2014美赛题目(翻译版)

问题A：右行左超规则在美国、中国和大多数除了英国、澳大利亚和一些前英国殖民地的国家，多车道高速公路常常有这样一种规则。

司机必须尽量在最右的车道行使，只有超车时，司机才可以向左移动一个车道来达成目的。

当司机超车完毕后必须回到原车道继续行使。

建立并分析一个数学模型，使得这个模型能够分析这个规则在交通高负荷和低负荷情况下的表现。

你可以从许多角度来思考这个问题，比如车流量和车辆安全之间的权衡，或者一个过快或过慢的车辆限速带来的影响等等。

这个规则可以使我们获得更好的交通流？如果不可以，请提出并分析一个替代方案使得交通流得到优化、安全得到保障、或者其他你认为重要的因素得到实现。

在靠左行使才是规则的国家，论证你的解决方案是否可以通过简单的变换或者通过增加一些新的要求来解决相同的问题。

最后，以上的规则的实行是建立在人们遵守它的基础上的，然而不是所有人都愿意去遵守。

那么现在我们使同一条道（可以只是一段，也可以是全段公路）上的交通车辆都在一个智能系统的严格控制下，这个变化对你之前的分析结果有多大的影响？问题B：体育画刊是一个为体育爱好者们设计的杂志。

这个杂志正在寻找上世纪女性或者男性的“历来最优秀的大学教练”。

建立一个数学模型，从男性或者女性体育教练中选择最好的大学教练（退役或者在役的都可以）。

这些体育教练可以是大学曲棍球、陆上曲棍球、足球、橄榄球、棒球、排球、篮球的教练。

你选择划分的时间会对你的分析有影响吗？也就是说，1913年的教练方式和2013年的会有什么不同吗？清楚的阐述你的评估方式。

讨论你的模型如何通用于两性教练和所有可能的运动项目上。

用你的模型为三项体育项目分别找到五个最佳教练。

再为体育画刊提供一篇1－2页的不涉及技术性问题解释的通俗易懂的文章来解释你们的结果，你们必须保证体育爱好者们能够理解。

PROBLEM A: The Keep-Right-Except-To-Pass RuleIn countries where driving automobiles on the right is the rule (that is, US A, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane(车道) freeways(快车道) often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they mov e one lane to the left, pass, and return to their former travel lane.Build and analyze a mathematical model to analyze the performance of th is rule in light and heavy traffic. You may wish to examine tradeoffs(权衡) between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/ or other factors that may not be explicitly(明确地) called out in this problem statement. Is this rule effective in promotin g better traffic flow? If not, suggest and analyze alternatives (to include p ossibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem(认为) important.In countries where driving automobiles on the left is the norm, argue whe ther or not your solution can be carried over with a simple change of orie ntation(方向), or would additional requirements be needed.Lastly, the rule as stated above relies upon human judgment for complian ce( 服从). If vehicle transportation on the same roadway was fully under the co ntrol of an intelligent system – either part of the road network or imbedde d(把……嵌入) in the design of all vehicles using the roadway – to what extent would this change the results of your earlier analysis?PROBLEM B: College Coaching LegendsSports Illustrated, a magazine for sports enthusiasts, is looking for the “be st all time college coach” male or female for the previous century. Build a mathematical model to choose the best college coach or coaches (past or present) from among either male or female coaches in such sports as colle ge hockey(冰球) or field hockey(曲棍球), football, baseball or softball(垒球), basketball, or soccer(英式足球). Does it make a difference which time line horizon that you use in yo ur analysis, i.e., does coaching in 1913 differ from coaching in 2013? Clearly articulate(善于表达的) your metrics(韵律学) for assessment. Discuss how your model can be applied in general acr oss both genders (性别) and all possible sports. Present your model’s top 5 coaches in each of 3 different sports.In addition to the MCM format and requirements, prepare a 1-2 page article(文章) for Sports Illustrated that explains your results and includes a non-technical explanation of your mathematical model that sports fans will un derstand。

