2001—2010MCM各题部分O奖论文_美赛国赛论文.pdf资源-CSDN文库

版权申诉

114 浏览量 2023-10-21 13:27:24 上传评论收藏 10.96MB PDF 举报

资源推荐

资源详情

资源评论

Contents

2001 MCM Problems……………………………………………………….…………1

2001 A Selection of a Bicycle Wheel Type…………………………….…..……..4

2001 B Traffic Flow Models and the Evacuation Problem………...…...…...…..19

2002 MCM Problems……………………………………………………… ..………39

2002 A Simulating a Fountain………………………………………..…….……40

2002 B Bumping for Dollars: The Airline Overbooking Problem……..…….….51

2003 MCM Problems………………………………………………………...………66

2003 A You Too Can Be James Bond……………………………………………68

2003 B A Sphere-Packing Model for the Optimal Treatment Plan………...……86

2004 MCM Problems………………………………………………………...………98

2004 A can not quite put our finger on it…….……………………………..……99

2004 B Developing Improved Algorithms for QuickPass Systems……....……113

2005 MCM Problems………………………………….……………………………131

2005 A Analysis of Dam Failure in the Saluda River Valley………………..…132

2005 B The Booth Tolls for Thee………………………………………………148

2006 MCM Problems………………….……………………………………………165

2006 A Fastidious Farmer Algorithms (FFA)……………………………..……167

2006 B Application of Min-Cost Flow to Airline Accessibility Services….…..181

2007 MCM Problems…………………………………………………………….…199

2007 A Why Weight?A Cluster-Theoretic Approach to Political Districting…..200

2007 B Boarding at the Speed of Flight

………

…………………………………218

2008 MCM Problems…………………………………………………….…………229

2008 A …………………………………………………230

2008 B A Difficulty Metric and Puzzle Generator for Sudoku………….…….257

2009 MCM Problems………………………………………………………….……281

2009 A Pseudo-Finite Jackson Networks and Simulation: A Round about

Approach to Traffic Control…………………...……...………….……283

2009 B America’s New Calling……………………………………..…………307

2010 MCM Problems……………………………………………………….………324

2010 A The Sweet Spot: A Wave Model of Baseball Bats……...……...………325

2010 B Centroids, Clusters, and Crime: Anchoring the Geographic Profiles

of Serial Criminals…………………………………………...………..343

2001 MCM Problems

Problem A: Choosing a Bicycle Wheel

Cyclists have different types of wheels they can use on their bicycles. The two basic types of

wheels are those constructed using wire spokes and those constructed of a solid disk (see

Figure 1) The spoked wheels are lighter, but the solid wheels are more aerodynamic. A solid

wheel is never used on the front for a road race but can be used on the rear of the bike.

Professional cyclists look at a racecourse and make an educated guess as to what kind of

wheels should be used. The decision is based on the number and steepness of the hills, the

weather, wind speed, the competition, and other considerations. The director sportif of your

favorite team would like to have a better system in place and has asked your team for

information to help determine what kind of wheel should be used for a given course.

Figure 1: A solid wheel is shown on the left and a spoked wheel is shown on the right.

The director sportif needs specific information to help make a decision and has asked your

team to accomplish the tasks listed below. For each of the tasks assume that the same spoked

wheel will always be used on the front but there is a choice of wheels for the rear.

•

Task 1. Provide a table giving the wind speed at which the power required for a solid

rear wheel is less than for a spoked rear wheel. The table should include the wind

speeds for different road grades starting from zero percent to ten percent in one

percent increments. (Road grade is defined to be the ratio of the total rise of a hill

divided by the length of the road. If the hill is viewed as a triangle, the grade is the

sine of the angle at the bottom of the hill.) A rider starts at the bottom of the hill at a

speed of 45 kph, and the deceleration of the rider is proportional to the road grade. A

rider will lose about 8 kph for a five percent grade over 100 meters.

•

Task 2. Provide an example of how the table could be used for a specific time trial

course.

•

Task 3. Determine if the table is an adequate means for deciding on the wheel

configuration and offer other suggestions as to how to make this decision.

Problem B: Escaping a Hurricane's Wrath (An Ill Wind...)

Evacuating the coast of South Carolina ahead of the predicted landfall of Hurricane Floyd in

1999 led to a monumental traffic jam. Traffic slowed to a standstill on Interstate I-26, which

is the principal route going inland from Charleston to the relatively safe haven of Columbia in

the center of the state. What is normally an easy two-hour drive took up to 18 hours to

complete. Many cars simply ran out of gas along the way. Fortunately, Floyd turned north and

spared the state this time, but the public outcry is forcing state officials to find ways to avoid a

repeat of this traffic nightmare.

The principal proposal put forth to deal with this problem is the reversal of traffic on I-26, so

that both sides, including the coastal-bound lanes, have traffic headed inland from Charleston

to Columbia. Plans to carry this out have been prepared (and posted on the Web) by the South

Carolina Emergency Preparedness Division. Traffic reversal on principal roads leading inland

from Myrtle Beach and Hilton Head is also planned.

A simplified map of South Carolina is shown. Charleston has approximately 500,000 people,

Myrtle Beach has about 200,000 people, and another 250,000 people are spread out along the

rest of the coastal strip. (More accurate data, if sought, are widely available.)

