1987 The Derivation of a Drag Coefficient Formula from Velocity-Voidage Correlations

1987年全国硕士研究生入学统一考试英语试题Section I: Structure and VocabularyIn each question, decide which of the four choices given will most suitably complete the sentence if inserted at the place marked. Put your choice in the brackets on the left. (10 points)EXAMPLE:I was caught ________ the rain yesterday.[A] in[B] by[C] with[D] atANSWER: [A]1. The skyscraper stands out ________ the blue sky.[A] in[B] against[C] under[D] beneath2. They have always been on good ________ with their next-door neighbors.[A] friendship[B] relations[C] connection[D] terms3. Hello! Is that 21035? Please put me ________ to the manager.[A] across[B] up[C] through[D] over4. Why do you look so ________? You never smile or look cheerful.[A] miserable[B] unfortunate[C] sorry[D] rude5. Eggs, though nourishing, have ________ of fat content.[A] large number[B] a large number[C] the high amount[D] a high amount6. Jim always ________ his classmates in a debate.[A] backs out[B] backs away[C] backs up[D] backs down7. Most of the people who ________ two world wars are strongly against arms race.[A] have lived out[B] have lived through[C] have lived on[D] have lived off8. There are many inconveniences that have to be ________ when you are camping.[A] put up[B] put up with[C] put off[D] put away9. Is it true that those old houses are being pulled down ________ new office blocks?[A] to accommodate[B] to provide for[C] to increase[D] to make room for10. Being in no great hurry, ________.[A] we went the long route with scenery[B] the long, scenic route was our preference[C] we took the long scenic route[D] our preference was taking the long, scenic routeSection II: Reading ComprehensionEach of three passages below is followed by five questions. For each question there are four answers, read the passage carefully and choose the best answer to each of the question. Put your choice in the ANSWER SHEET. (15 points)Text 1For centuries men dreamed of achieving vertical flight. In 400 A.D. Chinese children played with a fan-like toy that spun upwards and fell back to earth as rotation ceased. Leonardo da Vinci conceive the first mechanical apparatus, called a “Helix,” which could carry man straight up, but was only a design and was never tested.The ancient-dream was finally realized in 1940 when a Russian engineer piloted a strange looking craft of steel tubing with a rotating fan on top. It rose awkwardly and vertically into the air from a standing start, hovered a few feet above the ground, went sideways and backwards, and then settled back to earth. The vehicle was called a helicopter.Imaginations were fired. Men dreamed of going to work in their own personal helicopters. People anticipate that vertical flight transports would carry millions of passengers as do the airliners of today. Such fantastic expectations were not fulfilled.The helicopter has now become an extremely useful machine. It excels in military missions, carrying troops, guns and strategic instruments where other aircraft cannot go. Corporations use them as airborne offices, many metropolitan areas use them in police work, construction and logging companies employ them in various advantageous ways, engineers use them for site selection and surveying, and oil companies use them as the best way to make offshore and remote work stations accessible to crews and supplies. Any urgent mission to a hard-to-get-to place is a likely task for a helicopter. Among their other multitude of used: deliver people across town, fly to and from airports, assist in rescue work, and aid in the search for missing or wanted persons.11. People expect that ________.[A] the airliners of today would eventually be replaced by helicopters[B] helicopters would someday be able to transport large number of people from place to place as airliners are now doing[C] the imaginations fired by the Russian engineer’s invention would become a reality in the future[D] their fantastic expectations about helicopters could be fulfilled by airliners of today12. Helicopters work with the aid of ________.[A] a combination of rotating devices in front and on top[B] a rotating device topside[C] one rotating fan in the center of the aircraft and others at each end[D] a rotating fan underneath for lifting13. What is said about the development of the helicopter?[A] Helicopters have only been worked on by man since 1940.[B] Chinese children were the first to achieve flight in helicopters.[C] Helicopters were considered more dangerous than the early airplanes.[D] Some people thought they would become widely used by average individuals.14. How has the use of helicopters developed?[A] They have been widely used for various purposes.[B] They are taking the place of high-flying jets.[C] They are used for rescue work.[D] They are now used exclusively for commercial projects.15. Under what conditions are helicopters found to be absolutely essential?[A] For overseas passenger transportation.[B] For extremely high altitude flights.[C] For high-speed transportation.[D] For urgent mission to places inaccessible to other kinds of craft.Text 2In ancient Greece athletic festivals were very important and had strong religious associations. The Olympian athletic festival held every four years in honor of Zeus, king of the Olympian Gods, eventually lost its local character, became first a national event and then, after the rules against foreign competitors had been abolished, international. No one knows exactly how far back the Olympic Games go, but some official records date from 776 B.C. The games took place in August on the plain by Mount Olympus. Many thousands of spectators gathered from all parts of Greece, but no married woman was admitted even as a spectator. Slaves, women and dishonoredpersons were not allowed to compete. The exact sequence of events uncertain, but events included boy’s gymnastics, boxing, wrestling, horse racing and field events, though there were fewer sports involved than in the modern Olympic Games.On the last day of the Games, all the winners were honored by having a ring of holy olive leaves placed on their heads. So great was the honor that the winner of the foot race gave his name to the year of his victory. Although Olympic winners received no prize money, they were, in fact, richly rewarded by their state authorities. How their results compared with modern standards, we unfortunately have no means of telling.After an uninterrupted history of almost 1,200 years, the Games were suspended by the Romans in 394 A.D. They continued for such a long time because people believed in the philosophy behind the Olympics: the idea that a healthy body produced a healthy mind, and that the spirit of competition in sports and games was preferable to the competition that caused wars. It was over 1,500 years before another such international athletic gathering took place in Athens in 1896.Nowadays, the Games are held in different countries in turn. The host country provides vast facilities, including a stadium, swimming pools and living accommodation, but competing courtiers pay their own athletes’ expenses. The Olympics start with the arrival in the stadium of a torch, lighted on Mount Olympus by the sun’s rays. It is carried by a succession of runners to the stadium. The torch symbolized the continuation of the ancient Greek athletic ideals, and it burns throughout the Games until the closing ceremony. The well-known Olympic flag, however, is a modern conception: the five interlocking rings symbolize the uniting of all five continents participating in the Games.16. In ancient Greece, the Olympic Games ________.[A] were merely national athletic festivals[B] were in the nature of a national event with a strong religious colour[C] had rules which put foreign participants in a disadvantageous position[D] were primarily national events with few foreign participants17. In the early days of ancient Olympic Games ________.[A] only male Greek athletes were allowed to participate in the games[B] all Greeks, irrespective of sex, religion or social status, were allowed to take part[C] all Greeks, with the exception of women, were allowed to compete in Games[D] all male Greeks were qualified to compete in the Games18. The order of athletic events at the ancient Olympics ________.[A] has not definitely been established[B] varied according to the number of foreign competitors[C] was decided by Zeus, in whose honor the Games were held[D] was considered unimportant19. Modern athletes’ results cannot be compared with those of ancient runners because ________.