ICM1999原题

pcFresher · 发表于 2003-7-24 01:05:34

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 ICM:
 The Interdisciplinary Contest in Modeling 
 
 1999
 Contest Problem
 Ground
 Pollution 
 
 Background 
 
 Several practically important but theoretically difficult mathematical
 problems pertain to the assessment of pollution. One such problem consists
 in deriving accurate estimates of the location and amount of pollutants
 seeping inaccessibly underground, and the location of their source, on
 the basis of very few measurements taken only around, but not necessarily
 directly in, the suspected polluted region. 
 
 Example
 
 The data set (an Excel file at
 <a href="http://%20www.comap.com/mcm/procdata.xls" style="text-decoration: none">http://
 www.comap.com/mcm/procdata.xls</a>, downloadable into most spreadsheets)
 shows measurements of pollutants in underground water from 10 monitoring
 wells (MW) from 1990 to 1997. The units are micrograms per liter (μg/l).
 The location and elevation for eight wells are known and given in Table
 1. The first two numbers are the coordinates of the location of the
 well on a Cartesian grid on a map. The third number is the altitude in
 feet above Mean Sea Level of the water level in the well.
 
 Table
 1.
 
 Locations for
 eight wells in Problem C.
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 Well Number</td>
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 <span style="font-size: 11pt; font-family

alatino-Bold"> x-Coordinate(ft)</td>
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<span style="font-size: 11pt; font-family

alatino-Bold"> y-Coordinate(ft)</td>
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<span style="font-size: 11pt; font-family

alatino-Bold">Elevation(ft)</td>
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 MW-1
 
 MW-3
 
 MW-7
 
 MW-9
 
 MW-11
 
 MW-12
 
 MW-13
 
 MW-14</td>
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 4187.5
 
 9062.5
 
 7625.0
 
 9125.0
 
 9062.5
 
 9062.5
 
 9062.5
 
 4750.0</td>
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 6375.0
 
 4375.0
 
 5812.5
 
 4000.0
 
 5187.5
 
 4562.5
 
 5000.0
 
 2562.5</td>
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 1482.23
 
 1387.92
 
 1400.19
 
 1384.53
 
 1394.26
 
 1388.94
 
 1394.25
 
 1412.00</td>
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 The locations and elevations
 of the other two wells in the data set (MW-27 and MW-33) are not known.
 In the data set, you will also see the letter T, M, or B after the well
 number, indicating that the measurements were taken at the Top, Middle,
 or Bottom of the aquifer in the well. Thus, MW-7B and MW-7M are from the
 same well, but from the bottom and from the middle. Also, other measurements
 indicate that water tends to flow toward well MW-9in this area. 
 
 <b&gt

roblem One 
 
 Build a mathematical model to determine whether any new pollution has
 begun during this time period in the area represented by the data set.
 If so, identify the new pollutants and estimate the location and time
 of their source. 
 
 <b&gt

roblem Two 
 
 Before the collection of any data, the question arises whether the intended
 type of data and model can yield the desired assessment of the location
 and amount of pollutants. Liquid chemicals may have leaked from one of
 the storage tanks among many similar tanks in a storage facility built
 over a homogeneous soil. Because probing under the many large tanks would
 be prohibitively expensive and dangerous, measuring only near the periphery
 of the storage facility or on the surface of the terrain seems preferable.
 Determine what type and number of measurements, taken only outside the
 boundary or on the surface of the entire storage facility, can be used
 in a mathematical model to determine whether a leak has occurred, when
 it occurred, where (from which tank) it occurred, and how much liquid
 has leaked. 
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pcFresher · 发表于 2003-7-24 01:09:02

顺便说一句，那个xls文件的链接已经没有了，哪位高人有此文件，望能发给我：e3615471@sohu.com,谢谢！

happy2003 · 发表于 2003-7-26 05:44:04

我去帮你找找

pcfresher · 发表于 2003-7-26 19:52:27

谢谢！无什么内容!

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