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流体论坛 /bbs/工程流体网()傲雪论坛 /bbs/国际CFD论坛 /百思论坛 /振动论坛 /forum/三维网技术论坛 /仿真科技论坛 /forum/index.php康迈克计算力学论坛 中国机械CAD论坛 /thread-htm-fid-142-page-7.html补充：有关流体力学各类网址流体力学, 网址流体力学, 网址/dept5/stress.htm包括国家计算流体力学重点实验室（由李椿萱院士和张函信院士主持）和流体力学开放实验室2. 美国布朗大学流体机械研究中心了解流体机械的诸多方面3.美国ssesco公司CFD技术服务中心/files/cfd_main.html美国一个著名的计算流体服务机构，解决CFD计算和工程问题的专家4.英国Cranfield大学CFD研究中心/sme/cfd/主要介绍CFD的在各个领域的应用。
5.欧洲流体湍流及燃烧研究协会（European Research Community On Flow, TurbulenceAnd Combustion ）http://lmfwww.epfl.ch/lmf/ERCOFTAC/领导管理欧洲的流体，湍流及燃烧方面的科研教育和工业的联合组织。
6.美国国家航空和宇宙航行局/NASA的各项动态和进展，信息很多。
7. 加拿大计算流体力学学会(The CFD Society of Canada )http://www.cfdsc.ca/english/index.html介绍计算流体力学的进展和应用8. CFD免费软件下载中心(CFD codes list - free software)http://www.cfdsc.ca/english/index.htmlCFD免费软件下载(ftp)9. 美国普林斯顿大学空气动力学实验室(the Princeton Gas Dynamics Lab ) /~gasdyn/index.html进行流体力学的前沿研究10. 澳大利亚Monash 大学湍流研究所(The Turbulence Research Laboratory at Monash University ).au/~julio/TRL/进行湍流的理论和实验研究及应用11. 美国Syracuse 大学超音速中心(Syracuse University center for hypersonics) /~hysonics/介绍超音速材料,实验测量及超音速的CFD计算12. 美国流体动力学研究中心(The Fluid Dynamics Research Center (FDRC) )/流体力学研究中心13. 美国Cornell 大学流体力学研究实验中心（Charles Williamson教授领导） (The Fluid Dynamics Research laboratories of Professor Charles Williamson atCornell University)/主要研究涡,湍流和分离流动及其应用14. 荷兰Eindhoven科技大学流体力学实验室(fluid dynamics laborary of Eindhoven University of Technology)http://www.fluid.tue.nl/流体力学和热传导的科研和教育机构,主要研究涡,湍流及空气动力学15. 美国FLOMETRICS公司(FLOMETRICS)/研究流体力学,热力学,自动控制和测量设备的工业公司研究领域包括CFD,实验,理论及流体机械设备16.瑞士机械及机械处理工程能源系统试验室 (ETH Zentrum, Mechanical and Process Engineering, Energy Systems Laboratory )http://www.les.iet.ethz.ch/内容：研究建筑物内的空气流动，燃烧，能源和环境问题。
一份人口的报告英语Population ReportIntroduction:This report provides an overview of the current population trends and characteristics of a particular region. It aims to analyze the population growth, demographic composition, and key factors influencing the population dynamics in the region. The findings and conclusions of this report are based on the latest available data collected from reliable sources.1. Population Size:The current population of the region is estimated to be [population size]. This number has been progressively increasing over the past [time period] due to various factors such as natural birth rates, immigration, and improved healthcare facilities.2. Population Growth:The population growth rate in the region has been [growth rate] per year. This indicates a [positive/negative] population growth trend and highlights the need for continuous monitoring and planning to accommodate the increasing population.3. Demographic Composition:The population is divided into [number or percentage] of females and [number or percentage] of males, indicating a [gender] predominance. The age structure reveals that the largest demographic group is [age range], followed by [age range]. This distribution has implications for resource allocation, social services, and economic planning.4. Fertility Rates:The fertility rates in the region have experienced[increase/decrease] over the past [time period]. This can be attributed to factors such as changes in family planning practices, access to contraceptives, and cultural norms. The average number of children born to women of reproductive age is [fertility rate], which is [higher/lower] than the national average.5. Mortality Rates:The region also experiences [high/low] mortality rates, with [cause of death] being a significant contributor. This highlights the importance of healthcare infrastructure, disease prevention, and improving living conditions to reduce mortality rates and increase life expectancy.6. Migration:Migration has been a significant factor influencing population dynamics in the region. The region experiences [net migration rate], reflecting a [positive/negative] net inflow/outflow of people. The main reasons for migration include seeking better job opportunities, education, or escaping unfavorable living conditions. Conclusion:The population of the region has been steadily increasing, primarily due to natural population growth and migration. Understanding the demographic composition, fertility rates, mortality rates, and migration patterns is crucial for effective planning and decision-making in areas such as healthcare, education, and infrastructure development. Continuous monitoringand analysis of population trends will be essential to ensure sustainable development and address the challenges associated with an evolving population.。