[A] the Greeks had no means of recording the results[B] they are much better[C] details such as the time were not recorded in the past[D] they are much worse20. Nowadays, the athletes’ expenses are paid for ________.[A] out of the prize money of the winners[B] out of the funds raised by the competing nations[C] by the athletes themselves[D] by contributionsText 3In science the meaning of the word “explain” suffers with civilization’s every step in search of reality. Science cannot really explain electricity, magnetism, and gravitation; their effects can be measured and predicted, but of their nature no more is known to the modern scientist than to Thales who first looked into the nature of the electrification of amber, a hard yellowish-brown gum. Most contemporary physicists reject the notion that man can ever discover what these mysterious forces “really” are. “Electricity,” Bertrand Russell says, “is not a thing, like St. Paul’s Cathedral; it is a way in which things behave. When we have told how things behave when they are elec trified, and under what circumstances they are electrified, we have told all there is to tell.” Until recently scientists would have disapproved of such an idea. Aristotle, for example, whose natural science dominated Western thought for two thousand years, believed that man could arrive at an understanding of reality by reasoning from self-evident principles. He felt, for example, that it is a self-evident principle that everything in the universe has its proper place, hence one can deduce that objects fal l to the ground because that’s where they belong, and smoke goes up because that’s where it belongs. The goal of Aristotelian science was to explain why things happen. Modern science was born when Galileo began trying to explain how things happen and thus originated the methodof controlled experiment which now forms the basis of scientific investigation.21. The aim of controlled scientific experiments is ________.[A] to explain why things happen[B] to explain how things happen[C] to describe self-evident principles[D] to support Aristotelian science22. What principles most influenced scientific thought for two thousand years?[A] the speculations of Thales[B] the forces of electricity, magnetism, and gravity[C] Aristotle’s natural science[D] Galile o’s discoveries23. Bertrand Russell’s notion about electricity is ________.[A] disapproved of by most modern scientists[B] in agreement with Aristotle’s theory of self-evident principles[C] in agreement with scientific investigation directed toward “how” things happen[D] in agreement with scientific investigation directed toward “why” things happen24. The passage says that until recently scientists disagreed with the idea ________.[A] that there are mysterious forces in the universe[B] that man cann ot discover what forces “really” are[C] that there are self-evident principles[D] that we can discover why things behave as they do25. Modern science came into being ________.[A] when the method of controlled experiment was first introduced[B] when Galileo succeeded in explaining how things happen[C] when Aristotelian scientist tried to explain why things happen[D] when scientists were able to acquire an understanding of reality of reasoningSection III: Structure and V ocabularyFill in the blanks with the words which best complete the sentence. Put your choices in the ANSWER SHEET. (10 points)It was the largest experiment we have ever had, it ________ six hours.[A] ended[B] finished[C] was[D] lastedANSWER: [D]26. As scheduled, the communications satellite went into ________ round the earth.[A] circle[B] orbit[C] path[D] course27. When I saw Jane, I stopped and smiled, but she ________ me and walked on.[A] refused[B] ignored[C] denied[D] missed28. It was a good game, and at the end the ________ was Argentina 3, West Germany 2.[A] mark[B] account[C] record[D] score29. George took ________ of the fine weather to do a day’s work in his garden.[A] chance[B] interest[C] advantage[D] charge30. Is there anyone who ________ the plans put forward by the committee?[A] differs[C] disagrees[D] refuses31. All too ________ it was time to go back to school after the summer vacation.[A] often[B] quick[C] fast[D] soon32. In an accident when two cars run into each other, they ________.[A] hit[B] knock[C] strike[D] collide33. The noise was caused by a boy ________ a cat through the garden.[A] catching[B] fighting[C] following[D] chasing34. He drove fast and arrived an hour ________ of schedule.[A] in advance[B] ahead[C] abreast[D] in front35. This ticket ________ you to a free meal in our new restaurant.[A] gives[B] entitles[C] grants[D] creditsSection IV: Close TestFor each numbered blank in the following passage there are four choices labeled [A], [B], [C] and [D]. Choose the best one and put your choice in the ANSWER SHEET. Read the whole passage before making your choice. (10 points)EXAMPLE:For instance, the automobile tunnel might ________ huge ventilation problems.[A] make[B] bring[C] raise[D] createANSWER: [D]Cheques have __36__ replaced money as a means of exchange for they are widely accepted everywhere. Though this is very convenient for both buyer and seller, it should not be forgotten that cheques are not real money: they are quite valueless in themselves. A shop-keeper always runs a certain __37__ when he accepts a cheques and he is quite __38__ his rights if on occasion, he refuses to do so.People do not always know this and are shocked if their good faith is called __39__. An old and very wealthy friend of mine told me he had an extremely unpleasant experience. He went to a famous jewelry shop which keeps a large __40__ of precious stones and asked to be shown some pearl necklaces. After examining several trays, he decided to buy a particularly fine string of pearls and asked if he could pay by Cheques. The assistant said that this was quite __41__ but the moment my friend signed his name, he was invited into the manager’s office.The manager was very polite, but he explained that someone with exactly the same name had presented them with a worthless Cheque not long ago. My friend got very angry when he heard this and said he would buy a necklace somewhere else. When he got up to go, the manager told him that the police would arrive at any moment and he had better stay __42__ the wanted to get into serious trouble. __43__, the police arrived soon afterwards. They apologized to my friend for the __44__, but explained that a person who had used the same name as his was responsible for a number of recent robberies. Then the police asked my friend to copy out a note which had been used by the thief in a number of shops. The note __45__: “I have a gun in my pocket. Ask no questions and give me all the money in the safe.” Fortunately, my friend’s handwriting was quite unlike the thief’s. He was not only allowed to go without further delay, but to take the string of pearls with him.36. [A] exactly[B] really[C] largely[D] thoroughly37. [A] danger[B] chance[C] risk[D] opportunity38. [A] within[B] beyond[C] without[D] out of39. [A] in difficulty[B] in doubt[C] in earnest[D] in question40. [A] amount[B] stock[C] number[D] store41. [A] in order[B] in need[C] in use[D] in common42. [A] whether[B] if[C] otherwise[D] unless43. [A] Really[B] Sure enough[C] Certainly[D] However44. [A] treatment[B] manner[C] inconvenience[D] behaviour45. [A] read[B] told[C] wrote[D] informedSection V: Verb FormsFill in the blanks with the appropriate forms of the verbs given in the brackets. Put your answer in the ANSWER SHEET. (10 points)EXAMPLE:It is highly desirable that a new president ________ (appointed) for this college.ANSWER: (should) be appointed46. With all factors (consider) we think this program may excel all the others in achieving the goal.47. They had been working round the clock for a couple of days (hope) to get the design out before their competitors did.48. There’s a general understanding among the members of the Board of Directors that chief attention (g ive) to the undertaking that is expected to bring in highest profit.49. If we don’t start out now, we must risk (miss) the train.50. This test (intend) to reinforce what you have learnt in the past few weeks.51. The members of the delegation were glad (stay) longer than originally planned.52. With full knowledge of his past experience, we knew all along that he (succeed).53. (Know not) what appropriate measures to be taken to cope with the situation, he wrote to his lawyer for advice.54. It’s