美赛英文题目.docx
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美赛英文题目.docx
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美赛英文题目
2001年美国大学生数学建模竞赛MCM、ICM试题
2001MCMA:
ChoosingaBicycleWheel
Cyclistshavedifferenttypesofwheelstheycanuseontheirbicycles.Thetwobasictypesofwheelsarethoseconstructedusingwirespokesandthoseconstructedofasoliddisk(seeFigure1)Thespokedwheelsarelighter,butthesolidwheelsaremoreaerodynamic.Asolidwheelisneverusedonthefrontforaroadracebutcanbeusedontherearofthebike.
Professionalcyclistslookataracecourseandmakeaneducatedguessastowhatkindofwheelsshouldbeused.Thedecisionisbasedonthenumberandsteepnessofthehills,theweather,windspeed,thecompetition,andotherconsiderations.Thedirectorsportifofyourfavoriteteamwouldliketohaveabettersysteminplaceandhasaskedyourteamforinformationtohelpdeterminewhatkindofwheelshouldbeusedforagivencourse.
Figure1:
Asolidwheelisshownontheleftandaspokedwheelisshownontheright.
Thedirectorsportifneedsspecificinformationtohelpmakeadecisionandhasaskedyourteamtoaccomplishthetaskslistedbelow.Foreachofthetasksassumethatthesamespokedwheelwillalwaysbeusedonthefrontbutthereisachoiceofwheelsfortherear.
▪Task1.Provideatablegivingthewindspeedatwhichthepowerrequiredforasolidrearwheelislessthanforaspokedrearwheel.Thetableshouldincludethewindspeedsfordifferentroadgradesstartingfromzeropercenttotenpercentinonepercentincrements.(Roadgradeisdefinedtobetheratioofthetotalriseofahilldividedbythelengthoftheroad.Ifthehillisviewedasatriangle,thegradeisthesineoftheangleatthebottomofthehill.)Ariderstartsatthebottomofthehillataspeedof45kph,andthedecelerationoftheriderisproportionaltotheroadgrade.Ariderwillloseabout8kphforafivepercentgradeover100meters.
▪Task2.Provideanexampleofhowthetablecouldbeusedforaspecifictimetrialcourse.
▪Task3.Determineifthetableisanadequatemeansfordecidingonthewheelconfigurationandofferothersuggestionsastohowtomakethisdecision.
2001MCMB:
EscapingaHurricane'sWrath(AnIllWind...)
EvacuatingthecoastofSouthCarolinaaheadofthepredictedlandfallofHurricaneFloydin1999ledtoamonumentaltrafficjam.TrafficslowedtoastandstillonInterstateI-26,whichistheprincipalroutegoinginlandfromCharlestontotherelativelysafehavenofColumbiainthecenterofthestate.Whatisnormallyaneasytwo-hourdrivetookupto18hourstocomplete.Manycarssimplyranoutofgasalongtheway.Fortunately,Floydturnednorthandsparedthestatethistime,butthepublicoutcryisforcingstateofficialstofindwaystoavoidarepeatofthistrafficnightmare.
TheprincipalproposalputforthtodealwiththisproblemisthereversaloftrafficonI-26,sothatbothsides,includingthecoastal-boundlanes,havetrafficheadedinlandfromCharlestontoColumbia.Planstocarrythisouthavebeenprepared(andpostedontheWeb)bytheSouthCarolinaEmergencyPreparednessDivision.TrafficreversalonprincipalroadsleadinginlandfromMyrtleBeachandHiltonHeadisalsoplanned.
AsimplifiedmapofSouthCarolinaisshown.Charlestonhasapproximately500,000people,MyrtleBeachhasabout200,000people,andanother250,000peoplearespreadoutalongtherestofthecoastalstrip.(Moreaccuratedata,ifsought,arewidelyavailable.)
Theinterstateshavetwolanesoftrafficineachdirectionexceptinthemetropolitanareaswheretheyhavethree.Columbia,anothermetroareaofaround500,000people,doesnothavesufficienthotelspacetoaccommodatetheevacuees(includingsomecomingfromfarthernorthbyotherroutes),sosometrafficcontinuesoutboundonI-26towardsSpartanburg;onI-77northtoCharlotte;andonI-20easttoAtlanta.In1999,trafficleavingColumbiagoingnorthwestwasmovingonlyveryslowly.Constructamodelfortheproblemtoinvestigatewhatstrategiesmayreducethecongestionobservedin1999.Herearethequestionsthatneedtobeaddressed:
1.Underwhatconditionsdoestheplanforturningthetwocoastal-boundlanesofI-26intotwolanesofColumbia-boundtraffic,essentiallyturningtheentireI-26intoone-waytraffic,significantlyimproveevacuationtrafficflow?
2.In1999,thesimultaneousevacuationofthestate'sentirecoastalregionwasordered.Wouldtheevacuationtrafficflowimproveunderanalternativestrategythatstaggerstheevacuation,perhapscounty-by-countyoversometimeperiodconsistentwiththepatternofhowhurricanesaffectthecoast?
3.SeveralsmallerhighwaysbesidesI-26extendinlandfromthecoast.Underwhatconditionswoulditimproveevacuationflowtoturnaroundtrafficonthese?
4.WhateffectwouldithaveonevacuationflowtoestablishmoretemporarysheltersinColumbia,toreducethetrafficleavingColumbia?
