Transport coefficients in the early universe
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Mathematical Astronomy1.A brief history of cosmologyFour thousand years ago the Babylonians were skilled astronomers who were able to predict the apparent motions of the moon and the stars and the planets and the Sun upon the sky, and could even predict eclipses. But it was the Ancient Greeks who were the first to build a cosmological model within which to interpret these motions. In the fourth century BC, they developed the idea that the stars were fixed on a celestial sphere which rotated about the spherical Earth every 24 hours, and the planets, the Sun and the Moon, moved in the ether between the Earth and the stars. This model was further developed in the following centuries, culminating in the second century AD with Ptolemy's great system. Perfect motion should be in circles, so the stars and planets, being heavenly objects, moved in circles. However, to account for the complicated motion of the planets, which appear to periodically loop back upon themselves, epicycles had to be introduced so that the planets moved in circles upon circles about the fixed Earth.Despite its complicated structure, Ptolemy produced a model so successful at reproducing the apparent motion of the planets that when, in the sixteenth century, Copernicus proposed a heliocentric system, he could not match the accuracy of Ptolemy's Earth-centred system. Copernicus constructed a model where the Earth rotated and, together with the other planets, moved in a circular orbit about the Sun. But the observational evidence of the time favoured the Ptolemaic system!There were other practical reasons why many astronomers of the time rejected the Copernican notion that the Earth orbited the Sun. Tycho Brahe was the greatest astronomer of his the sixteenth century. He realised that if the Earth was moving about the Sun, then the relative positions of the stars should change as viewed from different parts of the Earth's orbit. But there was no evidence of this shift, called parallax. Either the Earth was fixed, or else the stars would have to be fantastically far away.It was only with the aid of the newly-invented telescope in the early seventeenth century that Galileo could deal a fatal blow to the notion that the Earth was at the centre of the Universe. He discovered moons orbiting the planet Jupiter. And if moons could orbit another planet, why could not the planets orbit the Sun?At the same time, Tycho Brahe's assistant Kepler discovered the key to building a heliocentric model. The planets moved in ellipses, not perfect circles, about the Sun. Newton later showed that elliptical motion could be explained by his inverse-square law for the gravitational force.But the absence of any observable parallax in the apparent positions of the stars as the Earth rotated the Sun, then implied that the stars must be at a huge distance from the Sun. The cosmos seemed to be a vast sea of stars. With the aid of his telescope, Galileo could resolve thousands of new stars which were invisible to the naked eye. Newton concluded that the Universe must be an infinite and eternal sea of stars, each much like our own Sun.It was not until in the nineteenth century that the astronomer and mathematicianBessel finally measured the distance to the stars by parallax. The nearest star (other than the Sun) turned out to be about 25 million, million miles away! (By contrast the Sun is a mere 93 million miles away from the Earth.)Most of the stars we can see are contained in the Milky Way - the bright band of stars that stretches across our night sky. Kant and others proposed that our Milky Way was in fact a lens shaped "island universe'' or galaxy, and that beyond our own Milky Way must be other galaxies.As well as stars and planets, astronomers had noted fuzzy patches of light on the night sky, which they called nebulae. Some astronomers thought these could be distant galaxies. It was only in the 1920's that the American astronomer Hubble established that some of these nebulae were indeed distant galaxies comparable in size to our own Milky Way.Hubble also made the remarkable discovery that these galaxies seemed to be moving away from us, with a speed proportional to their distance from us. It was soon realised that this had a very natural explanation in terms of Einstein's recently discovered General Theory of Relativity: our Universe is expanding!In fact, Einstein might have predicted that the Universe is expanding after he first proposed his theory in 1915. Matter tends to fall together under gravity so it was impossible to have a static universe. However, Einstein realised he could introduce a arbitrary constant into his mathematical equations, which could balance the gravitational force and keep the galaxies apart. This became known as the cosmological constant. After it was discovered that the Universe wa s actually expanding, Einstein declared that introducing the cosmological constant was the greatest blunder of his life!The Russian mathematician and meteorologist Friedmann had realised in 1917 that Einstein equations could describe an expanding universe. This solution implied that the Universe had been born at one moment, about ten thousand million years ago in the past and the galaxies were still travelling away from us after that initial burst. All the matter, indeed the Universe itself, was created at just one instant. The British astronomer Fred Hoyle dismissively called it the "Big Bang'', and the name stuck. There was a rival model, called the Steady State theory - advocated by Bondi, Gold and Hoyle - developed to explain the expansion of the Universe. This required the continuous creation of matter to produce new galaxies as the universe expanded, ensuring that the Universe could be expanding, but still unchanging in time.For many years it seemed a purely academic point, whether the universe was eternal and unchanging, or had only existed for a finite length of time. But a decisive blow was dealt to the Steady State model when in 1965 Penzias and Wilson discovered a cosmic microwave background radiation. This was interpreted as the faint afterglo w of the intense radiation of a Hot Big Bang, which had been predicted by Alpher and Hermann back in 1949.Following on from earlier work by Gamow, Alpher and Herman in the 1940's, theorists calculated the relative abundances of the elements hydrogen and helium that might be produced in a Hot Big Bang and found it was in good agreement with the observations. When the abundance of other light elements was calculated these toowere consistent with the values observed.Since the 1970's almost all cosmologists have come to accept the Hot Big Bang model and have begun asking more specific, but still fundamental, questions about our Universe. How did the galaxies and clusters of galaxies that we observe today form out of the primordial expansion. What is most of the matter in the Universe made of? How do we know that there are not black holes or some kind of dark matter out there which does not shine like stars? General relativity tells us that matter curves space-time, so what shape is the Universe? Is there a cosmological constant after all? We are only beginning to find answers to some of these questions. The cosmic microwave background radiation plays a key role as it gives us a picture of the universe as it was only a hundred thousand years after the Big Bang. It turns out to be so remarkably uniform, that it was only in 1992 that NASA's Cosmic Background Explorer satellite detected the first anisotropies in this background radiation. There are slight fluctuations in the temperature of the radiation, about one part in a hundred thousand, which may be the seeds from which galaxies formed.Since the early 1980's there has been an explosion of interest in the physics of the early universe. New technology and satellite experiments, such as the Hubble Space Telescope, have brought us an ever improving picture of our Universe, inspiring theorists to produce ever more daring models, drawing upon the latest ideas in relativity and particle physics.2.Greek astronomyToday the study of astronomy requires a deep understanding of mathematics and physics. It is important to realise that Greek astronomy (we are interested in the topic during the 1000 years between 700 BC and 300 AD) did not involve physics. Indeed, as Pannekoek points out in [7], a Greek astronomer aimed only to describe the heavens while a Greek physicist sought out physical truth. Mathematics provided the means of description, so astronomy during the 1000 