PROBLEM A: The Keep-Right-Except-To-Pass RuleIn countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane.Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this rule effective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important.In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirements be needed.Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system – either part of the road network or imbedded in the design of all vehicles using the roadway – to what extent would this change the results of your earlier analysis?问题A 除超车保持右行规则在有些国家，驾驶机动车在右车道行驶（如美国，中国和除了英国，澳大利亚以及前英国殖民地国家的其它大多数国家），多车道的高速公路所使用的规则要求驾驶人员右车道行驶，除非他们要超车行驶，在此情况下他们先开到左侧车道，超车，然后在回到之前的行驶车道。

A 题：除了超车以外都要靠右行驶的规则（靠右行驶规则）在某些国家，开车时规定要靠右行驶（如美国，中国以及除英国，澳大利亚和前英国殖民地的大多数国家）多车道高速公路往往会制定一个规则，要求司机在驾驶时靠最右车道行驶，除非在超车的时候可以行驶到左一个车道超车，超车结束后回归到原行驶车道。

建立一个数学模型，分析靠右行驶规则在交通畅通时和在交通拥挤的
情况下的性能表现。

你可以在交通流和安全之间，在限速中扮演的角色之间（也就是说限速过低或者过高）,和/或其他可能不会在这个问题中明确提出的因素之间权衡。

这是有效地改善交通流通性的规则吗？如果不是,提出并分析不同的方案选择(包括可能根本不存在的规则),这些方案可能改善交通流,安全性,和/或其他你认为重要的因素。

在靠左边驾驶汽车的国家中,讨论您的解决方案是否可以用一个简单的方向改变就可以转换,或者需要额外的要求。

最后,如上所述的规则依赖人类合规性判断。

如果相同道路的车辆运输是完全的控制在一个智能系统下,这个智能系统或者是道路网络的一部分或者是嵌入在道路中所有车辆的设计中-这在多大程度上改变你之前分析的结果?数学中国（w w w .m a d i o .n e t ）。

2010 MCM ProblemsPROBLEM A: The Sweet SpotExplain the “sweet spot” on a baseball bat.Every hitter knows that there is a spot on the fat part of a baseball bat where maximum power is transferred to the ball when hit. Why isn’t this spot at the end of the bat? A simple explanation based on torque might seem to identify the end of the bat as the sweet spot, but this is known to be empirically incorrect. Develop a model that helps explain this empirical finding.Some players believe that “corking” a bat (hollowing out a cylinder in the head of the bat and filling it with cork or rubber, then replacing a wood cap) enhances the “sweet spot” effect. Augment your model to confirm or deny this effect. Does this explain why Major League Baseball prohibits “corking”?Does the material out of which the bat is constructed matter? That is, does this model predict different behavior for wood (usually ash) or metal (usually aluminum) bats? Is this why Major League Baseball prohibits metal bats?MCM 2010 A题：解释棒球棒上的“最佳击球点”每一个棒球手都知道在棒球棒比较粗的部分有一个击球点，这里可以把打击球的力量最大程度地转移到球上。

问题A：保持向右行驶除非要超车的交通规则在一些国家，汽车行驶在右边是规则，比如，美国，中国和其他大多数国家，除了英国，澳大利亚和一些前英国殖民地。

多车道高速公路经常使用一个规则，就是要求司机在最右边的车道驾驶，除非它们要超车。

超车就是他们开到左边的一个车道，超越，并恢复到原来的行驶车道。

（1）建立和分析一个数学模型来分析这一规则在车流量少和车流量大的不同时刻的表现。

不妨检查权衡交通流量和其安全性。

这些保持原车道或者被超车的速度限制（即限制最大速度和最小速度），或者其他的因素，可以不用考虑到问题中。

（2）这个规则，能有效地促进了更多的车流量吗？如果不能，提出并分析备选方案（之中最好不要用到题目中这类规则），能够促进更多的交通流量，安全性，或者你认为重要的其他因素。

