Calculating Models on the Surface Tension of CaO-FeO-SiO2 Molten Slags
职称英语考试中的常见篇章及翻译
Sta ge FrightFall down as you come onstage. That’s an oddtrick. Not recommended. But it saved the pianist Vladimir Feltsman when he wasa teenager back in Moscow. The veteran cellist Mstislav Rostropovich trippedhim purposely to cure him of pre-performance panic,2 Mr. Feltsmansaid, “ All my fright was gone. I already fell. What else could happen?”Today, music schools are addressing the problem ofanxiety in classes that deal with performance techniques and careerpreparation. There are a variety of strategies that musicians can learn tofight stage fright and its symptoms: icy fingers, shaky limbs, racing heart,blank mind.3Teachers and psychologists offer wide-rangingadvice, from basics like learning pieces inside out,4 to mentaldiscipline, such as visualizi ng a performance and taking steps to relax. Don’tdeny that you’re jittery，they urge; some excitement is natural, even necessary for dynamicplaying. And play in public often, simply for the experience.Psychotherapist Diane Nichols suggests somestrategies f or the moments before performance, “Take two deep abdominalbreaths, open up your shoulders, then smile,’’ she says. “And not one of these‘please don’t kill me’ smiles. Then choose three friendly faces in theaudience, people you would communicate with andm ake music to, and make eyecontact with them.” She doesn’t want performers to think of the audience as ajudge.Extreme demands by mentors or parents are often atthe root of stage fright，says Dorothy Delay, awell-known violin teacher. She tells otherteachers to demand only what their students are able to achieve. When Lynn Harrell was 20，he became the principal cellist ofthe Cleverland Orchestra, and he suffered extreme stage fright. “There weretimes when I got so nervous I was sure the audience could see my chestresponding to the throbbing. It was just total panic. I came to a point where Ithought,‘ If I have to go through this to play music, I think I’m going to lookfor another job.”5 Recovery, he said, involved developinghumility-recognizing that whatever his talent, he was fallible，and that an imperfect concert wasnot a disaster.6It is not only young artists who suffer, ofcourse. The legendary pianist Vladimir Horowitz’s nerves were famous. The greattenor Franco Corelli is another example. “They had to push him on stage,”Soprano Renata Scotto recalled.Actually，success can make things worse. “In the beginning of your career,when you’re scared to death, nobody knows who you are, and they don’t have anyexpectations,” Soprano June Anderson said. “There’s less to lose. Later on, whenyou’re known, people are coming to see you, and they have certain expectations.You have a lot to lose.”Anderson added，“I never stop being nervous until I’ve sung my last note.”如何避免怯场上台就跌倒。
介绍算盘的作文150字
介绍算盘的作文150字英文回答，The abacus, also known as a counting frame,is a calculating tool that has been used for centuries. It consists of a rectangular frame with rods or wires running parallel to each other, and a series of beads that can be moved back and forth. Each rod represents a different place value, such as ones, tens, hundreds, and so on.The abacus is a versatile tool that can be used for addition, subtraction, multiplication, and division. It is particularly useful for teaching children the basics of arithmetic and place value. By moving the beads on the rods, users can perform mathematical operations quickly and accurately.In addition to its educational benefits, the abacus is also used by some people as a tool for mental calculation. By practicing with an abacus, individuals can developstrong mental math skills and improve their ability to perform complex calculations in their heads.Overall, the abacus is a valuable tool that has stood the test of time and continues to be used in various partsof the world.中文回答，算盘，又称为算筹，是一个计算工具，已经被使用了几个世纪。
七上英语牛津版电子书
七上英语牛津版电子书an animalscount,Hi?My cat do you know,Hi?I asked "What is6 minus 6" andit said ' manylanguages doyouknow?Everyone knowsat least two--his or her ownlanguage and theinternationallanguage numbersIn ancienttimes,peoplewrote numbers inmany allcounted in system ofnumbers todayconsists of thenumbers from 1to 9 and 0(zero).The Indiansfirst inventedand developedthe 1 to 9system theninvented invention ofzero helpedpeople write bignumbers andcalculate these tennumbers,we canwrite any numberfrom the biggestto the of the firstcalculatingmachines was arefast the abacus,the beads on thewires representones,tens,hundreds andthousands,starting fromthe bottom abacus inthe pictureshows a it down infigures,and thenin it byzero and thenadd isthe answer?Modernelectroniccalculatorscanadd,subtract,multiply can alsocalculatepercentages andsquare arevery puter cando millions ofcalculations ina andordinal numbers3 three5 five6 six9 nine13 thirteen15 fifteen16 sixteen19 nineteen30 thirty50fifty60 sixty90 ninety32 thirty-two54 fifty-four67 sixty-seven98 ninety-eight100 one hundred200 two hundred375three hundredand seventy-five1,000one thousand4,189four thousandone hundred andeighty-nine15,362fifteen thousandthree hundredand sixty-two100,000one hundredthousand284,653two