数学建模美赛写作各部分模板
数模美国赛总结部分英文
数模美国赛总结部分英文第一篇：数模美国赛总结部分英文Conclusions1、As our team set out to come up with a strategy on what would be the most efficient way to 我们提出了一种最有效的方法去解决……2、The first aspect that we took into major consideration was…….Other important findings through research made it apparent that the standard 首先我们考虑到……，其他重要的是我们通过研究使4、We have used mathematical modeling in a……to analyze some of the factors associated with such an activity。
为了分析这类问题的一些因素，我们运用数学模型……5、This “cannon problem” has been used in many forms in many differential equations courses in the Department of Mathematical Sciences for several years.这些年这些问题已经以不同的微分方程形式运用于自然科学部门。
6、In conclusion our team is very certain that the methods we came up with in 总之，我们很确定我们提出的方法7、We already know how well our results worked for…… 我们已经知道我们结果对……8、Now that the problem areas have been defined, we offer some ways to reduce the effect of these problems.既然已经定义了结果，我们提出一些方法减少对问题的影响。
美赛数学建模比赛论文模板
The Keep-Right-Except-To-Pass RuleSummaryAs for the first question, it provides a traffic rule of keep right except to pass, requiring us to verify its effectiveness. Firstly, we define one kind of traffic rule different from the rule of the keep right in order to solve the problem clearly; then, we build a Cellular automaton model and a Nasch model by collecting massive data; next, we make full use of the numerical simulation according to several influence factors of traffic flow; At last, by lots of analysis of graph we obtain, we indicate a conclusion as follow: when vehicle density is lower than 0.15, the rule of lane speed control is more effective in terms of the factor of safe in the light traffic; when vehicle density is greater than 0.15, so the rule of keep right except passing is more effective In the heavy traffic.As for the second question, it requires us to testify that whether the conclusion we obtain in the first question is the same apply to the keep left rule. First of all, we build a stochastic multi-lane traffic model; from the view of the vehicle flow stress, we propose that the probability of moving to the right is 0.7and to the left otherwise by making full use of the Bernoulli process from the view of the ping-pong effect, the conclusion is that the choice of the changing lane is random. On the whole, the fundamental reason is the formation of the driving habit, so the conclusion is effective under the rule of keep left.As for the third question, it requires us to demonstrate the effectiveness of the result advised in the first question under the intelligent vehicle control system. Firstly, taking the speed limits into consideration, we build a microscopic traffic simulator model for traffic simulation purposes. Then, we implement a METANET model for prediction state with the use of the MPC traffic controller. Afterwards, we certify that the dynamic speed control measure can improve the traffic flow .Lastly neglecting the safe factor, combining the rule of keep right with the rule of dynamical speed control is the best solution to accelerate the traffic flow overall.Key words：Cellular automaton model Bernoulli process Microscopic traffic simulator model The MPC traffic controlContentContent (2)1. Introduction (3)2. Analysis of the problem (3)3. Assumption (3)4. Symbol Definition (3)5. Models (4)5.1 Building of the Cellular automaton model (4)5.1.1 Verify the effectiveness of the keep right except to pass rule (4)5.1.2 Numerical simulation results and discussion (5)5.1.3 Conclusion (8)5.2 The solving of second question (8)5.2.1 The building of the stochastic multi-lane traffic model (9)5.2.2 Conclusion (9)5.3 Taking the an intelligent vehicle system into a account (9)5.3.1 Introduction of the Intelligent Vehicle Highway Systems (9)5.3.2 Control problem (9)5.3.3 Results and analysis (9)5.3.4 The comprehensive analysis of the result (10)6. Improvement of the model (11)6.1 strength and weakness (11)6.1.1 Strength (11)6.1.2 Weakness (11)6.2 Improvement of the model (11)7. Reference (13)1. IntroductionAs is known to all, it’s essential for us to drive automobiles, thus the driving rules is crucial important. In many countries like USA, China, drivers obey the rules which called “The Keep-Right-Except-To-Pass (that is, when driving automobiles, the rule requires drivers to drive in the right-most unless theyare passing another vehicle)”.2. Analysis of the problemFor the first question, we decide to use the Cellular automaton to build models,then analyze the performance of this rule in light and heavy traffic. Firstly,we mainly use the vehicle density to distinguish the light and heavy traffic; secondly, we consider the traffic flow and safe as the represent variable which denotes the light or heavy traffic; thirdly, we build and analyze a Cellular automaton model; finally, we judge the rule through two different driving rules,and then draw conclusions.3. AssumptionIn order to streamline our model we have made several key assumptions●The highway of double row three lanes that we study can representmulti-lane freeways.