2019美赛建模A题
2019年数学建模国赛a题目
2019年数学建模国赛A题目一、题目背景2019年数学建模国际赛A题目是建立在武汉市轨道交通运行时刻表数据上的模型研究。
轨道交通是城市快速、高效、环保的交通方式，为城市居民提供了便捷的出行方式。
而轨道交通的运行时刻表则对乘客的出行、等待时间等方面有着重要的影响。
研究轨道交通的运行时刻表对于优化城市交通运输系统，提高运输效率，改善城市居民的生活质量具有重要意义。
二、题目要求本题目要求选手建立数学模型研究武汉市轨道交通运行时刻表数据。
具体要求包括以下几点：1. 分析武汉市轨道交通的运行时刻表数据，并找出其中的规律和特点。
2. 建立数学模型，预测武汉市轨道交通在不同时间段的客流量。
3. 对轨道交通的运行时刻表进行优化，提出有效的调度方案。
三、题目分析1. 分析武汉市轨道交通的运行时刻表数据，需要选手具备分析大数据的能力和技巧，掌握数据挖掘、数据处理等相关知识。
2. 建立数学模型，需要选手熟练运用数学建模方法，如统计分析、回归分析、时间序列分析等。
3. 对轨道交通的运行时刻表进行优化，需要选手具备系统优化和调度的能力，能够结合数学模型和实际情况，提出合理的调度方案。
四、解题思路1. 选手需要对武汉市轨道交通的运行时刻表数据进行深入分析，了解不同线路、不同时间段的客流量分布情况，找出规律和特点。
2. 选手可以运用统计分析和回归分析的方法，建立数学模型，预测武汉市轨道交通在不同时间段的客流量。
3. 选手可以结合实际情况，提出针对性的调度方案，对轨道交通的运行时刻表进行优化。
五、题目意义本题目旨在培养选手的数据分析和数学建模能力，帮助选手提高解决实际问题的能力和水平。
通过研究轨道交通的运行时刻表数据，可以为城市交通运输系统的优化提供重要参考，促进城市交通运输领域的发展。
六、总结2019年数学建模国际赛A题目是一个具有一定难度和挑战性的题目，要求选手具备扎实的数学和数据分析基础，具备较强的综合应用能力和创新思维能力。
2019年美国大学生数学建模竞赛B题
2019 MCMProblem B: Send in the Drones: Developing an Aerial Disaster Relief Response SystemBackground: In 2017, the worst hurricane to ever hit the United States territory of Puerto Rico (see Attachment 1) left the island with severe damage and caused over 2900 fatalities. The combined destructive power of the hurricane’s storm surge and wave action produced extensive damage to buildings, homes, and roads, particularly along the east and southeast coast of Puerto Rico. The storm, with its fierce winds and heavy rain, knocked down 80 percent of Puerto Rico's utility poles and all transmission lines, resulting in loss of power to essentially all of the island's 3.4 million residents. In addition, the storm damaged or destroyed the majority of t he island’s cellular communication networks. The electrical power and cell service outages lasted for months across much of the island, and longer in some locations. Widespread flooding blocked and damaged many highways and roads across the island, making it nearly impossible for emergency services ground vehicles to plan and navigate their routes. The full extent of the damage in Puerto Rico remained unclear for some time; dozens of areas were isolated and without communication. Demands for medical supplies, lifesaving equipment, and treatment strained health-care clinics, hospital emergency rooms, and non-governmental organizations’ (NGOs) relief operations. Demand for medical care continued to surge for some time as the chronically ill turned to hospitals and temporary shelters for care.Problem: Non-governmental organizations (NGOs) are often challenged to provide adequate and timely response during or after natural disasters, such as the hurricane that struck the United States territory of Puerto Rico in 2017. One NGO in particular – HELP, Inc. - is attempting to improve its response capabilities by designing a transportable disaster response system called “DroneGo.” DroneGo will use rotor wing drones to deliver pre-packaged medical supplies and provide high-resolution aerial video reconnaissance. Selected drones should be able to perform these two missions – medical supply delivery and video reconnaissance – simultaneously or separately, depending on relief conditions and scheduling. HELP, Inc. has identified various candidate rotor wing drones that it would like your team to consider for possible use in designing its DroneGo fleet (see Attachments 2, 3).DroneGo’s pre-packaged medical supplies, called medical packages, are meant to augment, not replace, the supplies provided by local medical assistance organizations on-site within the country affected by the disaster. HELP, Inc. is planning on three different medical packages referred to as MED1, MED2, and MED3. Drones will carry these medical packages within drone cargo bays for delivery to selected locations (see Attachments 4, 5). Depending on the specific drone being used to transport medical supplies, it may be possible that multiple medical packages can be transported in a single drone cargo bay. Note that drones must land on the ground to offload medical supplies from the drone cargo bays. The video capability of the drones will provide high-resolution video of damaged and serviceable transportation road networks to HELP, Inc.’s command and contro l center for ground-based route planning.HELP, Inc. will use International Standards Organization (ISO) standard dry cargo containers to quickly transport a complete DroneGo disaster response system to a particular disaster area. The individual shipping containers for all drones in the DroneGo fleet, along with all requiredmedical packages, must fit within a maximum of three of the ISO cargo containers to be delivered to a single location, or up to three different locations if three cargo containers are used in the disaster area. Each shipping container’s contents should be packed in order to minimize any need for buffer materials for unused space. Table 1 shows the dimensions of an ISO standard dry cargo container.Table 1. Standard ISO Container DimensionsExterior Interior Door OpeningLength Width Height Length Width Height Width Height 20’20’8’8’6”19’3”7’8”7’ 10”7’8”7’5”StandardDryContainerHELP, Inc. is asking your team to use the 2017 situation in Puerto Rico to design a DroneGo disaster response system that will fit within the containers noted while meeting the anticipated medical supply demands during a potential similar future disaster scenario. It is possible that the demand requirements of this scenario may exceed the capabilities of the drone fleet your