years that interest us in this article was one of the branches of mathematics.The Greeks began to think of philosophy from the time of Thales in about 600 BC. Thales himself, although famed for his prediction of an eclipse, probably had little knowledge of astronomy, yet he brought back from Egypt knowledge of mathematics into the Greek world and possibly also some knowledge of Babylonian astronomy. It is reasonable to begin by looking at what 'astronomy' was in Greece around this time. However we begin by looking further back than this to around 700 BC.Basically at this time astronomy was all to do with time keeping. It is natural that astronomical events such as the day would make a natural period of time and likewise the periodic phases of the moon make the next natural time span. Indeed these provided the basic methods of time keeping around the period of 700 BC yet, of course, another important period of time, the year, was not easy to determine in terms of months. Y et a knowledge of the approximate length of the year was vital for food production and so schemes had to be devised. Farmers at this time would base their planting strategies on the rising and setting of the constellations, that is the times when certain constellations would first become visible before sunrise or were last visible after sunset.Hesiad, one of the earliest Greek poets, often called the "father of Greek didactic poetry" wrote around 700 BC. Two of his complete epics have survived, the one relevant to us here is Works and Days describing peasant life. In this work Hesiad writes that (see [5], also [1] and [7]):-... when the Pleiades rise it is time to use the sickle, but the plough when they are setting; 40 days they stay away from heaven; when Arcturus ascends from the sea and, rising in the evening, remain visible for the entire night, the grapes must be pruned; but when Orion and Sirius come in the middle of heaven and the rosy fingered Eos sees Arcturus, the grapes must be picked; when the Pleiades, the Hyades, and Orion are setting, then mind the plough; when the Pleiades, fleeing Orion, plunge into the dark sea, storms may be expected; 50 days after the sun's turning is the right time for man to navigate; when Orion appears, Demeter's gift has to be brought to the well-smoothed threshing floor.For many hundreds of years astronomers would write works on such rising and setting of constellations indicating that the type of advice given by Hesiad continued to be used.An early time scale based on 12 months of 30 days did not work well since the moon rapidly gets out of phase with a 30 day month. So by 600 BC this had bee n replaced by a year of 6 'full' months of 30 days and 6 'empty' months of 29 days. This improvement in keeping the moon in phase with the month had the unfortunate effect of taking the year even further out of phase with the period of the recurring seasons. About the same time as Thales was making the first steps in philosophy, Solon, a statesman in Athens who became known as one of the Seven Wise Men of Greece, introduced an improved calendar.Solon's calendar was based on a two yearly cycle. There were 13 months of 30 days and 12 months of 29 days in each period of two years so this gave a year of about 369 days and a month of 291/2days. However, the Greeks relied mainly on the moon as their time-keeper and frequent adjustments to the calendar were necessary to keep it in phase with the moon and the seasons. Astronomy was clearly a subject of major practical importance in sorting out the mess of these calendars and so observations began to be made to enable better schemes to be devised.Pythagoras, around 500 BC, made a number of important advances in astronomy. He recognised that the earth was a sphere, probably more because he believed that a sphere was the most perfect shape than for genuine scientific reasons. He also recognised that the orbit of the Moon was inclined to the equator of the Earth and he was one of the first to realise that V enus as an evening star was the same planet as V enus as a morning star. There is a pleasing appeal to observational evidence in these discoveries, but Pythagoras had a philosophy based on mathematical 'perfection' which tended to work against a proper scientific approach. On the other side there is an important idea in the Pythagorean philosophy which had a lasting impact, namely the idea that all complex phenomena must reduce to simple ones. One should not underestimate the importance of this idea which has proved so powerful throughout the development of science, being a fundamental driving force to the great scientists such as Newton and particularly Einstein.Around 450 BC Oenopides is said to have discovered the ecliptic made an angle of 24° with the equator, which was accepted in Greece until refined by Eratosthenes in around 250 BC. Some scholars accept that he discovered that the ecliptic was at an angle but doubt that he measured the angle. Whether he learnt of the 12 signs of the zodiac from scholars in Mesopotamia or whether his discoveries were independent Greek discoveries is unknown. Oenopides is also credited with suggesting a calendar involving a 59 year cycle with 730 months. Other schemes proposed were 8 year cycles, with extra months in three of the eight years and there is evidence that this scheme was adopted.About the same time as Oenopides proposed his 59 year cycle, Philolaus who was a Pythagorean, also proposed a 59 year cycle based on 729 months. This seemed to owe more to the numerology of the Pythagoreans than to astronomy since 729 is 272, 27 being the Pythagorean number for the moon, while it is also 93, 9 being the Pythagorean number associated with the earth. Philolaus is also famed as the first person who we know to propose that the earth moves. He did not have it orbiting the sun, however, but rather all the heavenly bodies went in circles round a central fire which one could never see since there was a counter earth between the earth and the fire. This model, certainly not suggested by any observational evidence, is more likely to have been proposed so that there were 10 heavenly bodies, for 10 was the most perfect of all numbers to the Pythagoreans.Meton, in 432 BC, introduced a calendar based on a 19 year cycle but again this is similar to one devised in Mesopotamia some years earlier. Meton worked in Athens with another astronomer Euctemon, and they made a series of observations of the solstices (the points at which the sun is at greatest distance from the equator) in order to determine the length of the tropical year. Again we do not know if the 19 year cycle was an independent discovery or whether Greek advances were still based on earlier advances in Mesopotamia. Meton's calendar never seems to have been adopted in practice but his observations proved extremely useful to later Greek astronomers such as Hipparchus and Ptolemy.That Meton was famous and widely known is seen from the play Birds written by Aristopenes in about 414 BC. Two characters are speaking, one is Meton [see D Barrett (trs.), Aristophanes, Birds (London, 1978)]:-Meton: I propose to survey the air for you: it will have to be marked out in acres. Peisthetaerus: Good lord, who do you think you are?Meton: Who am I? Why Meton. THE Meton. Famous throughout the Hellenic world - you must have heard of my hydraulic clock at Colonus?Meton and Euctemon are associated with another important astronomical invention of the time, namely a parapegma. A parapegma was a stone tablet with movable pegs and an inscription to indicate the approximate correspondence between, for example, the rising of a particular star and the civil date. Because the calendar had to be changed regularly to keep the civil calendar in phase with the astronomical one, the parapegma had movable pegs which could be adjusted as necessary. A parapegma soon also contained meteorological forecasts associated with the risings and settings of the stars and not only were stone parapegma constructed but also ones on papyri.Meton and Euctemon are usually acknowledged as the inventors of parapegmata and certainly many later astronomers compiled the data nessary for their construction. There is evidence for other observational work being undertaken around this time, for Vitruvius claims that Democritus of Abdera, famed for his atomic theory, devised a star catalogue. We have no knowledge of the form this catalogue took but Democritus may well have described the major constellations in some way.The beginning of the 4th century BC was the time that Plato began his teachings and his writing was to have a