●The data that we refer to has certain representativeness and descriptive●Operation condition of the highway not be influenced by blizzard oraccidental factors●Ignore the driver's own abnormal factors, such as drunk driving andfatigue driving●The operation form of highway intelligent system that our analysis canreflect intelligent system●In the intelligent vehicle system, the result of the sampling data hashigh accuracy.4. Symbol Definitioni The number of vehiclest The time5. ModelsBy analyzing the problem, we decided to propose a solution with building a cellular automaton model.5.1 Building of the Cellular automaton modelThanks to its simple rules and convenience for computer simulation, cellular automaton model has been widely used in the study of traffic flow in recent years. Let )(t x i be the position of vehicle i at time t , )(t v i be the speed of vehicle i at time t , p be the random slowing down probability, and R be the proportion of trucks and buses, the distance between vehicle i and the front vehicle at time t is:1)()(1--=-t x t x gap i i i , if the front vehicle is a small vehicle.3)()(1--=-t x t x gap i i i , if the front vehicle is a truck or bus.5.1.1 Verify the effectiveness of the keep right except to pass ruleIn addition, according to the keep right except to pass rule, we define a new rule called: Control rules based on lane speed. The concrete explanation of the new rule as follow:There is no special passing lane under this rule. The speed of the first lane (the far left lane) is 120–100km/h (including 100 km/h)；the speed of the second lane (the middle lane) is 100–80km8/h (including80km/h)；the speed of the third lane (the far right lane) is below 80km/ h. The speeds of lanes decrease from left to right.● Lane changing rules based lane speed controlIf vehicle on the high-speed lane meets control v v <, ),1)(min()(max v t v t gap i f i +≥, safe b i gap t gap ≥)(, the vehicle will turn into the adjacent right lane, and the speed of the vehicle after lane changing remains unchanged, where control v is the minimum speed of the corresponding lane.● The application of the Nasch model evolutionLet d P be the lane changing probability (taking into account the actual situation that some drivers like driving in a certain lane, and will not takethe initiative to change lanes), )(t gap f i indicates the distance between the vehicle and the nearest front vehicle, )(t gap b i indicates the distance between the vehicle and the nearest following vehicle. In this article, we assume that the minimum safe distance gap safe of lane changing equals to the maximum speed of the following vehicle in the adjacent lanes.Lane changing rules based on keeping right except to passIn general, traffic flow going through a passing zone (Fig. 5.1.1) involves three processes: the diverging process (one traffic flow diverging into two flows), interacting process (interacting between the two flows), and merging process (the two flows merging into one) [4].Fig.5.1.1 Control plan of overtaking process(1) If vehicle on the first lane (passing lane) meets ),1)(min()(max v t v t gap i f i +≥ and safe b i gap t gap ≥)(, the vehicle will turn into the second lane, the speed of the vehicle after lane changing remains unchanged.5.1.2 Numerical simulation results and discussionIn order to facilitate the subsequent discussions, we define the space occupation rate as L N N p truck CAR ⨯⨯+=3/)3(, where CAR N indicates the number ofsmall vehicles on the driveway,truck N indicates the number of trucks and buses on the driveway, and L indicates the total length of the road. The vehicle flow volume Q is the number of vehicles passing a fixed point per unit time,T N Q T /=, where T N is the number of vehicles observed in time duration T .The average speed ∑∑⨯=T it i a v T N V 11)/1(, t i v is the speed of vehicle i at time t . Take overtaking ratio f p as the evaluation indicator of the safety of traffic flow, which is the ratio of the total number of overtaking and the number of vehicles observed. After 20,000 evolution steps, and averaging the last 2000 steps based on time, we have obtained the following experimental results. In order to eliminate the effect of randomicity, we take the systemic average of 20 samples [5].Overtaking ratio of different control rule conditionsBecause different control conditions of road will produce different overtaking ratio, so we first observe relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.(a) Based on passing lane control (b) Based on speed control Fig.5.1.3Fig.5.1.3 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.It can be seen from Fig. 5.1.3:(1) when the vehicle density is less than 0.05, the overtaking ratio will continue to rise with the increase of vehicle density; when the vehicle density is larger than 0.05, the overtaking ratio will decrease with the increase of vehicle density; when density is greater than 0.12, due to the crowding, it willbecome difficult to overtake, so the overtaking ratio is almost 0.(2) when the proportion of large vehicles is less than 0.5, the overtaking ratio will rise with the increase of large vehicles; when the proportion of large vehicles is about 0.5, the overtaking ratio will reach its peak value; when the proportion of large vehicles is larger than 0.5, the overtaking ratio will decrease with the increase of large vehicles, especially under lane-based control condition s the decline is very clear.● Concrete impact of under different control rules on overtaking ratioFig.5.1.4Fig.5.1.4 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions. (Figures in left-hand indicate the passing lane control, figures in right-hand indicate the speed control. 1f P is the overtaking ratio of small vehicles over large vehicles, 2f P is the overtaking ratio of small vehicles over small vehicles, 3f P is the overtaking ratio of large vehicles over small vehicles, 4f P is the overtaking ratio of large vehicles over large vehicles.). It can be seen from Fig. 5.1.4:(1) The overtaking ratio of small vehicles over large vehicles under passing lane control is much higher than that under speed control condition, which is because, under passing lane control condition, high-speed small vehicles have to surpass low-speed large vehicles by the passing lane, while under speed control condition, small vehicles are designed to travel on the high-speed lane, there is no low- speed vehicle in front, thus there is no need to overtake. ● Impact of different control rules on vehicle speedFig. 