华罗庚英雄事迹用英语写成作文五句话全文共6篇示例，供读者参考篇1Hua Luogeng was a Really Great Mathematician from ChinaHua Luogeng was a very smart and important mathematician who lived in China. He was born in 1910 in a little village called Tongxiang near the city of Hangzhou. Even as a little kid, Hua Luogeng loved math more than anything! He was a math superstar in primary school. All the teachers were so impressed by how good he was at solving hard math problems.Hua Luogeng Fought Against the Japanese InvadersWhen Hua Luogeng grew up, Japan attacked China in 1937. This was a very sad time called the Second Sino-Japanese War. The big bully Japanese army invaded lots of Chinese cities and killed many innocent people. Hua Luogeng loved his country so much that he joined the fight against the evil Japanese invaders! He used his brilliant math brain to crack secret codes and help the Chinese resistance fighters. Hua was such a patriotic hero defending China from the Japanese.After World War 2, Hua Luogeng Became a Famous ProfessorAfter the brave Chinese people won the war against Japan in 1945, Hua Luogeng went to study more advanced mathematics at Cambridge University in England. He was the first Chinese person ever to get a PhD in mathematics from Cambridge! Hua then came back to China and became a respected math professor. He taught at many top universities like Peking University and helped train loads of new generations of Chinese mathematicians.Hua Luogeng's Creative Math Research Brought Glory to ChinaHua Luogeng did pioneering research in many different areas of higher mathematics. He made important discoveries in fields like number theory, algebra, topology, and geometry. Hua Luogeng loved solving the most difficult unsolved math problems that had stumped other genius mathematicians for years and years. His brilliant insights brought great honor and admiration for Chinese mathematics from all around the world!Hua Luogeng Taught Math the Fun and Easy WayNot only was Hua Luogeng an amazingly gifted mathematician, but he was also a wonderful teacher who cared deeply about education. He wrote many popular math books to share his passion for mathematics with students of all ages across China. Hua Luogeng always tried to explain complicated math concepts in the clearest and most simple way possible. His warm personality and humor made learning math feel like a fun game instead of a boring chore. Countless young Chinese kids were inspired to pursue mathematics as a career thanks to Hua's nurturing guidance and encouragement.Hua Luogeng was a true national treasure of China. He used his brilliant mind to defend his homeland from foreign invaders during World War 2. And he dedicated his life's work to advancing human knowledge through mathematics and nurturing China's next generation of top scholars and scientists. Isn't the amazing story of the humble village boy who became a world-renowned math genius just so inspiring? I hope reading about Hua Luogeng's heroic deeds has motivated you work really hard and chase your dreams too! The sky is the limit if you study diligently like he did.篇2Hua Luogeng Was a Really Cool Math Genius!Have you ever heard of Hua Luogeng? He was this awesome Chinese mathematician who lived from 1910 to 1985. Hua did some really neat stuff with math and numbers that made him pretty much a legend!When Hua was just a little kid, he was already a brainiac. He could do crazy hard math problems in his head before he even went to school! One time, his uncle asked him what 123,456 multiplied by 789 was. Most grown-ups would need a calculator or lots of scratch paper to figure that out. But little Hua just thought about it for a couple minutes and blurted out the right answer - 97,450,584! His family was like "Whoa, this kid is wicked smart."In school, Hua was always at the top of his class in every subject, especially math of course. His teachers were blown away by how quickly he could solve the toughest math problems they threw at him. Some of his classmates started calling him "The Number Tamer" because he seemed to have a magical power over numbers. Hua just made ultra-difficult math look easy peasy.After he graduated, Hua went on to have an amazing career as a mathematician. He made all kinds of important discoveries and came up with new math theories that changed the game.Probably his most famous contribution was in the field of analytic number theory. Hua was the first person to solve