in the linear theory. The Jeans instability in the linear theory gives a bound M<∼10MeV if we require that there is no exponential growth of the oscillatory potential within the age of the universe.However,the nonlinear dynamics is expected to cut offthe instability, and may weaken this bound.We argue below that the strongest bound comes from gravitational lensing due to regions of positive and negative energy produced by the Jeans instability.Demanding that the random walk of light rays due to the lensing does not smear out the observed CMB anisotropies gives the bound M<∼100GeV.We also consider other possible bounds on the ghost condensate from the grav-itational sector.The modifications of the gravitational potential are small due to velocity effects[13,14].We also consider energy loss in the nonlinear theory,as well as energy stored in would-be caustic singularities.Wefind that these effects are negligible,and we believe that the theory is safe for M<∼100GeV.3Nonlinear DynamicsWe now turn to the nonlinear dynamics of the theory.The nonlinear dynamics is veryrich and complex,and we emphasize that we do not claim a complete understandingin this work.It is therefore important to keep in mind that there is a simple limit ofthis theory,independent of the details of the nonlinear dynamics[5].The Ghostonesector naturally couples to matter only through gravity.(Gravitationally induceddirect couplings to standard modelfields are easily seen to be negligibly small.)Themaximum value of the gravitational energy in the Ghostone energy is of order M4,which does not affect even cosmology if M<∼(M Pl H0)1/2∼10−3eV.Such low values of M are still very interesting for cosmology,since the ghost may be a source of darkenergy and dark matter[5]and may drive inflation[8].Another general point to keep in mind in the following is that the modificationsof gravity vanish in regions whereΣ=0(X=1)and we neglect the( ∇2π)2term. This is because in this limit,the Lagrangian in‘unitary gauge’φ=t(φ=0)isL=√where∇2Φ=T00(X−1)=˙π−12Σ2−α2π2T NL∼√we have T2NL∼r3/2/R S,which is the Kepler relation.This is a very direct way of seeing that the nonlinear effects become important on the gravitational time scale.Solving Eq.(3.7)forπ,we obtain| ∇π|∼πΦ≪1.(3.9) That is,ghostone amplitudes are small for weak gravity,in agreement with our as-sumptions.On the other hand,in the linear approximation theα( ∇2π)2becomes comparable to˙π2at T Lin∼ML2.As a result,the nonlinear evolutions completely dominates for T NL<∼T Lin∼ML2,orΦL2>∼1M src M Pl(X−1)2=18Σ2gµν+Σuµuν ,(3.13)2whereuµ=∂µφ.(3.14) Note that uµis nonzero and timelike everywhere.This has the form of the stress-energy tensor for a perfectfluid with4-velocity uµ.Because uµis the gradient of a scalar,theflow of thefluid is irrotational.The conservation of the stess-energy tensor∇µTµν=0gives the equation of motion for the ghostonefield,and also gives the Euler equation for thefluid.ForΣ≪1we can read offthe density and pressure.(3.15)ρ=M4Σ,p=12M4This establishes the equivalence of the ghostone theory without theα( ∇2π)2term to the irrotationalflow of a perfectfluid2.It is also insightful to understand the equivalence directly in terms of the equa-tions of motion.For the ghostonefield,the equations of motion have the form of a conservation law˙Σ= ∇·[Σ ∇π],(3.16) whereΣis the charge density.For afluid made of particles carrying the conserved charge,the current is J=Σ v,so we identifyv=− ∇π.(3.17) Again we see that thefluidflow is irrotational.In thisfluid picture,the equations of motion are satisfied simply due to the fact that thefluid particles carry their charges with them.It remains only to satisfy the relation betweenΣandπ:Σ=˙π−1=− ∇(Φ+Σ),(3.19)Dt4πG Nρcorresponding to this equation of state is˜L J∼M P l/M2, where c s= ρ/M4is the sound velocity.Intriguingly,this agrees with the Jeans length (2.25)in the linear theory up to a constant of order unity.This equation of state ignores the k4 term,while the linear analysis does not take into account the nonlinear termΣ2in p.Hence,it is not a priori clear whether these two Jeans length should be the same or not.Nonetheless,they agree.whereD+ v· ∇(3.20)∂tis the time derivative along the particle worldline(also called the convective or Lagran-gian derivative).Eq.(3.19)is just Newton’s law for a particle moving in a potential Φ+Σ.Using the identifications Eq.(3.15)we can write− ∇Σ=−13Note that the equivalence between the ghostone andfluid pictures is a kind of duality,since it exchanges a constraint equation with an equation of motion.Noether charge of the original time translation symmetry,which we refer to as the ‘gravitational energy.’This is not the same as the Noether charge associated with the time translation symmetry that is unbroken in the vacuum,which we call the ‘inertial energy.’The inertial energy εis the energy associated with the unbroken time translation symmetry of the Lagrangian Eq.(3.6).