（3）在一些国家，汽车行驶在左边是常态，讨论你的解决方案是否能够转用，仅仅是要一个简单的方向改变，或者需要额外的要求。

（4）最后，如上所述的规则依赖于人的判断为标准。

如果运输车辆在相同的道路上完全被处于一个智能系统（无论是部分路网或是嵌入设计到所有车辆里）的控制下，在何种程度上这会改变你刚才分析的结果？问题B：大学传奇教练《体育画报》，一个给运动爱好者的杂志，正在寻找上个世纪（以前世纪）男女教练中“一直表现最佳的大学教练”。

（1）建立一个数学模型，选择最佳的大学教练（一个或多个，过去的或者现在的）。

根据男性或女性教练在高校曲棍球或曲棍球，足球，棒球或垒球，篮球，足等体育项目中的表现。

（2）清楚地说明你进行评估的指标。

讨论你在分析中使用的时间轴，是否对结果有所影响，也就是说，教练的执教能力在1913年是否不同于在2013年？（3）讨论你的模型是如何能在不同性别和所有可能的运动领域中普遍应用。

运用你的模型分别从3个不同的运动领域上展示你的前5名教练。

（4）除了MCM的格式和要求，为体育画报准备一份1-2页文章，解释你的结果，并包括你的数学模型的非技术性解释，以便体育迷们能够理解。

SIGNPage 1 of 2PART HIGHWAY SIGNS SECTION REGULATORY SIGNS RECOMMENDED PRACTICESSUB-SECTIONGeneralWhen traffic flow along a two-lane highway is near capacity and traffic operation deteriorates, often an auxiliary lane is introduced to alleviate congestion and traffic problems. Opening a third lane (i.e., a passing or a climbing lane) introduces new traffic rules for drivers who now have two lanes in the same direction.The primary function of an auxiliary lane is to accommodate passing manoeuvres. Consequently, all drivers travelling at their normal speeds with no intention of passing are required to utilize the right lane (i.e., the outside lane).The Traffic Safety Act, Regulation AR 304/2002 has provisions for the operation of traffic along a highway with three lanes. Under the Act, all drivers are required to use the right (i.e., the outside) lane unless they intend to pass. The inside or centre lane is reserved for overtaking and passing maneuvers.In Alberta, the regulation of the Act is supported with the use of the regulatory Keep Right Except to Pass sign. The sign is introduced to advise drivers that they must use the right lane except when they are passing a slower vehicle.The use of the Keep Right Except to Pass sign at the beginning of an auxiliary lane helps to channel travelling vehicles into the right lane and improves the overall operation of traffic along passing and climbing lanes.Provincial LegislationSections 16(1)(a),(b) and (c) of Part 1, Division 4 of the Traffic Safety Act , Regulation 304/2002 provide general provisions for traffic travelling along a three-lane highway.Based on Regulation AR 304/2002 of the Act:16 (1) Where a roadway consists of 3 trafficlanes, a person driving a vehicle shall not drive the vehicle in the centre traffic lane except for the following purposes:(a) when passing another vehicletraveling in the same direction; (b) when approaching anintersection where that person intends to turn left (c) when a traffic control deviceotherwise permits.StandardThe Keep Right Except to Pass sign is a regulatory information sign. The sign has a rectangular shape and consists of a black message on a white background. The size of the sign is 600 mm x 750 mm and it is the only size used in such situations.SIGNPage 2 of 2RB-34 600 mm x 750 mmColour Message and BorderBackgroundBlackWhiteSheeting ASTM, Type IIIGuidelines for UseIt is very common that drivers approachinga passing or climbing lane are unsure ofhow to properly use the auxiliary lane. Acommon mistake is to continue to travel inthe inside lane, which in consequence maycause delays to faster moving vehicles.It is therefore advisable to provide aregulatory Keep Right Except to Pass signfor each highway segment which has anauxiliary lane. The sign typically hasapplications at locations with steep grades(climbing lanes) or high traffic volumes(passing lanes) to minimize the effect ofslow moving vehicles on normal traffic flow.Guidelines for PlacementThe sign is placed on the right side of theroadway at the start of the taper for theclimbing lane or passing lane.A supplementary sign may be considered forpassing lanes longer than 2 km. The secondsign should be placed no closer than 1 kmfrom the end of the climbing or passing lane.References to StandardsTypical SignageDrawingsTEB 1.58Typical Signing for Passingand Climbing Lanes。