major influence of Greek thought. As far as astronomy is concerned Plato had a negative effect, for although he mentions the topic many times, no dialogue is devoted to astronomy. Worse still, Plato did not believe in astronomy as a practical subject, and condemned as lowering the spirit the actual observation of the heavenly bodies. Plato only believed in astronomy to the extent that it encouraged the study of mathematics and suggested beautiful geometrical theories.Perhaps we should digress for a moment to think about how the ideas of philosophy which were being developed by Plato and others affected the development of astronomy. Neugebauer [6] feels that philosophy had a detrimental affect:-I see no need for considering Greek philosophy as an early stage in the development of science ... One need only read the gibberish of Proclus's introduction to his huge commentary on Book I of Euclid's Elements to get a vivid picture of what would have become of science in the hands of philosophers. The real "Greek miracle" is the fact that a scientific methodology was developed, and survived, in spite of a widely admired dogmatic philosophy.Although there is some truth in what Neugebauer writes here, I [EFR] feel that he has overstated his case. It is true that philosophers came up with ideas about the universe which were not based on what we would call today the scientific method. However, the very fact that theories were proposed which could be shown to be false by making observations, must have provided a climate where the scientific approach could show its strength. Also the fact the philosophy taught that one should question all things, even "obvious" truths, was highly beneficial. Another important philosophical idea which had important consequences from the time of Pythagoras, and was emphasised by Plato, was that complex phenomena must be consequences of basic simple phenomena. As Theon of Smyrna expressed it, writing in the first century AD:-The changing aspects of the revolution of the planets is because, being fixed in their own circles or in their own shperes whose movements they follow, they are carried across the zodiac, just as Pythagoras had first understood it, by a regulated simple and equal revolution but which results by combination in a movement that appears variable and unequal.This led Theon to write:-It is natural and necessary that all the heavenly bodies have a uniform and regular movement.Perhaps the most telling argument against the above claim by Neugebauer is that our present idea of space-time, as developed from Einstein's theory of relativity, was suggested more by the basic philosophy of simplicity than by experimental evidence. The advances made not long after the time of Plato by Eudoxus, incorporating theidea of basic simplicity as expressed in Pythagorean and Platonic philosophy, were made by an outstanding mathematician and astronomer. In fact Eudoxus marks the beginning of a new phase in Greek astronomy and must figure as one of a small number of remarkable innovators in astronomical thought. Eudoxus was the first to propose a model whereby the apparently complex motions of the heavenly bodies did indeed result from simple circular motion. He built an observatory on Cnidus and from there he observed the star Canopus. The star Canopus played an important role in early astronomy, for it is seen to set and rise in Cnidus yet one does no have to go much further north from there before it can never be seen. The observations made at Eudoxus's observatory in Cnidus, as well as those made at an observatory near Heliopolis, formed the basis of a book concerning the rising and setting of the constellations. Eudoxus, another who followed Pythagorean doctrines, proposed a beautiful mathematical theory of concentric spheres to describe the motion of the heavenly bodies. It is clear that Eudoxus thought of this as a mathematical theory, and did not believe in the spheres as physical objects.Although a beautiful mathematical theory, Eudoxus's model would not have stood the test of the simplest of observational data. Callippus, who was a pupil of Polemarchus himself a pupil of Eudoxus, refined this system as presented by Eudoxus. The reason that we have so much information about the spheres of Eudoxus and Callippus is that Aristotle accepted the theory, not not as a mathematical model as originally proposed, but rather as spheres which have physical reality. He discussed the interactions of one sphere on another, but there is no way that he could have had enough understanding of physics to get anywhere near describing the effects of such an interaction. Although in many areas Aristotle advocated a modern scientific approach and he collected data in a scientific way, this was unfortunately not the case in astronomy. As Berry writes [2]:- There are also in Aristotle's writings a number of astronomical speculations, founded on no solid evidence and of little value ... his original contributions are not comparable with his contributions to the mental and moral sciences, but are inferior in value to his work in other natural sciences ...As Berry goes on to say, this was very unfortunate for astronomy since the influence of the writings of Aristotle had an authority for many centuries which meant that astronomers had a harder battle than they might otherwise have had in getting the truth accepted.The next development which was absolutely necessary for progress in astronomy took place in geometry. Spherical geometry was developed by a number of mathematicians with an important text being written by Autolycus in Athens around 330 BC. Some claim that Autolycus based his work on spherical geometry On the Moving Sphere on an earlier work by Eudoxus. Whether or not this is the case there is no doubt that Autolycus was strongly influenced by the views of Eudoxus on astronomy. Like so many astronomers, Autolycus wrote a work On Risings and Settings which is a book on observational astronomy.After Autolycus the main place for major developments in astronomy seemed to move to Alexandria. There Euclid worked and wrote on geometry in general but also making an important contribution to spherical geometry. Euclid also wrotePhaenomena which is an elementary introduction to mathematical astronomy and gives results on the times stars in certain positions will rise and set.Aristarchus, Timocharis and Aristyllus were three astronomers who all worked at Alexandria and their lives certainly overlapped. Aristyllus was a pupil of Timocharis and in Maeyama [23] analyses 18 of their observations and shows that Timocharis observed around 290 BC while Aristyllus observed a generation later around 260 BC. He also reports an astounding accuracy of 5' for Aristyllus' observations. Maeyama writes [23]:- The order of accuracy is an essential measure for the development of natural sciences. accuracy is in fact more than the mere operation of measuring. Accuracy increases only by virtue of active measuring. There cannot exist a high order of observational accuracy which is not connected with a high order of observations. Hence my assumption is that there must have been abundant accurate observations of the fixed stars made at least at the epochs 300 BC - 250 BC in Alexandria. They must have disappeared in the fires which frequently raged there. Maeyama also points out that this is the period when the coordinate systems for giving stellar positions originated. Both the equatorial and the ecliptic systems appear at this time. But why were these observations being made? This is a difficult question to answer for on the face of it there seems little point in the astronomers of Alexandria striving for observational accuracy at this time. In [34] van der Waerden makes an interesting suggestion related to the other important astronomer who worked in Alexandria around this time, namely Aristarchus.We know that Aristarchus measured the ratio of the distances to the moon and to the sun and, although his methods could never yield accurate results, they did show that the sun was much further from the earth than was the moon. His results also showed that the sun was much larger than the earth, although again his measurements were very inaccurate. Some historians believe that this knowledge that the sun was the largest of the three bodies, earth, moon and sun, led him to propose his heliocentric theory. Certainly it is for this theory, as reported by Archimedes, that Aristarchus has achieved fame. His sun-centred universe found little favour with the Greeks, however, who continued to develop more and more sophisticated models based on