hundred andeighty-fourthousand sixhundred andfifty-three1,000,000one million5,367,982five millionthreehundredand sixty-seventhousand ninehundred andeighty-twoWe use ordinalnumber to showthe order form mostordinals byadding -th tothe arealsoexceptions,likefirst,second first2nd second3rd third5th fifth8th eighth9th ninth12th twelfth13th thirteenth20thtwentieth21sttwenty-first22ndtwenty-second23thtwenty-second100th hundredtht100May is callingher friend, theirconversation andpractise work inpairs to checkthe otherhomeworkproblems inMay's 6521(two eight ninezero,six fivetwo one).MAY:Hello, is I do foryou?MAY:I made amistake with myhomework, Icheck it withyou?RITA: (zeropoint nine two)times (eighteen pointone eight)?RITA:No,itshould be (eighteen pointone six).MAY:Thanks, Jie askedOfficer Chenabout drew a theirconversationbelow and writethe figures onthe JIE:How manytrafficaccidents weretherein twothousand and twoin our city?CHEN:Threethousand sixhundred JIE:What wasthe number intwo thousand andthree?CHEN:Threethousand sevenhundred JIE:Whatabout in twothousand andfour?CHEN:Threethousand sixhundred JIE:And twothousand andfive?CHEN:Threethousand sevenhundred JIE:Whatabout in twothousandandsix?CHEN:Threethousand sixhundred JIE:Thankyou,Mr at about theinvention ofclocks andwatchesNow,we can telltime veryaccurately,butbefore theinvention ofclocks,it wasvery used theposition of thesun in the skyto tell time inancient times,but it wasimpossible to doit on cloudydays or 1099,Su Songinvented thefirst mechanicalclock in years later,in 1283,the British inventedthe first clockin 67 years later,in 1350,the Germansinvented thealarm Italiansinvented thefirstwatch watcheswere differentfrom today's intwo only hadone hand--thehour hadto keep them inyour calledthem 'pocketclocks'.The first wristwatches camefrom Switzerland328 years afterthe first pocketclock,but they did notbee popularfor a clocksand watches camefrom the UnitedStates and arethe latestinvention started tosell them in1971.。
ThestoryofLiBai（李白的故事）
The story of Li Bai（李白的故事）In the early years of Tianbao, when Tang Xuanzong just spoiled Yang Yuhuan, Li Bai met Aichi Aki. He Zhizhang Li Bai introduced to Tang Xuanzong, the emperor saw Li Bai's poems also greatly in the throne room, summoned Li Bai, when the poet far step on the stage, Tang Xuanzong has stepped forward to greet Li Bai, talk about political affairs at the time, Li Baineng on the spot according to the meaning of Tang Xuanzong, wrote an article "and the book", and a talk rapidly. With a hand Xuanzong talk, do not stop writing, Tang Xuanzong was happy to concoct a bowl of soup, gave Li Bai eat, since he was appointed academician.One night, Tang Xuanzong took his concubine Yang Yuhuan, by moonlight, transplanted to four strains of ornamental peony rare Shen Xiang pavilion. Xingqing lake, they walk along, and a row of empty chariot is behind the most outstanding operatic players. They laid songs and dances in the moonlight of flowers. When Li Guinian was busy the team to sing Tang Xuanzong said: "the reward of flowers, concubine, scene can't sing old words?" That Li Guinian took note of Jinhua gave to Li Bai, let Li Bai to write the words (i.e. sings seven poems). At that moment, Li Baizheng and some friends were lying in the restaurant. Li Guinian quickly with cold water to wake up excited him, sent Li Bai into the palace of Xingqing, half drunk Li Bai, wrote the three song "clear" tone:Cloud like clothes look, the spring breeze blows sill Revlon.If the Yushan group head, was next to Yaotai every month.A red flower with fragrant dews, sexual matters in vainheartbroken.May I ask who is like a palace, poor swallow hill new makeup.Energy-saving, long kings Daixiao look.Explain the sandpiper, Shen Xiang ting.The emperor saw good words, of course happy, but Li Bai think ancient poetry poems not otherworldly, see more, now sing three songs seven poems, I do not know how to write poems, and asked Li Bai to write a poem to ten songs "pleasure palace".Li Bai inebriated haze, also understand the emperor in test of his ability to play, in a way: "I have drunk today, unfortunately, if your Majesty gave me fearless courage, it can play" my slight skill."The emperor smiled: "all right."!" Call two Chamberlain hold the rickety Li Bai, let two Chamberlain hold Zhu silk bar.Li Bai commanded, "Yang Guozhong, bring me the ink!"! Gao Lishi, take my boots off!Yang Guozhong is her brother, was the most popular eunuch Gao Lishi, the two is the emperor's minions, the ministers have not qualified so rude, not do not want to be his head! But Tang Xuanzong was particularly carefree mood, see Li Bai's poems in tipsy write so perfect, let Yang Guo Zhong and Gao Lishi to serve Li Bai.Gao Lishi off his boots to Li Bai, Li Bai on the bench to sit down. Yang Guozhong took good ink. Li Bai took a pen slightly meditation, then brush hands, do not stop to write ten songs "palace word" picnicky. One of themSmall princess, Yingying in ziwei. Flowers inserted Baoji, Pink Embroidered dress.Each palace, often with the foot to. Only worry song and dance scattered, into the clouds fly.secondThe golden willows tender, pear white