(It is also the Hamiltonian density of the system.)Conservation of inertial energy states that˙ε=− ∇· p ,(3.22)whereε=M 4 12Σ( ∇π)2+αM 2( ∇2π) ∇π−˙π ∇( ∇2π) (3.24)is the momentum density.In the linearized approximation,ε=M 4 12M 2( ∇2π)2 ≥0.(3.25)However,in the nonlinear theory the inertial energy is not positive definite due to the second term in Eq.(3.23).The energy density can be negative only in regions where Σ<0.In fact it is easy to see that the energy is unbounded from below.For example,for π=c | x |we have ε=−1M 2 ∇( ∇2π).(3.27)If we neglect theα( ∇2π)2term,this conservation law is taken into account very directly in thefluid picture,to which we now turn.In this approximation,negative energy regions correspond precisely to regions whereΣ<0,so we consider such a region surrounded byΣ>0.5In thefluid picture,the conserved charge is carried by the individual particles,so theΣ<0region consists of particles with negative charge,while the boundary of theΣ<0region consists of particles of vanishing charge.Therefore,there can be noflux of charge across theΣ=0boundary,and the total charge inside the region does not change.On the other hand,theΣ=0boundary can move.Since ∇Σpoints outward at the boundary,the equation of motion forfluid particles Eq.(3.19)implies that the particles on the boundary experience an inward force due to the pressure.Therefore, theΣ<0region tends to shrink.These arguments show that the total shift charge integrated over aΣ<0regionQ= Σ<0d3xΣ(3.28)does not change with time.This can also be seen from the fact that the shift current J vanishes on theΣ=0boundary.The shift charge is not the same as the total inertial energyE= Σ<0d3xε.(3.29)However,if we neglect theα( ∇2π)2term,theflux of inertial energy across theΣ=0 boundary also vanishes,and therefore E also does not change with time.As with thefluid picture,these results hold beyond the approximations made here.This is discussed in the appendix.3.5Caustic SolutionsThefluid picture can be used to understand the structure of the caustic singularties that occur when we neglect theα( ∇2π)2term.We restrict attention to the case Σ=0,where there is no pressure and thefluid particles follow geodesics.In this case,it is clear that there are caustics without theα( ∇2π)2term.It is possible that the pressure resolves the caustics in important situations such as inside galaxy halos made of ghostone dark matter,but we will not consider that here.To introduce the subject of caustics,we consider the gravitational potential due to a uniform sphere of matter with densityρ0.Inside the sphere,the gravitational potential isρ0Φ=,(3.33)Twhere T is a constant that tells us how the initial velocity varies away from x0=0. Solving Eq.(3.31)for x0we obtainxx0=−TFig.4.The1-dimensional‘perfect caustic.’The shaded regions shows the region where we can expand the solution perturbatively about the perfect caustic.Since the velocity is constant along any trajectory,we havexv(x)=v0(x0)=−.(3.36)2(t−T)Note that this solution is scale-free,since T just gives the time to the caustic.Shifting t→t−T,we obtainx2π(x,t)=−=0(3.38)∂x0forfixed t.This gives the time to the caustic for a given value of x0as1t c(x0)=−In a realistic case,the function v0(x0)will be more complicated.We want to expand about the point where the causticfirst forms,i.e.the minimum of t c(x0), which we take to be x0=0.Expanded about this point,v0takes the formv0(x0)=−x06L2Tx30+O(L−3),(3.40)where we have performed a boost so that v0(0)=0.Because of the focussing of the geodesics,this expansion is valid only for|x|≪L t−Tt−T−T3(t−T)4+O(L−3).(3.42)and thereforev(x)=x6L2x3L21We can use Eq.(3.44)to estimate the time and distance scale where theα( ∇2π)2 term becomes important.This will happen whenα∂4xπML2 1/2,(3.46)where∆t=T−t is the time to the caustic.The distance scale where theα( ∇2π)2 term becomes important is therefore∆x∼LM 1/2.(3.47)Note that∆x,∆t≫M−1as long as L,T≫M−1and L/T≪1(i.e.the system is nonrelativistic),so this is within the regime of validity of the effective theory.4Numerical SimulationsIn this section we describe various numerical simulations of the ghostfield which allow us to understand the rather exotic features of its non-linear evolution.The test cases wefirst present assume symmetry to reduce the dynamics to a one dimensional problem,and will see that the various symmetries have different be-haviours.We will discuss how caustics do indeed form in the theory.As mentioned earlier,this is clear forα=0,but one would naively expect non-zeroαto amelio-rate this problem.However,as we will show,this is not the case,and for certain symmetries the‘perfect’caustic remains an attractor.As one might expect,the singular behaviour becomes less strong as one moves from planar through axisymmetry to spherical symmetry.Indeed without any grav-itational potential we will see the planar reduction exhibits singularities,while the spherical theory without potential does