this mega-hard problem called the "Waring's Problem" that mathematicians had been struggling with for centuries! His work on that helped unlock whole new areas of advanced math research.But you know what the coolest thing about Hua was? He didn't just keep all his brilliance locked away in some ivory tower. Nope, Hua used his mad math skills to help improve education in China so more kids could have access to quality teaching. He helped create better textbooks, teaching methods, and he trained up a fresh generation of math teachers across the whole country. Hua even persuaded the government to make math a much more important part of the school curriculum. Thanks to his efforts, millions more Chinese students got to learn and love math!So in my book, Hua Luogeng was an absolute legend. Not only was he a genius mathematician who made groundbreaking discoveries, but he went above and beyond to make sure his amazing knowledge benefitted everyone in China, especially the next generation of students. How awesome is that? If you ask me, Hua's tale proves that super smarts plus caring about others is awinning combo! Three cheers for the number-busting, education-boosting hero Hua Luogeng!篇3Hua Luogeng Was a Great Hero!Do you know Hua Luogeng? He was one of the best mathematicians ever in China! Hua Luogeng did so many awesome things that made him a true hero. Let me tell you all about his cool life.When Hua was just a little kid, he was super smart and good at math. Even as a young boy, he could solve really hard math problems that stumped grown-ups! Hua worked incredibly hard at his studies. He would stay up late at night reading books and doing Math by candlelight. His hard work paid off because he became a famous mathematician.During World War 2, the mean Japanese army invaded China. Hua Luogeng used his brilliant math mind to help fight the invaders. He set up a secretcodebook to send coded messages to the Chinese resistance fighters. The Japanese could never crack his super tricky math codes! Hua's codes helped the Chinese win many important battles against the Japanese.After the war, Hua Luogeng kept working super hard on higher level Mathematics. He made groundbreaking discoveries and solved problems that no one else could figure out. Hua loved sharing his passion for Math too. He trained generations of students who went on to make their own amazing Math discoveries. Hua's teachings still help mathematicians today!Hua Luogeng was selfless and always put others before himself. Despite his genius, he remained humble his whole life. He truly loved his country and dedicated himself to using Mathematics to make China stronger. For his brilliant mind, tireless work ethic, and patriotic spirit, Hua Luogeng will always be remembered as a great Chinese hero!篇4Hua Luogeng Was A Really Cool Math Guy!Hua Luogeng was a super smart Chinese mathematician who did lots of awesome things! He was born in 1910 in Jiangsu Province in China. When he was a kid, he loved math more than anything else in the whole world. He would stay up late at night solving tough math problems just for fun! His parents probably thought he was kind of a weirdo for liking numbers andequations so much. But little did they know, their son would grow up to be one of the greatest mathematicians ever!In 1936, when Hua Luogeng was 26 years old, he made a really important discovery in math called the Hua Composition Formulas. These formulas were a huge deal and helped advance the study of a tricky area of math called analytic number theory. Math nerds around the world were like "Wow, this Hua guy is a genius!" Even the famous English mathematician G.H. Hardy said Hua's work was "one of the few major discoveries made in recent years."But being a super genius mathematician wasn't enough for the amazing Hua Luogeng. When World War 2 started and the Japanese invaded China, he became a fighter in the resistance against the Japanese army! Can you imagine a math professor fighting on the battlefield? Hua helped to organize resistance efforts by Chinese mathematicians and scientists. He was so brave to risk his life defending his country like that. What a hero!After the war ended, Hua Luogeng worked really hard to help rebuild China's education system that had been destroyed by the fighting. He started a prestigious university called the Beijing Graduate School where he could train the nextgeneration of brilliant Chinese mathematicians. Hua wanted to make sure China became a world leader in math and science!Hua Luogeng accomplished so many unbelievable things in his 92 years of life. He made groundbreaking discoveries that changed mathematics forever. He fought courageously against the Japanese invasion during World War 2. And he dedicated his career to improving education in China. To me, Hua Luogeng seems like the coolest nerd ever! He's definitely one of the greatest Chinese heroes of the 20th century. I hope kids all over China learn about his amazing life and incredible achievements. What a legend!