Implicit-Explicit Numerical Methods in Models of Cardiac Electrical Activity By

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englishteaching英语教学法教程期末考试必考的知识点

englishteaching英语教学法教程期末考试必考的知识点Teaching grammarGrammar teaching depends on certain variables(learner and instructional ) in the language teaching/learning contextGrammar presentation methods-deductive method: relies on reasoning, analyzing and comparing teaching procedure:teacher’s example on the board,teacher’s explanation of the rules (in student’s native language),student’s practice application of the :good for selected and motivate students;save time to explain complex rules;increase students’ confidence in :grammar is taught iso latedly;little attention is paid to meaning;the practice is often mechanical-inductive method:teaching procedure;authentic language presentation(give grammar examples);let studentsobserve,analyse,compare examples;help students induct grammarrules,Advant ages:inspire students’ thinking activities;motivate students’ learning interests;grammar is taught in :the presen tation of grammar is more complex and time consumption;grammar is not taught directly;some rules can not be induced easily-guided discovery method: Similar to the inductive method:the students are induced to discover rules by themselves (similar);the process of the discovery is carefully guided and assisted by the teacher and the rules are then elicited and taught explicitly.(different)Implicit and explicit knowledge:Implicit knowledge refers to knowledge that unconsciously exists in our mind, which we can make use of automatically without making any effort;Explicit knowledge refers to our conscious knowledge about the language. We can talk about it, analyse it and apply it in conscious and acquiring (second language acquisitiontheory)The synthesis approaches to grammatical pedagogy:Collocational: grammar should be built on collocational relations between individual lexical items and their subcategories.Constructive: one’s knowledge of grammar is built bit by bit, which closely model the way language is learned and used.Contextual: Elements and structures are taught in relation to their context. Syntactic and lexical choices are explicitly related to pragmatic ones, and to social and cultural contexts.Contrastive: gra mmar involves drawing the learner’s attention to contrast the differences between the target language and other language. Grammar practice:Pre-learning;Volume and repetition: .Teacherpractice:activities that are aimed at form doing mechanical practice,students pay repeated attention to a key element in a of practice:Substitution and transformation drills2. Meaningful practice the focus is on the production, comprehension or exchange of meaning though the students “keep an eye on” the way ne wly learned structures are used in the process.prompts for practice:The prompts can be pictures, mimes, tables, charts or key words, etc.A good presentation should include both oral and written and form and meaning Visual materials can aid comprehensionIt’s the teacher’s involvement and his or her ability to personalise teaching and make activities engaging that often promotes successful learning.Teaching vocabularyThe first question need to know is what does knowing a word involve.A word:knowing its pronunciation and stress; spelling and grammatical properties; meaning; how and when to use it to express the intended meaning(freestanding and bound morphine)Vocabulary learning involves ate least two aspects of meaning: the understanding of its denotative and connotative meaning; and understanding the sense relations among wordsDenotative meaning of a word or a lexical item refers to those words that we use to label things as regards real objectsConnotative meaning of a word refers to ‘the attitudes or emotions of a language user in choosing a word and the influence of these on the listener or reader’s interpretation of the word. This words that may express a positive or negative attitude or subtle feelings toward something. Collocations refers to words that co-occur with high frequency and have been accepted as ways for the use of words. It is believed that teaching word collocations is a more effective way than just teaching one single word at a time. Synonyms refer to items that mean the same, or nearly the refer to items that mean the opposite of a word. Hyponyms refer to words which can be grouped together under the same superordinate concept Receptive and Productive vocabularyPassive vocabulary: the words they vocabulary: the words they use So the job for the teacher is to guide the students to those words which will help them to add to their active vocabularies, and to distinguish those words from the much larger number of passive items. At the beginning of language learning, all the words which are taught must be acquired for active use, later, at intermediate and advanced levels, most of the words students meet will only be needed for passive use. Ways of consolidating vocabulary:labelling,spot thedifference,descibe and draw,play a game,use word series,word bingo,word association,find a synonyms and antonym,categories,using wordnet-work,using the Internet resources for some ideasDeveloping vocabulary building strategies:review regularly,guessmeaning from context, Organize vocabulary effectively,using a dictionary,manage strategy useTeaching listeningListening problems:lack of teaching materials,both with print materials and audio or video tapes,lack of equipment in some schools;lack of real-life situations:lack of professional qualified instructors A number of people have frequently made the point that of the total time an individual is engaged in communication: approximately 9% is devoted to writing, 16% to reading, 30% to speaking,45% to listeningListening and reading are receptive skills, but listening can be more difficult than reading.Different speakers produce the same sounds in different waysThe listener has little or no control over the speed of the input of spoken material;Spoken material is often heard only once and in most cases，we cannot go back and listen again as we can when we read;The listener cannot pause to work out the meaning of the heard material as can be done when reading;Speech is more likely to be distorted by the media which transmit sounds or background noise that can make it difficult to hear clearly; The listener sometimes has to deal simultaneously with another task while listening, such as formal note-taking, writing down directions or messages from telephone calls, or operating while listening to instructions. Characteristics of the listening process,formal or informalrehearsed or non-rehearsedcan the listener interact with the speaker or notListening characteristics:Spontaneity,Co ntext,visualclues,listener’s response,speaker’s adjustmentListening purpose:for social reasons,to obtain and exchangeinformationPrinciples and models of teaching listeningFocus on process:(they have to hear what is being said,they have to pay attention and construct a meaningful message in their mind by relating what they hear to what they already know;it’s also possible to hear people talkingwithout paying attention;we also know that if we don’t have enough previous knowledge of what is being said,it’s more difficult to make sense of what is said)Combine listening with other skills;Focus on the comprehension of meaning;Grade difficulty level appropriatelyDesigning listening activity:give a clear purpose, a specific task,an appropriate context for doing themBottom-up model:Listening comprehension is believed to start with sound and meaning other words,‘we use information in the speech itself to try to comprehend the meaning’Listeners construct meaning of what they hear based on the sound they hear.Top-down model:listening for gist and making use of the contextual clues and background knowledge to construct meaning are otherwords,listening comprehension involves ‘knowle dge that a listener brings to a text,sometimes called ‘inside the head’ information,as opposed to the information that is available within the text itself’ In such a case,listeners can understand better if they know something about the speaker,the setting,the topic and the purpose of the knowledge or schematic knowledge—mental frameworks for various things and experience we hold in our long-term memoryPre-listening activities:aim to motivate students,to activate their prior knowledge,and to teach key words or key sentences to the students before listening begins predicting,setting the scene,listening for thegist and specific informationWhile-listening:no specific responses,listen and tick,listen and sequence,listen and act,listen and draw,listen and fill,listen and take notesPost-listening:multiple-choice questions,answeringquestions,note-taking and gap-filling ,dictogloss(preparation dictation reconstruction analysis and correction)Integrate listening with the practice of other language skills,role play,debate,discussion,writing back Teaching speakingSpeech characteristic:spontaneous,full of false starts repetitions incomplete sentences short phrases time-constraintspoken languages features:Using less complex syntax;Taking short cuts,(incomplete sentences);Using fixed conventional phrases/ chunks. Using devices such as fillers, hesitation device to give time to think before speaking.Both learners and teachers need to learn to acceptrepetitions,rephrase,hesitations,incomplete sentences,fillers or doesn’t mean we don’t encourage fluent training students’speaking skills,feat ures of natural speech should be doesn’t only have implication for teaching speaking but also for assessing students to speak up is the first and most important taskPrinciples:Balancing accuracy-based with fluency-based practices, Contextualising practice, Personalising practice, Building up confidence, Maximising meaningful interactions, Helping students develop speaking strategies Designing speaking tasks:meaningful motivationlinguistically appropriate cognitively challengeMaximum foreign talk even participation high motivation right language levelPre-communicative activities :structural,quasi-communicativeCommunicative activities :Functional communicative and Social interactionRole-play :perform in different moods,change different role relationship,actual word can be varied,make the dialogue longerLearners should be helped move from form to using what is learned in meaningful communication The problem is not having nothing to say but lacking the opportunity to say itTeaching readingReading aloud and silent reading:Reading aloud cannot replace silent reading as it involves only the skills of pronunciation and reading ability re-quires the reading skills of skimming, scanning, predicting Effective reading:clear purpose in reading; read silently; read phrase by phrase,rather than word by word; concentrate on the important bits,skim the rest,and skip the insignificant parts; use different speeds and strategies for different reading tasks; perceive the information in the target language rather than mentally translate; guess the meaning of new words from the context,or ignore them; use background information to help understand the text.Reading comprehension means extracting the relevant information from the text as efficiently as possible,connecting the information from written message with one’s own knowledge to arrive at an understanding (construction of meaning from printed or written message)Two broad levels in reading:1) a recognition task of perceiving visual signals from the printed page through the eyes;2) a cognitive task of interpreting the visual information,relating the receive info rmation with reader’s own knowledgeVocabulary role:efficient reading begins with a lightening-like automatic recognition of initial process of acc urate,rapid and automatic recognition of vocabulary frees one’s mind to use otherresources(reasoning abilities,,knowledge about topic)to construct meaningSight vocabulary:you can recognise with both sounds and meanings without special effort from your brainFluent reading depends on an adequate sight vocabulary,a general knowledge about the target language, some knowledge about the topic, wide knowledge about the world and enough knowledge about text types. Teaching model:bottom-up model top-down model interactive modelPre-reading:pooling existing knowledge about the topic;predicting the contents of the text,skimming and scanning the text or parts of the text for certain purpose;learning key words and structures(predicting setting the scene skimming scanning)While reading: Information presented in plain text form is not facilitative for information retention The way to transfer information from one form to another is called a transition device Reading comprehension questionsQuestions for literal and explicitly available in the answered in the words of the text itself. Questions involving reorganization or literal information from various parts and put it to-gether or reinterpret Questions for inferences. This type of questions require students to consider what is implied but not explicitly stated.Questions for evaluation or sophisticated ques-tions which involve making a judgment about the text in terms of what the writer is trying to convey.Questions for personal response. The answers to thes e questions depend most on the reader’s reaction to the content of the te xt.Post-reading:discussion questions,reproducing the text,role play,gap-filling,discussion,retelling,writingThe teaching of reading should focus on developing students’readingskill s and strategies and on maintaining students’motivation for readingTeaching writingWriting purpose:get things done and to form;maintain social relationships;give a voice for shy students;less threatening for anxious students as it gives them to think about their meaning and purpose;raise awareness of how language worksA communicative approach to writing:Writing for learning” and “writing for communication”Sense of authenticity and audience motivation for writing purpose for writing proper procedures for writing Problems in writing tasks：They are mainly are designed to practise a certain target is insufficient preparation before the writing is no sense of audience and are given ideas to express rather than being invited to inventtheir is no opportunity for creative writing, particular for expressing unusual or original of them are test-oriented.The important point is that they are given the freedom to write about themselves rather than to write what they are told to write and therefore what they write should be more meaningful and communicativeA process approach to writing: creating a motivation to write, brainstorming, mapping, freewriting, outlining, drafting, editing, revising, proofreading and conferencing.Motivating students to the topic of writing as close as possible to students’ students enough room for creativity and imagination. prepare students well before writing. encourage collaborative group writing as well as individual writing. provide opportunities for students to share their writings. provide constructive and positive feedback.treat students’ errors strategically. give students a sense of achievement from time to time. We have emphasized that the teaching ofwriting should focus on the process rather than the product, and that all the writing tasks should have communicative purposesSummative assessment is mainly based on testing,it’s done mostly at the end of a learning period or a school yearFormative assessment is based on information collected in the classroom during the teaching process for the purpose of improving teaching and learningTeacher’s observations continuous assessment student’sself-assessment project work portfolios。