not.However,once a gravitationally at-tractive potential is added,all three symmetries become singular under evolution of regular initial data.Clearly assuming symmetry can lead to unphysical behaviours,whilst the phy-sical situation we are ultimately interested,namely structure formation,is expectedto have very little symmetry.Hence this section will conclude with a study of a3-d numerical evolution where no continuous symmetry is present and a moving gravi-tational potential seeds the ghostfield growth.As expected from the1-d examples, we againfind singular caustics do develop,and interestingly appear to take a planar form.4.1One dimensional evolutions:Planar,axial and spherical symmetryWe will initially consider the case of evolution of the ghostfield in the absence of gravitational sources,seeded instead from a local perturbation in the ghostfield itself.Then reducing to planar symmetryπ=π(t,r)and we may write the equation for the ghost decoupled from gravity in a manifestlyflux conservative form,˙H=∂r Σ+1α/M,the second line is simply the definition ofΣand˙x,x′are the time and space derivatives of x.We then use a Crank-Nicholson method to evolve our initial data,which we take to be a Gaussian profile inππ(t=0)=π0e−r2(4.2) withΣ=0initially.As discussed previously,with L=0Σwould remain zero,but the higher derivative term sourcesΣ.In order to make contact with the epoch of structure formation we wish to have moderate initial amplitudes so|π0|<1but is still of order unity.From(4.2)we have chosen units to have initial data with unit spatial variation.We then wish to have L,the ghost length scale,to be L≪1.Naturally numerical methods limit our ability to separate the initial data length scale from the ghost length whilst maintaining accuracy.However we may separate the scale sufficiently to see the asymptotic properties of taking L very small.Thefirstfigures we show,5and6,illustrate the generic behaviour for the planar system for small L,showing both H andΣfor the evolution.We show both the evolution of data for L=0.005and also for L=0.for comparison,and the initial amplitude was taken to beπ0=0.1.As expected L=0.evolution leads to a caustic,whose time for formation scales as t caustic≃1/π0.Adding the higher derivative term changes the evolution dramatically around this time scale,completely smoothing out the ghostfield.However,we seefrom thefigure that the radiated waves scattered by the action of this higher derivative term in fact are attracted back to the origin where they grow and become singular. Obviously since the symmetry is planar,this growth is not due to a measure factor,but rather is due a‘perfect caustic’forming,which as mentioned before cannot be rescued by the higher derivative term we use here.Indeed this perfect caustic formation can be seen locally in detail fromΣnear the singularity.We note that taking sufficiently large L∼√π0when T→∞),or with decreasing L(so that the radiation from the increasingly perfect central caustic region is slower).Thus for small L a cartoon of the evolution is that the initially collapsing ghost field causes the higher derivative term to radiate strongly,but the process of radiation simply refines the collapsing region into the perfect caustic form where it eventually collapses.Suitable modification of the conservative equations of motion(4.1)introduce the geometric measure factor associated with axisymmetry.In this case wefind the behaviour essentially analogous to the planar case.Whilst the singular behaviour appears‘weaker’,taking longer to reach the singularity for the same parameters, the singularity does indeed form.However moving to spherical symmetry wefind a change in behaviour.For spherical symmetry we again take the initial data(4.2)and evolve this in the absence of any gravitational potential.Infigure8we plot the evolution of H for π0=0.1and L=0.005(as shown earlier for the planar case).The behaviour is clearly different with a totally non-singular evolution for all times,a portion of which is shown in thefigure.Whilst for L=0.obviously the spherically symmetric ghost field exhibits the usual caustic singularity,we see the higher derivative term,aided by the geometric measure factor,can now radiate sufficient energy to avoid any later energy build up.So far we have discussed the case of evolution of a local perturbation in the ghost field.We have seen that the symmetry of the initial data has a strong effect on whether the evolution is singular or not.Physically,however,we are interested more。