no good (write) to him, he never answers letters. The only thing to do is to go and see him.55. (Come) what may, we’re not going to make any concessions to his unreasonable demands.Section VI: Error-detection and CorrectionEach question consists of a sentence with four underlined parts (words or phrases). These parts are labeled [A], [B], [C], and [D]. Choose the part of the sentence that is incorrect and put your choice in the ANSWER SHEET. Then, without altering the meaning of the sentence, write down the correct word or phrase on the line in the ANSWER SHEET. (10 points)EXAMPLE:You’ve to hurry up if you want to buy something because [A] there’s [B] hardly something [C] left. [D] ANSWER: [C] anything56. In [A] his response to [B] the advertisement, Ed. replied that he was looking for a full-time position [C] not a part-time [D] one.57. No one who has seen [A] him work [B] in the laboratory can deny [C] that William has great capabilities of [D] research.58. Neither of the alternatives that had been outlined [A] at the last meeting [B] were [C] acceptable to [D] the executive committee.59. Airline companies today require [A] that all luggage’s [B] be inspected [C] before passengers are admitted into [D] the waiting rooms.60. Although Alice has been [A] to the mountains many times [B] be fore, she still [C] loves visiting it. [D]61. An important function of the World Health Organization is to improve [A] the healthy [B] and living conditions for the sick and the poor of [C] world [D]62. The element carbon is widely [A] found [B] in nature [C] in many forms including both diamonds as well as[D] coal.63. While still a young boy [A] Bizet knew to play [B] the piano well and as [C] he grew older, he wrote operas, the most famous of which [D] is Carmen.64. Despite the fact that [A] the South Pole is as snow-covered [B] and stormy-weathered [C] as the North Pole, it is colder [D] than the North Pole.65. Climate [A] conditions vary widely [B] from place to place and from season to season, but a certain order and pattern [C] can be identifiable. [D]Section VII: Chinese-English TranslationTranslate the following sentences into English (15 points)66. 所有那些努力工作的人都应得到鼓励。

CHAPTER3ATOMIC COLLISIONS3.1BASIC CONCEPTSWhen two particles collide,various phenomena may occur.As examples,one or both particles may change their momentum or their energy,neutral particles can become ionized,and ionized particles can become neutral.We introduce the funda-mentals of collisions between electrons,positive ions,and gas atoms in this chapter, concentrating on simple classical estimates of the important processes in noble gas discharges such as argon.For electrons colliding with atoms,the main processes are elastic scattering in which primarily the electron momentum is changed,and inelas-tic processes such as excitation and ionization.For ions colliding with atoms,the main processes are elastic scattering in which momentum and energy are exchanged, and resonant charge transfer.Other important processes occur in molecular gases. These include dissociation,dissociative recombination,processes involving negative ions,such as attachment,detachment,and positive–negative ion charge transfer,and processes involving excitation of molecular vibrations and rotations. We defer consideration of collisions in molecular gases to Chapter8.Elastic and Inelastic CollisionsCollisions conserve momentum and energy:the total momentum and energy of the colliding particles after collision are equal to that before collision.Electrons and fully stripped ions possess only kinetic energy.Atoms and partially stripped ions have internal energy level structures and can be excited,de-excited,or ionized, Principles of Plasma Discharges and Materials Processing,by M.A.Lieberman and A.J.Lichtenberg. ISBN0-471-72001-1Copyright#2005John Wiley&Sons,Inc.43corresponding to changes in potential energy.It is the total energy,which is the sum of the kinetic and potential energy,that is conserved in a collision.If the internal energies of the collision partners do not change,then the sum of kinetic energies is conserved and the collision is said to be elastic.Although the total kinetic energy is conserved,kinetic energy is generally exchanged between particles.If the sum of kinetic energies is not conserved,then the collision is inelas-tic.Most inelastic collisions involve excitation or ionization,such that the sumof kinetic energies after collision is less than that before collision.However,super-elastic collisions can occur in which an excited atom can be de-excited by acollision,increasing the sum of kinetic energies.Collision ParametersThe fundamental quantity that characterizes a collision is its cross section s(v R), where v R is the relative velocity between the particles before collision.To define this,we considerfirst the simplest situation shown in Figure3.1,in which aflux G¼n v of particles having mass m,density n,andfixed velocity v is incident on a half-space x.0of stationary,infinitely massive“target”particles having density n g.In this case,v R¼v.Let d n be the number of incident particles per unit volume at x that undergo an“interaction”with the target particles within a differential distanced x,removing them from the incident beam.Clearly,d n is proportional to n,n g,and d x for infrequent collisions within d x.Hence we can writed n¼Às nn g d x(3:1:1)where the constant of proportionality s that has been introduced has units of area and is called the cross section for the interaction.The minus sign denotes removal from the beam.To define a cross section,the“interaction”must be specified,for example,ionization of the target particle,excitation of the incident particle to a given energy state,or scattering of the incident particle by an angle exceeding p=2.Multiplying(3.1.1)by v,wefind a similar equation for theflux:d G¼Às G n g d x(3:1:2) FIGURE3.1.Aflux of incident particles collides with a population of target particles in the half-space x.0.44ATOMIC COLLISIONSFor a simple interpretation of s,let the incident and target particles be hard elastic spheres of radii a1and a2,and let the“interaction”be a collision between the spheres.In a distance d x there are n g d x targets within a unit area perpendicular to x.Draw a circle of radius a12¼a1þa2in the x¼const plane about each target.A collision occurs if the centers of the incident and target particles fall within this radius.Hence the fraction of the unit area for which a collision occurs is n g d x p a212.The fraction of incident particles that collide within d x is thend G G ¼d nn¼Àn g s d x(3:1:3)wheres¼p a212(3:1:4)is the hard sphere cross section.In this particular case,s is independent of v.Equation(3.1.2)is readily integrated to give the collidedfluxG(x)¼G0(1ÀeÀx=l)(3:1:5) with the uncollidedflux G0eÀx=l.The quantityl¼1n g s(3:1:6)is the mean free path or the decay of the beam,that is,the distance over which the uncollidedflux decreases to1=e of its initial value G0at x¼0.If the velocity of the beam is v,then the mean time between interactions ist¼lv(3:1:7)Its inverse is the interaction or collision frequencyn;tÀ1¼n g s v(3:1:8)and is the number of interactions per second that an incident particle has with the target particle population.We can also define the collision frequency per unit density,which is called the rate constantK¼s v(3:1:9)3.1BASIC CONCEPTS45and,trivially,from (3.1.8)and (3.1.9)n ¼Kn g(3:1:10)Differential Scattering Cross SectionLet us consider only those interactions that scatter the particles by u ¼908or more.For hard spheres,taking the angle of incidence equal to the angle of reflection,the 908collision occurs on the x ¼458diagonal (see Fig.3.2),therefore having a cross section s 90¼p a 2122,(3:1:11)which is a factor of two smaller than (3.1.4).Of course,multiple collisions at smaller angles (radii larger than a 12=ffiffiffi2p )also eventually scatter incident particles through 908.This indeterminacy indicates that a more precise way of determining the scat-tering cross section is required.For this purpose we introduce a differential scatter-ing cross section I (v ,u ).Consider a beam of particles incident on a scattering center (again assumed fixed),as shown in Figure 3.3.We assume that the scattering force is symmetric about the line joining the centers of the two particles.A particle incident at a distance b off-center from the target particle is scattered through an angle u ,as shown in Figure 3.3.The quantity b is the impact parameter and u is the scattering angle (see also Fig.3.2).Now,flux conservation