篇5Hua Luogeng was a Great Math Hero!Hua Luogeng was one of the most awesome math masters ever! He was born in 1910 in a small village called Jiaxing near the city of Shanghai. Even as a young kid, Hua was a super brainiac at numbers and algebra. By the time he was 12 years old, he had already read through advanced math books that most grown-ups couldn't understand!After finishing school, Hua went to university to study more crazy-hard math. But in 1935, something terrible happened. Themean Japanese army invaded China and made life very difficult for everyone. Instead of just doing math all day, Hua had to use his brilliant brain to fight against the invaders!Hua was one of the bravest heroes standing up to the Japanese bullies. He helped set up secret codes and ciphers to send messages back and forth without the enemy understanding. Whenever the Japanese tried to crack the codes, Hua'smega-mind was always 10 steps ahead! He outwitted them at every turn with his genius math skills.After World War 2 finally ended in 1945, Hua went back to teaching math and training new generations of students. He worked super hard to make China a world leader in mathematics and science. Thanks to the efforts of Hua Luogeng and other brilliant math warriors, China now has some of the most legendary genius mathematicians on planet Earth!Hua's courage, resilience, and passion for spreading math knowledge made him a true national hero. Even though he lived through very difficult times, he never lost his love for numbers and problem-solving. Hua Luogeng truly had one of the greatest math minds in history. What a totally awesome dude!篇6My Hero Hua LuogengMr. Hua Luogeng was a super amazing and super smart mathematician from China. He did so many awesome things in his life that made him a true hero! Let me tell you all about the heroic deeds of this incredible man.First of all, Mr. Hua was born in 1910 which was a really really long time ago. Even though he grew up in a poor family without much money, he worked extremely hard in school. He loved math more than anything and was already solving tricky math problems by the time he was a young kid! Can you imagine being that good at math when you were little? I can't!When Mr. Hua got older, he went to university to study mathematics. He was the best student and made all sorts of new discoveries in math. The professors were all totally blown away by how smart he was. After university, he started teaching math to other students and helping them understand all the confusing numbers and equations. Thousands of people learned from the great Mr. Hua over the years!But teaching wasn't even the most heroic thing Mr. Hua did. During World War 2 when China was fighting against other countries, the government asked Mr. Hua to use his brilliant math skills to help. You see, having really good mathematicianswas super important for making military weapons, breaking secret codes, and outsmarting the enemy. So Mr. Hua put his regular math work on hold and did everything he could to protect China using math! How cool is that?After the war ended, Mr. Hua kept working harder than ever to advance the field of mathematics in China. He established a prestigious math society, wrote lots of ground-breaking books, and trained future generations of great mathematicians. The math world in China wouldn't be what it is today without Mr. Hua's tireless efforts and genius mind dedicating his life to the subject he loved.In my opinion, Mr. Hua Luogeng is a true hero of China. He used his incredible talent and passion for math to serve his country during wartime and to educate countless students for decades after. Not only was he one of the smartest people ever, but he was selfless and worked for the greater good. Mr. Hua showed that mathematicians can be just as brave and heroic as soldiers on the battlefield. I hope to be as devoted to learning and as heroic as him when I grow up! The world needs more people like the legendary Mr. Hua Luogeng.。