新世纪高等院校英语专业本科生系列教材综合教程2第三单元课后答案

Text comprehensionI. CII. 1. F;2. T;3. F;4. T;5. F.III.1. Paragraph 4: She fled逃往from Germany to Belgium to escape fascism法西斯主义; then moved to Paris, surviving the occupation侵略占领时期by placing German subtitles字幕on French films.2. Anne is an independent and honest lady.3. Paragraph 10: Anne assured her husband that he’d done the right thing. This means she appreciated his decision.4. Paragraph 8: she could endure difficulties in the hardest time but she couldn’t tolerate her husband’s complaints and feel ing sorry for himself.自我难过/自责/自惭形秽.5. Paragraph 12: She believes in tough love, and doesn’t let him just lie around but forces him to overcome his troubles.IV.1. But I also made some effort to adjust myself.2. …because I am sometimes too proud of mysel f.Structural analysisChronological account (Paragraph 1—2) – (Paragraph 8) –(Paragraph 14).Flashback (Paragraph 3—4) –(Paragraph 5—7) –(Paragraph 9—10) –(Paragraph 11—13) Chronological account (1—2) –Flashback (3—4) –(5—7)–Chronological account (8) –Flashback (9—10) –(11—13)–Chronological account (14).Section Four Consolidation ActivitiesPart one. VocabularyI.Phrase1. tie the knot = get married2. given that = if one takes into account that考虑到，假定3. then and there = at that time and place, esp. without any delay当场，当时当地4. in the midst of = when在……之中，当……的时候5. set … apart = distinguish使分离，区别II.1. wrapped up;2. fatal;3. fluent;4. has undergone;5. stretch out;6. financed;7. consequences;8. neighbourhood.III.Word derivationFill in the blanks with the appropriate forms of the given words.1. The principal would be less insistent (insist) on kids wearing school uniforms if the school had to pay for them.2. It’s so depressing (depress) the way no one seems to care what’s happening to this country.3. I really miss my mother. My only consolation (console) is that her suffering was not prolonged.4. The progressive Chinese intellectuals in the early days of the 20th century drew much of their inspiration (inspire) from the revolutionary ideas flooding out of Europe at that time.5. Three people were killed in a head-on collision (collide) between a bus and a car.6. Much progress has been made in the diagnosis (diagnostic) of genetic disease.7. Then suddenly, despite all their assurance (assure) they broke the agreement and signed a deal with a rival company.8. A heavy concentration of the drug may produce dizziness or even unconsciousness (unconscious).1. insist (v.)坚持；强调insistence n.坚持，坚决主张；强调insistent a.坚持的2. depress v.使沮丧；降低，压下；压抑depressed a.沮丧的；降低的；不景气的depressing a.令人沮丧的depression n.沮丧；萧条3. console v.安慰，慰藉consolation n.安慰，慰藉consolatory a.慰问的，可慰藉的4. inspire v.使……感动；激发；煽动inspiration n.灵感，启示inspiring a.令人振奋的，激励人的，鼓舞人心的5. collide v.碰撞，互撞；抵触collision n.碰撞，冲突6. diagnose v.判断，诊断（疾病）diagnostic a.特征的；诊断的diagnosis n.诊断7. assure v.使确信，使放心；确保assurance n.保证；确信，肯定；自信assured a.确实的，保障的；有自信的8. unconscious a.失去知觉的unconsciously ad.无意识地，不知不觉地unconsciousness n.无意识，意识不清，失去知觉IV.1. A;2. B;3. C;4. D;5. C;6. D;7. A;8. D.V.Synonym / AntonymGive a synonym or an antonym of the word underlined in each sentence in the sense it is used. 1. My Stroke of LuckSynonym: fortune2. At dinner with friends, she’d set a place for me as if it were the most natural thing in the world to eat lying on the couch.Antonym: unnatural, artificial3. Noel and I survived, but the men in the plane died instantly.Synonym: immediately4. Anne has such good judgment and intuition, she rarely makes a wrong decision.Synonym: seldom, hardly5. When we went out, Anne would put me in the rear of the station wagon, where I could stretch out.Synonym: back6. In L.A., I could get the best care for my spinal injury and start seeing psychiatrists for my very real “survivor’s guilt”.Antonym: innocence7. Born in Hanover, Germany, she fled to Belgium to escape fascism as a teenager.Synonym: escaped8. After our first meeting, I called to invite her to supper at Tour d’Argent, one of Paris’s best restaurants, with fantastic views of the Seine.Synonym: marvelous, wonderful, terrific4Prefix / SuffixWrite in each space one word that has the same stem as underlined in each given word.1. intendpretend2. implicitexplicit3. occurrecur4. transferrefer5. admitcommit6. rejectinject7. expressdepress8. conformreformPart twoGrammar Exercises1. Negation and inversionInversion involves putting an auxiliary verb before the subject of a clause. In formal English, it is quite common to use inversion after negative adverbial expressions and restrictive words such as only, never, hardly, little and seldom.e. g. At no time did he get permission for what he was doing.Not until the next morning did she realize how serious it was.Only later did they learn his terrible secret.Hardly had we walked in the door when the phone started ringing.In some negative sentences, “not” is to negate the predicates in form, but actually it is used to negate other elements of those negative sentences. Therefore, while translating, we should transfer the negation in some cases.e. g. Every man cannot be a scientist.A high executive does not have a large vocabulary merely because of the opportunities of his position.A negative may be transferred from a certain part of the sentence to another in translation.e. g. We don’t believe that our moth er tongue is inferior to any other language in the world.I don’t think Father will fancy living an idle life like that.I.Change each sentence into a negative with the given word.1. I hope it will rain. (not)I hope it will not rain.2. She has seldom been so successful before.Seldom has she been so successful before.3. You will find gold in Iceland. (nowhere)Nowhere in Iceland will you find gold.4. Donald had never imagined that this strange incident would help him to find a job.Never had Donald imagined that this strange incident would help him to find a job.5. He had scarcely any time to pack his suitcase.Scarcely had he any time to pack his suitcase.6. In no circumstances must you tell him this secret.7. We rarely get more than three consecutive days of hot weather in summer.Rarely do we get more than three consecutive days of hot weather in summer.8. I had ever worked hard as I did yesterday. (hardly)I had hardly ever worked as hard as I did yesterday.Hardly had I ever worked as hard as I did yesterday.II.1.无爱之人不可能真正幸福。

相场法模拟悬浮熔融硅液滴内部对流及自由界面变形现象

相场法模拟悬浮熔融硅液滴内部对流及自由界面变形现象石万元;张凤超;田小红;塚田隆夫【摘要】为了模拟具有高密度比的两相流,提出采用牛顿迭代求解半隐式格式离散Cahn-Hilliard方程的方法,应用相场法模拟水的溃坝流和水下气泡的上升变形过程,发现水碰到右边壁面时,水面上卷,气泡在浮力作用下逐渐上升,从球形逐渐变为帽形,模拟结果与界面跟踪法模拟结果一致,验证了数值算法的正确性.在此基础上,数值模拟了悬浮熔融硅液滴的流动、变形过程,结果表明,具有初始变形的液滴在表面张力的作用下逐渐收缩,液滴内产生对流,然后,液滴逐渐变为长条状,液滴内分布着4个涡胞,沿纵向排列.%In order to simulate the two-phase flow with high density ratio, the algorithm of Newton iteration was utilized to solve a discretized semi-implicit Cahn-Hilliard equation- The dam-break flow problem and the interface deformation of a rising air bubble in water were numerically simulated using the phase field method. The result exhibits that when the water flow reaches the right side wall, it flows upward along the solid walL Driven by the buoyant force, the spherical bubble rises up, and deforms into a spherical-cap shape gradually. The results agree well with those obtained by the front tracking method, which indicates the validity of the numerical algorithm. By the phase field method, the internal convection and interface deformation of a levitated droplet of molten silicon is simulated with a given initial amplitude. The result shows that the droplet gradually shrinks and the internal convection occurs, driven by the surface tension force. After a while, the droplet extends again, and four vortexes locate in the droplet, aligning along the vertical direction.【期刊名称】《西南交通大学学报》【年(卷),期】2012(047)004【总页数】6页(P692-697)【关键词】相场模拟;硅熔体;液滴;半隐式格式;牛顿迭代【作者】石万元;张凤超;田小红;塚田隆夫【作者单位】重庆大学动力工程学院,重庆400044;重庆大学低品位能源利用技术及系统教育部重点实验室,重庆400044;重庆大学动力工程学院,重庆400044;重庆大学动力工程学院,重庆400044;日本东北大学化工系,仙台,980-8579【正文语种】中文【中图分类】O359;TK124在电磁悬浮法熔炼金属和测量金属熔体物性参数过程中，因洛伦兹力、浮力、粘性力和表面张力等引起的熔融液滴内部对流颇为复杂，并伴随自由界面的变形振荡等现象[1］.由于金属液滴不透明，难以直接观测其内部流动，数值模拟这类问题显得非常必要[2］.文献[3］中采用 Galerkin有限元法和拉格朗日法相结合模拟了电磁悬浮熔融液滴的变形和非线性振荡行为.文献[4］中模拟了静磁场对电磁悬浮铝熔融液滴振荡过程的影响.但这些方法需要跟踪自由界面的形状，计算比较复杂.文献[5］中采用水平集法模拟了自由液滴的振荡和旋转，但水平集法难以满足质量守恒，难以模拟具有较高密度比的金属液滴在气体环境中的行为.近年来，相场法被用于模拟复杂界面流动问题，文献[6］中运用该方法模拟了Rayleigh-Taylor不稳定现象，讨论了界面厚度对模拟结果的影响.文献[7］数值模拟了气泡在水中的上升行为、液滴的碰撞过程及Rayleigh-Taylor不稳定现象，模拟所采用的气液密度比达到1000∶1.文献[8］中模拟了固体表面液滴的流动和溃坝问题，模拟结果与实验结果十分吻合.目前还没有见采用相场法模拟金属或半导体液滴内部对流和界面变形过程的报道.本文采用一种快速稳定求解相场方程的数值方法，尝试模拟了悬浮熔融硅液滴的内部对流和变形过程.1 数学模型假设流体为不可压缩流体，在圆柱坐标系下，无量纲量的控制方程如下:连续性方程动量守恒方程Cahn-Hilliard方程(简称C-H方程)式(1)～(3)中:t为时间，时间的标尺为Lref/uref(Lref为特征长度，uref为特征速度);u为速度;p为压力，压力的标尺为ρ1u2ref(ρ1为模拟对象的密度);μ为化学势，化学势的标尺为ε/(αLref)(ε为界面厚度;α为常数φ为相场，φ的变化反映了界面形状的变化，当φ=1为模拟的主要对象，如气泡或液滴;φ=0为气泡或液滴周围的环境流体，0＜φ＜1为气液界面;ρ(φ)为无量纲密度，ρ(φ)=φ +(1－φ)λρ(λρ为密度比，λρ= ρ2/ρ1，ρ2为周围流体的密度);η(φ)为无量纲粘度，η(φ)=φ +(1－φ)λη(λη为粘度比，λη=η2/η1，η1和η2分别为主要模拟对象和周围流体的粘度);M(φ)为迁移率，M(φ)=φ(1－φ);g为重力加速度;Re为雷诺数，其中，σ12为气液界面张力;Fr为Froude数，Pe为Peclet数，其中，Mref为迁移率的标尺.本文中化学势定义为其中:Cn为Cahn数，计算时固体壁面采用无滑移边界条件，其它边界采用Neumann边界条件.初始时刻，液滴处于静止.气液界面的初始相场以平衡解析解[7］表示，即其中:r0为模拟对象的初始尺寸，例如气泡的初始半径;x、y为空间坐标.2 数值方法及验证在相场模拟中，相界面用一个很薄的有限厚度来表示，界面内的状态参数连续分布.在这个很薄的界面区域内，各种状态参数具有很高的梯度，尤其是当两相的密度比、粘度比较高的时候.采用高阶精度离散求解时极易产生数值振荡，准确、稳定求解C-H方程是相场模拟的关键.文献[9］中提出了一种求解该方程的半隐式格式，理论上具有无条件稳定的优点.由于C-H方程扩散项为四阶微分项，且其中的迁移率是相场的非线性函数，这使得求解该方程的收敛速度很慢.为了克服这一缺点，本文提出用牛顿迭代求解半隐式离散C-H方程的方法，期望既能保证数值计算的稳定性，又能提高收敛速度.具体方法如下.将C-H方程的右端的扩散项分为2部分，对流项并入第2部分，即式(4)右端第1项拟采用隐式格式，第2项采用显示格式.参照文献[10］的离散方式，时间项采用二阶半隐式向后差分[11］，时间项离散后的方程为式中:n为离散时刻;其中，f″(φ)=0.5(1 －6φ +6φ2).式(5)表示半隐式格式，可改写为式中:令其中:φn+1为未知量;φn和φn－1为已知量.有即离散并求解式(9)可得δφn+1.根据牛顿迭代式可迭代求解φn+1，其中，k为迭代层次.计算区域采用均匀交错网格离散，控制方程采用有限差分离散.其中:动量方程的对流项采用QUICK格式，扩散项采用二阶中心差分;C-H方程的对流项采用五阶加权本质无振荡法[12］，扩散项采用四阶中心差分;动量方程中速度和压力的耦合采用SIMPLEC法求解;离散的C-H方程和动量方程采用了 Bi-CGStab法[13］求解. 研究结果发现，采用牛顿迭代比采用高斯-赛德尔迭代快数倍甚至数十倍以上，计算采用的时间步长比用三阶龙格库塔法[12］离散时提高100倍以上，但仍能稳定求解，说明求解的稳定性大幅提高.为了验证以上数值方法和计算机程序的正确性，模拟了水的溃坝流问题.计算采用的物理模型如图1所示.在长×高为4a×3a的矩形容器左下角盛有尺寸为a×2a的水柱，周围充满空气. 假设在时刻t0将水柱的右边挡板移开，水在重力作用下开始流动.选取的计算参数为:空气/水密度比ρ2/ρ1=1.23 ×10 －3;空气/水粘度比η2/η1=1.56 ×10－2;网格数为80×60.图2为水柱在不同时刻的状态.图1 溃坝问题物理模型Fig.1 Physical model of dam-break problem由图2可知，水在重力作用下变形、流动，当碰到右边壁面时，水面上卷，该过程与文献[8］的数值模拟结果一致.图2 水柱在不同时刻的状态Fig.2 Evolution of the shape of water column水下气泡在浮力作用下的上升变形是另一个典型的复杂界面流动问题，轴对称模拟结果如图3所示.图3中:计算区域尺寸为2×5;图3 水下气泡的上升变形过程Fig.3 Evolution of the shape and position ofthe rising bubble气泡半径为1;网格数为40×100.图3为水下气泡的上升变形过程.图4 悬浮熔融硅液滴的变形过程Fig.4 Evolution of the shape of molten silicon droplet由图3可知，气泡在浮力作用下逐渐上升，形状从开始的球形逐渐变为帽形，模拟结果与文献[14］采用界面跟踪法的数值模拟结果一致.以上2个算例证明本文所采用的数值算法和计算机程序是正确的.3 结果与分析图4为相场模拟得到的微重力环境中悬浮熔融硅液滴的流动、变形过程.表面张力，顶部和底部表面张力较大，其余较平坦的地方表面张力相对较小，表面张力趋向于使液滴呈圆球形，经过一段时间后，液滴的形状有所收缩，如图4(b)所示.液滴的收缩驱动两极的流体沿中心向赤道区域流动，然后沿表面附近流回两极，液滴内上下各分布有一对反向旋转的涡胞，如图5(a)所示.假设:模拟区域为轴对称;模拟过程等温;模拟区域尺寸为2×4;液滴的初始形状为二阶Legendre多项式曲线，其中:θ为极角;r为液滴半径，r=1;ε为初始振幅，ε=0.38;网格数为40×80.初始状态如图4(a)所示.在图4(a)中，初始变形的液滴受到不均匀的当液滴逐渐接近于球形时，表面张力减小，但由于流体流动的惯性，液滴内部对流并不会立即停止，而是继续运动，经过一段时间后，液滴被沿两极的对流拉长为细长棒状，如图4(c)所示.此时涡胞被挤扁，沿竖直方向排列，涡胞增加为上下各4个，如图5(b)所示.继续计算发现，液滴的界面形状在球形和椭球形之间振荡[5］.由于粘滞力的作用，振荡随时间逐渐衰减，液滴最终变为球形，流动停止.完全模拟整个过程需要消耗相当长的CPU时间.图5 熔融硅液滴流场Fig.5 Evolution of the flow field of molten silicon droplet4 结论本文提出了牛顿迭代求解半隐式格式相场方程的方法，水的溃坝流和水下气泡的上升变形过程数值模拟表明该方法具有较强的稳定性和较快的收敛速度，模拟结果与文献结果一致，验证了数值算法和计算机程序的正确性.在此基础上，数值模拟了悬浮熔融硅液滴的流动、变形过程.模拟采用硅熔体和空气的密度比为2 066.1∶1.结果显示，具有初始变形的液滴在表面张力的作用下逐渐收缩，液滴内上下各分布着一对反向旋转的涡胞.由于惯性的作用，液滴又逐渐变为长条状，液滴内涡胞数增加为上下各4个，沿纵向排列.这些结果表明，本文提出的数值算法能够正确模拟高密度比、高粘度比金属或半导体熔融液滴的流动变形过程，为进一步开展这方面的数值计算提供了有效的途径.参考文献:【相关文献】[1]范建峰，袁章福，柯家骏.高温熔体表面张力测量方法的进展[J］.化学通报，2004(11):802-807.FAN Jianfeng， YUAN Zhangfu， KE Jiajun.Development in measuring surfacetension ofhigh temperature molten liquid[J］.Chemistry，2004(11):802-807.[2]鄢振麟，解文军，魏炳波.声悬浮条件下扇谐振荡液滴的内部流动规律[J］.中国科学:物理学力学天文学，2011，41(9):1096-1103.YAN Zhenlin，XIE Wenjun，WEI Bingbo.Internal flow of acoustically levitated water drops during sectorial oscillations[J］.Scientia Sinica Phys，Mech ＆ Astron，2011，41(9):1096-1103.[3]ASAKUMA Y， HIRATA T，TSUKADA T，et al.Nonlinearoscillations ofmolten silicon drops in electromagnetic levitator[J］.J.Chemical Engineering of Japan，2000，33(6):861-868.[4]BOJAREVICS V， PERICLEOUS K. 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SIAM Journal on Scientific and Statistical Computing，1992，13:631-644.[14]HUA J，HOU J.Numerical simulation of bubble riding in viscousliquid[J］. J. ComputationalPhysics，2007，222:769-795.。