an earth centred universe.Now Goldstein and Bowen in [16] attempt to answer the question of why Timocharis and Aristyllus made their accurate observations. These authors do not find a clear purpose for the observations, such as the marking of a globe. However van der Waerden in [34] suggests that the observations were made to determine the constants in the heliocentric theory of Aristarchus. Although this theory has strong attractions, and makes one want to believe in it, all the evidence suggests that Timocharis certainly began his observations some time before Aristarchus proposed his heliocentric universe.Goldstein and Bowen in [16] make other interesting suggestions. They believe that the observations of Timocharis and Aristyllus recorded the distance from the pole, and the distances between stars. They argued that the observations were made by means of an instrument similar to Heron's dioptra. These are interesting observations since the work of Timocharis and Aristyllus strongly influenced the most important of all of theGreek astronomers, namely Hipparchus, who made his major contribution about 100 years later. During these 100 years, however, there were a number of advances. Archimedes measured the apparent diameter of the sun and also is said to have designed a planetarium. Eratosthenes made important measurements of the size of the earth, accurately measured the angle of the ecliptic and improved the calendar. Apollonius used his geometric skills to mathematically develop the epicycle theory which would reach its full importance in the work of Ptolemy.The contributions of Hipparchus are the most important of all the ancient astronomers and it is fair to say that he made the most important contribution before that of Copernicus in the early sixteenth century. As Berry writes in [2]:- An immense advance in astronomy was made by Hipparchus, whom all competent critics have agreed to rank far above any other astronomers of the ancient world, and who must stand side by side with the greatest astronomers of all time.It is Hipparchus's approach to science that ranks him far above other ancient astronomers. His approach, based on data from accurate observations, is essentially modern in that he collected his data and then formed his theories to fit the observed facts. Most telling regarding his understanding of the scientific method is the fact that he proposed a theory of the motion of the sun and the moon yet he was not prepared to propose such a theory for the planets. He realised that his data was not sufficiently good or sufficiently plentiful to allow him to base a theory on it. However, he made observations to help his successors to develop such a theory. Delambre, in his famous work on the history of astronomy, writes:- When we consider all that Hipparchus invented or perfected, and reflect upon the number of his works and the mass of calculations which they imply, we must regard him as one of the most astonishing men of antiquity, and as the greatest of all in the sciences which are not purely speculative, and which require a combination of geometrical knowledge with a knowledge of phenomena, to be observed only by diligent attention and refined instruments. Although a great innovator, Hipparchus gained important understanding from the Babylonians. As Jones writes in [21]:- For Hipparchus, the availability of the Babylonian predictive methods was a boon.We will not describe the contributions of Hipparchus and Ptolemy in detail in this article since these are given fully in their biographies in our archive. Suffice to end this article with a quotation from [6]:- Alexandria in the second century AD saw the publication of Ptolemy's remarkable works, the 'Almagest' and the 'Handy Tables', the 'Geography', the 'Tetrabiblos', the 'Optics', the 'Harmonics', treatises on logic, on sundials, on stereographic projection, all masterfully written, products of one of the greatest scientific minds of all times. The eminence of these works, in particular the 'Almagest', had been evident already to Ptolemy's contemporaries. this caused an almost total obliteration of the prehistory of the Ptolemaic astronomy.Ptolemy had no successor. What is extant from the later Roman times is rather sad.....3.Mathematical discovery of planetsThe first planet to be discovered was Uranus by William and Caroline Herschel on 13 March 1781. It was discovered by the fact that it showed a disk when viewed through even a fairly low powered telescope. The only other planets which have been。
安徽省合肥市第一中学2024-2025学年高二上学期期中考试英语试卷一、阅读理解Impressive exhibitions in the US worth traveling for in 2024 Here are several museum exhibitions across the USA that are worth traveling for in 2024.1. Yayoi Kusama: Infinite LoveSFMOMA, San FranciscoOn view: now through September 7For six decades now, Japanese polymath Yayoi Kusama has been exploring the concept of the “infinity room.” These meditations on perception, the universe and existence itself combine bold colors, three-dimensional forms and mirror-generated visual illusions to transport viewers to an inclusive aesthetic world. In the exhibition Yayoi Kusama: Infinite Love, they have landed in Northern California for the first time. Featured works including the brand-new Dreaming of Earth’s Sphericity, I Would Offer My Love (2023) and the famous LOVE IS CALLING (2013) will be on display at SFMOMA through next fall. Be sure to reserve advance tickets the minute they go on sale.2. Matisse and the SeaSt Louis Art Museum, St LouisOn view: February 17-May 12,2024Henri Matisse lived for decades near the Mediterranean, and a number of blues carry through his entire oeuvre (全部作品), largely inspired by the reflection of light of the water. With the artist’s Bathers with Turtle (1907–8) as a museum highlight, the exhibition travels across both Matisse’s works and the world itself, with works by this 20th-century master in various media, depicting the sea as a subject and as a theme.3. Georgia O’ Keeffe: “My New Yorks”Art Institute of Chicago, ChicagoOn view: June 2-September 24,2024This show at the Art Institute of Chicago will explore how Georgia O’ Keeffe - an artist soclosely associated with the Southwest and nature - spent her formative years in the USA’s biggest city. Before she turned her eye to flowers and desert sunsets, Georgia O’ Keeffe captured the distinctive perspectives of New York City, looking up at skyscrapers from street level and down from her 30th-floor apartment.4. Whitney Biennial 2024: Even Better Than the Real ThingWhitney Museum of American Art, New Y ork CityOn view: starting March 20,2024Some leave angry. Others emerge inspired. Yet however you react, it’s hard to forget any Whitney Biennial. Multimedia pieces and political themes are never hard to detect. Organized by Chrissi e Iles and Meg Onli, the lineup at this year’s -Biennial has yet to be announced. But whoever the participants are, their work is sure to make a statement.1.What can we learn from the artist Yayoi Kusama and his works?A.His work Infinite Love has been on display for decades.B.His works feature incorporating varied colors boldly into the works.C.Dreaming of Earth’s Sphericity was inspired by the light of water.D.Four-dimensional forms will transport viewers to the universe.2.Who is most likely to be the target audience for the last exhibition?A.people concerned with current political affairs.B.people having a passion for economy.C.people fond of pursuing old fashion.D.people enthusiastic about different reactions. 