2019美赛数学建模A题论文

1/13Winterisapproaching,maythedragon’swingsgrowmoreabundantSummaryInthegameofthrones,DaenerysTargaryendepictstheimageofadragon.Ineasternandwesterncultures,thephenomenonofdragonsisnotuncommon.Ifdragonsliveinmodernsociety,howcanweraisethesewarmonsters?Research,andappliedthecrossdisciplinesofbiology,physics,andchemistrytobuildamathematicalmodelandsolveittoachievethemaximumgrowthofthedragon.Ofcourse,dragonsdonotexistinreallife,sowelikenedpterosaurs,modernAircraftandchemicalburnertoderivethespecificphysiologicalcharacteristicsofthedragontoensuretherationalityandscientificityoftheresearch.First,westudiedtheflightandfire-spittingmodelsofdragons.Throughanalogicalreasoning,ourhypotheticaldragon'sfire-spittingprincipleissimilartomodernalcoholflamethrowers.Fordragonflight,weusedfluidmechanicstogetthedragon'sflightspeed.Andglucoseenergyloss.Combiningthetwotogettheenergylossmodelofthedragon.Second,westudiedthebasicphysicalcharacteristicsofthedragon.Fortherelationshipbetweenthebodylengthandbodyageofthedragon,weestablishedanelasticmodelofgrowth.Becausetheweightandbodylengthofdragonshaveupperandlowerlimits,inordertocomplywithbasicecology,wehavedefinedthedragon'sbonesaturationvalueasthecut-offvalue,andconductedasegmentedstudy.Whenstudyingtherelationshipbetweenweightandbodylength,Weknowthattheweightofthedragonisproportionaltothecubeofthebodylength.Then,becausethedragonneedsresourcestoreplenishlikeotheranimals,webuiltadragon'sfoodsupplymodel.SupposethatthethreedragonshavethesamecompetitivenessandthedailysheepResourcesarethesame.Accordingtoecology,whenthenumberofsheepinacertainareareachesk/2,weneedtomigratethedragon.Finally,thetemperaturewillaffectthelivingenvironmentofthedragon,sothedragonneedstofollowMigrationwasselectedforchangesintemperature,andweselectedthreeareasofdrought,cold,andwarmthtostudythedragon,andintegratedthemodeloftheregionalareaofthedragonbytheappealingmodel.Inaddition,wewrotealettertotheauthoroftheSongofIceandFire,givingsomesuggestionsontheactualecologicalfoundationofthedragon,hopingtobeadopted.Althoughthedragondoesnotexistinourreallife,thedragoncanbebrokendownintoPartofourmodernsociety.Forthedragon'sflyingspitfireenergylossmodel,wecanfurtherstudytheaircraft'sfluidmechanicsandmodernflamethrowers.Thestudyofnon-existentorganismsalsopreparesusforthearrivalofnewspecies.2/13tableofContentsWinterisapproaching,maythedragon’swingsgrowmoreabundant.............................................1Summary...............................................................................................................................1tableofContents....................................................................................................................21Introduction........................................................................................................................31.1restatement...................................................................................................................31.2ProblemAnalysis.........................................................................................................32Assumptionsandreasons...................................................................................................43SymbolDefinition..............................................................................................................44.Mathematicalmodeling.....................................................................................................54.1AboutDragonFlightandSpitfireConsumption.........................................................54.2Abouttherelationshipbetweendragon'sbodylengthandweightandage.................74.3AboutDragon'sFoodSupply......................................................................................94.4Regulatingtheareaofdragonsbyregion....................................................................95Sensitivityanalysis...........................................................................................................106Modelevaluationandoutlook..........................................................................................116.1Modelevaluation.......................................................................................................116.2Furtherdiscussion......................................................................................................127toaletterfromGeorgeRRMartin...................................................................................128.Appendix:.........................................................................................................................138.1References.................................................................................................................138.2Matlabcode...............................................................................................................133/131Introduction1.1restatementInthemagicalTVseriesGameofThrones,DaenerysTargaryen,knownastheMotherofDragons,raisedthreedragonsasanaggressivearmy.Drago