requires that for incoming flux G ,G 2p b d b ¼ÀG I (v ,u )2p sin u d u (3:1:12)FIGURE 3.2.Hard-sphere scattering.46ATOMIC COLLISIONS3.1BASIC CONCEPTS47FIGURE3.3.Definition of the differential scattering cross section.that is,that all particles entering through the differential annulus2p b d b leave through a differential solid angle d V¼2p sin u d u.The minus sign is because an increase in b leads to a decrease in u.The proportionality constant is just I(v,u), which has the dimensions of area per steradian.From(3.1.12)we obtainI(v,u)¼bsin ud bd u(3:1:13)The quantity d b=d u is determined from the scattering force,and the absolute value is used since d b=d u is negative.We will calculate I(v,u)for various potentials in Section3.2.We can calculate the total scattering cross section s sc by integrating I over the solid angles sc¼2p ðpI(v,u)sin u d u(3:1:14)It is clear that s sc¼s for scattering through any angle,as defined in(3.1.2).It is often useful to define a different cross sections m¼2p ðp(1Àcos u)I(v,u)sin u d u(3:1:15)The factor(1Àcos u)is the fraction of the initial momentum m v lost by the incident particle,and thus(3.1.15)is the momentum transfer cross section.It is s m that is appropriate for calculating the frictional drag in the force equation(2.3.9).For asingle velocity,we would just have n m¼s m v,where s m is generally a function of velocity.In the macroscopic force equation(2.3.15),n m must be obtained by aver-aging over the particle velocity distributions,which we do in Section3.5.We illustrate the use of the differential scattering cross section to calculate thetotal scattering and momentum transfer cross sections for the hard-sphere modelshown in Figure3.2.The impact parameter is b¼a12sin x,and differentiating, d b¼a12cos x d x,so thatb d b¼a212sin x cos x d x¼12a212sin2x d x(3:1:16)From Figure3.2the scattering angle u¼pÀ2x,such that(3.1.16)can be written asb d b¼À1a212sin u d u(3:1:17)48ATOMIC COLLISIONSSubstituting(3.1.17)into(3.1.13),we haveI(v,u)¼14a212(3:1:18)Using the definitions of s sc and s m in(3.1.14)and(3.1.15),respectively,wefinds sc¼s m¼p a212(3:1:19) for hard-sphere collisions.In general,s sc=s m for other scattering forces.For electron collisions with atoms the electron radius is negligible compared to the atomic radius so that a12%a,the atomic radius.Although the value of a% 10À8cm gives s sc¼s m%3Â10À16cm2,which is reasonable,it does not capture the scaling of the cross section with speed.In the following sections of this chapter,we consider collisional processes in more detail.Except for Coulomb collisions,we confine our attention to electron–atom and ion–atom processes.After a discussion of collision dynamics in Section3.2,we describe elastic collisions in Section3.3and inelastic collisions in Section3.4.We reserve a discussion of some aspects of inelastic collisions until Chapter8,in which a more complete range of atomic and molecular processes is considered.In Section3.5,we describe the averaging over particle velocity distri-butions that must be done to obtain the collisional rate constants.Experimental values for argon are also given in Section3.5;these are needed for discussing energy transfer and diffusive processes in the succeeding chapters.A more detailed account of collisional processes,together with many results of experimental measurements,can be found in McDaniel(1989),McDaniel et al.(1993),Massey et al.(1969–1974),Smirnov(1981),and Raizer(1991).3.2COLLISION DYNAMICSCenter-of-Mass CoordinatesIn a collision between projectile and target particles there is recoil of the target as well as deflection of the projectile.In fact,both may be moving,and,in the case of like-particle collisions,not distinguishable.To describe this more complicated state,a center-of-mass(CM)coordinate system can be introduced in which projec-tiles and targets are treated equally.Without loss of generality,we can transform to a coordinate system in which one of the particles is stationary before the collision. Hence,we consider a general collision in the laboratory frame between two particles having mass m1and m2,position r1and r2,velocity v1and v2;0,and scattering angle u1and u2,as shown in Figure3.4a.We assume that the force F acts along the line joining the centers of the particles,with F12¼ÀF21.3.2COLLISION DYNAMICS49The center-of-mass coordinates may be defined by the linear transformationR ¼m 1r 1þm 2r 2m 1þm 2(3:2:1)andr ¼r 1Àr 2(3:2:2)with the accompanying CM velocityV ¼m 1v 1þm 2v 2m 1þm 2(3:2:3)and the relative velocityv R ¼v 1Àv 2(3:2:4)v 2´m 1m R center(a )(b )FIGURE 3.4.The relation between the scattering angles in (a )the laboratory system and (b )the center-of-mass (CM)system.50ATOMIC COLLISIONSThe force equations for the two particles are:m1_v1¼F12(r),m2_v2¼F21(r)¼ÀF12(r)(3:2:5) Adding these equations we get the result for the CM motion that_V¼0,such that the CM moves with constant velocity throughout the collision.Now dividing thefirst of (3.2.5)by m1and the second by m2,and using the definition in(3.2.4)we havem R_v R¼F12(r)(3:2:6) which is the equation of motion of a“fictitious”particle with a reduced massm R¼m1m2m1þm2(3:2:7)in afixed central force F12(r).Thefictitious particle has mass m R,position r(t), velocity v R(t),and scattering angle Q,as shown in Figure3.4b.This result holds for any central force,including the hard-sphere,Coulomb,and polarization forces that we subsequently consider.If(3.2.6)can be solved to obtain the motion,includ-ing Q,then we can transform back to the laboratory frame to get the actual scattering angles u1and u2.It is easy to show from momentum conservation(Problem3.2)thattan u1¼sin Q(m1=m2)(v R=v0R)þcos Q(3:2:8a)andtan u2¼sin Qv R=v0RÀcos Q(3:2:8b)where v R and v0R are the speeds in the CM system before and after the collision, respectively.For an elastic collision,the scattering force can be written as the gradient of a potential that vanishes as r¼j r j!1:F12¼Àr U(r)(3:2:9) It follows that the kinetic energy of the particle is conserved for the collision in the CM system.Hence v0R¼v R,and we obtain from(3.2.8)thattan u1¼sin Q1=m2þcos Q(3:2:10)3.2COLLISION DYNAMICS51and,using the double-angle formula for the tangent,u2¼1(pÀQ)(3:2:11) For electron collisions with ions or neutrals,m1=m2(1and we obtain m R%m1 and u1%Q.For collision of a particle with an equal mass target,m1¼m2,we obtain m R¼m1=2and u1¼Q=2.Hence for hard-sphere elastic collisions against an initially stationary equal mass target,the maximum scattering angle is908.Since the same particles are scattered into the differential solid angle 2p sin Q d Q in the CM system as are scattered into the corresponding solid angle 2p sin u1d u1in the laboratory system,the differential scattering cross sections are related byI(v R,Q)2p sin Q d Q¼I(v R,u1)2p sin u1d u1(3:2:12)where d Q=d u1can be found by differentiating(3.2.10).Energy TransferElastic collisions can be an important energy transfer process in gas discharges,and can also be important for understanding inelastic collision processes such as ioniz-ation,as we will see in Section3.4.For the elastic collision of a projectile of mass m1 and velocity v1with a stationary target of mass m2,the conservation of momentum along and perpendicular to v1and the conservation of energy can be written in the laboratory system asm1v1¼m1v01cos u1þm2v02cos u2(3:2:13)0¼m1v01sin u1Àm2v02sin u2(3:2:14)1 2m1v21¼12m1v012þ12m2v022(3:2:15)where the primes denote the values after the collision.We can eliminate v01and u1 and solve(3.2.13)–(3.2.15)to obtain1 2m2v022¼12m1v214m1m2(m1þm2)2cos2u2(3:2:16)Since the initial energy of the projectile is12m1v21and the energy gained bythe target is12m2v022,the fraction of energy lost by the projectile in the laboratory52ATOMIC COLLISIONSsystem isz L¼4m1m2(m12)cos2u2(3:2:17) Using(3.2.11)in(3.2.17),we obtainz L¼2m1m2(m1þm2)2(1Àcos Q)(3:2:18)where Q is the scattering angle in the CM system.We average over the differential scattering cross section to obtain the average loss:k z L l Q¼2m1m2(m1þm2)2Ð(1Àcos Q)I(v R,Q)2p sin Q d Q ÐI(v R,Q)2p sin Q d Q¼2m1m2 (m1þm2)2s ms sc(3:2:19)where s sc and s m are defined in(3.1.14)and(3.1.15).For hard-sphere scattering of electrons against atoms,we have m1¼m(electron mass)and m2¼M(atom mass),and s sc¼s m by(3.1.19),such that k z L l Q¼2m=M 10À4.Hence electrons transfer little energy due to elastic collisions with heavy particles,allowing T e)T i in a typical discharge.On the other hand,for m1¼m2,we obtain k z L l Q¼12,leading to strong elastic energy exchange among heavy particles and hence to a common temperature.Small Angle ScatteringIn the general case,(3.2.6)must be solved to determine the CM trajectory and the scattering angle Q.We outline this approach and give some results in Appendix A. Here we restrict attention to small-angle scattering(Q(1)for which the fictitious particle moves with uniform velocity v R along a trajectory that is practi-cally unaltered from a straight line.In this case,we can calculate the transverse momentum impulse D p?delivered to the particle as it passes the center of force at r¼0and use this to determine Q.For a straight-line trajectory,as shown in Figure3.5,the particle distance from the center of force isr¼(b2þv2R t2)1=2(3:2:20)where b is the impact parameter and t is the time.We assume a central force of the form(3.2.9)withU(r)¼C(3:2:21)3.2COLLISION DYNAMICS53where i is an integer.The component of the force acting on the particle perpendicu-lar to the trajectory is (b =r )j d U =d r j .Hence the momentum impulse isD p ?