3.What do the exhibition 2 and 3 have in common?A.Both artists prefer using city landscape in the works.B.Both exhibitions need to be reserved in advance.C.Both artists’ works focus on themes concerning surroundings.D.Both artists’ works embody political themes.My husband and I fell in love when we would sit and talk in the living room of my old apartment in front of the windows drinking cups of black coffee, sometimes until sunrise. I was so extremely fortunate to have finally found that one special person.However, it was soon after our honeymoon that my husband climbed into the tomb called “the office” and buried himself in piles of paperwork and clients, and I just kept silent for fear ofturning into a complaining wife. It seemed as if overnight an invisible wall had been put up between us. He just lay beside snoring like a hibernating bear unaware of my winter.When our daughter was born, my life was centred on her and I no longer seemed to care that my husband was getting busier and spending less time at home. Somewhere between his work timetable and our home and young daughter, we were losing contact with each other. That invisible wall was now being hardened by the mortar (砂浆) of indifference.Then tragedy struck our lives, when my husband’s younger brother was killed in 2001, together with thousands of other innocent people. He was identified only by the engraving (雕刻) on the inside of his wedding ring. Attending our brother’s memorial service was an eye-opening experience for both of us. For the first time, we saw our own marriage was almost like my in-laws. At the tragic death of the youngest son they could not reach out to comfort one another. It seemed as if somewhere between the oldest son’s first tooth and the youngest son’s graduation they had lost each other.Later one night, my husband told of his fear of dying and I spoke of trying to find myself in the writings of my journal. It seemed as if each of us had been hiding our soul-searching from the other.We are slowly working toward building a bridge - not a wall, so that when we reach out to each other, we do not find a barrier we cannot pass through or retreat from the stranger on the other side.4.what can we learn about the author’s husband From the second paragraph?A.He was fully involved in his work.B.He didn’t show any affection for her.C.He preferred his work to his family D.He got tired of his nagging wife5.What does the underlined word in Paragraph 4 mean?A.The author’s husband’s brothers.B.The author’s husband’s brothers-in-law.C.The author’s husband’s parents.D.The author’s husband’s sisters-in-law. 6.Which of the following best describe the author?A.Dependent and critical.B.Sensitive and sensible.C.Sympathetic and emotional.D.Ambitious and understanding.7.What can we infer from the passage about the couple?A.Attending the memorial service worsened their relationship.B.Their brother’s death set off their reflection on marriage.C.Communication was a most effective means to break the barrier.D.The fear of dying prevented the husband from reaching out.Nobel science prizes are awarded in three areas: physics, chemistry and physiology or medicine. But occasionally some noteworthy discovery comes along that does not really fit into any of them. Similar flexibility, though in an area with far more profound consequences than ethology (行为学), has been demonstrated with regard to this year’s physics prize.Showing a sense of timeliness not always apparent in its deliberations, Sweden’s Royal Academy of Science has stretched the definition of physics to include computer science, and given its recognition to two of the pioneers of the artificial-intelligence (AI) revolution.John Hopfield of Princeton University and Geoffrey Hinton of the University of Toronto both did their crucial work in the early 1980s, at a time when computer hardware was unable to take full advantage of it. Dr Hopfield was responsible for what has become known as the Hopfield network - a type of artificial neural network that behaves like a physical structure called a spin glass, which gave the academy a fa int reason to call the field "physics". Dr Hinton’s contribution was to use an algorithm (算法) known to train neural networks.Artificial neural networks are computer programs based loosely on the way in which real; biological networks of nerve cells are believed to work. In particular, the strengths of the connections between "nodes" (结点) in such networks are plastic. Hopfield networks, in which each node is connected to every other except itself, are particularly good at learning to extract patterns from sparse (稀疏的) or noisy data.Dr Hinton’s algorithm enhances neural networks’ learning ability by letting them work, in effect, in three dimensions. Hopfield networks and their types are, in essence, two-dimensional. Though they actually exist only as simulations in software, they can be thought of as a structure of physical layers of nodes. Dr Hinton adjusted Dr Hopfield’s networks using a branch of maths called statistical mechanics to create what are known as Boltzmann machines. Boltzmann machines can be used to create systems that learn in an unsupervised manner, spotting patterns in data without having to be explicitly taught.It is, then, the activities of these two researchers which have made machine learning reallysing. AI models can now not only learn, but create. Such tools have thus gone from being able to perform highly specific tasks, such as recognizing cancerous cells in pictures of tissue samples or streamlining particle-physics data, to anything from writing essays for lazy undergraduates to running robots.8.Why does the writer mention the three areas of Nobel science prizes?A.To inform readers of the specific information.B.To introduce the flexibility of this years’ Nobel physics prize.C.To share with readers the importance of the Nobel prizes.D.To highlight the critical role physics plays in the world.9.What can be the evidence that the two researcher’s activities can be called “physics”?A.The Hopfield Networks are two-dimensional.B.The nodes in the Hopfield Network connect each other.C.The Hopfield Network functions in a similar way to a spin glass.D.The Hopfield Network can extract patterns using a little data.10.How did Dr Hinton strengthen neural networks’ learning ability?A.He used special physical principles.B.He changed the function of the networks.C.He thought of a structure suitable for the networks.D.He made use of maths to transform their ways of working11.What can be the main idea of the passage?A.AI neural networks can be widely used.B.Two researchers will be awarded the Nobel Physics Prize.C.AI researchers have received the Nobel Prize for Physics.D.Physiology and medicine researchers are common in the Nobel Prize winners.The term parasocial interaction (虚拟社交) was introduced in the 1950s by the social scientists Donald Horton and R. Richard Wohl. It was the early days of home television, and they were seeing people form a close connection with actors who were appearing virtually in their home. Today, the definition is much broader. After all, actors, singers, comedians, athletes, and countless other celebrities are available to us in more ways than ever before. Forming parasocialbonds has never been easier.Psychologists document cases of parasocial relationships that can go much deeper, with severe consequences. Scholars note parasocial bonds range from casual talk about stars to intense emotions, to uncontrollable behavior and fantasies. At the deepest level, the parasocial relationship can be dangerous, such as when a fan loses touch with reality and secretly follows a star. It can also lead to confusion about one’s own identity, particularly in adolescents who are still forming their sense of self, as they may model themselves on the media figures with whom they have parasocial relationships.In 2021, two psychologists from York University, in Canada, found that forming parasocial bonds was strongly related to avoidant attachment. That is, people who tended to push others away in their day-to-day lives were more likely to relate to fictional characters. You can easily see how parasocial relationships could be a replacement when one finds real-life attachment difficult. This could start a feedback cycle, in which avoiding close relationships stimulates parasocial bonding, which in turn leads to reduced interactions with real-life family and friends as the fans spends their time and energy on someone who doesn’t know they exist.My purpose here is not to say that parasocial interactions are always bad for you, or even abnormal. Rather, it is to suggest that heavy parasocial bonding might be a signal that you are crowding out the real people who can give you the love you truly need. One way to address this is to get some more distance from your fictional friends, thus pausing the feedback cycle and giving yourself more space to pursue in-person connection.12.How has parasocial interaction changed according to Paragraph 1?A.It has become more accessible.B.It has affected more celebrities.C.It has lost much of its significance.D.It has turned into a two-way process. 13.What is Paragraph 2 mainly about?A.Reasons behind celebrity following.B.Origins of dangerous relationships.C.Different types of parasocial relationships.D.Potential harm of parasocialrelationships.14.Which of the following can lead to parasocial relationships?A.Socializing with strangers.B.Having strong family support.C.Participating in group activities.D.Struggling with relationships in reality.15.What might the author suggest for those with heavy parasocial relationships?A.Meeting fictional friends in real life.B.Seeking guidance from professionals.C.Hanging out more with real friends.D.Creating more space for being alone.We are overwhelmed by an unprecedented volume of information. 