目录2018 年美赛题目翻译 (3)问题A：多跳HF 无线电传播 (3)问题B：语言传播趋势 (3)问题C ：能源配置与预测 (5)问题D：从汽油驾驶到E （电）驾驶 (6)问题E：气候变化如何影响区域不稳定？ (7)问题F：隐私成本问题 (8)2017 年美赛题目翻译 (10)问题A：管理赞比西河 (10)问题B：收费后合并 (11)问题C：“合作和导航” (12)问题D：在机场安全检查站优化乘客吞吐量 (13)问题E：规划可持续城市的发展 (15)问题F：迁移到火星：2100城市社会的乌托邦劳动力 (17)2016 年美赛题目翻译 (20)Program A 浴缸的水温模型 (20)Program B 解决空间碎片问题 (20)Program C 优质基金挑战 (21)2015 年美赛题目翻译 (21)问题一：根除病毒 (21)问题B：寻找失踪的飞机 (22)2014 年美赛题目翻译 (22)问题A：（交通流、路况）优化 (22)问题B：（体育教练）综合评价 (23)2013 年美赛题目翻译 (23)A ：平底锅受热 (23)B：可利用淡水资源的匮乏 (24)2012 年美赛题目翻译 (25)A 题：一棵树的叶子 (25)B：沿着 Big Long River 野营 (25)2011 年美赛题目翻译 (26)A:单板滑雪场地 (26)B：中继站的协调 (26)2010 年美赛题目翻译 (27)A 题：解释棒球棒上的“最佳击球点” (27)B 题系列犯罪地理效应 (27)2018年美赛题目翻译问题A：多跳HF 无线电传播背景：在高频段（HF,定义为3-10MHz），无线电波可以在地球表面和电离层之间的多次反射以进行长距离的传输（从地球表面上的一个点到地球表面上的另一个远点）。

对于低于最大可用频率（MUF）的频率，来自地面源的HF 无线电波将随着每个连续的跳跃继续前进从电离层反射回地球，在那里它们可能再次反射回到电离层，也可能再次反射回地球，等等。

2014 ICM Problem使用网络来测量的影响和冲击Using Networks to Measure Influence and Impact确定学术研究的影响力的一种方法是构建和测量引文或合著者网络的属性.共同创作的文章通常意味着研究者之间的影响力有了重要的连接。

其中最有名的学术合著者是20世纪的数学家保罗·埃尔德什（Paul Erdös）他拥有超过500共同作者，并发表了超过1400的技术研究论文。

说埃尔德什（Erdös）是具有学科交叉特点的网络科学（science of networks）这一新兴研究的奠基人之一或许具有讽刺意味，或者也不。

特别是1959年，他和阿尔弗雷德的共同撰写的论文“关于随机图”（“On Random Graphs”）的发表，使得埃尔德什的作为合作者的角色在数学领域变得十分重要以至于数学家们经常会通过分析埃尔德什数量惊人的合作者来衡量自己与埃尔德什联系的紧密程度（their closeness to Erdös）。

(see the website http://www.oakla /enp/ )保罗.埃尔德什作为一个天才的数学家，天才的问题解决者，和著名合作者的不寻常和令人着迷的故事公布也在了许多书籍和在线网站上。

(例如,/Biographies/Erdos.html ).也许，他的生活方式就是经常和他的合作者待在一起或者住在一起。

或者把钱给他的学生作为解决问题的奖励，从而使他的合作蓬勃发展，并帮助他在数学的几个领域里建立了具有惊人影响力的网络。

为了衡量诸如埃尔德什等人产生的影响力，已经有了一些基于网络评价的工具（network-based evaluation tools）。

即是利用共同作者和引文数据来确定学者，出版物和学术期刊的影响因子，比如：科学文献索引（Science Citation Index，SCI的），H- factor（一种评价学术成就的新方法）Impact factor （期刊影响因子，SCI），Eigenfactor等等。