¼ð1À1b r d U d r d t (3:2:22)Differentiating (3.2.20)to obtaind t ¼r v R d r(r 2Àb 2)1=2substituting into (3.2.22),and dividing by the incident momentum p k ¼m R v R ,we obtainQ ¼D p ?p k ¼2b m R v R ð1b d U d r d r (r 22)(3:2:23)The integral in (3.2.23)can be evaluated in closed form (Smirnov,1981,p.384)to obtainQ ¼AW R b (3:2:24)where W R ¼12m R v 2R is the CM energy andA ¼C ffiffiffiffip p G ½(i þ1)=2 (3:2:25)FIGURE 3.5.Calculation of the differential scattering cross section for small-angle scattering.The center-of-mass trajectory is practically a straight line.54ATOMIC COLLISIONSwith G ,the Gamma function.ÃInverting (3.2.24),we obtainb ¼A W R Q1=i (3:2:26)and differentiating,we obtaind b ¼À1i A W R 1=i d Q Q (3:2:27)Substituting (3.2.26)and (3.2.27)into (3.1.13),with sin Q %Q ,we obtain the differ-ential scattering cross section for small angles:I (v R ,Q )¼1i A W R 2=i 1Q 2þ2=i (3:2:28)The variation of s ,n ,and K with v R are determined from (3.2.28)and the basic definitions in Section 3.1.If (3.2.28)is substituted into (3.1.14)or (3.1.15),then we see that a scattering potential U /r Ài leads to s /v À4=i R and n /K /v À(4=i )þ1R .These scalings are summarized in Table 3.1for the important scattering processes,which we describe in the next section.3.3ELASTIC SCATTERINGCoulomb CollisionsThe most straightforward elastic scattering process is a Coulomb collision between two charged particles q 1and q 2,representing an electron–electron,electron–ion,or ion–ion collision.The Coulomb potential is U (r )¼q 1q 2=4pe 0r such that i ¼1and TABLE 3.1.Scaling of Cross Section s ,Interaction Frequency n ,and Rate Constant K ,With Relative Velocity v R ,for VariousScattering Potentials UProcessU (r )s n or K Coulomb1/r 1/v R 41/v R 3Permanent dipole1/r 21/v R 21/v R Induced dipole1/r 41/v RConst Hard sphere 1/r i ,i !1Const v RÃG (l )¼(l À1)!¼l G (l À1)with G (1=2)¼ffiffiffiffip p .3.3ELASTIC SCATTERING 55we obtainA¼C¼q1q2 4pe0from(3.2.25).Using this in(3.2.28),wefindI¼b0Q2(3:3:1)whereb0¼q1q240W R(3:3:2)is called the classical distance of closest approach.The differential scattering cross section can also be calculated exactly,which we do in Appendix A,obtaining the resultI¼b04sin(Q=2)2(3:3:3)However,due to the long range of the Coulomb forces,the integration of I oversmall Q(large b)leads to an infinite scattering cross section and to an infinitemomentum transfer cross section,such that an upper bound to b,b max,must beassigned.This is done by setting b max¼l De,the Debye shielding distance for a charge immersed in a plasma,which we calculated in Section2.4.For momentumtransfer,the dependence of s m on l De is logarithmic(Problem3.5),and the exact choice of b max(or Q min)makes little difference.For scattering,s sc pl2De, which is a very large cross section that depends sensitively on the choice of b max. However,we are generally not interested in scattering through very small angles, which do not appreciably affect the discharge properties.The cross section for scattering through a large angle,say Q!p=2,is of more interest.There are two processes that lead to a large scattering angle Q for a Coulombcollision:(1)a single collision scatters the particle by a large angle;(2)the cumu-lative effect of many small-angle collisions scatters the particle by a large angle.Thetwo processes are illustrated in Figure3.6;the latter process is diffusive and,as wewill see,dominates the former.To estimate the cross section s90(sgl)for a single large-angle collision,we inte-grate(3.3.3)over solid angles from p=2to p to obtain(Problem3.6)s90(sgl)¼14p b2(3:3:4)To estimate s90(cum)for the cumulative effect of many collisions to produce a p=2deflection,wefirst determine the mean square scattering angle k Q2l1for a 56ATOMIC COLLISIONSsingle collision by averaging Q 2over all permitted impact parameters.Since the col-lisions are predominantly small angle for Coulomb collisions,we can use (3.2.24),which is Q ¼b 0=b .Hencek Q 2l 1¼1p b 2max ðb max b min q 1q 24pe 0W R 22p b d b b 2(3:3:5)The integration has a logarithmic singularity at both b ¼0and b ¼1,which is cut off by the finite limits.The singularity at the lower limit is due to the small-angle approximation.Setting b min ¼b 0=2is found to approximate a more accurate calcu-lation.The upper limit,as already mentioned,is b max ¼l De .Using these values and integrating,we obtaink Q 2l 1¼2p b 20p b 2max ln L (3:3:6)where L ¼2l De =b 0)1.The number of collisions per second,each having a cross section of p b 2max orsmaller,is n g p b 2max v R ,where n g is the target particle density.Since the spreadingof the angle is diffusive,we can then writek Q 2l (t )¼k Q 2l 1n g p b 2max v R tSetting t ¼t 90at k Q 2l ¼(p =2)2and using (3.3.6),we obtain (see also Spitzer,1956,Chapter 5)n 90¼t À190¼n g v R 8p b 20lnLFIGURE 3.6.The processes that lead to large-angle Coulomb scattering:(a )single large-angle event;(b )cumulative effect of many small-angle events.3.3ELASTIC SCATTERING 57Writing n90¼n g s90v R,we see thats90¼8p b 2ln L(3:3:7)Although L is a large number,typically ln L%10for the types of plasmas we are considering.Comparing s90(sgl)to s90,we see that due to the large range of the Coulomb fields,the effective cross section for many small-angle collisions to produce a root mean square(rms)deflection of p=2is larger by a factor(32=p2)ln L. Because of this enhancement,it is possible for electron–ion or ion–ion particle col-lisions to play a role in weakly ionized plasmas(say one percent ionized).Another important characteristic of Coulomb collisions is the strong velocity dependence. From(3.3.2)we see that b0/1=v2R.Thus,from(3.3.4)or(3.3.7)s90/1v4R(3:3:8)such that low-velocity particles are preferentially scattered.The temperature of the species is therefore important in determining the relative importance of the various species in the collisional processes,as we shall see in subsequent sections.Polarization ScatteringThe main collisional processes in a weakly ionized plasma are between charged and neutral particles.For electrons at low energy and for ions scattering against neutrals, the dominant process is relatively short-range polarization scattering.At higher energies for electrons,the collision time is shorter and the atoms do not have time to polarize.In this case the scattering becomes more Coulomb-like,but with b max at an atomic radius,inelastic processes such as ionization become important as well.The condition for polarization scattering is v R.v at,where v at is the charac-teristic electron velocity in the atom,which we obtain in the next section.Because of the short range of the polarization potential,we need not be concerned with an upper limit for the integration over b,but the potential is more complicated.We determine the potential from a simple model of the atom as a point charge of valueþq0,sur-rounded by a uniform negative charge sphere(valence electrons)of total chargeÀq0,such that the charge density is r¼Àq0=43p a3,where a is the atomic radius.An incoming electron(or ion)can polarize the atom by repelling(or attracting) the charge cloud quasistatically.The balance of forces on the central point charge due to the displaced charge cloud and the incoming charged particle,taken to have charge q,is shown in Figure3.7,where the center of the charge cloud and the point charge are displaced by a distance d.Applying Gauss’law to a sphere 58ATOMIC COLLISIONSof radius d around the center of the cloud,4pe0d2E ind¼Àq0d3 awe obtain the induced electricfield acting on the point charge due to the displaced cloudE ind¼Àq0d 4pe0a3The electricfield acting on the point charge