5.1.5 Relationships among vehicle density, proportion of large vehicles and average speed under different control conditions. (Figures in left-hand indicates passing lane control, figures in right-hand indicates speed control.a X is the average speed of all the vehicles, 1a X is the average speed of all the small vehicles, 2a X is the average speed of all the buses and trucks.).It can be seen from Fig. 5.1.5:(1) The average speed will reduce with the increase of vehicle density and proportion of large vehicles.(2) When vehicle density is less than 0.15,a X ,1a X and 2a X are almost the same under both control conditions.Effect of different control conditions on traffic flowFig.5.1.6Fig. 5.1.6 Relationships among vehicle density, proportion of large vehicles and traffic flow under different control conditions. (Figure a1 indicates passing lane control, figure a2 indicates speed control, and figure b indicates the traffic flow difference between the two conditions.It can be seen from Fig. 5.1.6：(1) When vehicle density is lower than 0.15 and the proportion of large vehicles is from 0.4 to 1, the traffic flow of the two control conditions are basically the same.(2) Except that, the traffic flow under passing lane control condition is slightly larger than that of speed control condition.5.1.3 ConclusionIn this paper, we have established three-lane model of different control conditions, studied the overtaking ratio, speed and traffic flow under different control conditions, vehicle density and proportion of large vehicles.5.2 The solving of second question5.2.1 The building of the stochastic multi-lane traffic model5.2.2 ConclusionOn one hand, from the analysis of the model, in the case the stress is positive, we also consider the jam situation while making the decision. More specifically, if a driver is in a jam situation, applying ))(,2(x P B R results with a tendency of moving to the right lane for this driver. However in reality, drivers tend to find an emptier lane in a jam situation. For this reason, we apply a Bernoulli process )7.0,2(B where the probability of moving to the right is 0.7and to the left otherwise, and the conclusion is under the rule of keep left except to pass, So, the fundamental reason is the formation of the driving habit.5.3 Taking the an intelligent vehicle system into a accountFor the third question, if vehicle transportation on the same roadway was fully under the control of an intelligent system, we make some improvements for the solution proposed by us to perfect the performance of the freeway by lots of analysis.5.3.1 Introduction of the Intelligent Vehicle Highway SystemsWe will use the microscopic traffic simulator model for traffic simulation purposes. The MPC traffic controller that is implemented in the Matlab needs a traffic model to predict the states when the speed limits are applied in Fig.5.3.1. We implement a METANET model for prediction purpose[14].5.3.2 Control problemAs a constraint, the dynamic speed limits are given a maximum and minimum allowed value. The upper bound for the speed limits is 120 km/h, and the lower bound value is 40 km/h. For the calculation of the optimal control values, all speed limits are constrained to this range. When the optimal values are found, they are rounded to a multiplicity of 10 km/h, since this is more clear for human drivers, and also technically feasible without large investments.5.3.3 Results and analysisWhen the density is high, it is more difficult to control the traffic, since the mean speed might already be below the control speed. Therefore, simulations are done using densities at which the shock wave can dissolve without using control, and at densities where the shock wave remains. For each scenario, five simulations for three different cases are done, each with a duration of one hour. The results of the simulations are reported in Table 5.1, 5.2, 5.3.●Enforced speed limits●Intelligent speed adaptationFor the ISA scenario, the desired free-flow speed is about 100% of the speed limit. The desired free-flow speed is modeled as a Gaussian distribution, with a mean value of 100% of the speed limit, and a standard deviation of 5% of the speed limit. Based on this percentage, the influence of the dynamic speed limits is expected to be good[19].5.3.4 The comprehensive analysis of the resultFrom the analysis above, we indicate that adopting the intelligent speed control system can effectively decrease the travel times under the control of an intelligent system, in other words, the measures of dynamic speed control can improve the traffic flow.Evidently, under the intelligent speed control system, the effect of the dynamic speed control measure is better than that under the lane speed control mentioned in the first problem. Because of the application of the intelligent speed control system, it can provide the optimal speed limit in time. In addition, it can guarantee the safe condition with all kinds of detection device and the sensor under the intelligent speed system.On the whole, taking all the analysis from the first problem to the end into a account, when it is in light traffic, we can neglect the factor of safe with the help of the intelligent speed control system.Thus, under the state of the light traffic, we propose a new conclusion different from that in the first problem: the rule of