-
2013 Contest Problems
MCM PROBLEMS
PROBLEM A:
The
Ultimate Brownie Pan
When
baking in a rectangular pan heat is concentrated
in the 4 corners and
the product gets
overcooked at the corners (and to a lesser extent
at the
edges). In a round pan the heat
is distributed evenly over the entire outer
edge and the product is not overcooked
at the edges. However, since most
ovens
are rectangular in shape using round pans is not
efficient with respect
to using the
space in an oven.
当在一个矩形的锅中烘烤时热量集中在烤箱的<
/p>
4
个角落中，
并在角落处的食物烤
的过了
（在某种程度上边缘也是这样）
。
在一个圆形盘的热量被均匀地分布在整
个外缘，在边缘处的食物烤的
不会过头。然而，因为大多数烤箱是方形的，使用
原型的平底锅效率是不高的相对于烤箱
中的空间。
Develop a model to
show the distribution of heat across the outer
edge of a
pan for pans of different
shapes - rectangular to circular and other shapes
in
between.
建立一个模型来说明不同形状的锅<
/p>
(
圆形方形或其他形状
)
的外边缘热量的不同
分布。
Assume
1. A width to length
ratio of
W/L
for the oven
which is rectangular in shape.
2. Each
pan must have an area of
A
.
3. Initially two racks in the oven,
evenly spaced.
假设
1.
矩形烤箱的的宽度与长度之比是
W /
L
。
2.
每个盘子的面积都是
A
3.
最初，两个机架在烤箱，间隔均匀。
Develop a model that can be used to
select the best type of pan (shape)
under the following conditions:
1. Maximize number of pans that can fit
in the oven (N)
2. Maximize even
distribution of heat (H) for the pan
3. Optimize a combination of conditions
(1) and (2) where weights p and
(1-
p
) are assigned to
illustrate how the results vary with different
values
of
W/L
and
p
.
建立一个模型，在下列情况下，可用于选择最佳的锅（形状）：
1.
可以放到烤箱中的锅的最大数量
是（
N
）
2.
烤箱里最大限度地均匀分布热量
为（
H
），
3.
优化的组合的条件（
1
）和（
2
）式的权重<
/p>
p
和
(1
–
p)
，用来说明如何随不同
的值的
W/L
和
P<
/p>
的变化而影响最终结果。
In addition to your MCM formatted
solution, prepare a one to two page
advertising sheet for the new Brownie
Gourmet Magazine highlighting your
design and results.
除了你的格式化的
解决方案
,
准备一个一到两页的广告页为新布朗尼美食杂志突<
/p>
出自己的设计和结果。
PROBLEM B:
Water, Water,
Everywhere
Fresh water is
the limiting constraint for development in much of
the world.
Build a mathematical model
for determining an effective, feasible, and
cost-efficient water strategy for 2013
to meet the projected water needs of
[pick one country from the list below]
in 2025, and identify the best water
strategy. In particular, your
mathematical model must address storage and
movement; de-salinization; and
conservation. If possible, use your model to
discuss the economic, physical, and
environmental implications of your
strategy. Provide a non-technical
position paper to governmental leadership
outlining your approach, its
feasibility and costs, and why it is the “best
water strategy choice.”
Countries: United States,
China, Russia, Egypt, or Saudi Arabia
问题
B:
水
,
水
,
到处都是
淡水已经是约束世界上大部分国家发展的一个限制条件。
建立一
个数学模型来确
定一个有效的、
可行的
,
和有成本效益的水侧罗
,
以满足从<
/p>
2013
年开始
[
选择一个
国家从下面的列表
]
到
2025
年的水需求
,
和确定最佳水策略。特别是
,
你
的数学模
型必须解决水的存储和移动
;
去盐碱化
;
环保等问题。
如果可能的话
,
用你的模型来
讨论经济、
物理和环境影响的战略。
提供一个非技术意见书给政府领导概述你的
方法
,
其可行性和成本
,
以及为什么它是“最好的水策略选择。”
国家
:
美国、中国、俄罗斯、埃及或沙特阿拉伯
ICM
PROBLEM
PROBLEM C:
Network Modeling of Earth's
Health
Click the title below
to download a PDF of the 2013 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.
Network Modeling of
Earth's Health
2013 ICM
Problem
Network Modeling of Earth's
Health
Background:
Society
is interested in developing and using models to
forecast
the biological and
environmental health conditions of our planet.
Many
scientific studies have concluded
that there is growing stress on Earth's
environmental and biological systems,
but there are very few global models to
test those claims. The UN-backed
Millennium Ecosystem Assessment
Synthesis Report
found that
nearly two-thirds of Earth's life-supporting
ecosystems
—
including clean water, pure air, and
stable climate
—
are being
degraded by
unsustainable use. Humans are blamed for much of
this damage.
Soaring demands for food,
fresh water, fuel, and timber have contributed to
dramatic environmental changes; from
deforestation to air, land, and water
pollution. Despite the considerable
research being conducted on local habitats
and regional factors, current models do
not adequately inform decision makers
how their provincial polices may impact
the overall health of the planet. Many
models ignore complex global factors
and are unable to determine the
long-
range impacts of potential policies. While
scientists realize that the
complex
relationships and cross-effects in myriad
environmental and biological
systems
impact Earth's biosphere, current models often
ignore these
relationships or limit the
systems' connections. The system complexities
manifest in multiple interactions,
feedback loops, emergent behaviors, and
impending state changes or tipping
points. The recent
Nature
article written by
22
internationally known scientists entitled
biosphere
models and the
importance of predicting potential state changes
of the
planetary health systems. The
article provides two specific quantitative
modeling challenges in their call for
better predictive models:
背
景：
建立并使用模型去预测我们星球的生态环境条件是现在社会最感兴趣的话
题。
许多科学研究表明，
地球的生态环境面临着越
来越大的压力。
但是也很少有
全球模型来验证那些推论。联合国
年生态系统评估的综合报告发现
,
近三分之二
< br>的地球维持生命的生态系统
-
包括纯净水
,
纯净的空气
,
和适宜的气候
——正在退
化
,
被不可持续的使用。<
/p>
这些都归咎于人类对生态环境的破坏。
大量对食物、
水、