跳跃-扩散模型资产定价公式的数值计算方法

跳跃-扩散模型资产定价公式的数值计算方法张鸿雁;李强;张志【摘要】假定资产价格变化过程服从跳跃-扩散过程,那么基于它的欧式期权就满足一个偏积分-微分方程(PIDE),本文利用差分法来离散这个PIDE方程,用两种迭代方法得到方程的数值解:基于雅可比正则分裂法和预条件共轭梯度法.【期刊名称】《经济数学》【年(卷),期】2010(027)002【总页数】6页(P51-56)【关键词】跳跃-扩散模型;差分法;FFT算法;欧式看涨期权【作者】张鸿雁;李强;张志【作者单位】中南大学,数学科学与计算技术学院,湖南,长沙,410083;中南大学,数学科学与计算技术学院,湖南,长沙,410083;中南大学,数学科学与计算技术学院,湖南,长沙,410083【正文语种】中文【中图分类】O241.82美国芝加哥大学教授Black和Scholes[1]在1973年发表了“The Pricing of Op tions and Corpo rate Liabilities”一文,提出了著名的Black-Scholes期权定价公式,在B-S公式中,假设股票的价格过程是连续的几何布朗运动,但是,在现实市场中,一些突发情况会引起股票价格发生跳跃.基于上述考虑,M erton在1976年首先提出了跳跃-扩散模型,在M erton模型中,资产价格在没有受到外界重大影响时服从布朗运动,当资产价格受到突发事件的影响而发生跳跃时,就用跳跃过程来描述.本文首先介绍 PIDE[2]的具体形式,在Merton模型下对其差分离散,得到一个Toep litz矩阵方程,用两种方法解这个矩阵方程,一是基于雅可比正则分裂的迭代方法[3-4],二是预条件共轭梯度方法.考虑到 Toep litz[5]矩阵的特殊性,在迭代的过程中,将其植入到一个循环矩阵中,利用循环矩阵和向量的乘积来计算 Toep litz和向量的乘积,而循环矩阵向量乘积可以通过快速富里叶变换(FFT)快速计算,这样就加快了迭代速度.共轭梯度法是解决 Toep litz线性方程组的主要方法之一,在利用共轭梯度法的情况下,快速傅里叶变换的作用是加快共轭梯度法的迭代速度,但不改变其收敛速度,共轭梯度法的收敛速度取决于线性方程组系数矩阵的条件数,基于此考虑,本文采用预条件共轭梯度算法,选用R.Chan优化循环预条件器[6],预条件器的使用是为了改善系数矩阵的条件数,以便提高收敛速度.假设市场是完备无套利的市场,在跳跃-扩散模型下,资产的价格变化过程服从随机微分方程:其中,υ(t)是漂移率,σ(t)是波动率,ω(t)标准布朗运动,d q(t)是泊松过程,d q(t)=0的概率是1-λd t,d q(t)=1的概率是λd t,λ是泊松到达强度,η-1是由 S跳跃到Sη的跳跃幅度函数,是一个随机变量,用ζ表示平均跳跃幅度E(η-1),泊松过程d q(t)与布朗运动ω(t)是相互独立的.由文献[7]可知,在上述假设下,基于资产价格S与时间τ的未定权益V(S,τ)满足PIDE:这里,对于时间的偏导,当m≥2时,用向后的二阶差分来近似对时间的微分,当m=1时,用向后的一阶差分近似;对于空间的偏导,用中心差分来近似.定义向量um=(um1,…,umn)T.由初始条件,初始向量:由式(13)～(16),则式(5)的有限差分离散能写成矩阵形式:定义1 假设矩阵A可用分裂成形式:其中,Q是单调矩阵(Q-1≥0)且R≥0,则称 A可以正则分裂.对于每一个形如式(21)的分裂,都存在相应的迭代方法:若A是单调矩阵,则迭代式(22)是收敛的(ρ(Q-1R)<1),证明过程见文献[8].给出雅可比正则分裂的形式:(A)A=Q1-R1,其中Q1是A的对角矩阵.如果满足:则分裂(A)是正则的,且证明过程见文献[9].在有限差分法中,若:则可以得到一个精确稳定的解.若保持 k/h固定不变而让h→0,则存在一个 h0>0使得在h≤h0时条件(i)～(iv)同时成立.本文中系数矩阵A是一个 Toeplitz矩阵,现选择R.Chan优化循环预条件器[10]加快迭代过程中的收敛速度.预条件器C:其中,是矩阵A中的元素,j=0,…,n-1.在所有的 n阶循环矩阵中,C极小化 Frobenius范数‖C-T‖F,在这个意义下,C被视为A的一个近似矩阵.在预条件共轭梯度法下,每一次迭代都要计算矩阵向量积Ax 和C-1y(x和y是n维向量),可以利用快速富里叶变换(FFT)快速计算.C可以被n阶离散富里叶矩阵对角化,即其中其中,τ=T-t,η=eσ2J-1,σ2m=σ2+mσ2J/τ,rm=r-λη+m log(1+η)/τ,VBS表示欧式看涨期权的价格.用M atlab编程进行数值试验.在所有的实验中,式(22)的迭代停止时刻由前后两个迭代矩阵之间的差的l-范数决定,即当‖Vl+1-Vl‖ <ε时停止,这里取ε=10-8.在M erton模型中用FD和BDF2对空间与时间进行差分,并用三对角分裂法处理Toep litz矩阵,到期时刻 T=1,截断点 x＊=4,r=0,波动率σ=0.2,跳跃方差σJ=0.5,跳跃强度λ=0.1,协定价格 K=1,xK=log(K).结果为:在M erton模型[12]下做数值实验,当μJ=0时,欧式看涨期权有解:由表1和表2,随着差分节点数的增加,计算的误差越来越小,从空间差分节点数129开始,差分节点数每增加一倍,雅克比正则分裂迭代算法的计算误差就下降一个数量级,对于预条件共轭梯度法,当差分节点数从65增加到129时,计算误差下降了两个数量级,而在节点数从129增加到1 025的过程中,误差都是在同一数量级内减少,这说明预条件共轭梯度法的收敛速度很快.从计算的精确度来说,雅克比正则分裂法和预条件共轭梯度法相差不大,但是从计算的速度来看,后者要比前者快.本文讨论了当市场有跳跃时欧式期权定价的数值计算方法,期权的价格是一个PIDE 方程的解,本文用差分法对这个方程进行离散,得到一个 Toep litz矩阵系统,本文用两种方法来处理这个系统,由表1和表2可以看出,二者在计算精度上差别不大,预条件共轭梯度法比雅可比正则分裂法的迭代结果误差更小些,而且迭代过程中的迭代次数更少,分析这些差别的原因,是由于预条件共轭梯度法对系数矩阵进行了处理,使系数矩阵的条件数减小,因而加快了迭代的收敛速度.Keywords jump-diffusion model;finite differences;FFT algo rithm;European call op tion【相关文献】[1] BLACK F,SCHOLESM.The p rice of options and corporate liabilities[J].Journal of Political Economy,1973,81(3),637-654.[2] AN ITA Mayo.Methods for the rapid solution of the p ricing PIDE in exponential andmerton models[J].Journal of Computational and Applied Mathematics:2008,22(34):128-143.[3] CONT R,VOLTCHKOVA E.A finite difference scheme foroption pricing in jump-diffusion and exponential levymodel[J].SIAM J 2005,43(67):1596-1626.[4] 杨向群,吴峦东.带跳的幂型支付欧式期权定价[J].广西师范大学学报:自然科学版,2007,25(34),56-58.[5] STANG G.A p roposal fo r toep litz calculations[J].Stud Appl M ath,1986,74(39):171-176.[6] CHAN T.An optimal circulant p reconditioner for Toeplitzsystems[J].SIAM,J,Sci,Stat,Comput,1988,9(13):766-771.[7] BRIAN T M,NA TAL IN IR,RUSSO G.Implicit-explicit numerical schemes for jump-diffusion p rocess[J].Technical Report,2004,38(37):35-45.[8] YOUNG D M.Iterative solution of large system s[J].New Yo rk:Academic,1971,5(23):25-35.[9] ARIEL Almendral,CORNEL ISW.Oosterlee.Numercial valuation of optionswith jumps in the underlying[J].Applied Numercial Mathematics,2005,53(29):1-18.[10]CHAN R,NAGY J,PLEMMONSR.Circulant p reconditioned:toeplitz least squares iterations[J].SIAM JMatrix Appl,1994,15(8):80-97.[11]BRIAN IM,Numericalmethods for option p ricing in jump-diffusionmarkets[D].Universita Degli Studi Di Roma“La Sapienza”Dottor to Di Ricerca in Miatematica Per Le Applicazioni Economiche e Finanziarie,2003.[12]ANDERSEN L,ANDREASEN J.Jump-diffusion p rocess:volatility smile fitting and numericalmethods for option p ricing[J].Rew.Derivatives Res,2000,4(17):231-262. Abstract The paper assume that the p rice p rocessof the assets is a jump-diffusion p rocess,then,the value of European op taon satisfies a general partial integro-differential equation(PIDE)under this assump tion.The equation was discretized by difference formula.The result was obtained by two iterative methods:Jacobi regular splitting method and p reconditioned conjugate gradient method.。

