美赛数学建模A题论文.docx
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美赛数学建模A题论文.docx
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美赛数学建模A题论文
Winterisapproaching,maythedragon’swingsgrowmoreabundant
Summary
Inthegameofthrones,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.
tableofContents
Winterisapproaching,maythedragon’swingsgrowmor..e...a..b..u..n..d..a..n..t1
Summary1
tableofContents2
1Introduction3
1.1restatement3
1.2ProblemAnalysis3
2Assumptionsandreasons4
3SymbolDefinition4
4.Mathematicalmodeling5
4.1AboutDragonFlightandSpitfireConsumption5
4.2Abouttherelationshipbetweendragon'sbodylengthandweightandage7
4.3AboutDragon'sFoodSupply8
4.4Regulatingtheareaofdragonsbyregion9
5Sensitivityanalysis10
6Modelevaluationandoutlook11
6.1Modelevaluation11
6.2Furtherdiscussion12
7toaletterfromGeorgeRRMartin12
8.Appendix:
13
8.1References13
8.2Matlabcode13
1Introduction
1.1restatement
InthemagicalTVseries"GameofThrones",DaenerysTargaryen,knownastheMotherofDragons,raisedthreedragonsasanaggressivearmy.DragonshavealwaysbeenthemostmysteriousmonstersinEasternandWesterncultures,butifDragonsliveinthepresentera,howshouldwefeedthethreedragonsinpursuitofmaximumgrowth?
Inthisarticle,weassumethatthegrowthrulesofdragonsareinlinewithbasicbiology.Tostudythem,webuildmathematicalmodelstosolveproblem.
a.Analyzethechangeofthedragon'sweightlengthwithage,andestimatethevalueofthedragon'sweightlengthcorrespondingtotheagegroup.
b.Investigatethelossofselfenergyduringdragonfire,flight,andbreathing,soastoestimatetheminimumsupplyvalueofdragonforexternalactivities
c.Dragonsneedfoodandsurvivalareaslikeotheranimalsintherealworld.Throughcertainassumptionsandcalculations,wecandeterminethetotalamountoffoodthatdragonsneeddailyandthesizeoflivingareasinthreeareas.
d.Sensitivityanalysis:
Astemperatureandclimatechange,dragonswillalsomigratetodifferentregions.Therefore,weneedtoanalyzethedifferencesintheimpactofdragonsonthesurvivalofaridregions,temperateregions,andcoldregions.
1.2ProblemAnalysis
Becausedragonsdonotexistinreallife,weneedtousesomethingsintherealworldtocomparedragonsinordertoachievethepurposeofstudyingdragons.Inanalyzingthebiologicalmorphologicalcharacteristicsofdragons,weusetheknowledgeofecologyandbasicelementsofbiologyLet'sconceivethebasicbiologicalcharacteristicsofthedragonsuchasweightandbodylength.Fortheenergylossmodelofthedragon,wehavestudiedthreeaspectstodescribeitsloss.Herewecomparethemodernflamethrowerandestablishrelatedchemicalequationstoachievetheresearchofthedragon.Spitfireloss.Inaddition,inTVseriessuchas"GameofThrones"wewillfindthatdragonscanflyincommonsense,sowehavederivedthedragon'sflightloss.Ofcourse,allaerobicorganismscanbreathe.Dragonsarenoexception,sothereisalossofbreathingtomaintainbodytemperature.Atthesametime,inordertomakeupforthelossofdragonsindailyactivities,wehaveestablishedamaterialreservemodel,inwhichmaterialsarecattleandsheepinreallife,etc.Finally,duringthecyclicalchangesinclimateandfood,thedragonswefeedwillalsomigratetosomeextent,soweanalyzedtheimpactofdifferentregionsonthegrowthofdragons.Intoaccountvariousfactorsthatwecanmorescientifictrainingofdragons,haveachievedourpurpose.
2Assumptionsandreasons
Afteracomprehensiveanalysisoftheproblem,inordertoincreasetheenforceability,wemakethefollowingassumptionstoensuretherationalityofourmodelestablishment.