PROBLEM A: The Keep-Right-Except-To-Pass RuleIn countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane.Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this rule effective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important.In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with asimple change of orientation, or would additional requirements be needed.Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system – either part of the road network or imbedded in the design of all vehicles using the roadway – to what extent would this change the results of your earlier analysis?PROBLEM B: College Coaching LegendsSports Illustrated, a magazine for sports enthusiasts, is looking for the “best all time college coach” male or female for the previous century. Build a mathematical model to choose the best college coach or coaches (past or present) from among either male or female coaches in such sports as college hockey or field hockey, football, baseball or softball, basketball, or soccer. Does it make a difference which time line horizon that you use in your analysis, i.e., does coaching in 1913 differ from coaching in 2013? Clearly articulate your metrics for assessment. Discuss how your model can be applied in general across both genders and all possible sports. Pre sent your model’s top 5 coaches in each of3 different sports.In addition to the MCM format and requirements, prepare a 1-2 page article for Sports Illustrated that explains your results and includes a non-technical explanation of your mathematical model that sports fans will understand.ICM PROBLEMPROBLEM C: Using Networks to Measure Influence and Impact Click the title below to download a PDF of the 2014 ICM Problem. Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.Using Networks to Measure Influence and Impact。

2014 年美国大学生数学建模竞赛MCM、ICM 试题2014 MCM A: The Keep-Right-Except-To-Pass RuleIn countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane.Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this rule effective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important.In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirements be needed.Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system –either part of the road network or imbedded in the design of all vehicles using the roadway – to what extent would this change the results of your earlier analysis?2014 MCM B: College Coaching LegendsSports Illustrated, a magazine for sports enthusiasts, is looking for the “best all time college coach” male or fem ale for the previous century. Build a mathematical model to choose the best college coach or coaches (past or present) from among either male or female coaches in such sports as college hockey or field hockey, football, baseball or softball, basketball, or soccer. Does it make a difference which time line horizon that you use in your analysis, i.e., does coaching in 1913 differ from coaching in 2013? Clearly articulate your metrics for assessment. Discuss how your model can be applied in general across both genders and all possible sports. Present your model’s top 5 coaches in each of 3 different sports.In addition to the MCM format and requirements, prepare a 1-2 page article for Sports Illustrated that explains your results and includes a non-technical explanation of your mathematical model that sports fans will understand.。

2014年数学建模美赛题目原文及翻译作者：Ternence Zhang转载注明出处：MCM原题PDF：PROBLEM A: The Keep-Right-Except-To-Pass RuleIn countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane.Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this ruleeffective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important.In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirements be needed.Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system –either part of the road network or imbedded in the design of all vehicles using the roadway –to what extent would this change the results of your earlier analysis?问题A：车辆右行在一些规定汽车靠右行驶的国家（即美国，中国和其他大多数国家，除了英国，澳大利亚和一些前英国殖民地），多车道的高速公路经常使用这样一条规则：要求司机开车时在最右侧车道行驶，除了在超车的情况下，他们应移动到左侧相邻的车道，超车，然后恢复到原来的行驶车道（即最右车道）。

2015年：A题一个国际性组织声称他们研发出了一种能够阻止埃博拉，并治愈隐性病毒携带者的新药。

建立一个实际、敏捷、有效的模型，不仅考虑到疾病的传播、药物的需求量、可能的给药措施、给药地点、疫苗或药物的生产速度，而且考虑你们队伍认为重要的、作为模型一部分的其他因素，用于优化埃博拉的根除，或至少缓解目前（治疗）的紧张压力。