team identifies. If this occurs, HELP, Inc. wants to clearly understand any tradeoffs that it must make for implementing solutions to address these shortcomings.Part 1. Develop a DroneGo disaster response system to support the Puerto Rico hurricane disaster scenario.Consider the background information, the requirements identified in the problem statement, and the information provided in the problem attachments to address the following.A.Recommend a drone fleet and set of medical packages for the HELP, Inc. DroneGodisaster response system that will meet the requirements of the Puerto Rico hurricanescenario. Design the associated packing configuration for each of up to three ISO cargocontainers to transport the system to Puerto Rico.B.Identify the best location or locations on Puerto Rico to position one, two, or three cargocontainers of the DroneGo disaster response system to be able to conduct both medicalsupply delivery and video reconnaissance of road networks.C.For each type of drone included in the DroneGo fleet:a.Provide the drone payload packing configurations (i.e. the medical packagespacked into the drone cargo bay), delivery routes and schedule to meet the identifiedemergency medical package requirements of the Puerto Rico hurricane scenario.b.Provide a drone flight plan that will enable the DroneGo fleet to use onboardvideo cameras to assess the major highways and roads in support of the Help, Inc.mission.Part 2. MemoWrite a 1–2 page memo to the Chief Operating Officer (CEO) of HELP, Inc. summarizing your modeling results, conclusions, and recommendations so that she can share with her Board of Directors.Your MCM team submission should consist of:∙One-page Summary Sheet,∙One- to Two-page memo to the HELP, Inc. CEO∙Your solution of no more than 20 pages, for a maximum of 23 pages with your summary and memo.∙Note: Reference list and any appendices do not count toward the 23-page limit and should appear after your completed solution.Attachments:1.Map of Puerto Rico2.Potential Candidate Drones for DroneGo Fleet Consideration (with Drone payloadcapability)3.Drone Cargo Bay Packing Configuration/Dimensions by Type4.Anticipated Medical Package Demand5.Emergency Medical Package Configuration/DimensionsAttachment 1: Map of Puerto RicoAttachment 2: Potential Candidate Drones for DroneGo Fleet Consideration (with Drone Payload Capability)Shipping ContainerDimensions PerformanceCharacteristics/CapabilitiesConfigurations CapabilitiesDroneLength (in.) Width (in.) Height (in.) Max PayloadCapability(lbs.) Speed(km/h)Flight Time No Cargo (min)Video Capable Medical Package Capable Drone Cargo Bay Type* A 45 45 25 3.5 40 35 Y Y 1 B 30 30 22 8 79 40 Y Y 1 C 60 50 30 14 64 35 Y Y 2 D 25 20 25 11 60 18 Y Y 1 E 25 20 27 15 60 15 Y Y 2 F 40 40 25 22 79 24 N Y 2 G 32 32 17 20 64 16 Y Y 2 H Tethered657541N/AN/AIndefiniteNNN/A*Note that cargo bays are affixed to the drone and that drone must be on the ground to offload cargo. SeeAttachment 3 for Drone Cargo Bay Type Configuration/Dimensions.Attachment 3: Drone Cargo Bay Packing Configuration/Dimensions by TypeDrone Cargo Bay Type Length (in) Width (in) Height (in)1 8 10 14 Top Loaded2 24 20 20 Top Loaded Attachment 4: Anticipated Medical Package DemandDelivery Location Emergency Medical Packages ** Location Name Latitude Longitude Requirement Quantity FrequencyCaribbean Medical Center 18.33 -65.65 MED 1 1 DailyJajardo MED 3 1 DailyHospital HIMA 18.22 -66.03 MED 1 2 DailySan Pablo MED 3 1 Daily Hospital Pavia Santurce 18.44 -66.07 MED 1 1 DailySan Juan MED 2 1 Daily Puerto Rico Children's Hospital 18.40 -66.16 MED 1 2 DailyBayamon MED 2 1 DailyMED 3 2 Daily Hospital Pavia Arecibo 18.47 -66.73 MED 1 1 DailyArecibo**See Attachment 5 for Emergency Medical Packages 1, 2, and 3 Configurations/Dimensions.A ttachment 5: Emergency Medical Package Configuration/DimensionsEmergency Medical Package ConfigurationPackage ID Weight(lbs.)Package Dimensions(in.)(L × W × H)MED 1 2 14 × 7 × 5 MED 2 2 5 × 8 × 5 MED 3 3 12 × 7 × 4Glossary:Cargo Container (Shipping Container): a large rectangular container with doors on the ends for loading and packing, and made of material suitable for shipping, storing, and handling in many weather and climate conditions.Drone (Unmanned Aerial Vehicle, UAV): a flying robot that can be remotely controlled or fly autonomously through software-controlled flight plans in their embedded systems that work in conjunction with onboard sensors and GPS.Drone Cargo Bay: For rotor wing drones, this is an externally carried “box” used to transport materials. For this problem, the drones under consideration have one of two types (sizes) of cargo bays. Note that each drone must land for the medical packages to be unloaded from the bay at its destination.Drone Fleet: a set of drones for a particular mission or purpose. For this problem, the total set of drones by type (A to H) and Payload Capability (Visual and Medical) needed to meet the requirements of HELP, Inc.Drone Payload Packing Configuration: how the drone payload bays are packed. For this problem, how the medical packages being transported by a drone are packed inside the drone cargo bay.Medical Package: a predetermined set of medical supplies packed in a single container. For this problem, there are three Medical Package Configurations (MED1, MED2, MED3) available for transport by a drone from a deployed cargo container location to the demand location.Non-governmental Organization (NGO): Usually non-profit and sometimes international organization independent of government and governmental organizations that is active in humanitarian, educational, healthcare, social, public policy, human rights, environmental and other areas in attempts to affect change.Payload Capability: the carrying capacity of an aircraft or launch vehicle, usually measured in terms of weight. For this problem, the capability/capacity of the drone to carry medical packages.。