snow incense. Gold cage nest jade, green water play Mandarin duck.People with carved chariot gyokudo, piano. Palace often wine, feast a total of chaoyang.thirdLu Chu orange tree, grape into the palace. The flowers reflected Laxia, drunk spring wire tube.Energy-saving, Xiao Mingfeng. Kings delight in many things, and with ten thousand parties.FourthYushu spring day, golden palace more fun. Not in the backyard at night is too light, chariot.Laugh out of the language, charming to the next song. Don't teach the bright moon to stay drunk.FifthEmbroidered households fragrant warm, screen new dawn. Palace flowers for laughter day, pond grass dark spring.The trees smell the song, the birds see the dancers. The sun and Luo Qi, from dating.The sixMingguang today,To travel. The purple breeze under the temple, Tianle Zhu lou.The Yin Fang, Sheng sound more secluded. Even the flower moon night, ladies wonderful voice.SevenHan Xuemei Zhong Zhong, the spring breeze, Liu GUI return. The palace Yingjiao drunk, swallows fly yan.Late Song riming seats, new flowers dress. Night shift color battle, fling up the rainbow.The eightAqua Dian, bonus North que floor. The smell too, Fengwu around japan.Zhupei motome Ming, and get the ball. One fine day, should swim into the weiyang."Tang Xuanzong read very happy, immediately let the musicians make music, musicians singing.Yang Guozhong and Gao Lishi where I can bear this tone, although on the surface to Li Bai, Li Bai had heart mantra many times, ready to pick up Li Bai. TheLi Bai fell asleep after he finished his poem. Li Guinian with Li Bai's poems singing clear tone, Yang Yuhuan see the poem is written in praise of their beauty, and also enjoy the flowers back to xuanzong.Two days later, Yang Yuhuan a person to sing that a few pieces of plain tune when you play, Gao Lishi took the opportunity to say: "I thought the empress Li's guts, how would you sing his word?"Yang Yuhuan was very surprised: "he is a member of the Imperial Academy, how can I hate him to this point?"Gao said: "the first second" clear tone in "" by the palace who resembles the poor swallow hill, new makeup ', that is not compare you to wanton Palace Zhao Feiyan?"Yang Yuhuan thinks it makes sense. From then on, Yang Yuhuanalways stops when Tang Xuanzong wants to reuse Li Bai.Li Bai waited a long time not see the emperor reuse, then guess there must be someone simply to resign Tang Xuanzong place obstacles in the way, it can only make the king happy imperial errand. Although Tang Xuanzong love Li Bai, but what Yang Yuhuan is not important, since she hate Li Bai, had to give Li Bai a lot of gold to let him out of Beijing travel.Since then, Li Bai riding a donkey wandering to Huayin, when drunk mountaineering, through Huayin county door but no ass. He didn't know Li Bai, see a little people dare to break on official, furious, ordered the Li Bai catch above the lobby all asked him: "what are you? Dare to be so rude?"Li Bai was the pen to write a strange confession, I did not write the name of origin, only said: "the emperor used handkerchief mouth; the Emperor himself for me Yang Guozhong I held for modulation soup; Yan; Gao Lishi boots for me; I can still ride in front of the emperor, the door was riding in Huayin county not a donkey."The magistrate was surprised and ashamed, busy with Li Bai to thank: "I do not know this sorry sorry, Hanlin!"Li Bai laughed, riding on his donkey to go wandering.Tang suzong Qianyuan years, over sixty years Li Bai still riding a donkey wandering. One day, he is walking on the way to Jinling, hot weather made him thirsty qiqiaoshengyan, suddenly saw in front of a door carrying a small flag, saying "good vinegar"two words. Li Bai came to the door and saw a vinegar shop. He thought it was good to drink without vinegar and thirst quenching. TheLi Bai took a donkey tied to a tree, slowly walked into the shop, a look, the store has a man sitting, dress like a seven product. Li Bai was too lazy to pay attention to him and went straight to the counter and said to the store owner:One man, one mouthful, one bamboo grove, no temple, no monk,A woman in her arms, twenty-one days when students.The store is a way to know the literati, this is a mystery, not for a while, he figured out the answer is "how good vinegar". So busy just smiled and answered: "this is Shanxi vinegar, Northland Jiapin, can taste good!"Li Bai is very happy, vinegar shop encounter bosom friend, drink side and store conversation. For a moment, Li Bai finished the vinegar, and returned the vinegar pot to the store owner:A goose, a bird, a bird is not there, a woman loves her,A big mouth to swallow, drops to.The store will soon work out the answer is "I want to go back," he says goodbye to Li Bai and "Sir, I wish you May you be safe throughout the journey!" Li Bai nodded and smiled "thank you!"The magistrate Li Bai from into the store to go with the storelaughing, saying what he did not understand, but his left side, liyebuli, he can't stand. Li Bai turned to go out, stood up and shouted: "wait a minute, you is who, how dare in front of me over!"Li Bai turned back and said:The beans in the root, the moon hanging in midair,To