除了竞赛需要的建模方案以外，为世界医学协会撰写一封1-2页的非技术性的发言稿，以便其公告使用。

B题回顾马航MH370失事事件。

建立一个通用的数学模型，用以帮助失联飞机的搜救者们规划一个有效的搜索方案。

失联飞机从A地飞往B地，可能坠毁在了大片水域（如大西洋、太平洋、印度洋、南印度洋、北冰洋）中。

假设被淹没的飞机无法发出信号。

你们的模型需要考虑到，有很多种不同型号的可选的飞机，并且有很多种搜救飞机，这些搜救飞机通常使用不同的电子设备和传感器。

此外，为航空公司撰写一份1-2页的文件，以便在其公布未来搜救进展的新闻发布会上发表。

2014美赛A题翻译问题一:通勤列车的负载问题在中央车站,经常有许多的联系从大城市到郊区的通勤列车“通勤”线到达。

大多数火车很长(也许10个或更多的汽车长)。

乘客走到出口的距离也很长，有整个火车区域。

每个火车车厢只有两个出口,一个靠近终端, 因此可以携带尽可能多的人。

每个火车车厢有一个中心过道和过道两边的座椅，一边每排有两个座椅，另一边每排有三个座椅。

走出这样一个典型车站,乘客必须先出火车车厢,然后走入楼梯再到下一个级别的出站口。

通常情况下这些列车都非常拥挤,有大量的火车上的乘客试图挤向楼梯，而楼梯可以容纳两列人退出。

大多数通勤列车站台有两个相邻的轨道平台。

在最坏的情况下,如果两个满载的列车同时到达,所有的乘客可能需要很长时间才能到达主站台。

建立一个数学模型来估计旅客退出这种复杂的状况到达出站口路上的时间。

假设一列火车有n个汽车那么长,每个汽车的长度为d。

站台的长度是p,每个楼梯间的楼梯数量是q。

Problem A: Hurricane preparednessThe recent super-storm Sandy was an unprecedented tragedy for the north-eastern coastal areas of the USA. Sandy and Irene (which occurred a year earlier) were both “100-year storms” (i.e., based on historical data, a storm of that strength has less than 1% probability of occurring on a given year). Both resulted in “100-year-floods” in New York City. Both have caused numerous casualties and damage in the billions of dollars.To protect the city of New York from floods, a group of scientists and engineers has recommended erecting several gigantic “sea gates” -- movable barriers that would be closed during hurricanes, preventing the storm surges from entering Hudson and East rivers. Such measures are quite expensive – the current rough estimates put construction costs at 10 billion dollars.To be realistic/conservative, you will assume a 20 billion construction cost + 500 million per year in additional costs (e.g., maintenance, security, impact on industry/trade/ecology) once they are built.a) Suppose Sandy never happened and that storms like Irene occur with probability P1=0.01 per year. Are the barriers economically justifiable?b) Many researchers have found that climate change and rising sea levels will dramatically increase the probability of such events in the future, making such costly flood-prevention measures more attractive. Find the lowest value of P1 that would justify erecting the sea gates to protect NYC.c) Suppose that Irene-strength storms happen with the annual probability of P1 while the corresponding annual probability of Sandy-strength storms is P2. Find all “lowest” (P1,P2) pairs that justify the sea gates.d) The high cost is not the only disadvantage of the sea gates. While protecting Manhattan and parts of other boroughs , they will likely also increase the flooding in several unprotected areas of Brooklyn, Queens and New Jersey. Develop a model for the future changes in real estate prices and/or population density in Breezy Point (Queens) and Manhattan Beach (Brooklyn) in the next 50/100 years. Your model should make predictions for two different scenarios (i.e., with and without sea gates).e) A preliminary version of your report somehow found its way to a journalist, who rushed to publicize the simulation results, alarming the general population & frustrating the engineers/scientists/authorities. Write a non-technical, half-page-long open “Letter to the Editor” to explain the limitations of your model‟s applicability.A few words of advice from the contest organizers:Always start with simpler models and then include additional features (and/or more realistic data) later – only if you have enough time.Much of the data you might need for your model can be easily found on the web.If the full problem is too long for your team, you can choose between solving subproblems (c) and (d).Several useful links (to save you some initial googling time):1)/Telegraph11-5.pdf2)/2012/09/11/nyregion/new-york-faces-rising-seas-and-slow-city-action.html3)/MESC/MESC%20distribution%20copy%2002-15-07.pdf4)/2012/11/04/opinion/sunday/deciding-where-future-disasters-will-strike.html5)/surgingseas/place/cities/NY/New_York6)/home_prices/New_York/Brooklyn-heat_map/7)/img/nyc_popdens_2010.pngProblem B: Explosion In Jellyfish PopulationsNuisance: A digger drops jellyfish cleared from the power station in Hadera, IsraelSlimy: Jellyfish cover the floor of the power station in IsaelDisruption: Containers filled with jellyfish at Orot Rabin coal-fired power stationA surge of jellyfish wreaked havoc in the U.S. during the co untry‟s big Fourth of July holiday weekend. Almost 2,000 beach-goers were stung as they celebrated Independence Day weekend in the surf at Volusia County, Florida. And in Israel a huge swarm clogged up the Orot Rabin power station in Hadera, a day after the Torness nuclear facility in Scotland was closed in a similar incident.Hadera ran into trouble when jellyfish blocked its seawater supply, which it uses for cooling purposes, forcing officials to use diggers to remove them.The report, published in December 2010 by the UN Environment Programme, warns that the acidification of oceans makes it harder for coral reefs and shellfish to form skeletons – threatening larger creatures that depend on them for food.The decline in creatures with shells could trigger an explosion in jellyfish populations. The report, written by Dr Carol Turley of Plymouth University, said: …Ocean acidification has also been tentatively linked to increased jellyfish numbers and changes in fish abundance.Jellyfish are immune to the effects of acidification. As other species decline, jellyfish will move in to fill the ecological niche.Populations have boomed at the seaside in recent years. Some marine scientists say the changing chemistry of the sea is to blame.Requirement 1: Present a mathematical model to explain why surge in the number of jellyfish.Requirement 2: Verify your model.Requirement 3: what is the total weight of the global jellyfish?Requirement 4: According to your conclusion, to control the number of jellyfish，what measures need to be taken to?。