Argument比较全的分类词汇和句式

Argument比较全的分类词汇和句式一、词汇(一) 动词支持：support, in support of, bolster, justify, substantiate, validate,保证：guarantee, warrant, demonstrate, prove, ensure that, assure (sb) that…Ø Say/tell/inform little more than/about, do littl e to…, lend no strong support to, lends little credible support to, is insufficient/far from being enough to support…, does not support/ensure/…,Ø fails to convince us that, fails to provide/produce/present any evidence/facts that... /information concerning..., provide no evidence that…, have no evidence to supportØ The author’s implicit claim that… is poorly supported/unconvincing.Ø there is no guarantee/ warrant/justification/proof/assurance/evidence that…, It does not naturally warrant that…, it is unwarranted that…,增强：solidify /strengthen/fortify/reinforce, enhance,弄清楚：make clear, elucidate, explain削弱：weaken, undermine, attenuate, dilute, invalidate评估，鉴别：evaluate, assess, appraise, identify怀疑：doubt, suspect相信：believe, be certain /sure that…, accept使用：employ (employs two lines of reasoning to), utilize, apply建立：establish (establish a causal relationship between), set up接受：accept,提出，呈现，显示：suggest, indicate, imply, show, present, reveal, introduce, propose提供：provide, be involved in, offer引用cite得出：it did not follow that…,This would go a long way toward explaining why…, reach, arrived at, get, draw有可能：there is a good chance that…有理由：have a good reason to…收集：gather, collect告诉：tell, inform指出：Point out建议：Proposal, recommendation, advocate依靠：Rest/depend/rely on, be based on, on the basis of推理：reason, infer, the reasoning that…过分… overemphasize, oversimplify宣称：assert/claim影响：affect, influence, account for, be more important than… in determining…, lead to, cause, give rise to, have some bearing on, have negative impact on有助于：help, facilitate, make for, contribute to, has done more to..., be advantageous to, benefit 归功于：owe a lot to, attribute to, ascribe to导致：lead to, result in, give rise to, cause, bring about, call... into existence由于：Result from,遭受：Suffer from, be influenced by,忽略：Ignores/overlooks; fails to take into account/consideration /consider/acknowledge/explain; fails to rule out其他因素：The possibility that, other factors that…, other likely benefits of…,other possible causes of…, other criteria for determining, the only attribute/reason/factor necessary to关心：Be concerned about, care for, consider as important喜欢：Prefer, incline最终证明是to prove to be in the result or end, turn out that/ to be, end up with意味着：mean, imply系动词：be, exist, remainIt句型：it is unwise to…, it is unwarranted to assume that…There句型：there is no guarantee that…(二) 名词证据：(the supporting) evidence (offered by the arguer), fact, information (about), data, justification for, statistical evidence, statistics,survey, study, experiment, investigation, observation, This observed phenomenon, experience, assurances, no evidence whatsoever,statistics showing that, a survey showing that, assurances from… that…假设：assumption-assume, claim, assert-assertion结论：conclusion-conclude, claim, what the arguer maintains原因：Reason, factor, cause, attribute, contingencies关注：concern about分析，检查：examination, investigations, inspection, analysis解释：explanation错误：fallacies /flaws部分：A small portion of, a fraction of作者：The arguer, This loan applicantThe… o f：the importance of, the necessity of, the reliability of, the combination of, the result of, the example of, the sign of/no sign ofThe… to：the desire to, the need to,名词后可跟的修饰其的小词Evidence available, which is of course unwarranted, A third problem with the argument, The conclusion reached in this argument, The evidence provided in this argument/ offered by the arguer, the statistical evidence upon which it relies, the evidence cited in the analysis, The statistics offered in the announcement, no evidence whatsoever, the difficulties inherent in this process, any evidence suggesting/shows that, all of which are ignored by the arguers, both of which are unknown from this argument, society as a whole(三) 形容词合理的：reliability, credibility, justifiable, reasonable, legitimacy, reliable, valid, credible, persuasive, sound无理的：unfounded, unwarranted, gratuitous, unreasonable, invalid, unconvincing , groundless, unproved, in lack of solid ground, no evidence whatsoever, untenable, poorly supported, vague, questionable, doubtful, suspect, uninformative, presumptuous, premature, ineffective, probablymisleading, Unfairly, oversimplified, counterproductive, impractical, meaningless强有力的：solid, strong, substantial很少的：trivial, trifling, slim information负的：Negative, adverse相关的，重要的：relevant严重的，主要的：Major, critical, serious, main不充分的：insufficient,具体的：specific, detailed, particular暗含的：Implicit-explicit仔细的：careful, thorough, comprehensive仅仅：mere在名词后修饰的形容词：enough /necessary to,(四) 副词不好poorly, seriously, unfairly,必然necessarily,可能probably,其他automatically, naturally, directly–indirectly, actually, only, equally, admittedly, merely, significantly, mutually, randomly, respectively, very, especially, particularly,非常：very, extremely, tremendously, enormously, heavily, deeply, great,节俭的：sparingly插入语：as we know; as is known to everyone, which is of course unwarranted单独：alone(五) 介词缺乏：in short of-in absence of-lacking-in lack of-without, unless尽管：regardless of, despite, in spite of根据，按照：according to，in terms of, in light of关于，就...而言：concerning, about, regarding, as to /for, in respect of, in so far as, with regard to, as far as... is/are concerned(六) 连词虽然：while, although, though, whereas, albeit, howbeit, Be that as it may然而：while, whereas, however, but, yet,并列：And-as well as例如：such as, e.g., for example/instance也就是：That is, i.e.所以：so, so that, therefore, thus, hence, consequently, accordingly, as a result, as a consequence, for this reason二、模板(一) 开头：1. 描述题干：1) 结论：however the author has committed several logical flaws. For example…also…and finally…a) 推论性的结论inferential conclusionthe arguer concludes/claims that, 特殊the conclusion in this argument is thatb) 建议the arguer advocates/recommends/claims that .().2) 证据：the arguer points out that, the arguer provides/present the evidence that..., 特殊this recommendation is based on the observation that; the arguer cites the result of a recent study that..., the arguer cites the example of,3) 假设：the arguer claims/assumes that.(假设，小结论).; the arguer reasons that .(推理论证reasoning: since...,...).2. 连接词：1) In this argumentThe first issue to be addressedThis argument also relies on the idea that2) To support/justify/substantiate/ bolster /in support of the conclusion /claim/ recommendation /prediction3) In addition/Meanwhile/Moreover3. 结论This argument suffers from/is unconvincing /problematic for several/two critical fallacies /flaws /reasons.This argument is fraught with vague, oversimplified and unwarranted assumptions.A careful examination of this argument would reveal how groundless the conclusion is.Although it seems to be an obvious conclusion, with further examination /inspection /analysis, you will find there are several critical/severe/serious/major/main flaws/fallacies in the argument.The conclusion reached in this argument is invalid and probably misleading.Careful examination of this supporting evidence, however, reveals that it lends little credible support to the applicant's claim.。

二语习得中的“显性”与“隐性”探析

二语习得中的“显性”与“隐性”探析-汉语言文学二语习得中的“显性”与“隐性”探析朱希芳摘要：本文在前人研究的基础上，对二语习得中的“显性”和“隐性”进行一系列的探讨。

通过分析学者们对“显性”与“隐性”的定义及观点，进一步提出两者之间的关系并不是相互独立的，而是可以相互转化的。

在一定程度上，显性知识可促进隐性知识的发展，隐性知识可以帮助显性知识的学习。

在语言学习方式的选择上，儿童或具有高语言分析能力的人更适合隐性学习，而成人或低语言分析能力的人更适合显性学习。

在二语习得过程中，应将两者有机结合，以取得最佳二语习得效果。

关键词：二语习得显性隐性一、引言显性学习与隐性学习是学习知识的两种必然途径，也是二语习得领域的基本问题之一。

显性学习处于有意识状态，而隐性学习处于无意识之中；前者需要付出努力和意志，而后者则是在不知不觉中获得知识的过程。

近年来，学术界已对二语习得中“显性”与“隐性”进行了大量的探讨和研究，并取得可观成果（如：代曼纯，2005；张宏武，2008；王敏，2008；江进林，2010；蒋慧、王艳敏，2012；周文美，2012；苏建红，2012）。

研究发现，语言学习者身份不同，他们学习语言所使用的方法也有所不同：本族语者多运用隐性学习法，二语学习者则多运用显性学习法。

对于这两种学习方式，究竟是显性学习效果好还是隐性学习效果更好，学界对此有多种观点，且说法不一。

我们认为“显性”和“隐性”之间具有很大联系，不能将二者割裂开来，而应该将其进行有机的结合，以此发挥二者的最佳效果。

二、显性与隐性的定义学习是一个复杂而又高级的心里过程，这一过程既受到语言学者们的关注，也受到心理学家们的重视。

在心理学和认知语言学领域，学习被看成一个心理认知过程，而认知主体则是我们人类自己，语言学习的本质就是在人类认知系统里的信息认知加工。

在二语习得领域，较早涉及显性学习和隐性学习以及相关知识研究的是Krashen。

Krashen（1982，1985）在他的监控模式中提出一系列假说，其中的“习得—学得”假说采用“意识”和“无意识”来划分二语的学习。

刚性微分方程组隐式龙格库塔方法

毕业设计题目：刚性系统的隐式RK方法学院：数理学院专业名称：信息与计算科学学号： ************学生姓名：**指导教师：***2016年05月15日摘要本文主要介绍单步隐式Runge – Kutta方法,简要的介绍了Gauss型隐式Runge – Kutta方法、Radau型隐式Runge – Kutta方法和Lobatto型隐式Runge – Kutta方法。

并利用这些基本的隐式Runge – Kutta方法来对刚性方程组进行数值求解，并将隐式Runge – Kutta方法与显式经典Runge – Kutta方法求解的结果进行对比，说明两种数值解法的优缺点。

关键词：刚性系统隐式Runge – Kutta方法单步方法Newton迭代法AbstractThis paper mainly introduces the Implicit Runge-Kutta Methods and a simple description of Gauss implicit Runge-Kutta method ,Radau implicit Runge-Kutta method and Lobatto implicit Runge-Kutta method . These basic Implicit Runge-Kutta methods are used to solve the stiff equations. These implicit Runge-Kutta methods iare compared with the classical explicit Runge-Kutta method. This paper explain the advantages and disadvantages of the two kind of numerical methods.Keywords: Stiff system Implicit Runge-Kutta method One step method Newton iterative method目录1.绪论 (1)1.1刚性方程 (1)1.2隐式RK方法的研究意义 (2)1.3 RK方法的研究现状 (3)2.单步RK方法的收敛性和稳定性 (5)2.1单步RK方法的收敛性 (5)2.2单步RK方法的稳定性 (6)3.三类隐式RK方法 (8)3.1引言 (8)3.2 Gauss型隐式RK方法 (9)3.3 Radau型隐式RK方法 (10)3.4 Lobatto型隐式RK方法 (11)4隐式RK方法的实现 (13)4.1非线性系统的改进 (13)4.2简化的Newton迭代法 (13)5数值实验与结果分析 (15)参考文献 (18)附录 (21)1.绪论1.1刚性方程对于一般的线性常系数系统y′=Ay+φ(t) A为m×m的矩阵，特征值为λi(i=1,2,⋯,m)。

微观经济学原理(第七版)-曼昆-名词解释(带英文)

微观经济学原理曼昆名词解释稀缺性（scarcity)：社会资源的有限性。

经济学（economics)：研究社会如何管理自己的稀缺资源。

效率(efficiency)：社会能从其稀缺资源中得到最多东西的特性。

平等(equality):经济成果在社会成员中公平分配的特性。

机会成本(opportunity cost)：为了得到某种东西所必须放弃的东西。

理性人(rational people）:系统而有目的地尽最大努力实现起目标的人。

边际变动（marginal change）：对行动计划微小的增量调整。

激励(incentive)：引起一个人做出某种行为的某种东西.市场经济（market economy）:当许多企业和家庭在物品与劳务市场上相互交易时，通过他们的分散决策配置资源的经济。

产权（property rights）：个人拥有并控制稀缺资源的能力。

市场失灵(market failure)：市场本身不能有效配置资源的情况。

外部性(externality）：一个人的行为对旁观者福利的影响。

市场势力(market power)：一个经济活动者（或经济活动者的一个小集团）对市场价格有显著影响的能力.生产率（productivity）：一个工人一小时所生产的物品与劳务量。

通货膨胀（inflation)：经济中物价总水平的上升。

经济周期(business cycle）：就业和生产等经济活动的波动（就是生产这类经济活动的波动.）循环流向图（circular—flow diagram）：一个说明货币如何通过市场在家庭与企业之间流动的直观经济模型.生产可能性边界(production possibilities frontier):表示一个经济在可得到的生产要素与生产技术既定时所能生产的产量的各种组合的图形.微观经济学（microeconomics)：研究家庭和企业如何做出决策，以及它们在市场上的相互交易。

宏观经济学（macroeconomics）：研究整体经济现象,包括通货膨胀、失业和经济增长。

英语六级翻译必背动词及分类词总汇

英语六级翻译必背动词及分类词总汇英语六级翻译必背动词今天为大家及时带来英语四六级考试相关资讯及备考技巧。

也为大家整理了大学英语六级翻译高频词汇，一起来看看吧！一、动词（18组）1. 强调stress/emphasize/underline例句：他们强调，人们应当读好书，尤其是经典著作。

They emphasize that people should read good books, especially the classics.2. 象征symbolize/signify/stand for例句：在中国文化中，红色通常象征着好运、长寿和幸福。

Red usually symbolizes fortune, longevity and happiness in Chinese culture.3. 变成、改变、演变become/change into/develop to/evolve into例句：珠江三角洲已成为中国和世界主要经济区域之一。

The Pearl River Delta has become one of the main economic zones in China and the world.4. 考虑consider/think about/take…into account/think over例句：但是好的烹饪都有一个共同点，总是要考虑到颜色、味道、口感和营养。

But good cooking shares one thing in common—always taking color,flavor, taste and nutrition into account.5. 举办、举行hold/conduct例句：今年在长沙举行了一年一度的外国人汉语演讲比赛。

The annual Chinese speech contest for foreigners was held in Changsha this year.6. 使用、利用use/utilize/make use of例句：核能是可以安全开发和利用的。

可重构计算

当前可重构计算或系统需要解决的问题
(1) 粒度问题.细粒度的可重构电路面积的使用效率很低. (2) 如何改进结构来减少重构时间.在数据重载时,FPGA端口对外呈高阻状态,重载后,才恢复对外的逻辑功能.这就是所谓的重构时隙,将影响系统功能的连续.如何克服或减少重构时隙,是实现动态重构系统的瓶颈问题. (3) 数据传输和存储问题.现在的可重构芯片提供的片上存储器太少,因而,许多重构计算的应用需要更大的外部存储器.当前设计中,最迫切需要优化解决的问题是Memory带宽和能耗.
可重构计算
可重构计算基于现场可编程门阵列——— FPGA.FPGA的编程技术主要有两种:一种是反熔丝技术,即通常所说的电可擦写技术,但是这种技术的可重构实时性太差;另一种是基于静态存储器 ( SRAM)可编程原理的FPGA编程技术,这种硬件包含计算单元阵列,这些计算单元的功能由可编程的配置位来决定.当前大多数的可重构设备是基于静态存储器的,其实现计算单元的粒度随不同的系统要求而不同.
可重构计算的分类
可重构计算又可按重构发生的时间分为静态重构和动态重构. 静态重构是指在可重构件运行之前对其进行预先配置, 在运行过程中其功能保持不变, 即运行过程中不能对其进行重构. 动态重构是指在可可重构件运行的过程中可根据需要对其实时进行配置, 改变其电路结构, 实现不同的功能.
可重构计算系统的分类
Garp 是加州大学伯克利分校提出的一种可重构体系结构, 其结构如图2 所示. 该结构中, 可重构阵列与一个通用的MIPS 处理器构成了一个混合式计算系统, 可重构阵列与通用处理器共享内存和数据缓冲, 二者之间形成一种主协处理器的关系. 该结构的优点是兼具了通用处理器的灵活性和可重构部件的高速性. 通用处理器完成通用程序的处理, 对于特定的循环和子程序, 则由可重构阵列在通用处理器的控制下实现加速处理. Garp 结构一般集成在一个芯片上, 形成一个片上系统.