The interstates have two lanes of traffic in each direction except in the metropolitan areas

where they have three. Columbia, another metro area of around 500,000 people, does not

have sufficient hotel space to accommodate the evacuees (including some coming from

farther north by other routes), so some traffic continues outbound on I-26 towards

Spartanburg; on I-77 north to Charlotte; and on I-20 east to Atlanta. In 1999, traffic leaving

Columbia going northwest was moving only very slowly. Construct a model for the problem

to investigate what strategies may reduce the congestion observed in 1999. Here are the

questions that need to be addressed:

1. Under what conditions does the plan for turning the two coastal-bound lanes of I-26

into two lanes of Columbia-bound traffic, essentially turning the entire I-26 into

one-way traffic, significantly improve evacuation traffic flow?

2. In 1999, the simultaneous evacuation of the state's entire coastal region was ordered.

Would the evacuation traffic flow improve under an alternative strategy that staggers

the evacuation, perhaps county-by-county over some time period consistent with the

pattern of how hurricanes affect the coast?

3. Several smaller highways besides I-26 extend inland from the coast. Under what

conditions would it improve evacuation flow to turn around traffic on these?

4. What effect would it have on evacuation flow to establish more temporary shelters in

Columbia, to reduce the traffic leaving Columbia?

5. In 1999, many families leaving the coast brought along their boats, campers, and

motor homes. Many drove all of their cars. Under what conditions should there be

restrictions on vehicle types or numbers of vehicles brought in order to guarantee

timely evacuation?

Selection of a Bicycle Wheel Type 225

Selection of a Bicycle Wheel Type

Nicholas J. Howard

Zachariah R. Miller

Matthew R. Adams

United States Military Academy

West Point, NY

Advisor: Donovan D. Phillips

Introduction

We present a model that compares the performance of various wheels over

auser-determined course. We approach the modeling problem by beginning

with Newton’s Second Law of Motion: The sum of the forces acting on an object

equals the mass of that object multiplied by its acceleration.

We identify the four principal forces that contribute to a cyclist’s motion:

applied force, drag force, gravity, and rolling resistance. We further classify

drag force into three components: the cyclist and bicycle frame, the front wheel,

and the rear wheel.

Drag force is dependent on a cyclist’s velocity, and the force of gravity is

dependent on a cyclist’s position. Thus, our force equation is a function of

cyclist position and cyclist velocity.

We can then arrange Newton’s Second Law to yield a second-order differ-

ential equation. Given position S,velocity dS/dt,acceleration d

S/dt

,mass

m, and a force function F,thedifferential equation is





To implement our model, we created a computer software program that

allows a user to input numerous pieces of data, including course layout, eleva-

tion proÞle, wind, weather conditions, and cyclist characteristics. The software

iterates the differential equation using the fourth-order Runge-Kutta method.

The software reports the preferred wheel choice based on the data.

As a real-world application of our model, we analyze the 2000 Olympic

Cycling time-trial race. Over that course, a disk wheel provided a considerable

advantage over a spoked wheel.

The UMAP Journal 22 (3) (2001) 225–239.

Permission to make digital or hard copies of part or all of this work for personal or classroom use

is granted without fee provided that copies are not made or distributed for proÞtorcommercial

advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights

for components of this work owned by others than COMAP must be honored. To copy otherwise,

to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP.

剩余362页未读，继续阅读

评论收藏

内容反馈

版权申诉

2301_77550592

粉丝: 17
资源: 7164

2001—2010MCM各题部分O奖论文_美赛国赛论文.pdf

2013MCM部分O奖F奖论文_美赛国赛论文.rar

MCM2012全部特等奖原文_美赛国赛论文_美赛国赛论文.rar

4-MCM2004A_M_美赛国赛论文.pdf

5-MCM2006A.sjtu06 copy_美赛国赛论文.pdf

3-MCM2005B_M_美赛国赛论文.doc

2-MCM2004B_M_美赛国赛论文.doc

1-MCM outstanding thesis_美赛国赛论文.doc

数学建模比赛超全经验合集美赛国赛资料大全.zip

2019数模美赛O奖论文.rar

2022年美赛（MCM）C题M奖论文

2021_MCM-ICM_美赛赛题翻译.rar

2021MCM_ProblemC_Vespamandarina.pdf

2013年美赛o奖论文

2017美赛A题O奖论文

2021MCM_ProblemC_ Images_by_GlobalID.xlsx

2017年美赛o奖论文集

2013-2016数学建模美赛o奖论文.rar

美赛O奖论文.zip

相关实用应用程序（Windows可用）

免费可用的ChatGPT网页版.zip

ChatGPT使用总结：150个ChatGPT提示词模板（完整版）

chromedriver-win64.zip

全国计算机二级WPSoffice精选350道选择题题库（含答案）.pdf

农村公交与异构无人机协同配送优化

李飞飞自传 我看见的世界 The World I see

哈尔滨工业大学-ChatGPT调研报告-2023.3.6-94页.pdf

4个亲测好用的ChatGPT4渠道

基于小波与卷积神经网络的多尺度时间序列分类.zip

最新资源

李飞飞自传我看见的世界 The World I see