2014年美赛数学建模A题翻译版论文D流入模型,或vehicle-generation模型,模拟了随机到达高速公路的入口处的车辆。

对于每一个车道,前六个细胞在元胞自动机中设置为vehicle-generation区域。

我们假设每辆车的到达服从二项概率分布。

让ts表示采样时间间隔和N表示在ts时间内车辆的总数。

然后N可以近似服从泊松概率分布。

让Pt(N)表示N的可能性，于是我们有ts表示在一秒,我们可以分配N的期望的值的范围从0到3.6。

N作为在每一秒中到达的总车辆,N的期望能有效地反映交通状况。

λ越小,交通越轻松。

因此我们能够模拟不同流量条件下,交通的轻或重,通过分配相应的值λ。

λ的值设定后,我们得到了进入高速公路的车辆模拟每一秒的随机号码。

每个车道然后随机分配进入。

我们的车辆模型支持两种不同的速度范围, 假设所有车辆的初始速度设置为20 m / s。

这种做法带来了简化而不削弱结果。

这是因为由于交通密度控制和加速度的分布概率的引入，所有车辆的速度往往是一个值。

当交通密度低,车辆可以自由加速到最大速度,而不用担心冲突,因此收敛速度在允许的最高速度而不用担心撞车。

当交通密度高,所有的通道将充满车辆,交通流的速度是由车道上速度最慢的车决定,因此收敛速度是在较低的速度限制。

经过初步分析，收敛速度模型稍后将合理的实现。

利用泊松概率分布使流入模型接近现实和实用。

由于收敛趋势,一样的初速度在不改变的情况下就能得到简化。

2.3 Vehicle-Following Model美国联邦公路管理局的部门定义司机的反应时间PIEV时间。

PIEV时间由四部分组成:•感知过程:司机在驾驶环境中感知的变化。

•理解过程:司机分析关于变化的信息。

•评估过程:司机决定根据他的驾驶行为分析。

•意志过程:司机执行驾驶行为我们应用PIEV在匀速行驶模型和超车模型。

在每次循环中,我们首先获得每辆车的速度和位置，计算差距，然后确定驾驶行为(无论继续或改变车道超车后)。