not see wood, Wang Li is a.Then, the solution under the donkey ride on the left.Li Bai was out of sight disappeared, the magistrate was still there over the poem.They knew ", also pretended not to understand There is no such a rule!", let the magistrate figure go! GuanShanYue, Li BaiBright moon out of the Tianshan Mountains, vast clouds between the sea. Changfeng tens of thousands of miles, blowing Yumen Pass.Under the Chinese Biden, Hu glimpse of Qinghai bay. From the war, no one else."The guest at the border, returning more bitter yan. Tall buildings, when this night, sigh, should not idle.The "GuanShanYue" is the old topic of the yuefu. "Ancient Yuefu" to: "GuanShanYue", also the sorrow of parting." Li Bai's poeminherited the ancient Yuefu in its content, but it has greatly improved.The first four sentences can be said to be a vast frontier fortress including three factors, namely, the mountain, the moon and the moon. We in the general literature, often see "Moonrise East" or "Moonrise Dongshan" category description, and the Tianshan Mountains in Western China, is likely to be the moon where, why say "moon out of the Tianshan Mountains"? This is the original point of view that the traveler. A guard in the Tianshan Mountains to the west, look east look, see the moon rises from the Tianshan scene. Although the Tianshan Mountains do not depend on the sea, there are some sea clouds lying across the mountains. The poet seems to be in the people the impression that only the sea is more common over the vast cloud on the scene, together with the magnificent Tianshan combination, appear fresh and spectacular. This state, in front of the general ability weak poets might have called Li difficult to follow up, but. Next, "Changfeng tens of thousands of miles, blowing Yumen Pass", the scope is much broader than the first two sentences. Yang Qixian of the Song Dynasty, "lest like tens of thousands of years", said: "not too far to the Tianshan Mountains to Yumen Pass, and said tens of thousands of years, with the moon out of Tianshan ear, not in Tianshan Mountains of." With the imagination of the moon and the distance from Yumen Pass to explain "tens of thousands of miles", it seems safe, but Li Bai is talking about "Changfeng" of the long, did not mention the moon and the earth's distance. In fact, these two are still from the perspective of the expedition, they were in the northwest frontier, the moonlight stands at home, but feel like traveling across the vast Central Plains land, tensof thousands of miles, across to Yumen Pass. If contact Li Bai, "midnight Wu Song" in "autumn wind blowing, always Jade Guan sentiment" to understand, the meaning of poetry is more clear. In this way, along with the description above, it features the Changfeng, the bright moon, the Tianshan Mountains and the Yumen Pass, forming a Wanli frontier map. Here seems to be just a natural scene, but as long as this is a look of the east look see, that Miss local mood is very easy to feel.Under the "Han Hu glimpse of Qinghai Bay Biden. From the war, no one else." This is in the first four words, the broad frontier, the natural picture, the war scenes. Point out the pawn. The Han Emperor Liu Bang Ling Bing Zheng Hun, was Hun in Bai Dengshan (now Shanxi Datong West) under siege for seven days. The Qinghai Bay area is the place where Tang and Tibet fought in successive years. The endless wars of the past made it impossible for the soldiers who had never set foot to live to return to their hometown. The four sentences in the structure play an important role in the description object by the frontier transition to war by war, the transition to the expedition."Shu guest looking toward the border, returning more bitter yan. Tall buildings, when this night, sigh, should not idle." The soldiers looked at the scene by the side,Longing for home, the face of the color of sorrow, they think of their high buildings on the wife, in this vast moonlight night, the sigh of the sound when it will not stop. "At the edge of color" three characters in Li Bai's works seem to just casually write, but above the inside and in the sight of Certeau million, with "" guest "tightly together. The sight was so,think also is broad and boundless. The soldiers in the imagination of building the thinking woman's affection and they sigh, against such a broad background, it seems extremely deep.Look at the ancient frontier fortress poet of ethnic conflict in the diffuse endless, revealing a huge sacrifice caused by war and soldiers and their families to millions of the pain, but the war did not simply condemn or praise, poets like generations of human beings is thought to pay a heavy price! In the face of such contradictions, the poet, collector, and the reader, it is easy to arouse a desire. This desire, the poem did not speak directly, but similar "is known it is a weapon, sage of last resort" ("South war") idea, is it easy for readers to read this article in the works.People think of women. In general, the poet, often written too delicate and sorrow, and accordingly the realm is often narrow. But Li Bai used "bright moon", Tianshan Mountains, vast clouds between. Changfeng tens of thousands of miles, blowing Yumen Pass "Wanli frontier map" scene to arouse this feeling. The only mind like Li Bai the great, so write. The Ming Dynasty Hu Yinglin commented: "muddy hero, how elegant." If the "elegant" as not cramped in the moment, with a more far-reaching, calm thinking, then, his comments is very appropriate. With vast space and time to do the background, and in such a thinking, the current homesickness, farewell sentiment merged into, so as to carry out a more far-reaching artistic conception, which other poets can not match.。