美赛数学建模A题翻译版论文
美赛数学建模A题翻译版论文The document was finally revised on 2021数学建模竞赛(MCM / ICM)汇总表基于细胞的高速公路交通模型自动机和蒙特卡罗方法总结基于元胞自动机和蒙特卡罗方法,我们建立一个模型来讨论“靠右行”规则的影响。
首先,我们打破汽车的运动过程和建立相应的子模型car-generation的流入模型,对于匀速行驶车辆，我们建立一个跟随模型,和超车模型。
然后我们设计规则来模拟车辆的运动模型。
我们进一步讨论我们的模型规则适应靠右的情况和,不受限制的情况, 和交通情况由智能控制系统的情况。
我们也设计一个道路的危险指数评价公式。
我们模拟双车道高速公路上交通(每个方向两个车道,一共四条车道),高速公路双向三车道（总共6车道)。
通过计算机和分析数据。
我们记录的平均速度,超车取代率、道路密度和危险指数和通过与不受规则限制的比较评估靠右行的性能。
我们利用不同的速度限制分析模型的敏感性和看到不同的限速的影响。
左手交通也进行了讨论。
根据我们的分析,我们提出一个新规则结合两个现有的规则(靠右的规则和无限制的规则)的智能系统来实现更好的的性能。
1介绍术语假设2模型设计的元胞自动机流入模型跟随模型超车模型超车概率超车条件危险指数两套规则CA模型靠右行无限制行驶规则3补充分析模型加速和减速概率分布的设计设计来避免碰撞4模型实现与计算机5数据分析和模型验证平均速度快车的平均速度密度超车几率危险指数6在不同速度限制下敏感性评价模型7驾驶在左边8交通智能系统智能系统的新规则模型的适应度智能系统结果9结论10优点和缺点优势弱点引用附录。
1 Introduction今天,大约65%的世界人口生活在右手交通的国家和35%在左手交通的国家交通流量。
[worldstandards。
欧盟,2013] 右手交通的国家,比如美国和中国,法规要求驾驶在靠路的右边行走。
多车道高速公路在这些国家经常使用一个规则,要求司机在最右边开车除非他们超过另一辆车,在这种情况下,他们移动到左边的车道、通过，返回到原来的车道。
2019年数学建模国赛A题
2019高教社杯全国大学生数学建模竞赛题目（请先阅读“全国大学生数学建模竞赛论文格式规范”）A题高压油管的压力控制燃油进入和喷出高压油管是许多燃油发动机工作的基础，图1给出了某高压燃油系统的工作原理，燃油经过高压油泵从A处进入高压油管，再由喷口B喷出。
燃油进入和喷出的间歇性工作过程会导致高压油管内压力的变化，使得所喷出的燃油量出现偏差，从而影响发动机的工作效率。
图1 高压油管示意图问题1. 某型号高压油管的内腔长度为500mm，内直径为10mm，供油入口A处小孔的直径为1.4mm，通过单向阀开关控制供油时间的长短，单向阀每打开一次后就要关闭10ms。
喷油器每秒工作10次，每次工作时喷油时间为2.4ms，喷油器工作时从喷油嘴B处向外喷油的速率如图2所示。
高压油泵在入口A处提供的压力恒为160 MPa，高压油管内的初始压力为100 MPa。
如果要将高压油管内的压力尽可能稳定在100 MPa左右，如何设置单向阀每次开启的时长？如果要将高压油管内的压力从100 MPa增加到150 MPa，且分别经过约2 s、5 s和10 s的调整过程后稳定在150 MPa，单向阀开启的时长应如何调整？图2 喷油速率示意图问题2. 在实际工作过程中，高压油管A处的燃油来自高压油泵的柱塞腔出口，喷油由喷油嘴的针阀控制。
高压油泵柱塞的压油过程如图3所示，凸轮驱动柱塞上下运动，凸轮边缘曲线与角度的关系见附件1。
柱塞向上运动时压缩柱塞腔内的燃油，当柱塞腔内的压力大于高压油管内的压力时，柱塞腔与高压油管连接的单向阀开启，燃油进入高压油管内。
柱塞腔内直径为5mm，柱塞运动到上止点位置时，柱塞腔残余容积为20mm3。
柱塞运动到下止点时，低压燃油会充满柱塞腔（包括残余容积），低压燃油的压力为0.5 MPa。
喷油器喷嘴结构如图4所示，针阀直径为2.5mm、密封座是半角为9°的圆锥，最下端喷孔的直径为1.4mm。
针阀升程为0时，针阀关闭；针阀升程大于0时，针阀开启，燃油向喷孔流动，通过喷孔喷出。
【2019年整理】全国大学生数学建模竞赛a题题目及参考答案-2019建模a题
2011高教社杯全国大学生数学建模竞赛题目（请先阅读“全国大学生数学建模竞赛论文格式规范”）A题城市表层土壤重金属污染分析随着城市经济的快速发展和城市人口的不断增加，人类活动对城市环境质量的影响日显突出。
对城市土壤地质环境异常的查证，以及如何应用查证获得的海量数据资料开展城市环境质量评价，研究人类活动影响下城市地质环境的演变模式，日益成为人们关注的焦点。
按照功能划分，城区一般可分为生活区、工业区、山区、主干道路区及公园绿地区等，分别记为1类区、2类区、……、5类区，不同的区域环境受人类活动影响的程度不同。
现对某城市城区土壤地质环境进行调查。
为此，将所考察的城区划分为间距1公里左右的网格子区域，按照每平方公里1个采样点对表层土（0~10 厘米深度）进行取样、编号，并用GPS记录采样点的位置。
应用专门仪器测试分析，获得了每个样本所含的多种化学元素的浓度数据。
另一方面，按照2公里的间距在那些远离人群及工业活动的自然区取样，将其作为该城区表层土壤中元素的背景值。
附件1列出了采样点的位置、海拔高度及其所属功能区等信息，附件2列出了8种主要重金属元素在采样点处的浓度，附件3列出了8种主要重金属元素的背景值。
现要求你们通过数学建模来完成以下任务：(1) 给出8种主要重金属元素在该城区的空间分布，并分析该城区内不同区域重金属的污染程度。
(2) 通过数据分析，说明重金属污染的主要原因。
(3) 分析重金属污染物的传播特征，由此建立模型，确定污染源的位置。
(4) 分析你所建立模型的优缺点，为更好地研究城市地质环境的演变模式，还应收集什么信息？有了这些信息，如何建立模型解决问题？题 目 A 题 城市表层土壤重金属污染分析摘 要：本文研究的是某城区警车配置及巡逻方案的制定问题，建立了求解警车巡逻方案的模型，并在满足D1的条件下给出了巡逻效果最好的方案。
在设计整个区域配置最少巡逻车辆时，本文设计了算法1：先将道路离散化成近似均匀分布的节点，相邻两个节点之间的距离约等于一分钟巡逻路程。
2019美国大学生数学建模竞赛赛前模拟成绩
队号成绩评语C_M0148一等奖论文整体模型较好，能解决好问题，有进行改进，图表可视化较好，在正式比赛中为 Finalist 特等奖候选奖B_M0066一等奖能较好地解决问题，需要加强图表的可视化，模型较好地解决问题，在正式比赛中为 Meritorious Winner 一等奖C_M0055一等奖论文整体模型较好，能解决好问题，有进行改进，图表可视化较好，在正式比赛中为 Meritorious Winner 一等奖D_M0138二等奖摘要过长，超过了一页，需要加强可视化，参考文献过少，在正式比赛中为二等奖 Honorable Mentions 奖B_M0135二等奖摘要过长，需要加强可视化，在正式比赛中为二等奖Honorable Mentions 奖B_M0139二等奖需要加强图表的可视化，模型较好地解决问题，在正式比赛中为 Meritorious Winner 一等奖B_M0145二等奖摘要过长，超过了一页，需要加强可视化，参考文献过少，在正式比赛中为二等奖 Honorable Mentions 奖B_M0146二等奖摘要过短，模型简单，需要加强可视化，在正式比赛中为二等奖 Honorable Mentions 奖B_M0157二等奖模型简单，可视化较好，在正式比赛中为二等奖 HonorableMentions 奖C_M0109二等奖模型简单，需要加强可视化，在正式比赛中为二等奖Honorable Mentions 奖B_M0018三等奖公式截图来自文献，均没有正确引用，全文没解决问题，图表也大部分截图来自参考文献，需要注意学术道德规范，在正式比赛中为Unsuccessful Participant 不成功参赛B_M0019三等奖摘要过短，模型过于简单，行间距过大，所做工作较少，在正式比赛中为 Successfully Participation 成功参与奖B_M0076三等奖论文格式不正确，不完整，论文没有完成，在正式比赛中为Successfully Participation 成功参与奖B_M0132三等奖摘要过短，模型过于简单，需要加强可视化，在正式比赛中为二等奖 Honorable Mentions 奖B_M0142三等奖摘要过短，模型过于简单，需要加强可视化，在正式比赛中为 Successfully Participation 成功参与奖B_M0153三等奖模型过于简单，需要加强可视化，在正式比赛中为二等奖Honorable Mentions 奖B_M0154三等奖图片不要截图，模型过于简单，需要加强可视化，在正式比赛中为二等奖 Honorable Mentions 奖B_M0159三等奖摘要过长，超过了一页，需要加强可视化，参考文献过少，在正式比赛中为二等奖 Honorable Mentions 奖C_M0038三等奖论文格式不正确，不符合比赛要求，模型简单，在正式比赛中为 Unsuccessful Participant 不成功参赛2019美国大学生数学建模竞赛赛前模拟成绩C_M0137三等奖摘要过短，模型简单，需要加强可视化，在正式比赛中为二等奖 Honorable Mentions 奖C_M0152三等奖第一问不是画出所有的图，模型过于简单，需要加强可视化，在正式比赛中为 Successfully Participation 成功参与奖C_M0156三等奖模型过于简单，需要加强可视化，在正式比赛中为Successfully Participation 成功参与奖C_M0160三等奖模型简单，需要加强可视化，在正式比赛中为二等奖Honorable Mentions 奖D_M0067三等奖不要截图，太模糊，模型过于简单，需要加强可视化，在正式比赛中为 Successfully Participation 成功参与奖D_M0128三等奖公式不要截图，模型简单，考虑因素较少，需要加强可视化，在正式比赛中为二等奖 Honorable Mentions 奖D_M0134三等奖模型简单，需要加强可视化，在正式比赛中为二等奖Honorable Mentions 奖D_M0150三等奖公式截图来自文献，均没有正确引用，全文没解决问题，图表也大部分截图来自参考文献，需要注意学术道德规范，在正式比赛中为 Unsuccessful Participant 不成功参赛D_M0190三等奖论文排版非常糟糕，公式截图来自文献，均没有正确引用，全文没解决问题，图表也大部分截图来自参考文献，需要注意学术道德规范，在正式比赛中为 Unsuccessful Participant 不成功参赛E_M0155三等奖摘要不符合要求，模型简单，需要加强可视化，在正式比赛中为二等奖 Honorable Mentions 奖F_M0144三等奖摘要过短，模型简单，需要加强可视化，在正式比赛中为二等奖 Honorable Mentions 奖B_M0212不成功参赛论文抄袭，并且不是本赛题的内容，严重违规，在正式比赛中为 Unsuccessful Participant 不成功参赛。
美赛A题讲解
4）位置更新规则： xi xi vi
车辆换道规则设计
“右行左超车”下的双车道换道规则
由于高速路上车速相对较高，因此，考虑到安全性的 因素，借鉴文献【1】中的换道规则，提出如下双车道 换道规则：
1）车辆由右向左变道规则。如果当前在右车道行驶的车辆 与前车的间距较小使得当前车辆的前行受阻，而其与相邻左 车道上的前车间距较大，同时与左车道上后方车辆的间距 大于安全距离，则车辆以概率 P 0 由右向左变道，即