大学英语四六级易混淆的单词(上)

大学英语六级考试听力易听混的单词(上）1.quite|quietquite[kwaɪt]adv.很，相当quiet['kwaɪət]adj.安静的tip：无论是从发音还是词义上，二者的差别都是极大的哟！只是形近而已~2.affect|effectaffect[ə'fekt]v.影响；使感动effect[ɪ'fekt]n.结果，影响v.造成tip：二者都有动词词性。

动词“影响”一般用affect，而effect一般作为名词使用。

3.adapt|adopt|adeptadapt[ə'dæpt]v.（使）适应；改变[词组]adapt toadopt[ə'dɒpt]v.采纳；收养adept[ə'dept]v.熟练的；内行的n.专家[词组]an adept intip：三者词形极像，但词义和发音都有区别，要注意区分哦~4.angel|angleangel['eɪndʒəl]n.天使；赞助人angle['æŋgl]n.角；观点tip：/ei/和/æ/的发音，大家一定要区别清楚哦~二者第二个音节的发音也非常不同哦~ 5.dairy|diarydairy['deərɪ]n.乳制品，牛奶厂diary['daɪərɪ]n.日记tip：/e/和/aɪ/的发音区别~读/aɪ/的时候一定要大大地张开口腔哦~6.contend|content|context|contestcontend[kən'tend]v.奋斗；斗争；声称content['kɒntent]n.内容，要旨adj.满足的context['kɒntekst]n.上下文，背景，语境contest['kɒntest]n./v.竞赛，争论tip:巧记方法：con-有“聚众、一起”的意思，tend是“走向、倾向”，一起倾向就是“声称”；tent是帐篷，一起帐篷具有“空间”的含义，因此是“容量、内容”；text是文本，一堆文本就是“语境、上下文”；test是比赛，一起比赛就是“竞赛、争论”啦！7.principal|principleprincipal['prɪnsəpl]n.校长adj.主要的，重要的principle['prɪnsəpl]n.原则；原理；信条tip：二者的发音倒是没啥区别，但注意拼写哦，一个是pal，一个是ple~8.implicit|explicitimplicit[ɪm'plɪsɪt]n.暗示的；含蓄的explicit[ɪk'splɪsɪt]n.明确的；清楚的；详尽的tip：二者互为反义词。

传热学专业英语词汇

Chapter 1 Thermodynamics and Heat Transfer主要内容:heat (thermal energy)、heat transfer、thermodynamics、total amount of heat transfer、heat transfer rate、heat flux、conduction、convection、radiation:1) The first law of thermodynamics (conservation of energy principle)2) Heat balance equation: a) closed system; b) open system (steady-flow)3) Fourier’s law of heat conduction4) Newton’s law of cooling5) Stefan-Boltzmann law主要专业词汇heat transfer 传热、热传递、传热学 thermodynamics热力学caloric 热素specific heat 比热 mass flow rate 质量流率latent heat 潜热 sensible heat 显热 heat flux 热流密度heat transfer rate热流量total amount of heat transfer 总热量conduction导热 convection对流 radiation 辐射thermal conductivity 热导率 thermal diffusivity 热扩散率convection/combined heat transfer coefficient 对流/综合换热系数emissivity 发射率 absorptivity 吸收率simultaneous heat transfer 复合换热Chapter 2 Heat Conduction Equation主要内容:temperature field、temperature gradient、heat generation、initial condition、boundary condition、steady\transient heat transfer、uniform\nonuniform temperature distribution:1) Fourier’s law of heat conduction (§2-1)v1.0 可编辑可修改2) Heat conduction equation (inrectangular\cylindrical\spherical coordinates) (§2-2、§2-3)3) Boundary conditions: (§2-4)a)Specified temperature B. C.b) Specified heat flux B. C. [special case(dt/dx=0):insulation、thermal symmetry];c) Convection .d) Radiation .e) Interface .4) Average thermal conductivity k ave (§2-7)5) Solution of one-dimensional, steady heat conduction inplane walls、cylinders and spheres (k =const)：a) no heat generation, specified .: T(x) or T(r) (§2-5)Q(x) or Q(r), Q=constb) with heat generation, Specified . or Convection . :(§2-6)∆T max=T o-T s= gs2/2nk ; q(x)=gx/n; T s=T+gs/nhcharacteristic length S, shape factor n:plane walls — s = L (half thickness), n = 1cylinders ——s =r o, n = 2spheres ——s =r o, n =3: Solve a heat transfer problem1) Mathematical formulation (differential equation & .)2) General solution of equation3) Application of Unique solution of the problem主要专业词汇temperature field\distribution温度场\分布 temperature gradient温度梯度heat generation热生成(热源) initial\boundary condition 初始\边界条件transient heat transfer瞬态(非稳态)传热 isothermal surface 等温面Heat conduction differential equation 导热微分方程trial and error method试算法iterate迭代convergence 收敛Chapter 3 Steady Heat Conduction主要内容:multilayer\composite wall overall heat transfer coefficient U thermal resistance R t thermal contact resistance R c critical radius of insulation R crfin efficiency fin effectiveness:Multiplayer plane wall、cylinders and spheres:Fin: fin equation——refer to the attachment.1) Uniform cross-section: refer to the attachment.2) Varying cross-section: refer to the attachment.主要专业词汇thermal resistance热阻 parallel 并联 in series串联thermal contact resistance 接触热阻 composite wall 复合壁面thermal grease 热脂 cross-section 横截面 temperature execess 过余温度hyperbolic 双曲线的 exponent 指数fin 肋(翅)片 fin base 肋基 fin tip 肋端fin efficiency 肋效率 fin effectiveness 肋片有效度Chapter 4 Transient Heat Conduction主要内容:lumped system analysis characteristic length (L c=V/A)Biot number (Bi=hL c /k) Fourier number ( τ = at/L):Bi≤0, lumped system analysis (§4-1)Bi>0, Heisler/Grober charts OR analytical expressions 1-D：a) infinite large plane walls, long cylinders and spheres (§4-2)b) semi-infinite solids (§4-3)multidimensional: product solution (§4-4)主要专业词汇lumped system analysis 集总参数法 characteristic length 特征长度（尺寸）dimension 量纲 nondimensionalize 无量纲化 dimensionless quantity 无量纲量semi-infinite solid 半无限大固体 complementary error function 误差余函数series 级数 production solution 乘积解Chapter 5 Numerical Methods in Heat Conduction主要内容:control volume (energy balance) method、 finite difference method、discretization、 node、space step、time step、mesh Biot number、mesh Fourier number、mirror image concept、explicit/implicit method、stability criterion (primary coefficients 0) Numerical error: 1) discretization/truncation error; 2) round-off error:Numerical solution:1) Discretization in space and time (x, t);2) Build all nodes’finite difference formulations (including interior and boundary nodes);difference methodbalance method . Control Volume method)3) Solution of nodal difference eqs. of heat conduction;method: Gaussian Eliminationmethod: Gauss-Seidel iteration主要专业词汇control volume 控制容积 finite difference有限差分Taylor series expression泰勒级数展开式mirror image concept 镜像法 Elimination method 消元法direct/iterative method 直接/迭代方法 explicit/implicit method 显式/隐式格式stability criterion 稳定性条件 primary coefficients 主系数unconditionally 无条件地 algebraic eq. 代数方程discretization/truncation error 离散/截断误差 round-off error 舍入误差Chapter 6、7 Forced Convection and NaturalConvection主要内容:Nu、Re、Gr、PrForce/natural convection、external/internal flow、velocity/thermal boundary layerflow regimes、laminar/turbulent flowhydrodynamic/thermal entry region、fully developed regionCritical Reynolds Number (Re c)、hydraulic diameter (D h)、film temperature (T f)、bulk mean fluid temperature (T b)logarithmic mean temperature difference ( T ln)volume expansion coefficient (β= 1/T)effective thermal conductivity (K eff = K Nu):Drag force ：F D = C f AρV2/2Heat transfer rate：Q = hA(T s-T)3．Typical Convection Phenomena:1) Forced convection：external flow——flow over flat plates (§6-4)——flow across cylinders and spheres (§6-5)internal flow——flow in tubes (§6-6)2) Natural convection： flow over surfaces (§7-2)flow inside enclosures (§7-3)主要专业词汇Force/natural convection 自然/强制对流 laminar/turbulent flow 层/湍流boundary layer 边界层 laminar sublayer 层流底层 buffer layer 缓冲层transition region 过渡区 flow regimes 流态inertia/viscous force 惯性/粘性力 shear stress 剪切应力friction/drag coefficient 摩擦/阻力系数 friction factor 摩擦因子dynamic/kinematic viscous 动力/运动粘度wake 尾流 stagnation point 滞止点 flow separation 流体分离vortex 漩涡 rotational motion 环流 velocity fluctuation 速度脉动hydrodynamic 水动力学的 hydraulic diameter 水力直径fully developed region 充分发展段 volume flow rate 体积流量arithmetic/logarithmic mean temperature difference 算术/对数平均温差volume expansion coefficient 体积膨胀系数interferometer 干涉仪 asymptotic渐近线的effective thermal conductivity 有效热导率analogical method 类比法 integral approach 积分近似法order of magnitude analysis 数量级分析法 similarity principle 相似原理Chapter 9 Radiation Heat Transfer主要内容:black body、gray body、diffuse surface、emissive power (E)emissivity (ε)、absorptivity (α)、reflectivity (ρ)、transmissivity (τ) irradiation(G)、radiosity(J)、reradiating(adiabatic) surfaceview factor (F ij)、radiation network、space resistance、surface resistance radiation shieldgas radiation、transparent medium to radiation、absorbing and transmitting medium:Blackbody： (1) Plank’s law(2) Stefan-Boltzmann’s law(3) Wien’s displacement lawGraybody： (4) Kirchhoff’s lawActual body：E (T) = ε E b(T) = εσT4 W/m2Gas： (5) Beer’s law3．Calculation:1) View factor：reciprocity/summation/superposition/symmetry Rulecrossed-strings method2) Radiation heat transfer：Radiation networkOpen system： between two surface . two large parallel plates) Enclosure： 2-surface enclosure；3-surface enclosureRadiation shield主要专业词汇thermal radiation热辐射、quantum theory量子理论、index of refraction 折射系数electromagnetic wave/spectrum 电磁波/波谱、ultraviolet (UV) rays紫外线、infrared (IR) rays 红外线absorptivity 吸收率、reflectivity 反射率、transmissivity 透射率、emissivity (ε) 发射率(黑度)、specular/diffuse reflection 镜反射/漫反射irradiation (incident radiation) 投入辐射、radiosity 有效辐射spectral/directional/total emissive power单色/定向/总辐射力fraction of radiation energy 辐射能量份额(辐射比)、blackbody radiation function 黑体辐射函数view factor 辐射角系数、crossed-strings method交叉线法、reciprocity/summation/superposition/symmetry Rule相互/完整/和分/对称性net radiation heat transfer 净辐射热流量radiation network 辐射网络图、space/surface radiation resistance 空间/表面辐射热阻、reradiating surface重辐射面、adiabatic 绝热的radiation shield遮热板transparent medium to radiation辐射透热体、absorbing and transmitting medium吸收-透过性介质Chapter 10 Heat Exchangers主要内容:heat exchanger type---- double-pipe、compact、shell-and-tube、plate-and-frame、regenerative heat exchangerparallel/counter/cross/multipass flowoverall heat transfer coefficient (U) fouling factor (R f)heat capacity rate capacity rationlog mean temperature difference (ΔT lm)heat transfer effectiveness (ε)number of transfer units (NTU):1) heat balance eq.: Q = C h (T h,in - T h,out)=C c(T c,out - T c,in)2) heat transfer eq.: Q = UAΔT lm ( LMTD method)or Q = εQ max = εC min (T h,in C T c,in) ( ε-NTU method) 3．Methods:1) LMTD Method：select a heat exchangerKnown: C h、C c、3‘T’Predict: 1‘T’、Q、A2) ε-NTU Method：evaluate the performance of a specified heat exchangerKnown: C h、C c、UA、T h,in、T c,inPredict: Q、T h,out、T c,out主要专业词汇double-pipe/compact/shell-and-tube/plate-and-frame/regenerative heat exchanger套管式/紧凑式/壳管式/板式/蓄热（再生）式换热器parallel/counter/cross/multipass flow 顺流/逆流/叉流/多程流area density 面积密度tube/shell pass 管程/壳程 static/dynamic type 静/动态型baffle 挡板 header 封头 nozzle管嘴 guide bar 导向杆 porthole 孔口gasket 垫圈 lateral 侧面的/横向的fouling factor 污垢因子 heat capacity rate 水当量heat transfer effectiveness (ε) 传热有效度number of transfer units (NTU) 传热单元数。