牛津深圳版 短语 卡片总会 -汉语部分留白-中考复习必备
1. A boy called simon2.Would like to do sth3.My favorite hobby4.Play chess5.Live with sb6.Be from/come from7.Own a Chinese restaurant8. A small house near our restaurant9.Work as an architect10.Form one11.Walk to school12.Be keen on13.Enjoy playing rugby14.My best subject15. A photo of myself16.in middle17.Write to sb18.Tell sb about sth19.Best wishes20.Reply to21.Make friends with sb22.One of the top students23.Write computer games24.All of her family25.Be still at school26.Get up at 6 am27.Put on school uniform28.Discuss the business29.At breakfast30.Drive me to school31.Make phone call to clients32.On the way to school33.Fail an exam34.Collect sb35.Return to school36.Attend a club37.Have meetings ，have a meeting38.Ask me to assist them，ask me to help them39.Once a week40.in one or two hours ，in an hour or two41.The business during the day42.Continue working43.Work on sth44.Wait for the ferry45.Two women tourists46.Begin arguing47.Hold out a bag48.Show it to sb、show sb sth49.Stare at sb /sth50.Go up ，go up to sb51.Talk to /with sb52.One of the women53.Find sth missing54.Run away55.Follow sb ，go after sb56.The bell rang57.Hurry aboard，go aboard in a hurry58.Let’s do sth，let us do sth59.Take the next ferry60.Hurry to sp, go to sp. in a hurry61.An ice cream shop62.Pick up sth63.Report a theft64.Steal sth from sp65.On the number 3 ferry66. A few minutes ago67.On the other side of the river/street68.Get on /off69.See sb doing sth70.Stand around the man71.Be in handcuff72.Well donest Friday morning74.Go to sp. for doing sth75.Cross the road、walk across the road76.trip on sth77.At that moment78.Get out 、get on 、get offe up to sb80.Take sb to sp81.Help sb to do sth82.Drive to sp83.The nearest hospital84.Tell sb to do sth85.The national flag86.Mineral water87.Summer holiday88.Spread your wings89. A big country with coasts on three sides90.Go skiing91.In central France92.Grow crops93.Such as94.One of the most beautiful scenic areased to do/be96.Famous attractions97.People with children98. A good place to visit99.An hour from。
模具镀层知识点总结
模具镀层知识点总结一、模具镀层的分类1. 金属镀层：主要包括电镀、热浸镀、喷涂等方法。
金属镀层可以有效提高模具的抗磨性和抗腐蚀性，常用的金属包括镍、铬、钛等。
2. 非金属镀层：如化学镀、喷涂等方法。
非金属镀层通常用于提高模具的耐蚀性和抗磨性，常用的非金属包括氮化物、氧化物、碳化物等。
二、模具镀层的优点1. 提高表面硬度：模具经过镀层处理后，表面硬度能够得到有效提高，提高了模具的耐磨性和抗压性。
2. 延长使用寿命：模具表面的镀层能够有效延长模具的使用寿命，减少更换和修理的次数，降低了生产成本。
3. 提高表面质量：模具经过镀层处理后，表面光洁度和精度得到了有效提高，提高了产品的质量。
4. 降低摩擦力：模具表面的镀层能够减少摩擦力，提高了模具的使用效率。
5. 提高产品精度：模具经过镀层处理后，能够提高产品的尺寸精度和表面质量，提高了产品的质量和市场竞争力。
6. 降低生产成本：镀层处理能够延长模具的使用寿命，减少了更换和修理的次数，降低了生产成本。
三、模具镀层的常见方法1. 电镀：电镀是最常见的模具镀层方法，采用电化学方法，在模具表面沉积一层金属或非金属覆盖层，形成均匀的镀层。
电镀方法有镀铬、镀镍、电镀铜、电镀锌、电镀银等。
2. 热浸镀：热浸镀是将模具浸入加热的液态金属溶液中，通过表面张力和元素扩散等过程，使金属沉积在模具表面形成均匀致密的镀层。
3. 喷涂：喷涂是将金属或非金属粉末通过喷枪喷洒到模具表面，然后进行烧结或烘干，形成均匀的镀层。
4. 化学镀：化学镀是利用化学还原或化学气相沉积等方法，在模具表面沉积一层金属或非金属镀层，形成均匀致密的镀层。
四、模具镀层的选材原则1. 选择合适的镀层厚度：镀层的厚度是影响模具使用寿命的重要因素之一，一般来说，金属镀层的厚度在几微米到几十微米之间，非金属镀层的厚度在0.1mm以下。
2. 根据使用条件选择镀层材料：根据模具的使用条件和要求，选择合适的镀层材料，如模具需要具有较高的表面硬度和耐磨性，选择具有高硬度的金属材料进行镀层，如需要具有较好的耐蚀性和氧化性，选择具有良好防腐蚀性能的材料进行镀层。
Electromagnetic instability of the Thomson Problem
a r X i v :c o n d -m a t /0506616v 1 [c o n d -m a t .s t a t -m e c h ] 23 J u n 2005Europhysics Letters PREPRINT Electromagnetic instability of the Thomson Problem Jayme De Luca (∗),Savio B.Rodrigues (∗∗)and Yan Levin (∗∗∗)∗Departamento de F´ısica,Universidade Federal de S˜a o Carlos,Rod.Washington Luiz km 235,13565-905,Caixa Postal 676,S˜a o Carlos,SP,Brazil ∗∗Departamento de Matem´a tica,Universidade Federal de S˜a o Carlos,Rod.Washington Luiz km 235,13565-905,Caixa Postal 676,S˜a o Carlos,SP,Brazil ∗∗∗Instituto de F´ısica,Universidade Federal do Rio Grande do Sul Caixa Postal 15051,CEP 91501-970,Porto Alegre,RS,Brazil –Order-disorder transformations;statistical mechanics of model systems.PACS.71.10.-w –Electron gas-theories and models.Abstract.–The classical Thomson problem of n charged particles confined to the surface of a sphere of radius a is analyzed within the Darwin approximation of electrodynamics.For n <n c (a )the ground state corresponds to a hexagonal Wigner crystal with a number of topological defects.However,if n >n c (a )the Wigner lattice is unstable with respect to small perturbations and the ground state becomes spontaneously magnetized for finite n .The Thomson problem,finding the ground state of electrons inside a sphere with a uniform neutralizing background,has a time honored position in the history of modern physics [1–7].The original question was posed by J.J.Thomson [8]after his discovery of the electron in 1897.Thomson conjectured that the knowledge of the positions of the electrons inside the atoms is essential to understanding