元胞自动机的微观规则设计
首先研究高速路一个方向两车道的超车问题。假设每一 车道分为1000个元胞，则2条车道划分为 21000 的元胞矩阵
定义每个元胞长度为5.5米，则模拟的实际道路长度为5.5km。
仿真的时间，步设为1秒。一个元胞的全部状态用一个5元组 表示： （ vi (t), xi (t), wi (t),ci (t), d i ( t ) ） 5个状态参数分别为：第i辆车在t时刻的速度，所处元胞
4、考虑到不同驾驶员的驾驶行为有所差异，车辆状态 的改变具有一定的随机性，因此，假设在行车过程中， 所有车辆状态的改变都按一定的概率发生。
5、在仿真过程中，通过在一个预先设定的区域，用定量 的汽车采用循环的方式来模拟整个高速交通情况。仿真路 段内汽车数量即车辆密度是常数，但是将对不同的密度进 行仿真。
2、是否存在更好的交通规则，如果存在，如何说明其更好。 3、新规则是否适合靠左行驶的国家，是否需要考虑其他因素。 4、在智能系统的控制下，上述规则表现如何，结果有何变化。 注：对该问题的研究可以归结为“右行左超车”规则下的交通
流模型的研究。
模型建立-元胞自动机模型
对于交通问题的研究中最经典的模型有跟车模型、流体 力学模型和元胞自动机模型。
2019美赛数学建模A题论文
Winter is approaching, may the dragon’s wings grow moreabundantSummaryIn the game of thrones, Daenerys Targaryen depicts the image of a dragon. In eastern and western cultures, the phenomenon of dragons is not uncommon. If dragons live in modern society, how can we raise these war monsters? Research, and applied the cross disciplines of biology, physics, and chemistry to build a mathematical model and solve it to achieve the maximum growth of the dragon. Of course, dragons do not exist in real life, so we likened pterosaurs, modern Aircraft and chemical burner to derive the specific physiological characteristics of the dragon to ensure the rationality and scientificity of the research.First, we studied the flight and fire-spitting models of dragons. Through analogical reasoning, our hypothetical dragon's fire-spitting principle is similar to modern alcohol flamethrowers. For dragon flight, we used fluid mechanics to get the dragon's flight speed. And glucose energy loss. Combining the two to get the energy loss model of the dragon. Second, we studied the basic physical characteristics of the dragon. For the relationship between the body length and body age of the dragon, we established an elastic model of growth. Because the weight and body length of dragons have upper and lower limits, in order to comply with basic ecology, we have defined the dragon's bone saturation value as the cut-off value, and conducted a segmented study. When studying the relationship between weight and body length, We know that the weight of the dragon is proportional to the cube of the body length. Then, because the dragon needs resources to replenish like other animals, we built a dragon's food supply model. Suppose that the three dragons have the same competitiveness and the daily sheep Resources are the same. According to ecology, when the number of sheep in a certain area reaches k / 2, we need to migrate the dragon. Finally, the temperature will affect the living environment of the dragon, so the dragon needs to followMigration was selected for changes in temperature, and we selected three areas of drought, cold, and warmth to study the dragon, and integrated the model of the regional area of the dragon by the appealing model.In addition, we wrote a letter to the author of the Song of Ice and Fire, giving some suggestions on the actual ecological foundation of the dragon, hoping to be adopted. Although the dragon does not exist in our real life, the dragon can be broken down into Part of our modern society. For the dragon's flying spitfire energy loss model, we can further study the aircraft's fluid mechanics and modern flamethrowers. The study of non-existent organisms also prepares us for the arrival of new species .table of ContentsWinter is approaching, may the dragon’s wings grow more abundant (1)Summary (1)table of Contents (2)1 Introduction (3)1.1 restatement (3)1.2 Problem Analysis (3)2 Assumptions and reasons (4)3 Symbol Definition (4)4. Mathematical modeling (5)4.1 About Dragon Flight and Spitfire Consumption (5)4.2 About the relationship between dragon's body length and weight and age (7)4.3 About Dragon's Food Supply (8)4.4 Regulating the area of dragons by region (9)5 Sensitivity analysis (10)6 Model evaluation and outlook (11)6.1 Model evaluation (11)6.2 Further discussion (12)7 to a letter from George RR Martin (12)8.Appendix: (13)8.1 References (13)8.2 Matlab code (13)1 Introduction1.1 restatementIn the magical TV series "Game of Thrones", Daenerys Targaryen, known as the Mother of Dragons, raised three dragons as an aggressive army. Dragons have always been the most mysterious monsters in Eastern and Western cultures, but if Dragons live in the present era, how should we feed the three dragons in pursuit of maximum growth? In this article, we assume that the growth rules of dragons are in line with basic biology. To study them, we build mathematical models to solve problem.a. Analyze the change of the dragon's weight length with age, and estimate the value of the dragon's weight length corresponding to the age group.b. Investigate the loss of self energy during dragon fire, flight, and breathing, so as to estimate the minimum supply value of dragon for external activitiesc. Dragons need food and survival areas like other animals in the real world. Through certain assumptions and calculations, we can determine the total amount of food that dragons need daily and the size of living areas in three areas.d. Sensitivity analysis: As temperature and climate change, dragons will also migrate to different regions. Therefore, we need to analyze the differences in the impact of dragons on the survival of arid regions, temperate regions, and cold regions.1.2 Problem AnalysisBecause dragons do not exist in real life, we need to use some things in the real world to compare dragons in order to achieve the purpose of