2.1Assumptions:
Thebasicbiologicalcharacteristicsofdragonsareinlinewiththelawofbiologicalgrowth.Inmodernlife,thegrowthanddevelopmentofdragonsshouldalsobesimilartootheranimalsandconformtobasicbiology.
2.2Assumption:
Thedragonwillspitfireandfly,anditsflightconformstothephysicalenvironmentoffluidmechanics
Reason:
InGameofThrones,theimageofthedragonwasonceabletoflyandspitfire.
2.3Assumption:
Inthesinglefieldwearestudying,theenvironmentofacertainareawillnotchangeabruptlyandmaintainadynamicstability.
2.4Hypothesis:
Dragonsaretoppredatorsinthefoodchain,butdragonsdonotcausedevastatingharmtothebiosphere.
2.5Assumption:
Theweightdistributionofthedragonisuniform,andthebodylengthreaches30to40cmatthetimeofbirth.
Reason2.6:
Werefertoancientbiologyandsomedinosaurfossils.
2.7Hypothesis:
Exceptfortheskull,heart,liver,lungs,kidneys,bones,etc.,thesumofotherbodymassesisproportionaltothecubeofheight.
Reason:
Thehypothesisisobtainedbycountingtherelationshipbetweenbodylengthandweightofmodernorganisms.
2.8Hypothesis:
Thedragonisaconstanttemperatureanimalwhosebodytemperatureisnotaffectedbyexternalfactors.
Reason:
Afewpterosaurfossilshavetracesof"hair"onthesurface,whilethedragonsinGameofThronesaresimilartopterosaurs.
2.9Hypothesis:
Thedragonisfullyaerobicduringtheflighttoprovideenergy
2.10Hypothesis:
Acertainfixedratiooftheamountofenergythatisnotassimilatedbythegrowthandmetabolismofthedragon'sbreathingandotherorganisms
2.11Hypothesis:
Dragon'sFlightSimilartoModernFighter
3SymbolDefinition
symbol
description
M
quality
L
Bodylength
a%
Unassimilatedamountisafixedratioofintake
b%
Respiratoryandotherbiologicalgrowthmetabolicconsumptioncanbeafixedratioofassimilationamount
t、T、i
time
A
Acceleration
W
Consumeenergy
N
Amountofcattleandsheep
d%
Assimilationrateofcattleandsheepgrazinginthearea
K
Environmentalcapacity
e%
Solarutilization
Q
Solarenergyperunitarea
S
Flyingdistanceofdragon
S
area
R
Parametersofenvironmentalcarryingcapacity
V
Speedorrate
Y
age
4.Mathematicalmodeling
4.1AboutDragonFlightandSpitfireConsumption
4.1.1Proposedmodel
Consideringthatdragonsflyandspitfireduringactivities,wehaveestablishedanenergylossmodel.Comparingtheprincipleofdragon'sspitfirewithmodernflamethrowers,modernflamethrowersconsumehydrocarbonsoralcohols.Itdoesnotcauseanyimpact,sothedragon'sfirebreathingprincipleisinlinewiththealcoholflame-throwerprinciple.Consideringthattheformaldehydeproducedbythemetabolismofmethanolintheanimalbodyisharmfultothebody,westipulatethatethanolisthefuelusedbythedragon'sflame.Intheprocess,therelationshipbetweenthedragon'sflightspeedandglucoseenergyconsumptionisobtainedaccordingtofluidmechanics.Inthisprocess,weassumethattheaerobicrespirationiscompletelyperformed,andtheenergyconsumedbythedragonduetoflightisobtainedaccordingtotheglucoseconsumption.Insummary,thedragonenergylossmodelisobtained..
4.1.2EstablishmentandSolutionofDragon'sSpitfireModel
Thethermochemicalequationforethanolcombustionis:
C2H50H(l)+3O2(g)=2CO2(g)+2H2O(l)△H=-12KJ/g
Specifytheenergyreleasedperunitmassofethanolcombustionx1
Whenthedragonspitfireinunittimet,theunitm
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