the regularity of the chemical elements in the periodic table.At the time,however,proton still had to wait 14years to be discovered,so in order to keep his atom neutral,Thomson was forced to introduce a uniform neutralizing background.The model became known as the “plum pudding”atom and the question that needed to be answered was:What are the positions of the electrons inside a uniformly (positively)charged sphere?Surprisingly,after more than a century this problem still has no general solution.If the background charge is made to vanish,the electrostatic energy will be a minimum only if all the electrons are located at the surface.This is a general consequence of the Earn-shaw theorem [9]which precludes existence of a stable equilibrium with purely electrostatic interactions.Curiously,the Coulomb potential is precisely on the border line where this be-havior is possible.If instead of 1/r ,the electrons would interact by a 1/r 1+ǫpotential with ǫ>0,the bulk occupation of the sphere would be energetically favorable for a sufficiently large number of electrons [10].Unfortunately,even the restricted surface Thomson problemsremains unsolved for an arbitrary number of electrons [11,12].2EUROPHYSICS LETTERS In this letter we will show that if the relativistic corrections to the Coulomb law are properly taken into account,even our intuitive picture of the ground state as consisting of stationary particles located atfixed positions on the surface of a sphere must be abandoned. Instead,wefind that for sufficiently large electron density,the energy is minimized by the particles undergoing a coherent motion and the sphere becomes spontaneously magnetized!The starting point for our analysis is the well known Darwin Lagrangian[13–23],which takes into account the relativistic corrections to the Coulomb law resulting from the particle motion,L=−mc2 ic2−1r ij+1r ij[v i·v j+(v i·ˆr ij)(v j·ˆr ij)].(1)Eq.(1)is correct to order v2/c2.The velocity-dependent correction to the Coulomb energy arises from the electromagnetic coupling between the moving particles.Since the Lagrangian (1)does not contain explicit time dependence,the energy of the systemE= i v i·∂Lc2+1r ij+1r ij[v i·v j+(v i·ˆr ij)(v j·ˆr ij)].(3) The ground state for n electrons on the surface of a sphere of radius a is then determined by the minimization of Eq.(3).We note that if the terms of order1/c2are neglected,we recover the classical formulation of the Thomson problem in which the electromagnetic coupling between the electrons is purely of the Coulomb form.In this case,the velocity dependent contribution to the Hamiltonian is positive or zero,and the ground state corresponds to stationary particles residing atfixed positions on the surface of the sphere.For large n,this structure resembles a hexagonal Wigner crystal containing some topological defects.In general,however,the1/c2terms can not be omitted and a full minimization of Eq.(3)must be performed.To proceed,it is convenient to rewrite the energy in adimensional form.Defining the reduced displacement and velocity as r∗=r/a and v∗=v/c,the reduced energy becomesE∗≡E r e 2a∗ i=j14a∗ i=j1Jayme De Luca,Savio B.Rodrigues and Yan Levin:The Thompson Problem3 electrons.This however,is not of great importance since the metastable states have energies very close to that of the exact ground state[10,25].Performing the minimization of E∗wefind that for reduced surface charge densityσ∗=n/a∗2such thatσ∗<σ∗c(subcritical region),the electrons form a stationary Wigner crystal with some topological defects.Above the critical charge densityσ∗>σ∗c(supercritical region),the Wigner crystal,however,becomes unstable and a new ground state with moving electrons is formed.In Fig.1we show the characteristic distribution of particles in this new ground state.The arrows indicate the relative magnitude and direction of the particle velocities.Thefigure shows bands of correlated antiferromagnetic8 v∗4i+1r∗ij,(5)where I is a2n×2n identity matrix and D is a position dependent matrix constructed from the last term of Eq.(4).The quadratic term in velocity is non-negative if all the eigenvalues of the matrix1A=I+4EUROPHYSICS LETTERS negative,the Wigner lattice will lose stability,and a new ground state,with energy below that of the Wigner crystal will be established.The phase transition occurs when λA min =0,where λA min is the minimum eigenvalue of the matrix A .It is important to note that the energetic bifurcation of Eq.