Mathematical Contest in Modeling, 1999

The event

The Mathematical Contest in Modeling is an annual event, sponsored by the Consortium for Mathematics and Its Applications, in which students at colleges and universities all over the world are asked to develop and analyze mathematical models of open-ended, practical problems for which no direct solutions are known. Participants work in teams of three and are permitted to use libraries, computers, and other inanimate sources of knowledge and inspiration. The organizers of the contest propose three problems; over the three days of the contest, each team selects one of these problems, designs, implements, and analyzes a model, and writes a substantial report presenting its results.

The fifteenth Mathematical Contest in Modeling was held on February 5-8, 1999. Grinnell's teams this year were:

The problems

Here are two of the problems that COMAP posed this year:

Problem A: Deep impact

For some time, the National Aeronautics and Space Administration (NASA) has been considering the consequences of a large asteroid impact on the earth.

As part of this effort, your team has been asked to consider the effects of such an impact were the asteroid to land in Antarctica. There are concerns that an impact there could have considerably different consequences than one striking elsewhere on the planet.

You are to assume that an asteroid is on the order of 1000 m in diameter, and that it strikes the Antarctic continent directly at the South Pole.

Your team has been asked to provide an assessment of the impact of such an asteroid. In particular, NASA would like an estimate of the amount and location of likely human casualties from this impact, an estimate of the damage done to the food production regions in the oceans of the southern hemisphere, and an estimate of possible coastal flooding caused by large-scale melting of the Antarctic polar ice sheet.

Problem B: Unlawful assembly

Many public facilities have signs in rooms used for public gatherings which state that it is unlawful for the rooms to be occupied by more than a specified number of people. Presumably, this number is based on the speed with which people in the room could be evacuated from the room's exits in case of an emergency. Similarly, elevators and other facilities often have maximum capacities posted.

Develop a mathematical model for deciding what number to post on such a sign as being the lawful capacity. As part of your solution discuss criteria, other than public safety in the case of a fire or other emergency, that might govern the number of people considered unlawful to occupy the room (or space). Also, for the model that you construct, consider the differences between a room with movable furniture such as a cafeteria (with tables and chairs), a gymnasium, a public swimming pool, and a lecture hall with a pattern of rows and aisles. You may wish to compare and contrast what might be done for a variety of different environments: elevator, lecture hall, swimming pool, cafeteria, or gymnasium. Gatherings such as rock concerts and soccer tournaments may present special conditions.

Apply your model to one or more public facilities at your institution (or neighboring town). Compare your results with the stated capacity, if one is posted. If used, your model is likely to be challenged by parties with interests in increasing the capacity. Write an article for the local newspaper defending your analysis.

Results

Both the team of Rachel Heck, Andrew Kensler, and Eric Nana Otoo and the team of Oleksiy Andriychenko, Dmitry Krivin, and Zorka Milin earned the Meritorious rating from COMAP's judges. The team consisting of Nikhil Sohonie, Yuriy Shchuchinov, and Shiva Kabra received Honorable Mention. The team of Andrew Meyer and Tim Andrews was ranked as a Successful Participant.

This year, 478 teams (representing 229 academic institutions in nine countries) submitted complete entries. Twelve of these entries were judged Outstanding; eighty-two, Meritorious. One hundred forty-nine received Honorable Mentions in COMAP's report. The remaining 235 teams were classified as Successful Participants.

This document is available on the World Wide Web as

http://www.math.grinnell.edu/mcm-1999.xhtml