studying dragons. In analyzing the biological morphological characteristics of dragons, we use the knowledge of ecology and basic elements of biology Let's conceive the basic biological characteristics of the dragon such as weight and body length. For the energy loss model of the dragon, we have studied three aspects to describe its loss. Here we compare the modern flamethrower and establish related chemical equations to achieve the research of the dragon. Spitfire loss. In addition, in TV series such as "Game of Thrones" we will find that dragons can fly in common sense, so we have derived the dragon's flight loss. Of course, all aerobic organisms can breathe. Dragons are no exception, so there is a loss of breathing to maintain body temperature. At the same time, in order to make up for the loss of dragons in daily activities, we have established a material reserve model, in which materials are cattle and sheep in real life, etc. Finally, during the cyclical changes in climate and food, the dragons we feed will also migrate to some extent, so we analyzed the impact of different regions on the growth of dragons.Into account various factors that we can more scientific training of dragons, have achieved our purpose.2 Assumptions and reasonsAfter a comprehensive analysis of the problem, in order to increase the enforceability, we make the following assumptions to ensure the rationality of our model establishment.2.1 Assumptions: The basic biological characteristics of dragons are in line with the law of biological growth. In modern life, the growth and development of dragons should also be similar to other animals and conform to basic biology.2.2 Assumption: The dragon will spit fire and fly, and its flight conforms to the physical environment of fluid mechanicsReason: In Game of Thrones, the image of the dragon was once able to fly and spit fire.2.3 Assumption: In the single field we are studying, the environment of a certain area will not change abruptly and maintain a dynamic stability.2.4 Hypothesis: Dragons are top predators in the food chain, but dragons do not cause devastating harm to the biosphere.2.5 Assumption: The weight distribution of the dragon is uniform, and the body length reaches 30 to 40 cm at the time of birth.Reason 2.6: We refer to ancient biology and some dinosaur fossils.2.7 Hypothesis: Except for the skull, heart, liver, lungs, kidneys, bones, etc., the sum of other body masses is proportional to the cube of height.Reason: The hypothesis is obtained by counting the relationship between body length and weight of modern organisms.2.8 Hypothesis: The dragon is a constant temperature animal whose body temperature is not affected by external factors.Reason: A few pterosaur fossils have traces of "hair" on the surface, while the dragons in Game of Thrones are similar to pterosaurs.2.9 Hypothesis: The dragon is fully aerobic during the flight to provide energy2.10 Hypothesis: A certain fixed ratio of the amount of energy that is not assimilated by the growth and metabolism of the dragon's breathing and other organisms2.11 Hypothesis: Dragon's Flight Similar to Modern Fighter3 Symbol Definition4. Mathematical modeling4.1 About Dragon Flight and Spitfire Consumption4.1.1 Proposed modelConsidering that dragons fly and spit fire during activities, we have established an energy loss model. Comparing the principle of dragon's spitfire with modern flamethrowers, modern flamethrowers consume hydrocarbons or alcohols. It does not cause any impact, so the dragon's fire-breathing principle is in line with the alcohol flame-thrower principle. Considering that the formaldehyde produced by the metabolism of methanol in the animal body is harmful to the body, we stipulate that ethanol is the fuel used by the dragon's flame. In the process, the relationship between the dragon's flight speed and glucose energy consumption is obtained according to fluid mechanics. In this process, we assume that the aerobic respiration is completely performed, and the energy consumed by the dragon due to flight is obtained according to the glucose consumption. In summary, the dragon energy loss model is obtained. .4.1.2 Establishment and Solution of Dragon's Spitfire ModelThe thermochemical equation for ethanol combustion is: C2H5OH (l) + 3O2 (g) = 2CO2 (g) + 2H2O (l) △H = -12KJ / gSpecify the energy released per unit mass of ethanol combustion x1When the dragon spit fire in unit time t, the unit mass of ethanol consumption is a fixed valueThe energy consumed by the fire time t1 is w1The mass consumed by the fire time T1 is m4Let the energy emitted by the combustion of unit mass of ethanol be w1 'Then W1 = x1 * tm4=W1/W1’Solve m4 = x1 * t / W1 '4.1.3 Establishment and Solution of Dragon Flight ModelDuring the flight of the dragon, it will be affected by the air resistance. In the ideal situation, the dragon's flight can be considered as a uniform acceleration and then a uniform speed, and it will decelerate when it is about to reach its destination.When Long uniform acceleration is specified, the acceleration is aSince the flight of the dragon is similar to that of a fighter, a = 30m / s ^ 2The speed of the dragon during uniform motion is v0The total flight length of the dragon during flight is sBecause air resistance is proportional to the speed of movement, that is, F1 = k * v (where k is a constant)Since the dragon's flight is similar to an airplane, we can get k = 3.2325Available