(5)is simultaneous with the dynamical instability of the Wigner lattice.If the Euler-Lagrange equations of motion are linearized around the stationary positions of the Wigner lattice,one can show that the Lya-punov instability occurs precisely when A loses convexity.Unfortunately,in the supercritical region,the equations of motion are differential-algebraic and due to the singularity of A are very difficult to integrate numerically [26].To determine the critical charge concentration at which the Wigner crystal loses stability,we adopt the following procedure.For a given number of electrons n ,the Coulomb energy is minimized to determine the positions of all the particles.For purely Coulombic interactions,the ground state location of the electrons is independent of the size of the sphere,since a scales out of the expression for the electrostatic energy.Once the ground state coordinates are known,the eigenvalues λD of the matrix D can be calculated numerically.The criticality condition λA min =0is then equivalent to the requirements that λD min =−a ∗.In Fig.2we show the result of this procedure.0 51015100 200 300 400 500 600 700 800 9001000Jayme De Luca,Savio B.Rodrigues and Yan Levin :The Thompson Problem 5Clearly,µ∗is just proportional to the total magnetic moment of the sphere.In the subcritical region,the electron velocities arezero and µ∗=0.The value of the magnetic moment in the supercritical region is plotted in Fig.3.We find that if the magnetic moment is scaled with n −2/5and is plotted as a function of the reduced surface charge concentration σ∗−σ∗c ,all the points for different values of a and n fall on the same universal curve,g (x )=0.545x 1/2.(9)Thus,although locally the orientation of the velocity vectors is antiferromagnetic,globally the symmetry is broken and the sphere acquires a net magnetic moment.The magnetic moment is sub-extensive and vanishes with a square root singularity as σ→σ+c .0 0.020.040.060.080.10 0.005 0.01 0.015 0.02d ,(11)6EUROPHYSICS LETTERS where M is the Madelung constant and d is the characteristic size of the Wigner-Seitz cell,πd2n=4πbining Eqs.(10)and(11)we arrive at a very simple expression for the Coulomb energy of n electrons on the surface of the sphereE C=n2q22a.(12)Eq.(12)with M=1.1046gives a very accuratefit to the ground state energy of the surface Thomson problem with purely Coulomb interactions[10,27].Note that for a planar OCP[29] M=1.1061,so that the topological defects affect very little the value of the Madelung constant.It is also important to notice that although E C is not extensive,∆E C≡12a(13)is.Therefore,if∆E C/n is plotted as a function of n/a2for different combinations of n and a,all points should fall onto one universal curve,f(x)=−Mx.(14)We can now check if this universality also holds for the Thomson problem with the Darwin coupling between the particles.That is if∆E∗≡E∗−1−n2Jayme De Luca,Savio B.Rodrigues and Yan Levin :The Thompson Problem 7-2.5-2-1.5-1-0.50 2 4 6 8 10 12 148EUROPHYSICS LETTERS[28]Y.Levin,Rep.Prog.Phys.65,1577(2002).[29]R.C.Gann,S.Chakravarty,and G.V.Chester,Phys.Rev.B20,326(1979).[30] A.Alastuey and W.Appel,Physica A276,508(2000).[31]W.Appel and A.Alastuey,Phys.Rev.E59,4542(1999).。
我想发明一个东西英语作文范文（精选5篇）
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The robot I want to invent, which is called ant robot, is a very small and powerful intelligent robot, mainly used for predicting dangerous situations and disaster relief.It is equipped with a natural disaster prediction system, which can accurately predict the time and place of natural disasters; its energy is an environmental protection robot converted from harmful substances in the air; at the same time, it can also be used in the search and rescue work of natural disasters. Once natural disasters occur, such as earthquakes, floods, snowstorms, etc., ant robots can quickly find the surrounding The trapped victims provide accurate information for rescue.If only I had invented this kind of robot earlier, this Wenchuan earthquake in Sichuan would not have killed so many innocent lives. I must work hard to learn scientific knowledge, invent it as soon as possible, and let it benefit mankind.what is my favorite invention?we knew there had been many inventions at the last century, for example, electric light bulb, telephone, phonograph, mimeograph machine, automobile, airplane, atomic weapon, computer and so on. what is my favorite invention?personally, my favorite invention should be computer. in the old days, many scientists took much time to calculate and deal with research data, so the effective time in doing research was relatively shortened. for millions of times of calculating per second by computer, the researchers may have enough time to study more important issues. the processing of expe riment results became very simple and easy. aren’t those all evidences that the computer is one of the greatest inventions in the last century, are those?so my favorite invention is computer.If I could invent something new, I’d invent a device or pil l that could put people to sleep immediately and would have no side effects. The proper amount of sleep is important for our concentration, mental health, and physical health.Getting enough sleep is a vital human need. For one thing, without sleep ourc oncentration is strongly affected. We’re easily distracted, we can’t remember things, and we don’t notice what’s happening around us. For example, a lot of car accidents are caused by tired drivers. When we get enough sleep, our powers of concentration are sharper. We’re more focused on what we’re doing. We perform better.Mental health is also affected by lack of sleep. It’s easy to tell if people don’t get enough sleep. They’re on edge, cranky, and out of sorts. They lose their tempers easily and over-react to situations. In fact, experiments have shown that lack of sleep over a long