due to the incoming charge isE appl¼q 4pe0rFor force balance on the point charge,the sum of thefields must vanish,yielding an induced dipole moment for the atom:p d¼q0d¼qa3r2(3:3:9)The induced dipole,in turn,exerts a force on the incoming charged particle:F¼2p d q4pe0r3^r¼2q2a34pe0r5^r(3:3:10)FIGURE3.7.Polarization of an atom by a point charge q.3.3ELASTIC SCATTERING59Integrating F with respect to r,we obtain the attractive potential energy:U(r)¼Àq2a38pe0r4(3:3:11)The polarizability for this simple atomic model is defined as a p¼a3.The relative polarizabilities a R¼a p=a30,where a0is the Bohr radius,for some simple atoms and molecules are given in Table3.2.The orbits for scattering in the polarization potential are complicated(McDaniel, 1989).As shown in Figure3.8,there are two types of orbits.For impact parameter b.b L,the orbit has a hyperbolic character,and for b)b L,the straight-line trajec-tory analysis in Section3.2can be applied(Problem3.7).For b,b L,the incoming particle is“captured”and the orbit spirals into the core,leading to a large scattering angle.Either the incoming particle is“reflected”by the core and spirals out again,or the two particles strongly interact,leading to inelastic changes of state.The critical impact parameter b L can be determined from the conservation of energy and angular momentum for the incoming particle having mass m and speed v0,with the mass of the scatterer taken to be infinite for ease of analysis.In cylindrical coordinates(see Fig.3.8a),we obtain1 2m v2¼12m(_r2þr2_f2)þU(r)(3:3:12a)m v0b¼mr2_f(3:3:12b)TABLE3.2.Relative Polarizabilities a R5a p/a03ofSome Atoms and Molecules,Where a0is the Bohr RadiusAtom or Molecule a RH 4.5C12.N7.5O 5.4Ar11.08CCl469.CF419.CO13.2CO217.5Cl231.H2O9.8NH314.8O210.6SF630.Source:Smirnov(1981).60ATOMIC COLLISIONSAt closest approach,_r¼0and r ¼r min .Substituting these into (3.3.12)and elimi-nating _f ,we obtain a quadratic equation for r 2min:v 20r 4min Àv 20b 2r 2min þa p q 240m¼0Using the quadratic formula to obtain the solution for r 2min ,we see that there is noreal solution for r 2min when(v 20b 2)2À4v 20a p q 20 0Choosing the equality at b ¼b L ,we solve for b L to obtains L ¼p b 2L ¼pa p q 2e 0 1=21v 0(3:3:13)which is known as the Langevin or capture cross section.If the target particle has a finite mass m 2and velocity v 2and the incoming particle has a mass m 1and velocity v 1,then (3.3.13)holds provided m is replaced by the reduced mass m R ¼m 1m 2=(m 1þm 2)and v 0is replaced by the relative velocity v R ¼j v 1Àv 2j .We (a )(b )FIGURE 3.8.Scattering in the polarization potential,showing (a )hyperbolic and (b )captured orbits.3.3ELASTIC SCATTERING 61。

1987年全国硕士研究生入学统一考试英语试题Section I Close TestFor each numbered blank in the following passage there are four choices labeled ［A］, ［B］, ［C］and ［D］. Choose the best one and put your choice in the ANSWER SHEET. Read the whole passage before making your choice. (10 points)①Cheques have 1 replaced money as a means of exchange for they are widely accepted everywhere. ②Though this is very convenient for both buyer and seller, it should not be forgotten that cheques are not real money: they are quite valueless in themselves. ③A shop-keeper always runs a certain 2 when he accepts a cheque and he is quite 3 his rights if on occasion, he refuses to do so.④People do not always know this and are shocked if their good faith is called 4 . ⑤An old and very wealthy friend of mine told me he had an extremely unpleasant experience. ⑥He went to a famous jewelry shop which keeps a large 5 of precious stones and asked to be shown some pearl necklaces. ⑦After examining several trays, he decided to buy a particularly fine string of pearls and asked if he could pay by Cheques. ⑧The assistant said that this was quite 6 but the moment my friend signed his name, he was invited into the manager’s office.⑨The manager was very polite, but he explained that someone with exactly the same name had presented them with a worthless Cheque not long ago. ⑩My friend got very angry when he heard this and said he would buy a necklace somewhere else. ○11When he got up to go, the manager told him that the police would arrive at any moment and he had better stay 7 he wanted to get into serious trouble. ○128 , the police arrived soon afterwards. ○13They apologized to my friend for the 9 , but explained that a person who had used the same name as his was responsible for a number of recent robberies. ○14Then the police asked my friend to copy out a note which had been used by the thief in a number of shops. ○15The note10 : “I have a gun in my pocket. Ask no questions and give me all the money in the safe.”○16Fortunately, my friend’s handwriting was quite unlike the thief’s. ○17He was not only allowed to go without further delay, but to take the string of pearls with him. [356 words]1. ［A］exactly ［B］really ［C］largely ［D］thoroughly2. ［A］danger ［B］chance ［C］risk ［D］opportunity3. ［A］within ［B］beyond ［C］without ［D］out of4. ［A］in difficulty ［B］in doubt ［C］in earnest ［D］in question5. ［A］amount ［B］stock ［C］number ［D］store6. ［A］in order ［B］in need ［C］in use ［D］in common7. ［A］whether ［B］if ［C］otherwise ［D］unless8. ［A］Really ［B］Sure enough ［C］Certainly ［D］However9. ［A］treatment ［B］manner ［C］inconvenience ［D］behaviour10.［A］read ［B］told ［C］wrote ［D］informedSection II Reading ComprehensionEach of the two passages below is followed by five questions. For each question there are four answers. Read the passages carefully and choose the best answer to each of the questions. Put your choice in the brackets on the left. (10 points)Text 1①For centuries men dreamed of achieving vertical flight. ②In 400 A.D. Chinese children played with a fan-like toy that spun upwards and fell back to earth as rotation ceased. ③Leonardo da Vinci conceive the first mechanical apparatus, called a “Helix,” which could carry man straight up, but was only a design and was never tested.①The ancient-dream was finally realized in 1940 when a Russian engineer piloted a strange looking craft of steel tubing with a rotating fan on top. ②It rose awkwardly and vertically into the air from a standing start, hovered a few feet above the ground, went sideways and backwards, and then settled back to earth. ③The vehicle was called a helicopter.①Imaginations were fired. ②Men dreamed of going to work in their own personal helicopters. ③People anticipate that vertical flight transports would carry millions of passengers as do the airliners of today. ④Such fantastic expectations were not fulfilled.①The helicopter has now become an extremely useful machine. ②It excels in military missions, carrying troops, guns and strategic instruments where other aircraft cannot go. ③Corporations use them as airborne offices, many metropolitan areas use them in police work, construction and logging companies employ them in various advantageous ways, engineers use them for site selection and surveying, and oil companies use them as the best way to make offshore and remote work stations accessible to crews and supplies. ④Any urgent mission to a hard-to-get-to place is a likely task for a helicopter. ⑤Among their other multitude of uses: deliver people across town, fly to and from airports, assist in rescue work, and aid in the search for missing or wanted persons.11. People expect that ________.[A] the airliners of today would eventually bereplaced by helicopters[B] helicopters would someday be able to transportlarge number of people from place to place asairliners are now doing[C] the imaginations fired by t he Russian engineer’sinvention would become a reality in the future[D] their fantastic expectations about helicopterscould be fulfilled by airliners of today12. Helicopters work with the aid of ________.[A] a combination of rotating devices in front andon top[B] a rotating device topside[C] one rotating fan in the center of the aircraft andothers at each end[D] a rotating fan underneath for lifting13. What is said about the development of thehelicopter?[A] Helicopters have only been worked on byman since 1940.[B] Chinese children were the first to achieveflight in helicopters.[C] Helicopters were considered moredangerous than the early airplanes.[D] Some people thought they would becomewidely used by average individuals.14. How has the use of helicopters developed?[A] They have been widely used for variouspurposes.[B] They are taking the place of high-flyingjets.[C] They are used for rescue work.[D] They are now used exclusively forcommercial projects.15. Under what conditions are helicoptersfound to be absolutely essential?