Numerical Methods in Engineering

&RS\ULJKW E\ 6SDWLDO $XWRPDWLRQ /DERUDWRU\6$/$ 0HVKIUHH 0HWKRG IRU ,QFRPSUHVVLEOH )OXLG '\QDPLFV 3UREOHPV, 7VXNDQRY 9 6KDSLUR 6 =KDQJA Meshfree Method for Incompressible Fluid Dynamics ProblemsI.Tsukanov a∗,V.Shapiro a,S.Zhang ba Spatial Automation LaboratoryUniversity of Wisconsin-Madison1513University AvenueMadison,WI53706,U.S.A.b General Motors R&D CenterWarren,MI48090,U.S.A.Accepted for publication in Int.Journal forNumerical Methods in EngineeringAbstractWe show that meshfree variational methods may be utilized for solution of incompressibleﬂuid dynamics prob-lems using the R-function method(RFM).The proposed approach constructs an approximate solution that satisﬁesall prescribed boundary conditions exactly using approximate distanceﬁelds for portions of the boundary,transﬁniteinterpolation,and computations on a non-conforming spatial grid.We give detailed implementation of the methodfor two common formulations of the incompressibleﬂuid dynamics problem:ﬁrst using scalar stream function for-mulation and then using vector formulation of the Navier-Stokes problem with artiﬁcial compressibility approach.Extensive numerical comparisons with commercial solvers and experimental data for the benchmark back-facing stepchannel problem reveal strengths and weaknesses of the proposed meshfree method.Keywords:meshfree method,distanceﬁeld,solution structure,Navier-Stokes problem,stream function,artiﬁcialcompressibility approach1Introduction1.1Towards meshfree solution of computationalﬂuid dynamics problemsModeling of the incompressibleﬂuidﬂow involves solution of the Navier-Stokes equations inside a geometric domain. The interaction between theﬂuid and the boundary of the geometric domain,in terms of the mathematical model is described by boundary conditions,formulated for viscousﬂuid as known velocity proﬁle at the inlet and zero velocity at the walls.The nature of this problem makes its treatment difﬁcult:the solution algorithm needs to incorporate two distinct types of information—(1)analytical information that describes the Navier-Stokes equations and func-tions given as boundary conditions;and(2)geometric information about boundaries where the boundary conditions are prescribed.Conventional methods of engineering analysis solve this problem by employingﬁrst,the spatial dis-cretization of the geometric domain(a mesh that conforms to the boundary of the geometric domain),and second,the discretization of the Navier-Stokes equations and the boundary conditions over the discretized geometry domain.The resulting approximation,therefore,uniﬁes both functional and geometric information.Such approach,despite its wide usage,has some drawbacks.For example,it is well known that the construction of a“good”mesh is a difﬁcult and time consuming task.In engineering practice design iterations require efﬁcient feedback from the analysis results to the geometric model.However,employment of conforming meshes for solution of engineering problems is not quite suitable for design purposes,because the spatial grid restricts changes of the parameters of the geometric model such that it is difﬁcult or even impossible to change the shape of the model without remeshing.∗Corresponding author.E-mail:igor@These difﬁculties in the conventional approaches led to the development of methods which use non-conforming1 meshes or no meshes at all.These new meshfree(sometimes they are also called meshless)methods represent a solu-tion of the problem by linear combination of basis functions which may be constructed over meshes not conforming to the shape of the geometric model[3,23,4,17,8,21,25,18,7,9].However,the employment of non-conforming spatial discretization makes the treatment of boundary conditions more difﬁcult.Proposed remedies include the combination of Element Free Galerkin Method(EFG)[4]withﬁnite element shape functions near the boundary[17],the use of modiﬁed variational principle[20],window or correction functions that vanish on the boundary[9],and Lagrange multipliers.Although these techniques appear promising,they often contradict the meshfree nature of the approxi-mation near the boundary,introduce additional constraints on solutions,or lead to systems with an increased number of unknowns[13].Several promising transformation-based approaches to satisfying essential boundary conditions at desired nodal locations have been recently proposed and compared by J.-S.Chen[8].The meshing problem can be substantially simpliﬁed by employment of the Cartesian grid methods[42,1,11,5]. These methods represent the geometric model by a hierarchical set of cubical/rectangular cells that simplify computa-tion of the partial derivatives using aﬁnite difference scheme.Instead of requiring that cells conform to the boundaries of the domain,the geometric model of the domain is approximated by quad/octtree spatial decompositions to any prescribed accuracy.This approach is accompanied by introduction of additional sources of errors and potentially exponential(in the subdivision depth)increase in computational cost.In contrast to Cartesian grid methods,immersed boundary methods[24,14,15]solve the problem using a uniform non-conforming grid of points that cover the geometric model.Inﬂuence of the boundaries and boundary conditions is accounted for by modiﬁcation of the differential equation of the problem,based on special case analysis.In this paper,we describe a method that also relies on a non-conforming uniform rectangular grid,but goes sub-stantially further.All prescribed boundary conditions are satisﬁed exactly by transﬁnitely interpolating individual boundary conditions inversely proportional to the approximate distance to each boundary portion.The technique can be applied systematically to any and all boundary value problems using the theory of R-functions[30],and the result-ing interpolant can be combined with just about any standard numerical solution method.The method is demonstrated with variational methods applied to the solution of incompressibleﬂuid dynamics problems:ﬁrst using scalar stream function formulation,and then using vector formulation of the Navier-Stokes problem with artiﬁcial compressibility approach.1.2Brief History of the MethodKantorovich showed that Dirichlet boundary conditions could be satisﬁed exactly using functions vanishing on the boundary of a geometric object[16].He proposed to represent a solution satisfying Dirichlet boundary conditionu|∂Ω=ϕin the following form:u=ωNi=1C iχi+ϕ,(1)whereωis a function taking on zero value on the boundary of the domain;{χi}N i=1is a system of linearly independent basis functions;{C i}N i=1is a vector of unknown coefﬁcients andϕis a function given as a boundary condition. Different sets of the coefﬁcients{C i}N i=1give different functions u but all of them satisfy the prescribed boundary condition.Numerical values of the unknown coefﬁcients can be obtained via variational or projectional methods. Application of Kantorovich’s method was limited to very simple geometric domains,because at that time it was unclear how to construct functionωfor arbitrary geometric domains.Several years later,Rvachev proposed that functions taking on zero value on the boundary of a geometric domain can be constructed for virtually any geometric object using R-functions[27,28,34].Informally,R-functions serve as a construction toolkit transforming a set-theoretic description of the boundary of a geometric object into a real valued function whose zero set coincides with the boundary.Detailed discussion on R-functions and construction techniques is outside of the scope of this paper,but it can be found in numerous references[28,34,35,26,29]and will be illustrated in section2.2.Functions constructed using R-functions are differentiable everywhere except a ﬁnite number of points[28,35]and behave as distances to the boundaries near the boundary points.We will refer 1This should not be confused with the another commonly used terminology of“conforming/non-conformingﬁnite element”.In this paper the non-conformance of the spatial grid to the shape of the geometric domain means that the grid is extended beyond,and unconstrained by the boundary of the geometric domain.to such functions as approximate distanceﬁelds.Besides techniques based on the theory of R-functions[28],other methods may also be applied for construction of approximate distanceﬁelds.For example,the level set method [33,32]results in a distance-like functions,albeit deﬁned at a discrete set of points and usually implicitly.In contrast, the approximate distanceﬁelds constructed using R-functions are explicitly deﬁned at all points of the space.The successful employment of the level set method to model holes and inclusions was discussed in[38].Similar technique was used to model crack development and propagation in[37].Approximate distanceﬁelds can be used for interpolation of the functions and their derivatives prescribed on the boundary pieces of a geometric object[31].Representation of boundaries of a geometric object by approximate distanceﬁelds made possible the extension of the Kantorovich’s method into the R-function method(RFM).The RFM allows the satisfaction of many types of boundary conditions exactly by employing solution structures that incorporate boundary conditions,approximate distanceﬁelds,and basis functions with unknown coefﬁcients[30]. RFM is essentially a meshfree method because it places no restriction on the choice of the basis functions:they can be constructed over conforming or non-conforming mesh.For example,ﬁnite elements can be used as basis functions;in this case,RFM can be viewed as an enhancedﬁnite element method that treats all given boundary conditions exactly. But in this paper,all computations were performed over a uniform rectangular grid of B-splines and performed within the SAGE system developed by authors[41].In[36],we showed that the method is particularly effective in dealing with moving and deforming boundaryconditions.Figure1:Parametrization of the geometry of a back facing step channel1.3Scope and outlineThis paper serves two purposes.First,the application of the RFM to Computational Fluid Dynamics(CFD)is illus-trated through two different formulations;second,the numerical properties(accuracy and convergence)of the RFM, applied to these formulations,are investigated.The paper will show that the RFM approach to CFD provides a unique andﬂexible method to link both the functional and geometric information in a uniﬁed manner.It will also be shown that the artiﬁcial compressibility approach gives good results for low Reynolds numberﬂow(Re<400).For higher Reynolds numbersﬂows the RFM needs to be implemented either with Finite V olume(FV)/Finite Difference(FD) numerical schemes or using the regularization approach described in[10].Throughout the paper,we assume thatﬂow is laminar,ﬂuid is Newtonian,and we focus on two-dimensional problems.In this case incompressible two dimensional viscousﬂow is described by Navier-Stokes equations and the continuity equation[19]:u ∂u∂x+v∂u∂y−1Re∇2u=−Eu∂p∂x;u ∂v∂x+v∂v∂y−1Re∇2v=−Eu∂p∂y∂u ∂x +∂v∂y=0,(2)where variables u and v are the velocity components in the x and y coordinate directions respectively,p is thepressure variable,Re=23u max2h inletνand Eu=Pρu2maxare Reynolds and Euler numbers respectively.We explorethe accuracy of the RFM and its convergence properties,solving a standard textbook benchmark problem:an incom-pressible viscousﬂuidﬂow in a two-dimensional back-facing step channel,whose parametrization is shown in Figure 1.For this problem experimental data[2],as well as the computer simulation results given by the conventionalﬂuiddynamics systems,are available.For concreteness we let the geometric parameters take on the following numericalvalues:L inlet=5,L channel=12,h inlet=0.5and s=0.471.In order to simplify the comparison of the RFM modeling results with experimental data,we use the same ratio between h inlet and s as in[2].Boundary conditions areformulated as a parabolic velocity proﬁle with u max=1.5at the inlet and zero velocity at the walls of the channel.Most meshfree methods employ some variational principle in order to solve the problem,and the RFM is no ex-ception.Since RFM treats the given boundary conditions exactly,the variational principle is applied to the differentialequation(s)of the problem only.Because viscousﬂuidﬂows do not conserve energy,we employ a least squares method.In the paper we discuss the application of the RFM to two different formulation of the incompressibleﬂuid dynamics problem:stream function and artiﬁcial compressibility formulations.The stream function formulation discussed in Section2substantially simpliﬁes the initial problem reducing the system of the Navier-Stokes and continuity equations to a single equation.We use the stream function formulation as an introductory example in order to explain the concept of the RFM solution structure and the RFM solution procedure. The velocity proﬁles given by the RFM are in good agreement with the experimental data for Reynolds number100. For higher Reynolds numbers the RFM overestimates the position of the reattachment point.The accuracy of the modeling results can be improved by applying the RFM to the primitive variables of the Navier-Stokes equations via an artiﬁcial compressibility approach,detailed in Section3.In contrast to the stream function formulation,the artiﬁcial compressibility formulation allows modeling ofﬂuidﬂows in channels with arbitrary geo-metric shape including multiple connected channels.Further,it can be easily extended to model three-dimensional and turbulentﬂows.Since the artiﬁcial compressibility formulation leads to solution of a vector problem,application of the RFM to this formulation of incompressibleﬂuid dynamics problem results in vector solution structures whose construction we explain in Section3.2.Section2.5and Section3.4contain the analysis of the RFM modeling results and their comparison with exper-imental data and numerical results obtained using the commercialﬂuid analysis system Fluent.Distributions of the velocity components and the pressureﬁeld given by the RFM are in good agreement with experimental data,however the employment of variational methods appears to raise some issues.These observations and possible ways to improve effectiveness of the method are discussed in Section4.2RFM with stream function formulation2.1Stream function formulation and solutionIntroduction of a stream functionψsuch that u=∂ψ∂y and v=−∂ψ∂xallows us to satisfy the continuity equation andto exclude the pressure p from the momentum equations.Substitution of the stream functionψinstead of derivatives of velocity components gives a differential equation for the stream function[19]:1 Re ∇4ψ−∂ψ∂y∂∂x∇2ψ+∂ψ∂x∂∂y∇2ψ=0.