period of time can cause a complete mental breakdown. When we get our proper rest, we’re more alert and responsive. Our outlook is positive, and we’re much easier to get alo ng with.Our physical health shows the strain of sleeplessness, too. We have less energy, and everything seems like a major effort. Over a long period of time, we become slow and unresponsive. The wear and tear on the body from lack of sleep can be a very serious health problem. Every doctor will tell you that getting enough sleep is a basic factor in maintaining good health.Wouldn’t it be great to go to bed every night knowing you’d have no problem getting to sleep, no matter what’s going on in your l ife? Getting enough sleep is always going to be an important part of how you respond to your situation. I think this device would be very helpful to all of us.When I grow up, I want to be a scientist, to find out the earth, what is the cause of the earthquake, I want to invent a super strong seismic tester, which will automatically alarm in advance when there is an earthquake, and never let disaster happen again! Let the earth full of vitality, so that tens of thousands of children can grow up happily!As long as I study hard on the ground, I think I will reach my ideal when I grow up!When I was a child, I was always dreaming of what I could become when I grew up. Become a singer? Become a painter? Become an actor? These are some glamorous professions, and what I want to be the most is an inventor.Although the inventor is a behind-the-scenes worker, he can make a great contribution to human development. It can make peoples lives less tired and make people happier every day.If I were an inventor, I would invent many things that would be convenient for people to live on. Start with peoples housing starts! If I were an inventor, I would invent a very advanced door. The shape of this door is not different from the ordinary one, but it has many functions. First of all, when the noise coming from the corridor, the door can be according to the masters voice as he opened the door ahead of time, when the owner came to the door it say: "master, welcome home!" Then the door closes. The advantage of this design is that the owners no longer have to go out with keys. Second, if there is a bad guy to destroy the door, the door have a security alarm system, can let the neighbors know there is a thief, the thief will soon be away. And the door will also send the information to the owners mobile phone for the first time, telling the host that there is a bad guy and need to deal with it as soon as possible. Finally, the door has the function of weather forecasting. At seven o clock in the morning, it will report on time and report the weather and the situation of the day. If the weather forecast says its going to rain, the door will offer an umbrella before its owner goes out, and if its a big summer it will also offer a sunblock and sunscreen. The invention guarantees home safety, improves living standards and makes peoples lives more comfortable.If I were an inventor, I wanted to invent a medicine that would delay peoples life slightly. Because I know that it is impossible to live forever, and if you can live forever, there will be more and more people in the world. A slight delay is the ability to make a persons life a little longer. The invention is mainly used for the immediate death of the hospital, but to the people who want to see the last of their loved ones. Or people who are in a car accident or other sudden death. Because of this invention, they can be able to see the last part of their family, leaving them with the words they want to say, without regret.If I were an inventor, I would invent an emotional robot. Scientists say robots are mechanical, unemotional and cant understand what people really need. And Im going to invent this robot, which has its own personality, apart from being able to do the housework, the laundry, the cooking. Owners can choose robots with different personalities.There are gentle, considerate, or tyrants. The charm value of the robot can be acquired by itself. At that time, the robot is more than just a machine, it can be your family, your friends, more like your child. Hes hungry and needs you to feed him. When you are sad it will hug you, stand beside you and comfort you and tell you jokes. When youre nervous, it encourages you and tells you its ok. When you are happy, it will give you all kinds of celebrations, standing next to you and dancing, more than you are happy. But the baby robot also dies, for example, when it dies of starvation, or parts that are too long and die. But you can rest assured that the life of the robot baby is usually a hundred years old, enough to accompany you forever.If I am the inventor, I would also like to invent a lot of things to benefit mankind, Im notin order to let everyone thank me, let me earn a lot of money, but in order to let people all over the world have a safe, happy, happy, carefree, so I am very satisfied. I would like to be an inventor. For this dream, I must study hard and go to a good university in the future. I can get rid of the word "if" and realize my dream.。