美国数学建模竞赛培训.ppt

1、赛 前 培 训,数 学 建 模 竞 赛,take a bath,MCM2008年A题,Consider the effects on land from the melting of the north polar ice cap due to the predicted increase in global temperatures. Specifically, model the effects on the coast of Florida every ten years for the next 50 years due to the melting, with particular

2、attention given to large metropolitan areas. Propose appropriate responses to deal with this. A careful discussion of the data used is an important part of the answer.,给大陆洗个澡 研究一下由于全球气温升高造成的北极冰帽融化对大陆的影响。具体来说，为佛罗里达海岸今后50年，每十年由于融化造成的影响建立模型，要特别注意大型都市区。提出一些适当的回应来处理这些问题。对所使用的数据的详细讨论是答案的一个重要部分。,中文翻译：,美国赛题

3、特点： 1、语言简练！ 2、没有一个数字！ 那数据从哪里来？ 我们的学生在这一点（资料收集）上吃了很大的亏！,题目要求： 1、收集过去海平面上升的精确数据！ 2、分析海平面上升对佛罗里达的影响！ 、给出相应的措施来尽可能减少因全球变暖而导致海平面上升带来的灾难！,考虑： 1、对海平面上升的最重要的因素：冰川的融化和海洋本身的热膨胀； 2、冰川的融化主要是气候变暖！ 、主要使用的是冰川积累与融化的质量平衡模型和海洋的热膨胀模型,假设(assumption),1.The sea level rise is primarily due to two factors, the balance of a

4、ccumulation/ablation of the Greenland Ice Sheet and the thermal expansion of the ocean. This ignores the contribution of processes such as calving and direct human intervention, which are difficult to model accurately and have minimal effect on sea level rise .,假设(assumption),2.The air is the only h

5、eat source for melting the ice. Greenlands land is permafrost, and because of large amounts of ice on its surface it is assumed at a relatively constant temperature. This allows us to use convection as a mode of heat transfer. 3.The temperature within the ice changes linearly at the steady-state. Th

6、is assumption allows us to solve the heat equation for Neumann conditions. By subtracting the steadystate term from the heat equation, we can solve for the homogeneous boundary conditions.,假设(assumption),4.Sublimation and melting processes do not interfere with each other. This assumption drasticall

7、y simplifies the computation needed for the model since sublimation and melting can be considered separately. Additionally, the assumption is very reasonable. Sublimation primarily occurs at below freezing temperatures, a condition during which melting does not normally occur. Thus, the two processe

8、s are temporally isolated as in our model.,假设(assumption),5.The surface of the ice sheet is homogeneous with regards to temperature, pressure, and chemical composition. This assumption is necessary because high-resolution spatial temperature data for Greenland cannot be obtained in our framework. Ad

9、ditionally, we lack the computational resources and time to simulate such a variation, which would require the use of finite element methods and mesh generation for a complex topology.,Defining the problem,Let M denote the mass balance of the Greenland Ice Sheet. Given a temperature forcing function

10、, we must quantitatively estimate the sea level increases SLR that occur as a result. These increases are a sum of M and thermal expansion TE effects, corrected for local trends. Further, we must quantitatively and qualitatively the long-term (50 years) effect on Floridas major cities and metropolit

11、an areas from global warming, as a result of high SLR. This analysis can be used to make recommendations as to how to best prepare for and reduce SLR effects.,全球海平面数据： http:/www.bodc.ac.uk/data/online_delivery/international_sea_level/ 美国气象数据： /oa/ncdc.html 中国气象数据： 气候变化国家评估报告：

12、,这里提供几个相关资料的网址,常备一些文献数据资料网址：这个是在竞赛期间有效的节省时间，快速的搜索相关的资料。大家在竞赛前多找一些国外大学图书馆的网站，里面有大量的科技文献电子资源库，以备竞赛期间使用。,小提示:,对赛题的理解：,本题主要解决气候变暖与冰洋融化之间（温室气体排放量与融化速度之间的关系）、北冰洋融化与大陆影响（以目前的融化趋势，预测佛州几个大城市将在什么时候毁灭，或者50年内佛州的受灾程度）之间关系模型：大陆影响主要有：海平面上升、恶劣气候（飓风）、大西洋暖流变冷等情况。以佛洲为例，考虑佛州几个重要城市的地理位置，指出减缓温室气体排放及减缓北冰洋融化速度对海平面上升、恶劣气候等的

13、作用。,Problem B: Creating Sudoku Puzzles,Develop an algorithm to construct Sudoku puzzles of varying difficulty. Develop metrics to define a difficulty level. The algorithm and metrics should be extensible to a varying number of difficulty levels. You should illustrate the algorithm with at least 4 difficulty levels. Your algorithm should guarantee a unique solution. Analyze the complexity of your algorithm. Your objective should be to minimize the complexity of the algorithm and meet the above requirements.,B题：