[A] For overseas passenger transportation.[B] For extremely high altitude flights.[C] For high-speed transportation.[D] For urgent mission to places inaccessible toother kinds of craft.Text 2①In ancient Greece athletic festivals were very important and had strong religious associations. ②The Olympian athletic festival held every four years in honor of Zeus, king of the Olympian Gods, eventually lost its local character, became first a national event and then, after the rules against foreign competitors had been abolished, international. ③No one knows exactly how far back the Olympic Games go, but some official records date from 776 B.C.①The games took place in August on the plain by Mount Olympus. ②Many thousands of spectators gathered from all parts of Greece, but no married woman was admitted even as a spectator. ③Slaves, women and dishonoredpersons were not allowed to compete. ④The exact sequence of ev ents uncertain, but events included boy’s gymnastics, boxing, wrestling, horse racing and field events, though there were fewer sports involved than in the modern Olympic Games.①On the last day of the Games, all the winners were honored by having a ring of holy olive leaves placed on their heads. ②So great was the honor that the winner of the foot race gave his name to the year of his victory. ③Although Olympic winners received no prize money, they were, in fact, richly rewarded by their state authorities.④How their results compared with modern standards, we unfortunately have no means of telling.①After an uninterrupted history of almost 1,200 years, the Games were suspended by the Romans in 394 A.D.②They continued for such a long time because people believed in the philosophy behind the Olympics: the idea that a healthy body produced a healthy mind, and that the spirit of competition in sports and games was preferable to the competition that caused wars. ③It was over 1,500 years before another such international athletic gathering took place in Athens in 1896.①Nowadays, the Games are held in different countries in turn. ②The host country provides vast facilities, including a stadium, swimming pools and living accommodation, but competing courtries pay th eir own athletes’ expenses.①The Olympics start with the arrival in the stadium of a torch, lighted on Mount Olympus by the sun’s rays.②It is carried by a succession of runners to the stadium. ③The torch symbolized the continuation of the ancient Greek athletic ideals, and it burns throughout the Games until the closing ceremony. ④The well-known Olympic flag, however, is a modern conception: the five interlocking rings symbolize the uniting of all five continents participating in the Games.16. In ancient Greece, the Olympic Games________.[A] were merely national athletic festivals[B] were in the nature of a national event with astrong religious colour[C] had rules which put foreign participants in adisadvantageous position[D] were primarily national events with fewforeign participants17. In the early days of ancient OlympicGames ________.[A] only male Greek athletes were allowed toparticipate in the games[B] all Greeks, irrespective of sex, religion orsocial status, were allowed to take part[C] all Greeks, with the exception of women,were allowed to compete in Games[D] all male Greeks were qualified to competein the Games18. The order of athletic events at the ancientOlympics ________.[A] has not definitely been established[B] varied according to the number of foreigncompetitors[C] was decided by Zeus, in whose honor theGames were held[D] was considered unimportant19. Modern athletes’results cannot becompared with those of ancient runners because_____.[A] the Greeks had no means of recording theresults[B] they are much better[C] details such as the time were not recordedin the past[D] they are much worse20. Nowadays, the athletes’ expenses are paidfor ________.[A] out of the prize money of the winners[B] out of the funds raised by the competingnations[C] by the athletes themselves[D] by contributionsText 3①In science the meaning of the word “explain” suffers with civilization’s every step in s earch of reality. ②Science cannot really explain electricity, magnetism, and gravitation; their effects can be measured and predicted, but of their nature no more is known to the modern scientist than to Thales who first looked into the nature of the electrification of amber, a hard yellowish-brown gum. ③Most contemporary physicists reject the notion that man can ever discover what these mysterious forces “really” are. ④“Ele ctricity,” Bertrand Russell says, “is not a thing, like St. Paul’s Cathedral; it is a way in which things behave. ⑤When we have told how things behave when they are electrified, and under what circumstances they are electrified, we have told all there is to tell.”⑥Until recentlyscientists would have disapproved of such an idea. ⑦Aristotle, for example, whose natural science dominated Western thought for two thousand years, believed that man could arrive at an understanding of reality by reasoning from self-evident principles. ⑧He felt, for example, that it is a self-evident principle that everything in the universe has its proper place, hence one can deduce that objects fall to the ground because that’s where they belong, and smoke goes up because that’s where it belongs. ⑨The goal of Aristotelian science was to explain why things happen. ⑩Modern science was born when Galileo began trying to explain how things happen and thus originated the method of controlled experiment which now forms the basis of scientific investigation.21. The aim of controlled scientificexperiments is ________.[A] to explain why things happen[B] to explain how things happen[C] to describe self-evident principles[D] to support Aristotelian science22. What principles most influenced scientificthought for two thousand years?[A] the speculations of Thales[B] the forces of electricity, magnetism, andgravity[C] Aristotle’s natural science[D] Galileo’s discoveries23. Bertrand Russell’s notion about electricityis ________.[A] disapproved of by most modern scientists[B] in agreement with Aristotle’s theory ofself-evident principles[C] in agreement with scientific investigationdirected toward “how” things happen[D] in agreement with scientific investigationdirected toward “why” things happen24. The passage says that until recentlyscientists disagreed with the idea ________.[A] that there are mysterious forces in theuniverse[B] that man cannot discover what forces“really” are[C] that there are self-evident principles[D] that we can discover why things behave asthey do25. Modern science came into being________.[A] when the method of controlled experimentwas first introduced[B] when Galileo succeeded in explaining howthings happen[C] when Aristotelian scientist tried to explainwhy things happen[D] when scientists were able to acquire anunderstanding of reality of reasoningSection III English-Chinese TranslationTranslate the following passage into Chinese. Only the underlined sentences are to be translated. (20 points)Have there always been cities? (26) Life without large urban areas may seem inconceivable to us, but actually cities are relatively recent development. Groups with primitive economics still manage without them. The trend, however, is for such groups to disappear, while cities are increasingly becoming the dominant mode of man’s social existence. (27) Historically, city life has always been among the elements which form a civilization. Any high degree of human endeavor and achievement has been closely linked to life in an urban environment. (28) It is virtually impossible to imagine that universities, hospitals, large businesses or even science and technology could have come into being without cities to support them. To most people, cities have traditionally been the areas where there was a concentration of culture as well as of opportunity. (29) In recent years, however, people have begun to become aware that cities are also areas where there is a concentration of problems. What has happened to the modern American city? Actually, the problem is not such a new one. Long before this century started, there had begun a trend toward the concentration of the poor of the American society into the cities. Each great wave of immigration from abroad and from the rural areas made the problem worse. During this century, there has also been the development of large suburban areas surrounding the cities, for the rich prefer to live in these areas. Within the cities, sections may be sharply divided into high and low rent