keep right except to pass is more effective than that of lane speed control.And when it is in the heavy traffic, for sparing no effort to improve the operation efficiency of the freeway, we combine the dynamical speed control measure with the rule of keep right except to pass, drawing a conclusion that the application of the dynamical speed control can improve the performance of the freeway.What we should highlight is that we can make some different speed limit as for different section of road or different size of vehicle with the application of the Intelligent Vehicle Highway Systems.In fact, that how the freeway traffic operate is extremely complex, thereby,with the application of the Intelligent Vehicle Highway Systems, by adjusting our solution originally, we make it still effective to freeway traffic.6. Improvement of the model6.1 strength and weakness6.1.1 Strength●it is easy for computer simulating and can be modified flexibly to consideractual traffic conditions ,moreover a large number of images make the model more visual.●The result is effectively achieved all of the goals we set initially, meantimethe conclusion is more persuasive because of we used the Bernoulli equation.●We can get more accurate result as we apply Matlab.6.1.2 Weakness●The relationship between traffic flow and safety is not comprehensivelyanalysis.●Due to there are many traffic factors, we are only studied some of the factors,thus our model need further improved.6.2 Improvement of the modelWhile we compare models under two kinds of traffic rules, thereby we come to the efficiency of driving on the right to improve traffic flow in some circumstance. Due to the rules of comparing is too less, the conclusion is inadequate. In order to improve the accuracy, We further put forward a kinds of traffic rules: speed limit on different type of cars.The possibility of happening traffic accident for some vehicles is larger, and it also brings hidden safe troubles. So we need to consider separately about different or specific vehicle types from the angle of the speed limiting in order to reduce the occurrence of traffic accidents, the highway speed limit signs is in Fig.6.1.Fig .6.1Advantages of the improving model are that it is useful to improve the running condition safety of specific type of vehicle while considering the difference of different types of vehicles. However, we found that the rules may be reduce the road traffic flow through the analysis. In the implementation it should be at the 85V speed of each model as the main reference basis. In recent years, the85V of some researchers for the typical countries from Table 6.1[ 21]:Author Country ModelOttesen and Krammes2000 AmericaLC DC L DC V C ⨯---=01.0012.057.144.10285Andueza2000Venezuela ].[308.9486.7)/894()/2795(25.9885curve horizontal L DC Ra R V T++--=].[tan 819.27)/3032(69.10085gent L R V T +-= Jessen2001America][00239.0614.0279.080.86185LSD ADT G V V P --+=][00212.0432.010.7285NLSD ADT V V P -+=Donnell2001 America22)2(8500724.040.10140.04.78T L G R V --+=22)3(85008369.048.10176.01.75T L G R V --+=22)4(8500810.069.10176.05.74T L G R V --+=22)5(8500934.008.21.83T L G V --=BucchiA.BiasuzziK. And SimoneA.2005Italy DCV 124.0164.6685-= DCE V 4.046.3366.5585--=2855.035.1119.0745.65DC E DC V ---=FitzpatrickAmericaKV 98.17507.11185-= Meanwhile, there are other vehicles driving rules such as speed limit in adverseweather conditions. This rule can improve the safety factor of the vehicle to some extent. At the same time, it limits the speed at the different levels.7. Reference[1] M. Rickert, K. Nagel, M. Schreckenberg, A. Latour, Two lane trafficsimulations using cellular automata, Physica A 231 (1996) 534–550.[20] J.T. Fokkema, Lakshmi Dhevi, Tamil Nadu Traffi c Management and Control inIntelligent Vehicle Highway Systems,18(2009).[21] Yang Li, New Variable Speed Control Approach for Freeway. (2011) 1-66。
建模美赛获奖范文
建模美赛获奖范文全文共四篇示例，供读者参考第一篇示例：近日，我校数学建模团队在全国大学生数学建模竞赛中荣获一等奖的喜讯传来，这是我校首次在该比赛中获得如此优异的成绩。
本文将从建模过程、团队合作、参赛经验等方面进行详细介绍，希望能为更多热爱数学建模的同学提供一些借鉴和参考。
让我们来了解一下比赛的背景和要求。
全国大学生数学建模竞赛是由中国工程院主办，旨在促进大学生对数学建模的兴趣和掌握数学建模的基本方法和技巧。
比赛通常会设置一些实际问题，参赛队伍需要在规定时间内通过建立数学模型、分析问题、提出解决方案等步骤来完成任务。
最终评选出的优胜队伍将获得一等奖、二等奖等不同级别的奖项。
在本次比赛中，我们团队选择了一道关于城市交通拥堵研究的题目，并从交通流理论、路网优化等角度进行建模和分析。
通过对城市交通流量、拥堵原因、路段限制等方面的研究，我们提出了一种基于智能交通系统的解决方案，有效缓解了城市交通拥堵问题。
在展示环节，我们通过图表、数据分析等方式清晰地呈现了我们的建模过程和成果，最终赢得了评委的认可。
在整个建模过程中，团队合作起着至关重要的作用。
每个成员都发挥了自己的专长和优势，在分析问题、建模求解、撰写报告等方面各司其职。
团队内部的沟通和协作非常顺畅，大家都能积极提出自己的想法和看法，达成共识后再进行实际操作。
通过团队合作，我们不仅完成了比赛的任务，也培养了团队精神和合作能力，这对我们日后的学习和工作都具有重要意义。
参加数学建模竞赛是一次非常宝贵的经历，不仅能提升自己的数学建模能力，也能锻炼自己的解决问题的能力和团队协作能力。
在比赛的过程中，我们学会了如何快速建立数学模型、如何分析和解决实际问题、如何展示自己的成果等，这些能力对我们未来的学习和工作都将大有裨益。
在未来，我们将继续努力，在数学建模领域不断学习和提升自己的能力，为更多的实际问题提供有效的数学解决方案。
我们也希望通过自己的经验和教训，为更多热爱数学建模的同学提供一些指导和帮助，共同进步，共同成长。
数学建模美赛写作各部分实用模板
摘要第一段：写论文解决什么问题1．问题的重述a. 介绍重点词开头：例1：“Hand move” irrigation, a cheap but labor-intensive system used on small farms, consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexities.例3：An (effective plan) is crucial to………b. 直接指出问题：例 1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes: the number of tollbooths that minimizes average delay experienced by cars.例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.例4: After mathematically analyzing the …… problem, our modeling group would like to present our conclusions, strategies, (and recommendations )to the …….例5：Our goal is... that (minimizes the time )……….2．解决这个问题的伟大意义反面说明。
美国大学生数学建模大赛英文写作
写作要求 ： 1. 简短 论文标题一般在10个字内，最多不超 过15个词。
多用复合词
如：self-design, cross-sectional, dust-free, water-proof, input-orientation, piece-wiselinear 利用缩略词 如：e.g., i.e., vs.（与…相对), ibid.(出处相同）， etc., cit.(在上述引文中), et al.(等人), viz.(即,就是), DEA (data envelopment analysis), OLS(Ordinary least-squares)