5.In1999,manyfamiliesleavingthecoastbroughtalongtheirboats,campers,andmotorhomes.Manydrovealloftheircars.Underwhatconditionsshouldthereberestrictionsonvehicletypesornumbersofvehiclesbroughtinordertoguaranteetimelyevacuation?
6.Ithasbeensuggestedthatin1999someofthecoastalresidentsofGeorgiaandFlorida,whowerefleeingtheearlierpredictedlandfallsofHurricaneFloydtothesouth,cameupI-95andcompoundedthetrafficproblems.Howbiganimpactcantheyhaveontheevacuationtrafficflow?
Clearlyidentifywhatmeasuresofperformanceareusedtocomparestrategies.Required:
Prepareashortnewspaperarticle,nottoexceedtwopages,explainingtheresultsandconclusionsofyourstudytothepublic.
Clearlyidentifywhatmeasuresofperformanceareusedtocomparestrategies.
Required:
Prepareashortnewspaperarticle,nottoexceedtwopages,explainingtheresultsandconclusionsofyourstudytothepublic.
2001ICM:
OurWaterways-AnUncertainFuture
Zebramussels,Dreissenapolymorpha,aresmall,fingernail-sized,freshwatermollusksunintentionallyintroducedtoNorthAmericaviaballastwaterfromatransoceanicvessel.Sincetheirintroductioninthemid1980s,theyhavespreadthroughalloftheGreatLakesandtoanincreasingnumberofinlandwaterwaysintheUnitedStatesandCanada.Zebramusselscolonizeonvarioussurfaces,suchasdocks,boathulls,commercialfishingnets,waterintakepipesandvalves,nativemollusksandotherzebramussels.Theironlyknownpredators,somedivingducks,freshwaterdrum,carp,andsturgeon,arenotnumerousenoughtohaveasignificanteffectonthem.ZebramusselshavesignificantlyimpactedtheGreatLakesecosystemandeconomy.Manycommunitiesaretryingtocontroloreliminatetheseaquaticpests.SOURCE:
GreatLakesSeaGrantNetwork http:
//www.sgnis.org/.
ResearchersareattemptingtoidentifytheenvironmentalvariablesrelatedtothezebramusselinfestationinNorthAmericanwaterways.Therelevantfactorsthatmaylimitorpreventthespreadofthezebramusselareuncertain.Youwillhaveaccesstosomereferencedatatoincludelistingsofseveralchemicalsandsubstancesinthewatersystemthatmayaffectthespreadofthezebramusselthroughoutwaterways.Additionally,youcanassumeindividualzebramusselsgrowatarateof15millimetersperyearwithalifespanbetween4-6years.Thetypicalmusselcanfilter1literofwatereachday.
RequirementA:
Discussenvironmentalfactorsthatcouldinfluencethespreadofzebramussels.
RequirementB:
Utilizingthechemicaldataprovidedat:
ap/undergraduate/contests/icm/imagesdata/LakeAChem1.xls,andthemusselpopulationdataprovidedat:
ap/undergraduate/contests/icm/imagesdata/LakeAPopulation1.xls modelthepopulationgrowthofzebramusselsinLakeA.BesuretoreviewtheInformationaboutthecollectionofthezebramusseldata.
RequirementC:
UtilizingadditionaldataonLakeAfromanotherscientistprovidedat:
ap/undergraduate/contests/icm/imagesdata/LakeAChem2.xls andadditionalmusselpopulationdataprovidedat:
ap/undergraduate/contests/icm/imagesdata/LakeAPopulation2.xls corroboratethereasonablenessofyourmodelfromRequirementB.Asaresultofthisadditionaldata,adjustyourearliermodel.Analyzetheperformanceofyourmodel.Discussthesensitivityofyourmodel.
RequirementD:
UtilizingtheChemicaldatafromtwolakes(LakeBandLakeC)intheUnitedStatesprovidedat ap/undergraduate/contests/icm/imagesdata/LakeB.xls andap/undergraduate/contests/icm/imagesdata/LakeC.xls determineiftheselakesarevulnerabletothespreadofzebramussels.Discussyourprediction.
RequirementE:
ThecommunityinthevicinityofLakeB(inrequirementD)isconsideringspecificpoliciesforthede-icingofroadwaysnearthelakeduringthewinterseason.Provideguidancetothelocalgovernmentofficialsregardingapolicyon“de-icingagents.”Inyourguidanceincludepredictionsonthelong-termimpactofde-icingonthezebramusselpopulation.
RequirementF:
IthasbeenrecommendedbyalocalcommunityintheUnitedStatestointroduceroundgobyfish.Zebramusselsarenotofteneatenbynativefishspeciessotheyrepresentadeadendecologically.However,roundgobiesgreaterthan100mmfeedalmostexclusivelyonzebramussels.Ironically,becauseofhabitatdestruction,thegobyisendangeredinitsnativehabitatoftheBlackandCaspianSeasinRussia.Inadditiontoyourtechnicalreport,includeacarefullycraftedreport(3-pagemaximum)writtenexplicitlyforthelocalcommunityleadersthatrespondstotheirrecommendationtointroducetheroundgoby.Alsosuggestwaystohelpreducethegrowthofthemusselwithinandamongwaterways.
Informationaboutthecollection
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