districts, the “right side of town” and the slums.Of course, everyone wants to do something about this unhappy situation. But there is no agreement as to goals. Neither is there any systematic approach or integrated program. Opinions are as diverse as the people who give them. (30) But one basic difference of opinion concerns the question of whether or not the city as such is to be preserved. Perhaps transportation and the means of communication have really made it possible for there to be an end to the big cities. Of course, there is the problem of persuading people to move out of them of their own free will. (31) And there is also the objection that the city has always been the core from which cultural advancement has radiated. Is this, however, still the case today in the presence of easy transportation and communication? Does culture arise as a result of people living together communally, or is it too the result of decisions made at the level ofgovernment and the communications industry?It is probably true to say that most people prefer to preserve the cities. Some think that the cities could be cleaned up or totally rebuilt. This is easy to say; it would not be so easy to do. (32) To be sure, a great rebuilding project would give jobs to many of those people who need them. Living conditions could not help but improve, at least for a while. But would the problems return after the rebuilding was completed?Nevertheless, with the majority of the people living in urban areas, the problem of the cities must be solved.(33) From agreement on this general goal, we have, unfortunately, in the past proceeded to disagreement on specific goals, and from there to total inaction. At the basis of much of this inaction is an old-fashioned concept -- the idea human conditions will naturally tend to regulate themselves for the general goal.考研英语真题。

小学下册英语第6单元真题[含答案]考试时间：90分钟（总分:110）A卷一、综合题(共计100题共100分)1. 填空题：I love to play ______ (户外运动) with my friends. It keeps us active and healthy.2. 听力填空题：Learning new languages fascinates me. It opens doors to understanding different cultures and communicating with more people. I want to learn __________ next.3. 听力题：A solution with a low concentration of ions is called a ______ solution.4. 填空题：A _____ (草原) is filled with wildflowers in spring.5. 听力题：The ______ helps with digestion in the stomach.6. 听力题：The chemical formula for calcium carbonate is ______.7. 听力题：The study of the interactions between matter and energy is called _______.8. 选择题：What do you call the end of a story?A. BeginningB. MiddleC. ConclusionD. Chapter答案: C9. 填空题：The city of Rome is known for its ancient ________ (罗马以其古老的________而闻名).10. 选择题：How many months have 30 days?A. 7B. 8C. 9D. 10答案: A11. 选择题：What do you call a place where animals are kept?A. ZooB. FarmC. AquariumD. Park12. 听力题：The chemical formula for amyl acetate is ______.13. 选择题：What do you call a person who studies rocks?A. BiologistB. GeologistC. ChemistD. Astronomer答案:B14. 选择题：What do we call the act of joining two things together?A. ConnectionB. AttachmentC. BondingD. Linking答案：D15. 选择题：What is the process of taking in oxygen and expelling carbon dioxide?A. PhotosynthesisB. RespirationC. DigestionD. Circulation答案: B16. 选择题：What is the process of water turning into vapor called?A. EvaporationB. CondensationC. PrecipitationD. Sublimation17. 填空题：My cat loves to chase after ______ (昆虫).18. 听力题：I help my mom _____ (洗碗).19. 选择题：What do we call a baby horse?A. CalfB. FoalC. LambD. Kid20. 填空题：A ________ (植物繁殖方法) can differ greatly.21. 听力题：The reaction between an acid and a base produces _____.22. 选择题：What is the capital of Malta?A. VallettaB. MdinaC. RabatD. Birkirkara答案: A23. 选择题：What do we call the traditional Japanese art of folding paper?A. OrigamiB. CalligraphyC. IkebanaD. Sumi-e答案:A24. 选择题：What is the term for the process of water falling to the Earth?A. EvaporationB. PrecipitationC. CondensationD. FiltrationThe teacher is ______ (kind) to all students.26. 填空题：We should _______ (尊重) our elders.27. 听力填空题：I love reading mystery books. My favorite author is __________.28. 选择题：How do you say "goodbye" in Japanese?A. SayonaraB. KonnichiwaC. ArigatoD. Adiós29. 听力题：The dog is ________ to the park.30. 听力题：A lizard can be found ______ on a rock.31. 填空题：The ______ (蜘蛛) spins a web to catch its ______ (昆虫).32. 填空题：The first successful powered flight lasted _______ seconds. (12)33. 听力题：A polar molecule has a slight _____ charge.34. 听力题：The ______ teaches us about animal care.35. 听力题：The capital of Vietnam is __________.36. 选择题：What is the main source of light during the day?A. StarsB. SunC. MoonD. Lamp37. 听力题：I saw a _______ (deer) in the forest.The _______ of a light wave can be affected by its color.39. 选择题：What is the name of the imaginary line that runs from the North Pole to the South Pole?A. EquatorB. Prime MeridianC. International Date LineD. Longitude答案: D40. 填空题：The _____ (藤蔓) climbs up the trellis in my backyard.41. 选择题：What do you call the story of someone's life?A. BiographyB. NovelC. FictionD. Poem答案: A42. 填空题：My sister loves to play with her __________. (玩具)43. 选择题：Which season comes after summer?A. SpringB. WinterC. FallD. Summer答案:C44. 选择题：What do you call the layer of gases surrounding the Earth?a. Hydrosphereb. Biospherec. Atmosphered. Lithosphere答案:C45. 选择题：What is the name of the largest desert in the world?A. SaharaB. GobiC. ArcticD. Antarctic答案:A46. 听力题：She sings _____ (beautifully).47. 填空题：The jackal is a clever ______ (动物).48. 听力题：The Boston Tea Party was a protest against _______ taxes.49. 听力题：A radioactive element has an unstable _______.50. 听力题：She wears _____ (眼镜) to read.51. 填空题：The _____ (蜜蜂) buzzes around the flowers collecting nectar. 蜜蜂在花丛中嗡嗡作响，采集花蜜。

东北财经大学--工商管理专业学位外语考试参考试卷一、语音题（每空1分，共10分）01、notice['nəutis]A. stomachs['stʌməks]B. houses ['hauziz]C. mouths[mauθ]D. reasonable ['ri:zənəbl]02、winkle ['wiŋkl]A. windy ['windi]B. drink[driŋk]C. footprint ['futprint]D. interesting [ˈɪntrɪstɪŋ]03、shook [ʃuk]A. shoot [ʃu:t]B. food [fu:d]C. shoe [ʃu:]D. wood[wud]04、occasionally [ə'keiʒənəli]A. population[pɔpju'leiʃən]B. Russian['rʌʃən]C. question['kwestʃən]D. television['teli,viʒən]05、pressure ['preʃə]A. directly['direkli]B. oxygen 'ɔksidʒən]C. absence ['æbsəns]D. camera ['kæmərə]06、float [fləut]A. flower ['flauə]B. brown [braun]C. hometown ['həʊmtaʊn]D. bellows['beləuz]07、bulletin ['bulitin]A. bury ['beri]B. Prussian ['prʌʃən]C. bullet['bulit]D. punishment['pʌniʃmənt]08、breach [bri:tʃ]A. break [breik]B. theatre ['θiətə]C. meadow['medəu]D. least[li:st]09、opposite A. companion B. balloon C. stroll D. historic['ɔpəzit] [kəm'pænjən] [bə'lu:n] [strəul] [his'tɔrik] 10、scatter A. laboratory B. separate C. gravity D. various['skætə] [lə'bɔrətəri] ['sepərit] ['ɡræviti] ['vεəriəs] 11、essay A. holiday B. says C. away D. mayor[e'sei]['hɔlədi][sez][ə'wei]['mεə]12、singer A. anger B. tongue C. eager D. single['siŋə]['æŋɡə][tʌŋ]['i:ɡə]['siŋɡl]13、splendid A. watched B. refused C. wretched D. impressed['splendid][wɔtʃd][ri'fju:z ]['retʃid]['impres ]14、owner A. powerful B. brown C. narrow D. power ['əunə]['pauəful][braun]['nærəu][pauə]15、latent A. squirrel B. centigrade C. level D. mend['leitənt]['skwə:rəl]['sentiɡreid]['levəl][mend]16、flood A. loose B. blood C. moon D. noon[flʌd][lu:s][blʌd][mu:n][nu:n]17、mud A. music B. human C. huge D. lung[mʌd]['mju:zik]['hju:mən][hju:dʒ][lʌŋ]18、creature A. effect B. energy C. reduce D. belief['kri:tʃə] [i'fekt] ['enədʒi] [ri'dju:s] [bi'li:f]19、mountain A. explain B. remain C. campaign D. captain ['mauntin][ik'splein][ri'mein][kæm'pein]['kæptin]20、cookie A. frog B. oxygen C. wolf D. obvious['kuki] [frɔɡ] ['ɔksidʒən] [wulf] ['ɔbviəs]21、period A. request B. perseverance C. RecognizeD. require['piəriəd][ri'kwest][pə:si:'viərəns]['rekəɡnaiz][ri'kwaiə]22、geographyA. regretB. envy C. remark D. deck[dʒi'ɔɡrəfi] [ri'ɡret] ['envi] [ri'mɑ:k] [dek]23、replied A. entered B. askedC. stepped D. added [ri'plaid]['entəd][æskt] [stept]['ædid]24、counterA. country B. south C. tough D. enough ['kauntə]['kʌntri][sauð][tʌf][i'nʌf]25、eyebrow A. town B. followC. slow D. fellow['aibrau] [taun] ['fɔləu] [sləu] ['feləu]26、schoolyard A. coo B. cook C. poor D. childhood['sku:ljɑ:d] [ku:] [kuk] [pɔ:] ['tʃaildhud] 27、master A. Alsace B. tiresome C. impress D. unable['mæstə] ['a:əθas] ['taiəsəm] ['impres] [ʌn'eibl]28、twinkle A. windy B. drink C. footprint D. interesting['twiŋkl] ['windi] [driŋk] ['futprint] [ˈɪntrɪstɪŋ]二、单选题（每空1.5分，共30分）01、Since your supervisor has __specified___ the time for a talk, you must make sure that you will be there on time.因为你的上司有特定的时间谈谈,你必须保证你会准时到那儿的。