“Investigation on …”, “Observation on …”, “The Method of …”, “Some thought on…”, “A research on…”等冗余套语 。
4. 少用问题性标题 5. 避免名词与动名词混杂使用 如:标题是 “The Treatment of Heating and Eutechticum of Steel” 宜改为 “Heating and Eutechticuming of Steel” 6. 避免使用非标准化的缩略语 论文标题要 求简洁,但一般不使用缩略语 ,更不能使用 非标准化的缩略语 。
关键词（Keywords)
基本功能：顾名思义；便于检索 语言特点：多用名词；字数有限（4-6）； 出处明确 写作要求 :论文的关键字一般列在作者与单 位之下，论文摘要之上。也有列在论文摘 要之下的。关键词除第一个字母大写外， 一般不要求大写。关键词间用逗号、分号 或大间隔隔开。最末一个关键词一般不加 用逗号、分号或句号。
美赛-数学建模-写作模板课件-摘要
使用专业术语
摘要中应使用与论文主题 相关的专业术语，以体现 论文的专业性和深度。
突出关键词
摘要中应突出关键词，以 便读者快速了解论文的主 题和主要内容。
突出重点
强调研究目的
摘要应明确指出研究的目 的和目标，以及研究的重 要性和意义。
突出主要发现
摘要中应突出论文的主要 发现或结论，以引起读者 的兴趣和好奇心。
强调研究方法
对于实验或实证研究，摘 要中应简要介绍研究方法， 以增加论文的可信度和说 服力。
保持连贯性
逻辑清晰
使用过渡句
摘要的逻辑应清晰，各部分内容之间 应相互衔接，形成一个完整的整体。
在摘要的不同部分之间，应使用过渡 句来连接，以增强摘要的连贯性和流 畅性。
结构完整
摘要应包含引言、方法、结果和结论 等部分，以确保内容的完整性和连贯 性。
帮助编辑和审稿人评估文章
总结和概括整篇文章
摘要也是编辑和审稿人在评估文章是否适 合发表或是否值得审稿时的重要依据。
摘要需要对整篇文章或报告的内容进行总 结和概括，因此需要作者对文章或报告有 深入的理解和把握。
02 摘要的写作技巧
精炼语言
01
02
03
避免冗余和重复
摘要应简洁明了，避免使 用过多的修饰语和重复的 表述。
精炼内容
删除不必要的描述，突出重点， 使摘要更加紧凑。
调整结构
合理安排摘要的逻辑结构，使其 条理清晰、层次分明。
05 摘要的示例与点评
优秀摘要示例
摘要应简明扼要地概括整个论文 的主要内容和结论，包括问题定 义、模型建立、求解方法和主要
结果。
优秀摘要应具有清晰的结构，使 用简洁明了的语言，避免冗长和
美赛memo的格式
美赛memo的格式英文回答：As a team member of the MCM/ICM contest, I understand the importance of a well-structured and well-written memo. The format of the memo is crucial in conveying our ideas and solutions effectively. Therefore, it is essential to follow a clear and organized structure when writing the memo.The memo should begin with a brief introduction, providing background information on the problem at hand. This sets the stage for the reader and helps them understand the context of the issue. It is important to be concise yet informative in this section, as it lays the foundation for the rest of the memo.Following the introduction, the memo should present the analysis of the problem. This is where we delve into the details of the problem, using mathematical models, dataanalysis, and any other relevant methods to provide a thorough understanding of the issue. It is crucial to be clear and logical in our explanations, ensuring that the reader can follow our thought process.After the analysis, the memo should propose solutions to the problem. This is the crux of the memo, where we showcase our creativity and critical thinking skills. It is important to present multiple solutions, weighing the pros and cons of each, and ultimately recommending the most effective approach. Providing real-life examples or case studies can further strengthen our argument.Finally, the memo should conclude with a summary of the key points and recommendations. This section should reiterate the main findings and emphasize the proposed solutions. It is important to leave the reader with a clear understanding of our conclusions and the next steps to be taken.Overall, the memo should be well-organized, clear, and persuasive. By following a structured format and providingcompelling content, we can effectively communicate ourideas and solutions to the judges.中文回答：作为数学建模竞赛的团队成员，我深知一份结构良好、写作规范的备忘录的重要性。
美国赛写作模版模板
CONTENTSAbstract (1)Ⅰ Introduction (2)ⅡGeneral Assumptions (3)ⅢKey Terminology (3)ⅣModel Development.......................................................................... (3)4.1 (4)4.1.1 (4)4.1.2 (4)4.1.3 (4)4.2 (5)4.2.1 (5)4.2.2 …………………………………................................................................ .64.2.3 (9)4.3 (9)4.3.1 (9)4.3.2 (10)4.3.3 (10)4.4 (10)4.4.1 (10)4.4.2 (10)4.4.3 (10)4.5 (13)4.5.1 (13)4.5.2 (13)4.5.3 (13)ⅤStrengths and Weakness (14)ⅥConclusion (15)ⅦReferences (16)ⅧAppendix (16)TITLEAbstract♦In our essay, we first develop a basic model to account for the fundamental but important phenomena in baseball game and then three improved models for some details. When developing the basic model, in order to analyze overall hitting process clearly, we focus on simplifying the practical problem into a mechanical model.We resolve basic model through three steps, each step considering one important part of the model that greatly impacts our searching for the “sweet spot”. After resolving the basic model, we begin to revise the model to make it more practical.♦Before resolving the basic model, we establish a criteria for evaluation-the proportion of effective energy transmission r, a criteria used to determine at which spot of the bat the maximum proportion of energy output by human is transferred to the ball. Our three steps are designed as follows:⑴In our first step, we mainly investigate the action process between the simplified baseball bat andbaseball. Ignoring other influencial factors, we find one “sweet spot”.⑵In our second step, our focus moves to the relationship between the hand and the bat. Ignoringother influencial factors, we find another “sweet spot”.⑶In our last step, we integrate merits of each “sweet spot ” in above two steps so that we find out a“sweet spot zone”. Then we figure out the variation of r in “sweet spot zone”and find the maximum r.♦After resolving the basic model, we revise our model in three aspects to make it more practical.⑴In our first improvement, we restore the simplified line and particle with objects of different shapeand find out the “sweet spot”after revision.⑵In our second improvement, we consider the shape change of the baseball bat when the bat hits theball and also calculate the lost energy consumed by the shape change of bat made of different material.After revision, we find that the position of the practical “sweet spot”should be a bit more closely than that of “sweet spot”calculated in basic model to the thin end of the bat.