16 if we don’t actively engage with it.In order to stay focused and retain more information, it’s important to be highly engaged with the content. 17 It mostly relies on critical thinking. Active reading transforms passive absorption into an interactive, analytical process. There are many active reading strategies, but here are some of the most immediately useful.Understand the author’s purpose. 18 Take a few minutes to read the introduction or any other material available to become aware of the reason and intent of writing.Adjust your reading rate. Instead of using a constant rate, adapt yourself to the content you’re reading. 19 , and speeding up when it’s information you are already familiar with.Annotate the content. Taking notes is a great way to stay engaged with the content. Use the margins to write ideas that pop into your mind when reading something.Paraphrase. Whenever a new concept seems a bit more complex to grasp, stop reading and try to paraphrase it using your own words. This will force you to assess your level of understanding.Organize the information visually. Map the content into a graphic to better visualize it and make it your own. You can craft a simple mind map, or be creative with collages and other forms of visual thinking.Evaluate the content. Every so often, take a step back and think critically about what you’re reading. 20Consult a reference. Whenever you’ re in doubt, use a dictionary or another external reference to make sure you understand a new concept or an unfamiliar word’s meaning and have all the necessary background information.Summarize the ideas. Once you’ re done reading a book, sit down and write your own summary. Get bonus points if you publish it online to learn in public and get feedback and additional perspectives from other readers.Active reading will help you make the most of the time you spend reading books and blog posts by ensuring you retain more of the relevant content and can apply it in your day-to-day life and work.A.This means slowing down to comprehend better new or more complex information. B.Yet, research suggests that we forget up to 70% of new information within 24 hours.C.It matters for you to assess what you read.D.Active reading basically means reading something with the determination to understand, evaluate, and remember relevant aspects of what you read.E.Is it well structured, are there gaps in the argument, does the author sound biased?F.Is the goal of the author to inform, entertain, or advertise their product or services?G.Our life is packed with varied information.二、完形填空Michael Surrell and his wife had just parked the car when they got a call from their daughter, “The house next door is on fire!” He immediately went to 21 and saw an old woman cried. “The baby is inside!” “The baby” was 8-year-old Tiara Roberts, the woman’s 22 .Though the fire department had been called, Surrell 23 rushed into the burning house. The thick 24 caused him to stumble blindly around and made it impossible to 25 . After a few minutes in the smoke-filled house, he moved outside to 26 his breath.“Where is Tiara?” he asked 27 .“The second floor,” her grandma shouted back.Taking a deep breath, Surrell went in a second time. Because the house had a 28 layout to his, he found the stairs 29 and made it to the second floor.But the darkness was overwhelming. All he could feel was the crackling and popping of burning wood. Then a soft but 30 moan emerged. He crawled toward the sound, feeling around for any 31 of the little girl. Finally, he 32 something. He scooped Tiara into his arms, 33 through the smoke.Fortunately, Surrell managed to help Tiara out; she was 34 from the hospitalafter a few days. However, the fire worsened Surrell’s pulmonary (肺的) condition, which he suffered before, and he feels the effects even two years later. “It’s a small 35 to pay,” he says. “I would do it again without a second thought.”21.A.stimulate B.witness C.investigate D.innovate 22.A.niece B.granddaughter C.cousin D.daughter 23.A.consciously B.passionately C.instantly D.occasionally 24.A.mist B.smoke C.dust D.smog 25.A.escape B.distinguish C.see D.breathe 26.A.hold B.save C.waste D.catch 27.A.randomly B.cautiously C.nervously D.desperately 28.A.opposite B.similar C.different D.striking 29.A.mysteriously B.thrillingly C.threateningly D.effortlessly 30.A.distinct B.loud C.massive D.sharp 31.A.sense B.symbol C.sound D.sign 32.A.touched B.found C.explored D.got 33.A.running B.breaking C.struggling D.going 34.A.rescued B.composed C.suspended D.released 35.A.fee B.bill C.check D.price三、语法填空阅读下面短文,在空白处填入一个适当的单词或括号内单词的正确形式。
高二英语外星人来地球的作文 Last night, the sky was not the same. A strange glow illuminated the horizon, and whispers of an extraterrestrial visit filled the air.
In the early hours, a spacecraft touched down gently in the outskirts of town. It was unlike anything we had ever seen, its metallic surface reflecting the moonlight with an eerie shimmer.
Curiosity drew us to the site, where we found beings from another world. They were not the monstrous creatures of our wildest fears, but rather, they possessed a serene and intelligent demeanor.
The aliens communicated with us through a universal language of symbols and sounds, expressing a desire for peace and knowledge exchange. Their technology was far beyond our comprehension, yet they shared it with us, eager to learn about our planet and its inhabitants.
As the day broke, the aliens showed us images of their home planet, a place of breathtaking beauty and advanced civilizations. It was a moment of unity, bridging the gap between worlds.
拒绝盲目跟风的英文作文Individuality and independent thinking are essential qualities in a world that often encourages conformity. The tendency to blindly follow the crowd can lead to a lack of critical analysis, stifle creativity, and prevent personal growth. In this essay, I will explore the importance of resisting the urge to simply go along with the masses and the benefits of forging one's own path.At the core of blindly following the crowd is a desire for acceptance and a fear of being an outsider. We are social creatures by nature, and the pull of belonging to a group can be strong. However, this desire should not come at the expense of our own beliefs and values. True belonging comes from being authentic and true to oneself, not from simply mirroring the actions of those around us.One of the primary dangers of blindly following the crowd is the loss of independent thought. When we rely on the opinions and decisions of others, we abdicate our own ability to think critically and form our own conclusions. This can lead to a lack of innovation and a stagnation of ideas. History is filled with examples of individuals whochallenged the status quo and pushed the boundaries of what was considered possible, precisely because they refused to simply go along with the crowd.Consider the case of Galileo Galilei, the renowned Italian astronomer and physicist. In the early 17th century, the prevailing belief was that the Earth was the center of the universe, a view that was strongly supported by the Catholic Church. Galileo, however, championed the heliocentric model, which placed the sun at the center of the solar system. Despite facing intense persecution and even imprisonment for his beliefs, Galileo remained steadfast in his convictions, ultimately paving the way for a scientific revolution that transformed our understanding of the cosmos.Similarly, the civil rights movement of the 1950s and 1960s in the United States was driven by individuals who refused to conform to the prevailing social norms of the time. Leaders like Martin Luther King Jr. and Rosa Parks challenged the status quo and sparked a movement that led to significant progress in the fight for racial equality. These individuals understood that true change often requires the courage to stand apart from the crowd and challenge the established order.Furthermore, blindly following the crowd can stifle creativity and personal growth. When we simply mirror the actions and choices ofthose around us, we limit our own potential to explore new ideas, take risks, and discover our unique talents and abilities. Conformity can lead to a sense of complacency and a lack of motivation to push beyond our comfort zones.In contrast, those who resist the urge to blindly follow the crowd often find greater fulfillment and a deeper sense of purpose. By forging their own path, they are able to cultivate a stronger sense of self-identity and authenticity. They are also more likely to make meaningful contributions to their communities and society as a whole, as they are not constrained by the limitations of group-think.Of course, it is important to acknowledge that there are times when it is appropriate and beneficial to follow the lead of others. In certain situations, such as during a crisis or when dealing with complex problems, it may be wise to seek the guidance and expertise of those who have more experience or knowledge. The key is to do so with a critical eye, carefully evaluating the information and opinions presented, rather than simply accepting them at face value.In conclusion, the ability to resist the urge to blindly follow the crowd is a crucial skill in today's world. By maintaining our independence of thought and the courage to challenge the status quo, we can foster innovation, personal growth, and a deeper sense of purpose. While the path of the individual may not always be the easiest or mostpopular, it is often the one that leads to the most meaningful and lasting achievements.。