according to the relevant kinematic formulaThe flying distance of the dragon during uniform acceleration is s1 = (v0) ^ 2 / 2aThe flying distance of the dragon during uniform deceleration is s3 = (v0) ^ 2 / 2aThe flying distance of the dragon during uniform motion is s2 = s-s1-s3Average air resistance during uniform acceleration F1 '= k * (0 + v0) / 2The average air resistance during uniform motion is F1 '' = k * v0Average air resistance during uniform deceleration f1 '' '= k * (v0 + 0) / 2According to the law of conservation of energyThe energy w2 consumed by the dragon during flight is all used for air resistance workW2=F1’*s1+F1’’*s2+F1’’’*s3Solve W2 = 3.2325 * v0 * s-3.2325 * (v0) ^ 3 / (2 * 30)During the flight of the dragon, the principle of energy provided by aerobic respiration isC6H12O6+6O2=6CO2+6H2OAmong them, the energy produced when 1g of glucose is completely consumed is 16KJThen the weight consumed in this process is m6 = W2 / 16[v,s]=meshgrid(0:0.1:100;0:0.1:100);m=3.2325*v*s-3.2325*v^3/60mesh(v,s,m)4.2 About the relationship between dragon's body length and weight and age4.2.1 Proposed ModelFirst, in order to study the relationship between the weight, length, and age of the dragon, that is, morphological characteristics, we established a model of elasticity during growth. The above-mentioned change curve is continuous, so we use the weight of the dragon at birth, and consider the weight and length of the dragon. The relationship between age changes can be used to derive the normal weight and body length of dragons in all ages. When analyzing the weight changes of dragons, biological knowledge shows that the amount of assimilation of the dragon is equal to the intake amount minus the amount of unassimilated amount Considering that the growth rate of the dragon in adulthood is a watershed, we use the saturation value of the dragon's head, heart, and liver as a cutoff value to estimate the relationship between the dragon's weight and age, respectively. When studying the body length of the dragon, according to the existing morphological knowledge, the head to hip of the dragon is used as the length standard. Because the weight of the dragon is proportional to the cube of the dragon's length, we get the weight and length Functional relationship. Of course, the daily weight gain of the dragon must be less than the daily energy consumption. In summary, we have a dragon intake model.4.2.2 Model establishmentSpecify the weight of the dragon as mDragon was born with a weight of m0 (known m0 = 10kg)Assume that the mass of cattle and sheep fed by a train every day is m2The assimilation amount of the dragon is fixed at a%A certain fixed ratio of the amount of unabsorbed energy due to growth and metabolism of organisms such as dragon's respiration, recorded as b%The weight gain of the dragon is m 'The sum of the weight of the dragon's head, heart, liver, lungs, kidneys, bones, etc. m1 increases with age y until adulthoodDragon is y1 when he is an adultThe growth rate of m1 is v1The mass of m1 at birth is m0Before the dragon reaches y1m1=m0+v1*yAfter the dragon reaches y1m1’=m0+v1*y14.2.3 Model Solvingm’=m2*(1-a%)*(1-b%)-m4-m6So the weight of the dragon m = m '+ m0Except for the dragon, except for the head, heart, liver, lungs, kidneys, bones, etc., the sum of other body masses is proportional to the cube of height, and the body length is recorded as l When the age of the dragon does not reach y1, l = (m-m1) ^ (1/3)When the age of the dragon reaches y1, l '= (m-m1') ^ (1/3)M2 =y=0:0.1:20function[y]= (m2*(1-a%)*(1-b%)-m4-m6-v1*y)y=20:0.1:100function[y]= (m2*(1-a%)*(1-b%)-m4-m6-v1*20)power(y,1/3)4.3 About Dragon's Food Supply4.3.1 Proposed modelBased on the above analysis, we studied the living area of the three dragons in the region andtheir impact on the ecological community in the region. For the sake of research, we assume that the other creatures in the region are cattle and sheep, and the competitiveness of the three dragons is comparable, Being a top predator in the food chain.4.3.2 Model establishmentThe local food chain can be approximated as: grass → cow or sheep → dragonAssume that the weight of the grass in the arid region, the warm temperate region, and the Arctic region is the same as m8.Remember that the mass of each cow and sheep is the same as m7We provide the same initial number of cattle and sheep in all three regionsAssume that the daily growth rate of cattle and sheep is c%The initial number of cattle and sheep is n1And n1 is the number of populations reaching k in the regionDragons live in this area. When the number of cattle and sheep reaches k / 2, in order to ensure the balance of the ecological environment, the dragons need to be moved to other regions.4.3.3 Model SolvingThe initial amount of cattle and sheep on day 1 is: n1The initial amount of cattle and sheep on the second day is: N2 = (N1-3 * m2 / m7) * (1 + c%) The initial amount of cattle and sheep on the third day is: N3 = ((N1-3 * m2 / m7) * (1 + c%)-3 * m2 / m7) * (1 + c%)……From this we can get the initial amount of Ni of cattle and sheep on day iI can be solved by the equation Ni = K / 2That is, the dragon needs to change a living area after living in the area for i days.4.4 Regulating the area of dragons by region4.4.1 Proposed modelIn order to ensure the normal growth of the dragon, we provide fixed-quality cattle and sheep as the supply of resources for the survival of the dragon