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2001_年美国大学生数学建模竞赛_mcm_icm_试题 [2008/02/08 15:55]
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2001_年美国大学生数学建模竞赛_mcm_icm_试题 [2014/12/30 22:36] (当前版本)
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| {{mcm-icm:2001-mcm-b-fig1.jpg|}} | {{mcm-icm:2001-mcm-b-fig1.jpg|}} |
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| ===== 2001 ICM: Our Waterways - An Uncertain Future ===== | ===== 2001 ICM: Our Waterways - An Uncertain Future ===== |
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| Zebra mussels, Dreissena polymorpha, are small, fingernail-sized, freshwater mollusks unintentionally introduced to North America via ballast water from a transoceanic vessel. Since their introduction in the mid 1980s, they have spread through all of the Great Lakes and to an increasing number of inland waterways in the United States and Canada. Zebra mussels colonize on various surfaces, such as docks, boat hulls, commercial fishing nets, water intake pipes and valves, native mollusks and other zebra mussels. Their only known predators, some diving ducks, freshwater drum, carp, and sturgeon, are not numerous enough to have a significant effect on them. Zebra mussels have significantly impacted the Great Lakes ecosystem and economy. Many communities are trying to control or eliminate these aquatic pests. SOURCE: Great Lakes Sea Grant Network [[http://www.sgnis.org/]]. | {{mcm-icm:2001-icm-fig1.gif|}} |
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| | Zebra mussels, Dreissena polymorpha, are small, fingernail-sized, freshwater mollusks unintentionally introduced to North America via ballast water from a transoceanic vessel. Since their introduction in the mid 1980s, they have spread through all of the Great Lakes and to an increasing number of inland waterways in the United States and Canada. Zebra mussels colonize on various surfaces, such as docks, boat hulls, commercial fishing nets, water intake pipes and valves, native mollusks and other zebra mussels. Their only known predators, some diving ducks, freshwater drum, carp, and sturgeon, are not numerous enough to have a significant effect on them. Zebra mussels have significantly impacted the Great Lakes ecosystem and economy. Many communities are trying to control or eliminate these aquatic pests. SOURCE: Great Lakes Sea Grant Network http://www.sgnis.org/. |
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| Researchers are attempting to identify the environmental variables related to the zebra mussel infestation in North American waterways. The relevant factors that may limit or prevent the spread of the zebra mussel are uncertain. You will have access to some reference data to include listings of several chemicals and substances in the water system that may affect the spread of the zebra mussel throughout waterways. Additionally, you can assume individual zebra mussels grow at a rate of 15 millimeters per year with a life span between 4 - 6 years. The typical mussel can filter 1 liter of water each day. | Researchers are attempting to identify the environmental variables related to the zebra mussel infestation in North American waterways. The relevant factors that may limit or prevent the spread of the zebra mussel are uncertain. You will have access to some reference data to include listings of several chemicals and substances in the water system that may affect the spread of the zebra mussel throughout waterways. Additionally, you can assume individual zebra mussels grow at a rate of 15 millimeters per year with a life span between 4 - 6 years. The typical mussel can filter 1 liter of water each day. |
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| **Requirement A** : Discuss environmental factors that could influence the spread of zebra mussels. | **Requirement A**: Discuss environmental factors that could influence the spread of zebra mussels. |
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| **Requirement B** : Utilizing the chemical data provided at: | **Requirement B**: Utilizing the chemical data provided at: |
| http://www.comap/undergraduate/contests/icm/imagesdata/LakeAChem1.xls, and the mussel population data provided at: | http://www.comap/undergraduate/contests/icm/imagesdata/LakeAChem1.xls, and the mussel population data provided at: |
| http://www.comap/undergraduate/contests/icm/imagesdata/LakeAPopulation1.xls | http://www.comap/undergraduate/contests/icm/imagesdata/LakeAPopulation1.xls |
| model the population growth of zebra mussels in Lake A. Be sure to review [[the Information about the collection of the zebra mussel data]]. | model the population growth of zebra mussels in Lake A. Be sure to review the Information about the collection of the zebra mussel data. |
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| | **Requirement C**: Utilizing additional data on Lake A from another scientist provided at : |
| | http://www.comap/undergraduate/contests/icm/imagesdata/LakeAChem2.xls |
| | and additional mussel population data provided at: |
| | http://www.comap/undergraduate/contests/icm/imagesdata/LakeAPopulation2.xls corroborate the reasonableness of your model from Requirement B. As a result of this additional data, adjust your earlier model. Analyze the performance of your model. Discuss the sensitivity of your model. |
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| | **Requirement D**: Utilizing the Chemical data from two lakes (Lake B and Lake C) in the United States provided at http://www.comap/undergraduate/contests/icm/imagesdata/LakeB.xls and http://www.comap/undergraduate/contests/icm/imagesdata/LakeC.xls determine if these lakes are vulnerable to the spread of zebra mussels. Discuss your prediction. |
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| | **Requirement E**: The community in the vicinity of Lake B (in requirement D) is considering specific policies for the de-icing of roadways near the lake during the winter season. Provide guidance to the local government officials regarding a policy on “de-icing agents.” In your guidance include predictions on the long-term impact of de-icing on the zebra mussel population. |
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| | **Requirement F**: It has been recommended by a local community in the United States to introduce round goby fish. Zebra mussels are not often eaten by native fish species so they represent a dead end ecologically. However, round gobies greater than 100 mm feed almost exclusively on zebra mussels. Ironically, because of habitat destruction, the goby is endangered in its native habitat of the Black and Caspian Seas in Russia. In addition to your technical report, include a carefully crafted report (3-page maximum) written explicitly for the local community leaders that responds to their recommendation to introduce the round goby. Also suggest ways to help reduce the growth of the mussel within and among waterways. |
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| | **Information about the collection of the zebra mussel data** |
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| | The developmental state of the Zebra mussel is categorized by three stages: veligers (larvae), settling juveniles, and adults. Veligers (microscopic zebra mussel larvae) are free-swimming, suspended in the water for one to three weeks, after which they begin searching for a hard surface to attach to and begin their adult life. Looking for zebra mussel veligers is difficult because they are not easily visible by the naked eye. Settled juvenile zebra mussels can be felt on smooth surfaces like boats and motors. An advanced zebra mussel infestation can cover a surface, even forming thick mats sometimes reaching very high densities. The density of juveniles was determined along the lake using three 15X15 cm settling plates. The top plate remained in the water for the entire sampling season (S - seasonal) to estimate seasonal accumulation. The middle and bottom plates are collected after specific periods (A – alternating ) of time denoted by “Lake Days” in the data files. |
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| | {{mcm-icm:2001-icm-fig2.gif|}} |
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| | The settling plates are placed under the microscope and all juveniles on the undersides of the plate are counted and densities are reported as juveniles/m^2. |
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| | {{mcm-icm:icm2001.zip|PDF version of the problem}} |