⑶In our last improvement, we take into account the vibration that might also impact our searchingfor the “sweet spot”.After detailed analysis, we calculated the lost energy consumed by vibration when the ball hits different spot on the bat and figure out that the position of the practical “sweet spot”should also be a bit more closely than that of “sweet spot”calculated in basic model to the thin end of the bat.♦ⅠIntroductionOn the softball field, hitters usually attempt their best to hit the baseball.In addition to the physical strength the player applied to the baseball, the hitting spot also has great influence on our searching for the sweet spot. Usually, according to the moment of momentum theorem, it seems that the fat end of the baseball bat should be the best hitting spot. However, this is known to be empirically incorrect. Experienced player usually chooses a spot called “sweet spot”to be the best hitting spot, at which the maximum power is transferred to the baseball, thus the hit ball travelling the longest distance. Howard Brody(1989) conducted a series of experiments and investigated that vibration of the baseball would affect the choice of the best hitting spot. Rod Cross(1998) proved that both center of percussion and vibration of the bat affect the searching for the sweet spot through a series of experiment. However, none of scientistshas given a theoretical method to find out the solution. In our essay, we attempt to find out and explain that the sweet spot does not lies on the end of the bat.ⅡGeneral Assumption♦The baseball and baseball bat are assumed to move at uniform velocity. Air friction and gravity can be neglected♦The direction of the velocity of the particle is assumed to collinear that of the linear veloc ity of the action point.♦Baseball bats made of different materials are assumed to attain identical energy after accelerated by human.ⅢKey TerminologyTable 1.Symbols.Symbols Description UnitsⅣModel Development4.1 Simplifying the situationIn order to address the problem, we need to simplify the hitting process. It is reasonable to abstract the process as follows: replacing the baseball bat with a single line, on which the mass is distributed uniformly, and substituting a particle for the baseball; fixing one end of the line so that the line can oscillate on the smooth ground freely; using the process that a baseball hits an oscillating rod to simulate the process that a baseball hits a bat.This is the basic and simplest model that we can extract from hitting process, based on which we can analyze the most basic motion of these two objects. However, we cannot ignore the importance of the elasticity, the vibration and the antihunt action, which might also have impact on our searching for the sweet spot.4.1.1 Basic ModelWe analyze the whole hitting process:Step oneAt the beginning of hitting, the particle moves at a fixed velocity to the line that is oscillating at a fixed angular velocity and linear velocity. The moment of the momentum of the overall system with respect to o is:1112o L m v d J ω=-+, (1) After the hitting, the particle and the line separate and move respectively. The moment of the momentum ofthe overall system with respect to o is2112o L m v d J ω''=+As exterior impulsive moment vanishes, we can then get:12o o L L =that is112112m v d J m v d J ωω''-+=+ (2) Given the material of the line and the particle, we can achieve the coefficient of the restitution between the line and the particle, a coefficient that will help us to achieve the relationships of the linear velocity of the line and the particle.1212v v k v v ''-=+ (3)22v d ω= , 22v d ω''= (4)Putting .Eq (1),(2),(3)and (4) together, we have junctions()221122121221233d m v l m v k v v v m d m l-+++⎡⎤⎣⎦'=+ (4) ()22111222222123133d k m v d km L m d m l m ωωω-+-+'=+ (5)When considering at which spot of the line the maximum power is transferred to the particle, we attempt to work out a spot at which the hit particle reaches the fastest velocity. Differentiating 1v 'with respect to d , we will achieve that when123d m ω=(6)the hit particle reaches the fastest velocity. We just define this spot as the spot of moment(SOM).Step twoIt is necessary for us to take the function of the hands into account if we want to simulate the hitting process exactly. At the instant of hitting the particle, the impulse of the particle will rotate the line unless the particle hits a specified spot on the line-the center of percussion(COP) at which the impulse will only move the translationally with no rotation. According to the momentum theorem()22221111122ox I m l m l m v v ωω''=--+ (7)If the particle hits the COP exactly, the momentum theorem o x I should be 0. Inserting .Eq (4) and (5) into .Eq (7)leads to equation:()()()1212212132062w k d l lm mvd d m l m ω+-+=+ (8)Because all of the parameters in .Eq (8)are greater than 0, only under condition that 320d l -= can the .Eq (8) result in a proper solution. Then we can know the position of the COP:23C O P d l =(9)Step threeAccording to the investigation of ……..(), if viewing hand as soft tissue, we can get the relationship between the force pressed on the tissue and the degree at which the hands ’ shape changes012aseF a-= (10)where♦ 0F represents the force pressed on hands♦ s denotes the relative displacement of the point on palm♦ b and c are constants which have been discussed in !!!!!!!!!!!!!!!!!!!!!!!!!