navier stokes方程组的方程Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, represent the fundamental principles of fluid dynamics. These equations describe the motion of viscous fluid substances, taking into account the forces acting on the fluid and the changes in pressure, velocity, and density. They are a set of partial differential equations that govern the flow of fluids, and are widely used in various fields such as aerodynamics, hydrodynamics, and meteorology.Navier-Stokes方程组是以克劳德-路易·纳维尔和乔治·加布里埃尔·斯托克斯的名字命名的，它代表了流体动力学的基本原理。
这组方程描述了粘性流体物质的运动，考虑了作用在流体上的力以及压力、速度和密度的变化。
它们是一组偏微分方程，支配着流体的流动，并被广泛应用于空气动力学、水动力学和气象学等多个领域。
The equations consist of a momentum equation that expresses the conservation of momentum, and a continuity equation that expresses the conservation of mass. The momentum equation takes into account the effects of pressure gradients, viscous stresses, and external forces on the fluid. On the other hand, the continuity equation ensures that mass is conserved within the fluid as it flows.方程组包含动量方程和连续性方程。
Fluid-Structure Interaction Fluid-structure interaction (FSI) is a complex and challenging problem that arises in various engineering and scientific fields. It involves the interaction between a deformable structure and a fluid flow, and understanding and accurately modeling this interaction is crucial for the design and analysis of many engineering systems, such as aircraft wings, wind turbines, and cardiovascular devices. The behavior of the structure is influenced by the fluid flow, and vice versa, making FSI a highly coupled and multidisciplinary problem. From a mechanical engineering perspective, FSI presents a unique set of challenges and opportunities. On one hand, the coupling between the fluid and structure introduces nonlinearities and complexities that are not present in either fluid dynamics or structural mechanics alone. This requires advanced numerical methods and computational tools to accurately simulate and analyze FSI problems. On the other hand, FSI offers the potential for innovative designs and optimization of engineering systems by exploiting the interaction between the fluid and structure to improve performance and efficiency. In the field of computational fluid dynamics (CFD), FSI is a topic of great interest and research. Simulating FSI problems requires solving the governing equations for both the fluid flow and the structural deformation, and then coupling these equations to account for the interaction between the two. This often involves using specialized FSI algorithms and solvers, as well as high-performance computing resources to handle the computational demands of FSI simulations. Additionally, experimental validation and verification of FSI simulations are essential to ensure their accuracy and reliability. From a biomedical engineering perspective, FSI is particularly relevant in the study of cardiovascular dynamics and the behavior of blood flow in the human body. Understanding how blood interacts with the walls of blood vessels and how this interaction affects the cardiovascular system is crucial for the diagnosis and treatment of cardiovascular diseases. FSI simulations can provide valuable insights into the hemodynamics of blood flow, the formation of arterial plaques, and the performance of medical devices such as stents and artificial heart valves. In the aerospace industry, FSI plays a critical role in the design and analysis of aircraft and spacecraft. The interaction between the aerodynamicforces acting on the aircraft and the structural response of the wings, fuselage, and control surfaces is essential for ensuring the safety and performance of the vehicle. FSI simulations are used to predict the structural loads and deformations under different flight conditions, as well as to optimize the aerodynamic shape of the aircraft to improve fuel efficiency and reduce emissions. In conclusion,fluid-structure interaction is a multifaceted problem that presents challenges and opportunities across various engineering disciplines. From a mechanical engineering perspective, FSI requires advanced computational tools and methods to accurately simulate and analyze the complex interaction between a fluid flow and a deformable structure. In the fields of biomedical engineering and aerospace engineering, FSI is particularly relevant for studying cardiovascular dynamics and designing aircraft and spacecraft. Overall, FSI is a critical area of research and development with far-reaching implications for the design and analysis of engineering systems.。