region, and assume that the number of cattle and sheep is proportional to the size of the regional living area. Considering the growth rate of cattle and sheep, we have established a differential The equation draws the relationship between the growth rate of cattle and sheep and the age of the dragon. However, cattle and sheep will reach a growth saturation value at a certain moment, we will consider it in segments to ensure that the data is more scientific. In order to comply with ecology, cattle The supply of sheep should also have a lower limit. In summary, we have established a dragon-cow-sheep-living area function model.4.4.2 Model establishmentRemember that the assimilation rate of cattle and sheep grazing in this area is d%Because the solar energy received by the surface area of the three areas is different, the total area required for the grass under the same quality conditions is different. The utilization rate of the solar energy is required to be e% (0.5 <e <1 under the natural conditions of the search data)The solar energy per unit area in the arid area is q1Unit area solar energy in warm zone is q2Solar energy per unit area in the Arctic is q34.4.3 Model SolvingAccording to the utilization of solar energy, we can find:Area required to support the arid areas where the three dragons live: S1 = m8 / (q1 * e%)Warm zone: S2 = m8 / (q2 * e%)Arctic region: S3 = m8 / (q3 * e%)5 Sensitivity analysisImpact of climatic conditions on dragon lifeThe effect of climatic conditions on dragon growth can be obtained from the logistic growth model dm/dt=r*m*(1-m/k)That is m = 15 / (4 * t + 20);(Where m is the mass that the dragon can eventually grow into)Where m0 = 10 (k is the maximum carrying capacity of the ecosystem and r is a parameter of the environmental carrying capacity)k is 0.75r is 0.8dm/dt=0.8*m*(1-m/0.75)t=0:0.1:100;m=15./(4*t+20);plot(t,m)6 Model evaluation and outlook6.1 Model evaluationFor the idealized model of Yanglong, we have performed various aspects of modeling and solving, and the scope is relatively broad. Of course, the content has been streamlined to facilitate understanding and application. We have used physical and biological models based on The mathematical formulas are also encountered in the middle school stage. In these more basic models, we have solved efficiently, and at the same time, for the interdisciplinary problems of question a, we have considered the field that the ideal biology of dragons may involve and solve The process is relatively complete. In addition, the four models are closely related and logical. First, we consider the consumption of dragons in daily life, and use the results of consumption to calculate the weight and length of the dragon at various ages. In order to meet the requirements of all ages, we have established the ecological supply model of dragons, and discussed the problem of periodic alternating fields. Second, the fields are also scoped. Therefore, we calculated the scope of three areas with different climates. Interval problems. However, the models we build are idealized, the data is also streamlined, and the assumptions set are also fallible. In reality,The data is diverse and complex, and our considerations are obviously lacking, and further optimization is needed in the later stage. In summary, the model we built is very consistent with the solution of the problem. Although there are some flaws, it does not affect the specific Specific analysis of the problem.6.2 Further discussionCombining the models and evaluations described above, we will improve in the later stages. If this model is used in a specific environment, by statistic large amounts of real data, we can optimize the model. At the same time research also It will be more scientific and rigorous, and it will be more efficient for raising a fictional creature.7 to a letter from George RR MartinDear George RR MartinHope you are wellAfter reading the Song of Ice and Fire, we watched the "Game of Thrones". We became very curious about the mysterious giant that appeared in it-the dragon. Dragons are not uncommon in Eastern and Western cultures. In previous impressions However, there are few studies on dragons. So if we imagine that dragons live in modern times, what would it look like?According to the description of the dragon in the novel, we discussed the following questions. What are the ecological impacts and requirements of the dragon? What is the energy consumption of the dragon, what are their calorie intake requirements? How much area is needed to support the three dragons? Energy loss during fire? In response to these problems, we constructed a multivariate non-linear objective programming model of dragon's growth index and function, size, diet, growth changes, and other animal-related features. Considering the physical characteristics of dragons, we will Its fire-spitting ability is analogized to modern flame-throwers to ensure scientific and rational research.Based on these, we have established a mathematical model. The weight and length of the dragon also grows with the age of the dragon. When the dragon grows slowly at the initial 10 kilograms, the mass of sheep it needs each year also varies The growth of the supply chain of resources and the size of the ecological community should also change. The fire and flight of the dragon will also have a certain impact on the ecological environment. As the dragon and other creatures will migrate