1.Ancient Greek culture is the major foundation in the Western culture and makes apowerful impact on the development of human civilization. 西方文化的奠基石古希腊文化2.Mycenaean culture benefited much from Cretan culture on its social andeconomic development.迈锡尼文明大多受益于克里特文化3.The Trojan War broke out at the end of the Mycenaean Civilization. 特洛伊战争是在迈锡尼文明结束的时候爆发的4.The Trojan War had helped to produce two famous epics,Odyssey and Iliad. 《奥德赛》和《伊利亚特》的产生得益于特洛伊战争5.Since the 8th Century BC, Greece stepped into an important period when irontools were universally used as a substitute for bronze. With further economic development, the city-states were founded one after another. Among them, Athens and Sparta were the most developed and powerful. 城邦雅典斯巴达6.Cleisthenes submitted a method called ostracism to decide whether a prosecutedperson should be exiled by casting pieces of pottery.7.The boule was led by ten archons whose term of office was one year.五百人会议8.Greek Civilization came to its peak during Pericles’reign and then began todecline.完善时期之后是没落时期9.Hera is the goddess responsible for marriage and family.赫拉宙斯的妻子10.Aphrodite is the sensual goddess of love and beauty.阿佛洛狄特11.Heraclitus claims that fire is the fundamental substance in the universe, and theuniverse is in a state of ongoing change, struggle or flux. 赫拉克利特选择题12.Protagoras is famous for his saying that “Man is the measure of all things”.普罗塔哥拉13.Democritus developed his teacher’s autonomic theory by saying that entire material world is composed of tiny, inseparable particles called atoms.德谟克利特选择题原子14.Plato established the Academy. 柏拉图建立了学院制度15.Plato’s writing usually takes up the form of dialogues. 柏拉图的写作通常是采用对话的形式16.Among the early works, his Apology is famous of the homage Plato paid to his great teacher.17.The Symposium is full of life, set against dinner parties, drinking, jokes and social graces.研讨会18.Plato’s view of class is based on three elements of human nature, namely reason, will and lust.柏拉图的阶级观点是基于人性的三个要素,即原因,意志和欲望。
英语作文航天日的时间和简介The exploration of space has been a captivating and awe-inspiring endeavor for humanity since the dawn of the space age. Marked by a significant milestone, Space Day is an annual celebration that commemorates the remarkable achievements and advancements in space exploration. This international observance serves as a platform to inspire and educate people about the wonders of the cosmos and the remarkable feats accomplished by space agencies and individuals around the world.Space Day is officially observed on the first Friday of May each year. This date was chosen to commemorate the historic launch of the first American astronaut, Alan Shepard, into space on May 5, 1961. Shepard's successful suborbital flight aboard the Mercury-Redstone 3 spacecraft marked a pivotal moment in the space race between the United States and the Soviet Union, igniting a renewed sense of wonder and curiosity about the vast expanse of the universe.The origins of Space Day can be traced back to 1997 when the Lockheed Martin Corporation, a leading aerospace and defensecompany, established the event as a way to inspire and educate students about the exciting field of space exploration. The company recognized the importance of fostering a passion for science, technology, engineering, and mathematics (STEM) among the younger generation, as these disciplines are crucial for the continued advancement of space exploration.Over the years, Space Day has grown in scope and significance, with organizations and individuals around the world joining in the celebration. Schools, museums, planetariums, and space agencies organize a variety of educational and interactive events to engage the public, particularly students, in the wonders of space exploration. These activities can include lectures, workshops, rocket-building competitions, stargazing events, and virtual tours of space facilities.One of the primary goals of Space Day is to inspire the next generation of space explorers, scientists, and engineers. By exposing young minds to the incredible achievements and ongoing discoveries in space, organizers hope to ignite a spark of curiosity and passion that will lead to future advancements in space technology and exploration. The event also serves as a platform to highlight the diverse career opportunities available in the space industry, from astronauts and aerospace engineers to mission controllers and scientific researchers.In addition to its educational focus, Space Day also provides an opportunity to celebrate the remarkable accomplishments of space agencies and individual space pioneers. From the first human footsteps on the Moon to the successful landing of robotic probes on distant planets, the history of space exploration is filled with remarkable feats that have expanded our understanding of the universe and our place within it.One of the most significant milestones in recent space exploration history is the launch of the James Webb Space Telescope in 2021. This groundbreaking observatory, a joint project between NASA, the European Space Agency, and the Canadian Space Agency, has revolutionized our understanding of the early universe and the formation of galaxies. The stunning images and data collected by the Webb Telescope have captivated the public and inspired a renewed sense of wonder and curiosity about the cosmos.Another notable achievement in space exploration is the ongoing work of the International Space Station (ISS). This orbiting laboratory, a collaborative effort between space agencies from around the world, has served as a hub for scientific research and technological advancements for over two decades. Astronauts aboard the ISS conduct a wide range of experiments, from studying the effects of microgravity on human physiology to testing new technologies that could benefit life on Earth.As we look to the future, the space industry is poised for even greater advancements and discoveries. Private companies, such as SpaceX and Blue Origin, have made significant strides in developing reusable launch vehicles and making space travel more accessible. Meanwhile, space agencies are planning ambitious missions to explore the Moon, Mars, and beyond, with the goal of establishing a permanent human presence beyond our home planet.The celebration of Space Day serves as a reminder of the incredible potential of space exploration and the boundless opportunities it presents for scientific discovery, technological innovation, and human exploration. By inspiring and educating the public, particularly the younger generation, Space Day helps to foster a greater appreciation for the wonders of the cosmos and the tireless efforts of those who have dedicated their lives to unlocking the secrets of the universe.As we continue to push the boundaries of space exploration, the significance of Space Day will only grow. It is a day to celebrate our achievements, acknowledge the challenges we have overcome, and look forward to the exciting future that awaits us among the stars. Through the continued dedication and innovation of space agencies, private companies, and individuals around the world, the promise ofspace exploration will continue to captivate and inspire generations to come.。