Part I Writing (30 minutes)Directions: For this part，you are allowed 30 minutes to writea short essay on the importance of writing ability and howto develop it. You should write at least 120 words but nomore than180 words.【参考范文】No body could deny that writing is one of the basic abilities for men. Put it another way, it is unlikely to imagine human civilization without writing ability.At the top of the list, if we overlook the significance of writing ability, we will suffer a great difficulty in our daily written communication. In addition to what has been mentioned above, it is advisable for us to attach importance to this ability because writing plays a key in our academic performance. To summarize,writing does carry a positive implication for our life and study.In view of the great value of writing ability, we should take actions to develop this capability. For my part, initially, we are supposed to keep in mind that reading is the first step of writing, so we should read great books as many as possible, learning from the great works how to write concisely and effectively. Moreover, owing to the fact that practicemakes perfect, we should frequently practice writing; for example, we may develop the habit of keeping a diary.PartⅡListening Comprehension ( 25 minutes)Section ADirections:In this section, you will hear three news reports. Atthe end of each news report, you will hear two or threequestions. Both the news report and then questions will bespoken only once. After you hear a question, you must choosethe best answer from the four choices marked A），B), C) andD).Then mark the corresponding letter on Answer Sheet1with a single line through the centre.Questions l and 2 are based on the news report you have just heard. Questions 3 and 4 are based on the news report you have just heard. Questions 5 to 7 are based on the news report you have just heard.Section BDirections: In this section, you will hear two longconversations. At the end of each conversation, you will hearfour questions. Both the conversation and the questions willbe spoken only once. After you hear a question, you mustchoose the best answer from the four choices marked A），B），C)and D). Then mark the corresponding letter on AnswerSheet 1 with a single line through the centre.Questions 8 to 11 are based on the conversation you have just heard.Questions 12 to 15 are based on the conversation you have just heard.Section CDirections:In this section, you will hear three passages. At theend of each passage, you will hear three or four questions.Both the passage and the questions will be spoken onlyonce. After you hear a question, you must choose the bestanswer from the four choices marked A), B), C) and D）．Thenmark the corresponding letter on Answer Sheet 1 with a singleline through the centre.Questions 16 to 18 are based on the passage you have just heard.Questions 19 to 21 are based on the passage you have just heard. Questions 22 to 25 are based on the passage you have just heard.【参考答案】暂缺Part ⅢReading Comprehension ( 40 minutes) Section ADirections: In this section, there is a passage with ten blanks.You are required to select one word for each blank from a listof choices given in a word bank following the passage. Readthe passage through carefully before making your choices.Each choice in the bank is identified by a letter. Please markthe corresponding letter for each item on Answer Sheet 2 witha single line through the centre. You may not use any of thewords in the bank more than once．Questions 26 to 35 are based on the following passage.Since the 1940s, southern California has had a reputation for smog. Things are not as bad as they once were but, according to the American Lung Association, Los Angeles is still the worst city in the United States for levels of 26 . Gazing down on the city from the Getty Center, an art museum in the Santa Monica Mountains, one would find the view of thePacific Ocean blurred by the haze (霾). Nor is the state’s had air 27 to its south. Fresno, in the central valley, comes top of the list in America for year-round pollution. Residents’hearts and lungs are affected asa 28 .All of which, combined with California’s reputation as the home oftechnological 29 , makes the place ideal for developing and testing systems designed to monitor pollution in 30 . And that is just what Aclima, a new firm in San Francisco, has been doing over the past few months. It has been trying out monitoring that are 31 to yieldminute-to-minute maps of 32 air pollution. Such stations will also be able to keep an eye on what is happening inside buildings, including offices.To this end, Aclima has been 33 with Google’s Street View system.Davida Herzl, Aclima’s boss, says they have revealed pollution highs on days when San Francisco’s transit workers went on strike and the city’s 34 were forced to use their cars. Conversely, “cycle to work”days have done their job by 35 pollution lows.A.assistedB.collaboratingC.consequenceD.consumersE.creatingF.detailG.domesticH.frequentlyI.inhabitantsJ.innovationK.intendedL.outdoorM.pollutantsN.restrictedO.Sum【参考答案】.M pollutants . .N restricted .. C consequence . .J innovation .. F detail ..K intended ..L outdoor .33. B collaborating .34. I inhabitants .35. E creating.26. M pollutants . 解析：of前边是levels级别，等级的意思，of后应该是名词形式，翻译为_____的级别，根据文章首句说南加利福尼亚的雾霾是出了名的差可判断这篇文章关于坏境。