(3)Boundary conditions for the stream function at the inlet can be derived from the velocity proﬁle at the inlet which is usually known:ψ|inlet=sV(x,y)cos(n,V)dS,(4)where V=u i+v j is the velocity vector and n is the normal vector to the inlet section.Assuming a parabolic proﬁle for the u component of the velocity vector,as shown in Figure1,with u max=1.5and v=0at the inlet,we obtain the boundary condition for stream function as:ψ|inlet=2h2inlety3+3h inlety2;∂ψ∂n|inlet =0.(5)On the walls of the channel the stream function should satisfy the following boundary conditions:ψ|lower wall =0;ψ|upper wall =h inlet .(6)Since we are dealing with viscous ﬂow,velocity is assumed to be zero on all walls.This condition is expressed in terms of homogeneous Neumann boundary condition for the stream function:∂ψ∂n |walls =0.(7)Boundary conditions for the stream function at the outlet can be derived from two conditions:(a)the total discharge at the outlet should be the same as at the inlet,and (b)the velocity components at the outlet should respectively be:v =0,and u should possess a parabolic proﬁle as is shown in Figure 1.After simpliﬁcation we get:ψ|outlet =m −y 33+h inlet −s 2y 2+h inlet sy +k ;m =6h inlet (h inlet +s )3;k =m 4 3s 2h inlet +s 3 ;∂ψ∂n |outlet=0.(8)The geometry of the channel,equation (3)together with boundary conditions (4–8)constitutes a complete mathe-matical formulation of the problem.The ﬁrst steps of solving this problem with RFM are construction of approximate distance ﬁelds for boundary pieces and the RFM solution structure for the problem.The solution structure interpolates all given boundary conditions over the speciﬁed geometry,but also includes a set of basis functions with undetermined coefﬁcients.The subsequent solution procedure will determine the coefﬁcients that best approximate the govern-ing differential equation in some sense.The solution structure,as well as approximate distance ﬁelds,are usually constructed automatically without user’s intervention,but below we show all the construction details manually and explicitly.2.2Theory of R -functions and approximate distance ﬁeldsThe theory of R -functions was originally developed in Ukraine by V .L.Rvachev and his students [28,26,29].A complete list of references through 2001can be found in [22].A brief English summary of the theory of R -functions written by Shapiro in 1988[34]is available as a technical report.An R -function is real-valued function whose sign is completely determined by the signs of its arguments.For example,the function xyz can be negative only when the number of its negative arguments is odd.A similar property is possessed by functions x +y + xy +x 2+y 2and xy +z +|z −yx |,and so on.Such functions ‘encode’Boolean logic functions and are called R -functions .Every Boolean function is a companion to inﬁnitely many R -functions,which form a branch of the set of R -functions.For example,it is well known that min(x 1,x 2)is an R -function whose companion Boolean function is logical “and”(∧),and max(x 1,x 2)is an R -function whose companion Boolean function is logical “or”(∨).But the same branches of R -functions contain many other functions,e.g.x 1∧αx 2≡11+α x 1+x 2− x 21+x 22−2αx 1x 2 ;x 1∨αx 2≡11+α x 1+x 2+x 21+x 22−2αx 1x 2 ,(9)where α(x 1,x 2)is an arbitrary symmetric function such that −1<α(x 1,x 2)≤1.The precise value of αmay or may not matter,and often it can be set to a constant.For example,setting α=1yields the min and max respectively,but setting α=0results in much nicer functions ∨0and ∧0that are analytic everywhere except when x 1=x 2=0.Similarly,R -functionsx 1∧m αx 2≡(x 1∧αx 2)(x 21+x 22)m 2;x 1∨m αx 2≡(x 1∨αx 2)(x 21+x 22)m 2(10)(a)(b)Figure2:(a)Halfspaces that constitute a CSG representation of the channel;(b)the corresponding approximate distanceﬁeld(a)(b)Figure3:Approximate distanceﬁelds for the portions of the boundary where non-slip boundary conditions are pre-scribed:(a)for the car presented in Figure23(b);(b)for the car presented in Figure23(c)are analytic everywhere except the origin(x1=x2=0),where they are m times differentiable.Many other systems of R-functions are studied in[28].The choice of an appropriate system of R-functions is dictated by many considerations, including simplicity,continuity,differential properties,and computational convenience.Just as Boolean functions,R-functions are closed under ing R-functions,any object deﬁned by a predicate on“primitive”geometric regions(e.g.regions deﬁned by a system of inequalities)can now also be represented by a single inequality,or equation.The latter can be evaluated,differentiated,and possesses many other useful properties.In particular:•the functions are constructed in a‘logical’fashion and can be controlled through intuitive user-deﬁned parame-ters;•functions can be normalized,in which case they behave as distance functions near the boundary of the object and can be differentiated everywhere[28,35];•functions can also be constructed for individual cells and cells complexes,given prescribed values for the func-tions and their gradients;•the functions can be used to deﬁne time-varying geometry and used for modeling various complex physical phenomena.Theory of R-functions provides the connection between logical and set operations on geometric primitives and analytic constructions.For every logical or set-theoretic construction,there is a corresponding approximate distance function with the above properties.Furthermore,the translation from logical and set-theoretic description is a matter of simple syntactic substitution that does not require expensive symbolic computations.For example,the geometric domain of the channel in Figure2(a)can be deﬁned as a Boolean(Constructive Solid Geometry)combination of six primitives:Ω=(f1∪f2)∩f3∩f4∩f5∩f6,where x denotes the regularized complement of x,and individual primitives f1through f6are deﬁned by the following inequalities:f1=y≥0;f2=x−L inlet≥0;f3=y−s≥0;f4=L inlet+L channel−x≥0;f5=h inlet−y≥0;f6=x≥0Naturally,all numeric constants can be viewed as speciﬁc values for some parameters(size,position,etc.).The constructed Boolean representation can be translated into the approximate distanceﬁeld shown in Figure2(b)using R-functions:ω=(f1∨0f2)∧0f3∧0f4∧0f5∧0f6,(11) which is also parameterized by h inlet,s,L inlet and L channel.This example clearly shows that any Boolean representation may be translated into the corresponding approximate distanceﬁeld.Similarly,boundary representation of a solid is a union of solid’s faces,each face is a subset of some surface bounded by edges,and so on.This logical description can also be directly translated into a function such that is zero for every point on the boundary and positive elsewhere. Our recent results[35,41]indicate that such functions can be constructed directly from the commercially available solid modeling representations,as well as from a variety of other geometric data structures,such as cell complexes. For example,Figures3(a)and(b)show approximate distanceﬁelds for the portions of the boundary where non-slip boundary conditions are prescribed(compare to the car shapes in Figures23(b)and(c)respectively).In the next Section we explain the usage of approximate distanceﬁelds for construction of the RFM solution structures and transﬁnite interpolation of the prescribed boundary conditions.2.3RFM solution structure for stream functionA solution structure is a function that satisﬁes exactly all prescribed boundary conditions.In general,any RFM solution structure can be represented as a sum of two functions:ψ=ψ0+ψ1(12) whereψ0satisﬁes homogeneous boundary conditions and contains necessary degrees of freedom in order to approxi-mate the differential equation of the problem;functionψ1interpolates the functions given as boundary conditions(5),Figure4:The RFM solution structure that satisﬁes boundary conditions(4-8)exactly(6)and(8).The interpolation term is constructed using the transﬁnite interpolation method[31]which is a generaliza-tion of the inverse distance weighting technique;it matches all speciﬁed boundary conditions and extends them inside the domain by some arbitrary but well behaved function.For the problem considered here,it takes:ψ1=ψoutletω2outlet+ψinletω2inlet+ψupper wallω2upper wall+ψlower wallω2lower wall1ω2outlet+1ω2inlet+1ω2upper wall+1ω2lower wall,(13)whereωoutlet,ωinlet,ωupper wall andωlower wall are approximate distanceﬁelds that describe outlet,inlet and walls of the channel as it is shown in Figure4.Rasing these functions to the second power assures that boundary condition∂ψ∂n|whole boundary =0is satisﬁed.Functionψ0in the solution structure(12)serves for approximation of the differential equation of the problem.In our case it can be represented as a product of the second power of an approximate distance to the boundary of the channelωand unknown functionΦwhose sole purpose is the approximation of the differential equation of theproblem:ψ0=ω2Φ.Sinceωtakes on zero value on boundary of the geometric domain,ψ0vanishes on the boundary together with itsﬁrst normal derivative.Therefore,regardless of the chosen functionΦ,functionψ0satisﬁes thehomogeneous boundary conditions exactly.In many practical situations functionΦcannot be determined exactly,which is why it is usually represented by a linear combination of basis functions{χi}N i=1:Φ=Ni=1C iχi.(14)The basis functions{χi}N i=1have to be smooth enough in order to approximate the differential equation of the problem. Thus,the RFM solution structure(12)may be rewritten as follows:ψ=ψoutletω2outlet+ψinletω2inlet+ψupper wallω2upper wall+ψlower wallω2lower wall1ω2outlet+1ω2inlet+1ω2upper wall+1ω2lower wall+ω2Ni=1C iχi.(15)This solution structure corresponds to the space that contains functions satisfying the prescribed boundary conditions and is sufﬁciently complete in the sense of being able to approximate the exact solution with an arbitrary degree of accuracy[30].Employment of the RFM solution structures to represent a solution of a physical problem offers several advantages. In particular:an RFM solution structure treats the prescribed boundary conditions exactly;an RFM solution structure contains no information about the differential equation of the problem which means that the same solution structure can be used to represent solutions of different physical problems with similar types of boundary conditions;basis functions in the solution structure can be constructed over a mesh conforming or non-conforming to a geometric model;solution structure can be easily adjusted to a new geometric model—only approximate distanceﬁelds have to be reconstructed in order to represent the boundary pieces of new geometric model;an RFM solution structure can be evaluated and differentiated at any point inside the computational domain;ﬁnally,an RFM solution structure can be integrated over the geometric model using adaptive numerical procedures[41].2.4Computation of the coefﬁcients in the solution structureSince the RFM solution structure satisﬁes the given boundary conditions exactly,to solve the problem we need to ﬁnd the set of the unknown coefﬁcients{C i}N i=1in the RFM solution structure that gives the best approximation to the differential equation of the boundary value problem.Numerical values of these coefﬁcients can be determined via variational or projectional methods.The differential equation(3)for the stream function contains non-linear terms that have to be linearized before the solution method is applied.After substitution of solution structure(12)into differentialequation (3)and application of Newton-Kantorovich linearization scheme we obtain:1Re ∇4ψn +10− ∂ψn +10∂y ∂∇2ψn 0∂x +∂ψn 0∂y ∂∇2ψn +10∂x −∂ψn +10∂x ∂∇2ψn 0∂y −∂ψn 0∂x ∂∇2ψn +10∂y−∂ψn +10∂y ∂∇2ψ1∂x −∂ψ1∂y ∂∇2ψn +10∂x +∂ψn +10∂x ∂∇2ψ1∂y +∂ψ1∂x ∂∇2ψn +10∂y=−1Re ∇4ψ1+∂ψ1∂y ∂∇2ψ1∂x −∂ψ1∂x ∂∇2ψ1∂y −∂ψn 0∂y ∂∇2ψn 0∂x +∂ψn 0∂x ∂∇2ψn 0∂y .(16)This equation is formulated for the function ψ0satisfying the homogeneous boundary conditions ψ0|∂Ω=0,∂ψ0∂n |∂Ω=0.Equation (16)is solved by an iterative algorithm,and the superscripts n +1and n in the equation denote solutions at the current and previous iterations respectively.The iterative process ﬁnishes as soon as the difference between twoconsecutive solutions becomes sufﬁciently small.At each iteration the least squares method is applied to equation (16)minimizing the residual of the equation:F = Ω1Re ∇4ψn +10− ∂ψn +10∂y ∂∇2ψn 0∂x +∂ψn 0∂y ∂∇2ψn +10∂x −∂ψn +10∂x ∂∇2ψn 0∂y −∂ψn 0∂x ∂∇2ψn +10∂y −∂ψn +10∂y ∂∇2ψ1∂x −∂ψ1∂y ∂∇2ψn +10∂x +∂ψn +10∂x ∂∇2ψ1∂y +∂ψ1∂x ∂∇2ψn +10∂y+1Re ∇4ψ1−∂ψ1∂y ∂∇2ψ1∂x +∂ψ1∂x ∂∇2ψ1∂y +∂ψn 0∂y ∂∇2ψn 0∂x −∂ψn 0∂x ∂∇2ψn 0∂y 2d Ω→min.(17)From the necessary condition of the existence of minimum ∂F ∂C i =0,i =1,...,N we obtain a system of linear equations AC =B whose solution gives the numerical values of the unknown coefﬁcients in the solution structure.Elements of the matrix A and vector B are deﬁned as follows:a ij = Ω 1Re ∇4 ω2χi − ∂∂y ω2χi ∂∇2ψn 0∂x +∂ψn 0∂y ∂∂x ∇2 ω2χi −∂∂x ω2χi ∂∇2ψn 0∂y −∂ψn 0∂x ∂∂y ∇2 ω2χi −∂∂y ω2χi ∂∇2ψ1∂x −∂ψ1∂y ∂∂x ∇2 ω2χi +∂∂x ω2χi ∂∇2ψ1∂y +∂ψ1∂x ∂∂y ∇2(ωχi ) 1Re ∇4 ω2χj − ∂∂y ω2χj ∂∇2ψn 0∂x +∂ψn 0∂y ∂∂x ∇2 ω2χj −∂∂x ω2χj ∂∇2ψn 0∂y −∂ψn 0∂x ∂∂y ∇2 ω2χj −∂∂y ω2χj ∂∇2ψ1∂x −∂ψ1∂y ∂∂x ∇2 ω2χj +∂∂x ω2χj ∂∇2ψ1∂y +∂ψ1∂x ∂∂y∇2 ω2χj d Ω;(18)b i = Ω 1Re ∇4 ω2χi − ∂∂y ω2χi ∂∇2ψn 0∂x +∂ψn 0∂y ∂∂x ∇2 ω2χi −∂∂x ω2χi ∂∇2ψn 0∂y −∂ψn 0∂x ∂∂y ∇2 ω2χi −∂∂y ω2χi ∂∇2ψ1∂x −∂ψ1∂y ∂∂x ∇2 ω2χi +∂∂x ω2χi ∂∇2ψ1∂y +∂ψ1∂x ∂∂y ∇2 ω2χi −1Re ∇4ψ1+∂ψ1∂y ∂∇2ψ1∂x −∂ψ1∂x ∂∇2ψ1∂y −∂ψn 0∂y ∂∇2ψn 0∂x +∂ψn 0∂x ∂∇2ψn 0∂yd Ω(19)Integrals (18)and (19)are computed using adaptive integration algorithm based on the Gauss-Legendre quadrature rule in conjunction with hierarchical space decomposition technique [41].。