---[Opening shot: A breathtaking view of the night sky, stars twinklinglike diamonds scattered across the velvet canvas of the universe.]Narrator:Welcome to a cosmic odyssey that takes you beyond the confines of our little blue planet. Today, we embark on a visual journey through the vast and mysterious cosmos, where the wonders of the universe unfold before our eyes.---[Transition to a montage of galaxies, nebulae, and planets, accompanied by an ethereal piece of music.]Narrator:The universe, an endless sea of stars and galaxies, stretches out infinitely, each containing countless celestial bodies. Let's dive in and explore some of the marvels that make up our cosmic neighborhood.---[Scene: The Milky Way, with its spiral arms and bright center.]Narrator:First, there's our very own Milky Way galaxy, a spiral beauty that spans over 100,000 light-years. Home to over 400 billion stars, including our sun, it's the galaxy we call home. But what lies beyond its shimmering arms?---[Transition to a close-up of the Andromeda Galaxy, which is approaching our Milky Way.]Narrator:The Andromeda Galaxy, also known as M31, is the closest major galaxy to the Milky Way. At about 2.5 million light-years away, it's a massive spiral galaxy that will eventually collide with our Milky Way, a cosmic spectacle that awaits in about 4.5 billion years.---[Scene: A nebula, with its swirling colors and intricate patterns.]Narrator:Nebulae are cosmic clouds of gas and dust, often the birthplace of new stars. The Pillars of Creation in the Eagle Nebula, for example, are columns of gas and dust where new stars are being born, illuminated by the intense light of nearby stars.---[Transition to a view of a black hole, with its swirling accretion disk.]Narrator:Black holes, the most mysterious objects in the universe, are regions of space where gravity is so strong that nothing, not even light, can escape. The event horizon of a black hole is the boundary beyond which escape is impossible, a boundary that remains a cosmic enigma.---[Scene: A close-up of a planet with a blue and green atmosphere, resembling Earth.]Narrator:Planets are the building blocks of solar systems, and beyond our solar system, there are countless exoplanets waiting to be discovered. Some, like Kepler-452b, are in the habitable zone of their stars, where conditions could support liquid water and perhaps life.---[Transition to a view of the cosmic microwave background radiation, a relic from the Big Bang.]Narrator:The cosmic microwave background radiation is the leftover glow from the Big Bang, the event that marked the beginning of our universe. Thisfaint glow, detected in 1965, provided evidence for the Big Bang theory and gave us insights into the early conditions of the universe.---[Scene: A view of the universe from the outside, with the Earth as a small dot in the vastness.]Narrator:From this perspective, we see the Earth, a pale blue dot floating in the inky blackness of space. It's a humbling reminder of our place in the cosmos, a tiny speck of life amidst the infinite expanse.---[Closing shot: The Earth from space, with the moon in the background.]Narrator:The universe is a place of wonder, mystery, and endless possibilities. As we continue to explore and learn, we come to appreciate the beauty and complexity of the cosmos we inhabit. So, let your imagination soar, and join us on this journey through the cosmos.[End with a fade to black, accompanied by the same ethereal music.]Narrator:Journey through the cosmos. Keep looking up.---[End of Video]。
arXiv:hep-ph/9801434v1 29 Jan 1998TransportcoefficientsintheearlyuniverseJarkkoAhonen1DepartmentofPhysics,P.O.Box9,FIN-00014UniversityofHelsinki,FinlandFebruary1,2008
AbstractWecalculatenumericallytheelectricalconductivityσ,heatconductivityκandshearviscosityηofthehotplasmapresentintheearlyuniverseforthetemper-atureinterval1MeV<∼T<∼10GeV.WeusetheBoltzmanncollisionequationtocomputeallthescatteringmatrixelementsandregulatethembythethermalmassesofthet-andu-channelparticles.Noleadingorderapproximationisneededbecauseofthenumericalintegrationroutinesused.1IntroductionThetransportpropertiesofthehotplasmapresentintheearlyuniverseareofgreatinterest.Thetransportcoefficientsplayasignificantroleinthephasetransitionsoftheearlyuniverse[1,2,3,4],thecreationanddevelopmentoftheprimordialmagneticfields[5,6]andfinallyinthecreationoftheprimordialdensityperturbationsandthereforeinthegalaxyformation[7,8].Therehasbeenmanyattemptstoestimatethetransportcoefficients.(Textbookestimatesforthermalconductivity,shearandbulkviscosityintheultrarelativisticplasmaweregivenin[9]and[10].)In[11]theviscositiesofapuregluonplasmaandofaquark-gluonplasmawerecomputedintheweakcouplinglimitfromavariationalsolutiontotheBoltzmannequation.In[12]thetransportcoefficientswerecalculatedforplasmasinteractingthroughstrong,electromagneticandweakinteractionstolead-ingorderintheinteractionstrength.Theratesofmomentumandthermalrelaxation,electricalconductivityandviscositiesofquark-gluonandelectrodynamicplasmaswerealsoincludedin[12].In[13]thetransportcoefficientsandrelaxationtimeswerecal-culatedtoleadingordersinthecouplingconstantfordegeneratequarkmatterwithinperturbativeQCDfortemperaturesandinversescreeninglengthsmuchsmallerthanthequarkchemicalpotential.TheviscositiesoftheQCD-plasmawereconsideredin[14].Textbookestimatesforthermalconductivityandviscosityintheultrarelativisticplasmaweregivenin[9]and[10].Theconductivityofarelativisticplasmahasalsobeenconsideredin[15]byreformulatingthecollisionoperatorforarelativisticplasmaintermsofanexpansioninsphericalharmonics.However,allthepreviousestimatesinvolveapproximations.Thecalculationshavebeenperformedonlytotheleading(logarithmic)ordersandcertainscatteringreac-tionspresentinthehotprimordialplasmahavebeenneglected.Inthepresentpaper,theonlyapproximationwemakeistoassumethatwhenparticlesappearintheheatbathoftheprimordialplasma,theirthermalvelocitiesarehighenoughtoallowustotreatthemultrarelativisticandthereforemassless.Weconsiderradiationdominatedplasmawithtemperaturesfromabout1MeVtoabout10GeV.Theviscousdampingandheatconductingeffectsaffectthefirstorderphasetran-sitionsintheearlyuniverse.Duringsuchphasetransitions,instabilitiesmayoccurwhenthetransportoflatentheatisdominatedbythefluidflow.In[1]thiswasstudiedintheEWtransitioninthesmallvelocitylimit,in[2]intheQCDtransition,in[3]forcosmologicaldetonationfrontsandin[4]forgeneralfirstordertransitionswitheitherlargeorsmallbubblewallvelocities.Theinstabilitiescanbedampedbyfiniteviscosityandheatconductivityduetothediffusionofradiationonsmalllengthscales.Whenconsideringthecreationanddevelopmentofprimordialmagneticfieldsitisalsoofimportancetoknowthetransportcoefficientsofthesurroundingprimordialplasma[5,6].Finiteelectricalconductivityleadstothediffusionofmagneticfieldsandthereforeisofimportancewhentryingtoexplainthefurtherevolutionofaninitialseedmagneticfield(seee.g.[16]).Theinstabilitiesinthefirstorderphasetransitionscanbeshowntocreateseedmagneticfields[6].Thereforetheseedprimordialmagneticfieldsalsodependonthesizeofthetransportcoefficientsintheprimordialplasmainacrucialway.Inparticular,theseedfieldscreatedintheQCDphasetransitionarehighlydependentontheneutrinoviscosity[6].Galaxyformation[7]islikewiseaffectedbythethermalcoefficientsintheprimor-dialplasma[8].Viscositytendstoheatuptheplasma,andontheotherhandthermalconductiontransfersheatfromregionsofhightemperaturetoregionsatlowertem-perature.Theeffectsaffectthestructureformationandthusinordertomakeprecisemodelsofthegalaxyformationitisimportanttoknowthevaluesofthetransportcoefficients.Itshouldbenotedthattwomajoreffectsareinvolvedwhenheattransportandviscosityarestudied.Theseeffectsarethenumberofpossiblescatteringreactions,i.e.thenumberofparticlespresentintheplasma,andtheDebyemasspresentinthepropagator.AswewilldiscussinSection4,thefirsteffectwilldecreasethetransportcoefficientswhilethesecondeffectwillincreasethem.Thenetbehaviourofthecoefficientsdependontheexactinterplaybetweenthesetwoeffects.Thedifferentinteractionsgivecontributionsofdifferentstrengthstotheelectricalconductivityaswasshownin[17].However,in[17]onlystrongandelectromagneticinteractionswereconsidered.Herewealsodealwiththescatteringreactionsinvolvingneutrinos.Thepaperisorganizedasfollows.Insection2weintroducethereadertothemethodofcalculationand,usingthefulldefinitionoftheenergy-stresstensorTµν,wedefinethetransportcoefficientspresentedhere.Insection3wereconsiderelectricalconductivity.WefirstdiscusswhatistheproperwaytointroducetheDebyescreen-ingtothepropagatorsinthematrixelements.Wethenincludeadditionalscatteringreactionsnotpresentinpreviousworkandpresentanewvaluefortheelectricalcon-ductivity.Wealsocompareourresultswithotherrecentestimatesfortheelectricalconductivityinthehotplasma.InSection4and5weapplyourtechniquetocalcu-latingthermalconductivityandshearviscosityinthehotplasma,respectively,andcompareourresultswithotherrecentestimates.Section6containsasummaryoftheresultsandabriefdiscussionontheirrelevancefortheearlyuniverse.