with changes in temperature, we choose The three regions of the cold zone, temperate zone and arid zone were taken as key research objects to find out the impact of climate change on Long.Therefore, we make the following suggestions, hoping that the survival of the dragon in the realm of science is more reasonable and scientific.When the herd resource is saturated, the dragon needs to expand the area living area.Dragons like warm, hydrated areas, and migrate to warm areas in the cold winter.A dragon has a certain weight and length when it is just born, and it will grow over time, but it also has an upper limit. It cannot grow endlessly.The daily energy intake of the dragon is limited, and the dragon spitfire flight consumes energy, which requires that the dragon's flight distance and spitfire time are limited, and it is related to the age of the dragon body.Because the living conditions of the three areas are different, the unit area will also receive solar energy differently, resulting in different resource distributions in each area, which means thatthe speed of dragon growth should also be different in different areas.The environmental carrying capacity of each area is limited, and the dragon does not stay in one place for long.The above content is the result of our research on the Queen of Dragons. We sincerely hope that you can adopt it, and we have been looking forward to your new book.Your fans: 27 groupsJanuary 7, 20208.Appendix:8.1 References1) Chen Yun.Research on Environmental Carrying Capacity of Yuhuan County [j] .Energy and Energy Conservation, 2014 (4): 31-33.2) Zhu Ziqiang.Aerodynamic design of modern aircraft [m] .Beijing: National Defense Industry Press, 2011-10-13) Jin Lan.Environmental Ecology [m] .Higher Education Press, 19928.2 Matlab codeModeling the flight of a dragon[v,s]=meshgrid(0:0.1:100;0:0.1:100);m=3.2325*v*s-3.2325*v^3/60mesh(v,s,m)Sensitivity Analysis of the Impact of Climate Conditions on Lifet=0:0.1:100;m=15./(4*t+20);plot(t,m)。
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2019MCM
Problem A:A Hot Youbot
Background:Thermal Analysis,using finite element techniques,is carried out as a steady-state or transient analysis.Conductive heat transfer is handled directly by finite element techniques; conduction occurs in a solid due to temperature differences.However,radiation heat transfer analysis may require additional particle-tracking or ray-tracing techniques to approximate the radiant energy arriving at a given surface.
The material is assumed to be a magnesium alloy and to have a thermal conductivity of52W/m∙K. Material properties were taken from"Thermal Conductivity of Magnesium Alloys".Since the model is in inches you can use symunit to rewrite the value in inches.Now you need remove the units to obtain the value for the thermal properties.Unless overwritten,all of the side faces are set to have a natural convection coefficient of25W/m2∙K representing heat transfer to an ambient air temperature of288.15K(25℃).Convert and calculate the convection coefficient to W/inch2∙K to be consistent with the model dimensions.
Explore different material selections for the robotic pute the change in max body temperature as a function of increasing thermal conductivity.Before begining calculate the expected run time from the previous run time.Run the models using a parfor loop to speed up the simulation by parallelizing the iterations across Parallel Computing Toolbox workers.If you do not have the Parallel Toolbox change parfor to for.
Problem:
Part I:Develop a mathematical model for the heat transfer among the gripper pivot.In the youBot,the gripper pivot sits underneath the electronics board and is exposed to the heat coming off the circut board.Here you will create the pde model,import the STL file of the gripper pivot, and plot it.Create and visualize a tetrahedral mesh of the component with a maximum value of 0.09inches.Measure the x,y and z dimensions of the mesh.
Part II:The bottom face is given a fixed temperature assuming that the rest of the robotic arm acts as a heat sink.The top face and inner hole is arbitrarily given a heat flux to represent the heat off the circuit board.Solve the model and calculate the max and bulk body temperatures and time how long the solve pute the max temperature in K and rewrite that to℃and F,then plot the distribution of temperature of the gripper pivot in3D.
Part III:Develop a mathematical model for predicting the relationship between thermal conductivity and max temperature for this geometry and material.Assume the robotic arm shuts off at a max temperature of311K,find the associated allowable heat transfer coefficient for the alloy.Which materials are appropriate for being made into the the gripper pivot?
Part IV:Prepare a short(1to2pages)synopsis of your results suitable for publication as a short note in IEEE Communications Magazine.
Your submission should consist of:
●One-page Summary Sheet,
●Two-page synopsis,
●Your solution of no more than20pages,for a maximum of23pages with your summary
and synopsis.
●Note:Reference list and any appendices do not count toward the23-page limit and
should appear after your completed solution.
Reference:
Lee,Sanghyun,et al."Thermal Conductivity of Magnesium Alloys in the Temperature Range from-125℃to400℃."International Journal of Thermophysics34.12(2013):2343-2350. Appendix:
The structure of Gripper Pivot in youBot plotted by AutoCAD:
ProblemAData：youBot.stl。