叶轮机械非定常流动及气动弹性计算

中图分类号：V211.3 论文编号：1028701 18-B061 学科分类号：080103博士学位论文叶轮机械非定常流动及气动弹性计算研究生姓名周迪学科、专业流体力学研究方向气动弹性力学指导教师陆志良教授南京航空航天大学研究生院航空宇航学院二О一八年十月Nanjing University of Aeronautics and AstronauticsThe Graduate SchoolCollege of Aerospace EngineeringNumerical investigations of unsteady aerodynamics and aeroelasticity ofturbomachinesA Thesis inFluid MechanicsbyZhou DiAdvised byProf. Lu ZhiliangSubmitted in Partial Fulfillmentof the Requirementsfor the Degree ofDoctor of PhilosophyOctober, 2018南京航空航天大学博士学位论文摘要气动弹性问题是影响叶轮机械特别是航空发动机性能和安全的一个重要因素。

作为一个交叉学科，叶轮机械气动弹性力学涉及与叶片变形和振动相关联的定常/非定常流动特性、颤振机理以及各种气弹现象的数学模型等的研究。

本文基于计算流体力学(CFD)技术自主建立了一个适用于叶轮机械定常/非定常流动、静气动弹性和颤振问题的综合计算分析平台，并针对多种气动弹性问题进行了数值模拟研究。

主要研究内容和学术贡献如下：由于叶轮机械气动弹性与内流空气动力特性密切相关，真实模拟其内部流场是研究的重点之一。

基于数值求解旋转坐标系下的雷诺平均N–S(RANS)方程，首先构造了适合于旋转机械流动的CFD模拟方法。

特别的，针对叶片振动引起的非定常流动问题，采用动网格方法进行模拟，通过一种高效的RBF–TFI方法实现网格动态变形；针对动静叶排干扰引起的非定常流动问题，采用一种叶片约化模拟方法，通过一种基于通量形式的交界面参数传递方法实现转静子通道之间流场信息的交换。

explicit和implicit的用法区别

explicit和implicit的用法区别explicit [?k?spl?s?t] 和 implicit [?m?pl?s?t] 两者拼写很接近，但是意思完全不同，那么如何区分它们呢？一、explicit 作形容词，意为“清楚明白的，易于理解的；直言的，坦率的；直截了当的，不隐晦，不含糊的”，例如：I gave her very explicit directions about how to get here.怎么到这里，我给了她很明确的指示。

The law was explicit in whose tax rates were to be raised.法律明确规定要提高谁的税率。

Marathon runners set explicit goals.马拉松运动员设定明确的目标。

二、implicit 作形容词1、意为“含蓄的，不直接言明的”，例如：The attention on young middle class protestors was far less direct but often implicit.对年轻的中产阶级抗议者的关注远没有那么直接，但往往是含蓄的。

Some reporters thought there was an implicit threat in the president’s speech.一些记者认为总统的讲话中暗含威胁。

2、意为“完全的；无疑问的”，常用的组合是implicit trust 或implicit faith 等，例如：She had the implicit trust of her staff.她得到了全体职员的绝对信任。

He had implicit faith in the noble intentions of the Emperor.他对皇帝的高尚意图深信不疑。

3、意为“内含的，固有的”，例如：The ability to listen is implicit in the teacher's role.教师的角色包括了懂得倾听。

六级词汇

Pro往前prospect 往前看prospective 有可能的，有潜力的前缀表方向，后缀表词性Spectator 观众spector 幽灵 audience 听众，读者Speculate on 推测Speculate in 投机取巧（贬义）Spectacular 壮观的，极好的Spectrum 范围,光谱 gum forum论坛（r不发音） iron（r不发音）Spectacle s n.壮观的景象，眼镜Contact lens隐形眼镜 lens 镜头Vehicle 交通工具Perspective透视，观点 from my perspective = I think objective 客观的Panorama 全视，全景前缀 com con coContest 竞赛（文化类的）protest 抗议,争取 protest againstContestant 竞赛者 protester 竞争者Commemorate 纪念in memory of 为了纪念in support of为了支持in favor of 为了支持in badly need of 很需要in pursuit of 为了追求Confront 面对，面临We are confronted with a huge challenge.指人用被动，指物用主动The difficulty confronting me is very huge. Coincide 巧合（时间，地点，想法的巧合）coincident adj.-coincidence n. What a coincidence! 太巧了Compromise vt.妥协，危害 Finally they compromised to each other.Combat 与作…斗争combat crime与犯罪作斗争 Our government should take immediate measures to combat crime.criminal罪犯bat 蝙蝠，球拍 bat man 蝙蝠侠 debate 争论 I feel hot. Heated debate concerning sth 关于。

显式与隐式（ExplicitAndImplicit）

显式与隐式（ExplicitAndImplicit）显式与隐式（Explicit And Implicit）1.概念1.1 显式实现的单词Explicit意思是清楚的、明确的、详述的。

所以，显式的“显”是指明显且清楚的实现，相对于接⼝来说，就是明显⽽清楚的指定了接⼝的实现。

对于其他的逻辑来说，显式就是清楚且明确的指定了实现内容。

1.2 隐式实现的单词Implicit意思是隐匿的、不⾔明的、绝对的。

所以，隐式的实现是指想当然的实现，相对于接⼝来说，只要实现类的⽅法签名和返回值与接⼝定义的⼀致即视为接⼝的实现，并⽆显式的（清晰的、明确的）指定。

2.例⼦2.1 代码1using System;2namespace ExplicitAndImplicit{3//⼑⼦4public interface IKnife{5void KillPeople();6 }7//枪8public interface IGun{9void KillPeople();10 }11//隐式实现12public class WrongKillMachine:IKnife,IGun{13public void KillPeople(){14 Console.WriteLine("切切切脑袋");15 }16 }17//显式实现：18//1.实现接⼝⽅法不需要加访问定义符19//2.实现接⼝⽅法前⾯要加接⼝名.⽅法名，⽤来指定其实现的接⼝20//2.实现接⼝⽅法只能被显式的调⽤，不能被隐式的调⽤：21// 显式调⽤：22public class KillMachine:IKnife,IGun{23void IKnife.KillPeople(){24 Console.WriteLine("切切切");25 }26void IGun.KillPeople(){27 Console.WriteLine("啪啪啪");28 }29 }30public static class Case31 {32public static void Begin(){33 Console.WriteLine("Design Pattern —— Explicit And Implicit：");34//隐式实现35 WrongKillMachine w = new WrongKillMachine();36 w.KillPeople();3738//显式实现39 IKnife k = new KillMachine();40 k.KillPeople();41 IGun g = new KillMachine();42 g.KillPeople();43 }44 }45 }2.2 结果2.3 例⼦解释2.3.1 隐式实现即为WrongKillMachine类，并没有指定每个接⼝的实现⽅法，⽽是通过⼀个签名与返回值⼀致的⽅法来隐式实现（Implicit、不⾔明的、绝对的、隐匿的）。

中考英语阅读理解之推理判断题的解题技巧

relationships between senses or paragraphs, understanding their relationships and connections, and using them to help you understand the content of the text
Part
03
Example analysis of reasoning
Inference questions about details
Summary word
Inferring details and problems
Detailed description
This type of question requires candidates to infer certain details based
Common problems and misconceptions
Common problems
Some students may account for differences in distinguishing between differences and true They may misunderstand the meaning of inference and true, leading to errors in answering questions
目录Part01源自Overview of Inference and True
Definition and Type
• Definition: Inference refers to the process of reasoning and drawing conclusions based on known information It requires readers to use their prior knowledge and background information to analyze and understand the content of the text True references to the accuracy and authenticity of the statement It requires readers to determine which statement is true or false based on the given information and their prior knowledge

显式与隐式算法区别

显式与隐式算法区别显式（explicit）和隐式（implicit）这两个词在有限元分析中⼤家可能经常看到，特别是涉及到动⼒学分析时。

但其实⼴义的说他们分别对应着两种不同的算法：显式算法（explicit method）和隐式算法（implicit method）。

所以不论在动⼒学或者静⼒学中都有涉及到。

显式算法：不直接求解切线刚度，不进⾏平衡迭代，计算速度快，时间步长只需要⾜够⼩，⼀般不存在收敛问题，需要的内存也⼩。

隐式算法：每⼀增量步都需要对静态⽅程进⾏平衡迭代，且每次迭代需要求解⼤量的线性⽅程组，这⼀特点使之占⽤⼤量的资源。

但该算法增量步可以很⼤，⾄少⽐显式算法⼤的多，实际计算中会受到迭代次数及⾮线性程度的影响我们都知道有限元分析FEA在计算微分⽅程（differential equations）时，由于计算本⾝的局限，⽐如计算机储存的位数有限，以及⽅程本⾝的复杂性，计算机运⽤的是数值算法（numerical algorithm）来逼近真实解的。

有限元分析中数值算法的基础是欧拉法（Euler method），欧拉法⼜分为forward Euler method 和backward Euler method，这两种⽅法被简称为显式法（explicit method）和隐式法（implicit method）。

中⼼差分法：（动⼒学分析）⽤有限差分代替位移对时间的求导，将运动⽅程中的速度与加速度⽤位移的某种组合来标⽰，这样就将常微分⽅程组的求解问题转化为代数⽅程组的求解问题，并假设在每个⼩的时间间隔内满⾜运动⽅程。

⾸先我们来看看这两种算法的区别。

显式算法（explicit method）（forward Euler method）考虑常微分⽅程：初始条件：设为每⼀步的时间步长，在Tn时刻，. （n=0,1,2,3...)，在T(n+1)时刻有：所以在显式算法中，T(n+1)时刻的值由T(n)时刻决定，也就是说当前时刻的值由上⼀时刻的值决定。

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i
Acknowledgements
I would like to thank Dr. Raymond Spiteri for all the time, encouragement, constructive criticism, ﬁnancial support, and eﬀort he has given to myself and this project. This project would not have been possible without him I would also like to thank Mary MacLachlan and Sarah Healy for supplying Matlab code to help debug the odeToJava code, and for some helpful comments along the way.
ii
Contents
Abstract Acknowledgements Contents List of Tables List of Figures 1 Introduction 2 Electrical Activity of the Heart 2.1 Relevant Background on the Heart 2.2 The Model of Luo and Rudy . . . 2.3 The Model of Courtemanche et al. 2.4 The Model of Winslow et al. . . . 2.5 The Model of Puglisi and Bers . . 3 Mathematical Background 3.1 Diﬀerential Equations . . . . . . 3.2 Numerical Methods . . . . . . . . 3.2.1 Basic Concepts . . . . . . 3.2.2 Error and Stability . . . . 3.2.3 Runge-Kutta Methods . . 3.2.4 Implicit-Explicit Methods 3.2.5 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1 Parameters for the Luo-Rudy Phase I model . . . . . . . . . . . . . . . . . . . . . . . 36
iv
List of Figures
2.1 3.1 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 Transmembrane potential over time in the Luo-Rudy model. . . . . . . . . . . . . . . 5
Implicit-Explicit Numerical Methods in Models of Cardiac Electrical Activity
By Ryan C. Dean
Abstract
Mathematical models of electric activity in cardiac tissue are becoming an increasingly powerful tool in the study of the heart and cardiac arrhythmias. The ordinary diﬀerential equations contained within these mathematical models are challenging to solve. This challenge often means that the physiological accuracy of a model is limited by how eﬃcient we can make the numerical solution process. In this thesis, we examine the eﬃciency of the numerical solution of four cardiac electrophysiological models using Implicit-Explicit (IMEX) methods. We ﬁnd that a particular IMEX method, ARK5, can be up to 275 times faster than some methods most frequently used in practice.
Forward Euler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Sparsity pattern for the Jacobian of the LБайду номын сангаасo-Rudy model. . . . . . . Sparsity pattern for the Jacobian of the Courtemanche et al. model. Sparsity pattern for the Jacobian of the Winslow et al. model. . . . Sparsity pattern for the Jacobian of the Puglisi-Bers model. . . . . . Eigenvalues for the Jacobian of the Luo-Rudy model. . . . . . . . . . Eigenvalues for the Jacobian of the Courtemanche et al. model. . . . Eigenvalues of the Jacobian of the Winslow et al. model. . . . . . . . Eigenvalues for the Jacobian of the Puglisi-Bers model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 23 24 25 26 27 28 29
iii
List of Tables
4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 Initial values for V . . . . . . . . . . . . . . . ERK with Contant Step Size . . . . . . . . . NSFD with Constant Step Size . . . . . . . . Luo-Rudy Dormand Prince Results . . . . . . Luo-Rudy ARK5 Results . . . . . . . . . . . Courtemanche et al. Dormand-Prince Results Courtemanche et al. ARK5 Results . . . . . . Winslow et al. Dormand-Prince Results . . . Winslow et al. ARK5 Results . . . . . . . . . Puglisi-Bers ARK5 Results . . . . . . . . . . Puglisi-Bers Dormand-Prince Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 17 18 18 18 19 19 20 20 21 21