文献As the the force pressed on palm generates the relative displacement, the hand apply negative force on the line, thereby absorbing part of the energy transferred from our arms to the particle. We can easily figure out the lost energy through definite integral:100s w F ds =⎰(11)212ase asa-+-=At the instant of hitting, the energy transferred from the line to the particle is:22222221126w J m l ωω== (12)The energy achieved by the particle is:22011111122w m v m v '=- (13) To transfer the maximum proportion of power output from the human body to the particle, we define this proportion as12w p w w =+ (14)Plugging .Eq (4),(5),(10),(11),(12),(13) into .Eq (14),we have()()()2222211121222112222122231122310.3672as m d m v K l m v dl m K m v d m l mp easaωω-+++-++=-+-+空As the value of p varies when the hitting spot on the rod changes, the variation of p with respect to0d and K is pictured in Fig.14.1.2 Improvement ⅠWith the purpose of improving the practicability, we have to restore the single line and the particle with bodies of axisymmetry (In effect, both the baseball and the bat are axisymmetry). In this way, our model more closely resembles the real hitting process. In this situation, we regard the two bodies as rigid bodies. Unlike the moment of inertia of a line, the moment of inertia of the bat has to be calculated through definite integral. Since we cannot attain the equation of the generating line of the equation, here is an example to compute the moment of inertia of a circular cone to illustrate our methods.In practice, the motion state of an axisymmetrical body, the mass of which is distributed uniformly, is usually equivalent to that of its axis line, on which the mass of the body concentrates. However, the mass is unevenly distributed on the axis line. By computing the moment of inertia of the axis line, we will reach the same result as calculating the moment of inertia of the circular cone. Like circular cone, all of the axisymmetrical bodies can also be figured out in this way.4.1.4 Improvement ⅡAssume that the ball is completely elastic and the energy dissipation mainly stems from the deformation of the bat. As suggested by Adair (2002), the hitting between the bat and the baseball can be reasonably modeled by a ball and a flat without introducing large error. This collision can be simply described as Figure 1. Denoting by R the radius of the ball and by δ the depth of the indentation, the equation of the sphere, on the surface of contact, is[]222()r z R R δ++-= (14)Figure 1. The indentation by a baseball.For shallow indentations /1R δ and /1z R , where in the second inequality the coordinate z is meant to be on the indented surface. According to Asaro and Lubarda (2006), the distributed force takes theform1/2202()1r q r q a ⎛⎫=- ⎪⎝⎭ (15)The total hitting force is1/22200202213a r P q rdr a q a ππ⎛⎫=-=⎪⎝⎭⎰(16)The displacement of the indented surface is given as22212a r w R a ⎛⎫=- ⎪⎝⎭r a ≤ (17) or alternatively, in terms of the depth δ of the indentation,22rw Rδ=-r ≤ (18)Consequently, the energy bat E absorbed by the bat can be expressed as4200232d 55a bat q a a P E qwr r RRππ==⎰(19)4.1.4 Improvement ⅢBy employing the d ’Alembert ’s Principle, one gets the equilibrium equation:()()22,s s s F y x dx F F dx f x t dx t x ρ∂∂⎛⎫=-++ ⎪∂∂⎝⎭(20)where()x ρdenotesthe quality of the unit lengths F is shear force(),f x t is external excitation.Here the shear deformation and the rotation of the cross section are neglected. The small element satisfies the momentum balance which requires(),02s Mdx M dx M F dx f x t dxx ∂⎛⎫+---= ⎪∂⎝⎭(21)Droping the high order small quantity yieldss M F x∂=∂ (22)According to the mechanics of materials, the moment relates the deflection by:()()()2,,y x tM x t E I x x∂=∂ (23) Inserting .Eq (22) and (23) into (21) leads to:()()()()()222222,,,y x t y x t EI x x f x t x x t ρ⎡⎤∂∂∂+=⎢⎥∂∂∂⎣⎦(24)The dynamic equation (24) provides unified theoretical framwork for considering the vibration arbitrayrod or beam. When the rod is uniform, in both quality and shape, the .Eq (24) reduces to()()()4242,,,y x t y x t EIfx t xtρ∂∂+=∂∂ (25)Under our current interest, namely, the hitting between the baseball and the rod, the impulse reads()(),,0F x d tfx t δ⎧-=⎨⎩(26)Where F represents the impulse force By writing()()(),y x t x q t φ=we have()()()2200qt q t E I x ωφωρφ⎧+=⎪⎨''''-=⎪⎩(27) ()()()440x x φβφ-= (28)Obiviously, the solution of ()q t is()()sin q t A t ωθ=+ (29)The homogeneous solution of (27)is()1234cos sin cosh sinh x c x c x c x c x φββββ=+++ (30) Where ()1,2,3,4i c i =are constants which are yet to be determined by following boundary conditions:()()()()()00, 000EI K l l φφφφφ'''=-=⎧⎪⎨'''''==⎪⎩(31) From .Eq (31),we obtain the frequency equation()()()()()()c o s h s i n c o s s i n h 0K l K c o n s l E I l E I l l βββββββ+⋅+-= (32)If 0K =, .Eq (32) reduces tot a n t a n h l l ββ=(33)Normalizing .Eq (32)as:()()()()()00cosh cos sin cos sinh 0K l K l l l l βββββ++-=⎡⎤⎣⎦ (34)with 0K K EI β=Assigning K with a certain value ranged from 0 to 1, we attempt to find out the numerical solution offrequency.The variation of .Eq (34) with respect to l β is illustrated in Fig.1. As can be seen from the figure, the first two-oder frequencies are 3.87701 and 7.01587, respectively, when 0.1K =.重画图4.2 Model ⅡBecause wood has been removed from the bat and replaced by some substance with a s maller density than the wood, not only is the bat lighter, but the center of the gravity of the bat moves closer to the thin end. Since center of percussion(COP) and is relavant to the center of the gravity , the COP also movesJ M α=212t t ωαϕα=⎧⎪⎨=⎪⎩22αϕω⇒= We can get the mechanical energy of the bat:212E J ω=122E J J αϕαϕ=⋅=E Mϕ=4.2.14.2.24.2.34.3 Model Ⅲ4.3.14.3.24.3.34.44.4.14.4.24.4.34.54.5.14.5.24.5.3ⅤStrengths and WeaknessesStrengths♦Our basic model’s strength is that we consider the whole process of energy transmission, energy from hand to bat to baseball.♦We view the palm of the hand as soft tissue and consider the shape change of the hand so that we can model the strengths the hand press on the bat.♦The improvement in basic model take into account the energy loss from vibration, and we develop the “simple support and spring” model to model the function of human hand.♦We consider and compute the lost energy consumed by the shape change of the bat.WeaknessesSince neglecting the data of several parameters in the model, we have difficulty in deducing a perfect solution. We introduce some examples so as to illustrate our method.ⅥConclusionⅦReferencesⅧAppendix。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