Frobenius MethodFrobenius method is a powerful mathematical technique used to find solutions to differential equations, especially those with singular points. It was developed by Ferdinand Georg Frobenius, a German mathematician, in the late 19th century. The method has applications in various fields of science and engineering, including physics, chemistry, and biology.IntroductionDifferential equations are mathematical equations that involve derivatives of unknown functions. They are used to model a wide range of phenomena in the physical and natural sciences. Solving these equations is crucial in understanding the behavior of systems governed by differential equations.The Frobenius method is particularly useful when dealing with second-order linear differential equations that have regular singular points. A regular singular point is a point at which the coefficients of the differential equation become infinite or indeterminate.ProcedureTo apply the Frobenius method, we follow these steps:1.Assume a power series solution: We assume that the solution to thedifferential equation can be expressed as an infinite series ofpowers of x.2.Substitute the power series into the differential equation: Wesubstitute the assumed power series into the original differential equation and equate coefficients of like powers of x.3.Determine recurrence relations: By equating coefficients, weobtain recurrence relations that relate each coefficient toprevious coefficients in the power series.4.Solve for initial values: Using initial conditions or boundaryconditions, we can solve for some or all of the initial values in terms of known quantities.5.Determine convergence: We analyze the radius and interval ofconvergence for the power series solution to ensure its validitywithin a certain domain.6.Construct the general solution: Once we have determined allnecessary coefficients, we can construct the general solution as a linear combination of terms involving these coefficients.ExampleLet’s consider an example to illustrate how to apply the Frob enius method:We want to solve Bessel’s equation:x^2 y’’ + x y’ + (x^2 - n^2) y = 0where n is a constant.1.Assume a power series solution:We assume that the solution can be expressed as a power series:y(x) = Σ(a_n * x^(n+r))where r is an arbitrary constant.2.Substitute the power series into the differential equation: Substituting the power series into Bessel’s equation, we obtain:Σ[(n+r)(n+r-1) * a_n * x^(n+r-2) + (n+r) * a_n * x^(n+r-1) + (x^2 - n^2) * a_n * x^(n+r)] = 03.Determine recurrence relations:By equating coefficients of like powers of x, we obtain the following recurrence relation:a_(n+2) = -((n+r)^2 - n^2)/(n+1)(n+2) * a_n4.Solve for initial values:To solve for initial values, we need to consider the behavior of the coefficients as n approaches negative infinity. We can chooseappropriate values for r to ensure convergence and determine all necessary initial values.5.Determine convergence:We analyze the recurrence relation to determine the radius and interval of convergence for the power series solution.6.Construct the general solution:Once we have determined all necessary coefficients, we can construct the general solution by combining terms involving these coefficients.ApplicationsThe Frobenius method has various applications in science and engineering. Some examples include:1.Quantum mechanics: The Frobenius method is used to solveSchrödinger’s equation in atomic physics and quantum mechanics.2.Heat conduction: The Frobenius method can be applied to solvepartial differential equations governing heat conduction invarious materials.3.Fluid dynamics: The Frobenius method is used to solve differentialequations describing fluid flow and turbulence in fluid dynamics.4.Electromagnetism: The Frobenius method is used to solve Maxwell’sequations, which describe the behavior of electric and magneticfields.ConclusionThe Frobenius method provides a systematic approach for findingsolutions to differential equations with regular singular points. By assuming a power series solution and equating coefficients, we can determine the necessary recurrence relations and initial values to construct the general solution. This method has wide-rangingapplications in various scientific and engineering disciplines, makingit an essential tool for researchers and practitioners alike.。