第一段：写论文解决什么问题1．问题的重述a. 介绍重点词开头：例1：“Hand move” irrigation, a cheap but labor-intensive small farms, a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexities.例3：An (effective plan) is crucial to………b. 直接指出问题：例1：number of tollbooths in a highway toll-plaza for a given number of highway lanes: the number of tollbooths that minimizes average delay experienced by cars.例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe the engineering parameters of sprinklers available in the market.数学建模美赛论文例4: After mathematically analyzing the …… problem, our modeling group would like to present our conclusions, strategies, (and recommendations )to the …….例5：Our goal is... that (minimizes the time )……….2．解决这个问题的伟大意义反面说明。
如果没有……implementing defensive measure, the university is exposed to an expected of $8.9 million per year.3．总的解决概述a．通过什么方法解决什么问题例：amusement park enjoyment through distributing Quick Passes (QP), reservation slips that ideally allow an individual to spend less time waiting in line.b．实际问题转化为数学模型例1 a network flow vertices are the locations of escorts and wheelchair passengers.例2 : A naïve strategy would be to employ the minimum number of escorts to guarantee that all passengers reach their gates on time.c.将问题分阶段考虑例3：the jump three : flying through the air, punching through the stack, and landing on the ground.第二、三段：具体分析1．在什么模型中/ 建立了什么模型a. 主流模型例1：We formulate a differential model to account for the rates of change of these uses, and how this change the overall consumption of water within the studied region.例2:We examined the mathematical effects of……. We developed a detailed …… (simulation methodology) to test our ideas and to quantify the differences between (among) different …… (strategies).例3：Based on (write your basis .such as the theory of supply and demand), we establish a model (such as differential equation system that includes demand, supply).例4：To (write the aims), we establish a criterion (write the criterion).b. 模型非主流例5：We build a model to determine how to lay out the pipe each time the equipment is moved. 例6：We determine …………例7：We build a model to determine……….例8：We formulate a model for………By analyzing …and examining…..2．分析模型（使用什么数据，怎么做，一般三句话）a. 写历史数据例1：Using historical data from the United States, we determine initial conditions for our model. b. 写计算机模拟例1：this model leads to a computer simulation of catch-can tests of the irrigation system and ……例2:Software packing reaches………by calculating and comparing………..c. 运用数据模拟例1：to ground this model in reality, we incorporate extensive demographic data and run…… 例2：We fit the modified model to data (such as 1970-2003.). We conclude that (write the last conclude).d. 讲详细分析例1：We physically characterize the syste m that…例2：We provide a strategy (write the logical strategy).例3：The …model is (efficient, intuitive, and flexible) and could be applied to…例4：To meet the needs of people today without, we establish a criterion of rational(合理的标准) oil allocation(分配).3．总结该模型的结果/得到什么结论a. 说明不是最优但能产生作用例：We show that this strategy is not optimal but can be improved by assigning differentnumbers……b. 说明如果用这个模型，结果如何例1：If Delta Airlines were to utilize the naïve strategy at Atlanta International Airport, the cost woul d be ……例2：We modify the model to reflect (some trend such as exponentially increasing……) and generalize the model to (other field).例3：Our results are summarized in the formula for the optimal number Bof tollbooths for c．通过其上情况的列举得到的结论例：For various situations, we propose an optimal solution.d. 得出了结论例1：we elicit that a conclusion.例2：We conclude with a series of recommendations for how best to…e.进一步说明其他因素对模型的影响例：In addition to the model, we also discuss policies for …..f.用真实数据检验模型例:To demon strate how our model works, we apply it to ………..最后一段：写总的结论a. 说明结论的可行性例：Our suggested solution, which is easy to implement, includes a detailed timetable and the arrangement of pipes.b.说明算法的广泛性例1：Our algorithm is broad enough to accommodate various airport concourses, flight schedules, and flight delays.例2：Our analysis began by determining what factor impact……, Our conclusions are presented……c.说明模型可用于其他领域例：Since our model is based on…… it can be applied to (other domain).其他（承上启下的连接词/常用词组）例:In addition to the model, we also discuss……引言部分（1）回顾研究背景，常用词汇有review, summarize, present, outline, describe等（2）说明写作目的，常用词汇有purpose, attempt, aim等，另外还可以用动词不定式充当目的状语来表达（3）介绍论文的重点内容或研究范围，常用词汇有study, present, include, focus, emphasize, emphasis, attention等方法部分（1）介绍研究或试验过程，常用词汇有test study, investigate, examine, experiment, discuss, consider, analyze, analysis等（2）说明研究或试验方法，常用词汇有measure, estimate, calculate等（3）介绍应用、用途，常用词汇有等结果部分（1）展示研究结果，常用词汇有show, result, present等（2）介绍结论，常用词汇有summary, introduce, conclude等讨论部分（1）陈述论文的论点和作者的观点，常用词汇有suggest, repot, present, expect, describe等（2）说明论证，常用词汇有等support, provide, indicate, identify, find, demonstrate, confirm, clarify（3）推荐和建议，常用词汇有suggest, suggestion, recommend, recommendation, propose, necessity, necessary, expect等。