Mathematical Models and Methods for Planet Earth PDF
Preview Mathematical Models and Methods for Planet Earth
Springer INdAM Series 6 Alessandra Celletti Ugo Locatelli Tommaso Ruggeri Elisabetta Strickland Editors Mathematical Models and Methods for Planet Earth Springer INdAM Series Volume 6 Editor-in-Chief V.Ancona SeriesEditors P.Cannarsa C.Canuto G.Coletti P.Marcellini G.Patrizio T.Ruggeri E.Strickland A.Verra Forfurthervolumes: http://www.springer.com/series/10283 · · Alessandra Celletti Ugo Locatelli · Tommaso Ruggeri Elisabetta Strickland Editors Mathematical Models and Methods for Planet Earth Editors AlessandraCelletti TommasoRuggeri DipartimentodiMatematica DipartimentodiMatematica UniversitàdegliStudidiRoma UniversitàdegliStudidiBologna “TorVergata” Bologna,Italy Roma,Italy UgoLocatelli ElisabettaStrickland DipartimentodiMatematica DipartimentodiMatematica UniversitàdegliStudidiRoma UniversitàdegliStudidiRoma “TorVergata” “TorVergata” Roma,Italy Roma,Italy ISSN:2281-518X ISSN:2281-5198(electronic) SpringerINdAMSeries ISBN978-3-319-02656-5 ISBN978-3-319-02657-2(eBook) DOI10.1007/978-3-319-02657-2 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2013949326 ©SpringerInternationalPublishingSwitzerland2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection withreviewsorscholarlyanalysisormaterialsuppliedspecificallyforthepurposeofbeingenteredand executedonacomputersystem,forexclusiveusebythepurchaserofthework.Duplicationofthispub- licationorpartsthereofispermittedonlyundertheprovisionsoftheCopyrightLawofthePublisher’s location,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Permis- sionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violationsareliable toprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateofpublica- tion,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityforanyerrors oromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,withrespecttothe materialcontainedherein. CoverDesign:RaffaelaColombo,GiochidiGrafica,Milano,Italy TypesettingwithLATEX:PTP-Berlin,ProtagoTEX-ProductionGmbH,Germany(www.ptp-berlin.de) SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface More than ahundred scientific societies, universities, research institutes and orga- nizationsfromaroundtheworldhavebandedtogethertodedicate2013asaspecial year for the Mathematics of Planet Earth. The Italian partner which endorsed the MPE2013 initiative is INdAM, the National Institute of Advanced Mathematics. First founded in 1939 by the noted mathematician Francesco Severi, the aims of INdAM are the training of researchers in mathematics, especially in the emerging branches,inordertofosterthetransferofknowledgetotechnologicalapplications andpromotecontactbetweenItalianandinternationalmathematicalresearch.Inor- der to achieve its objectives in training researchers and in supporting excellence programs, INdAM offers fellowships from undergraduate level to experienced re- searchers,aswellasorganizingworkshops,meetingsandschools. INdAM has decided to share in and support the mission of the MPE2013, as it shares the desire of the world’s mathematical community to learn more about thechallengesfacedbyourplanetandtheunderlyingmathematicalproblems.The MPE2013initiativeorganizedbyINdAMtookplaceinRome,Italy,onMay27–29, 2013,andconsistedintheWorkshop“MathematicalmodelsandmethodsforPlanet Earth”, organized by Alessandra Celletti (Università di Roma Tor Vergata), Ugo Locatelli (Università di Roma Tor Vergata), Tommaso Ruggeri (Università di Bologna)andElisabettaStrickland(UniversitàdiRomaTorVergata). Overthecourseoftheworkshopaninternationalgroupofmathematicians(name- lyallcorrespondingauthorsofthefollowingchaptersandotheroutstandinginvited speakers) with a very wide range of expertise in various branches presented find- ings on several themes related to the MPE2013: Earth as a planet to discover, a planetsupportinglife,aplanetorganizedbyhumans,andaplanetatriskfromceles- tialthreats.Thetopicsofthetalksconcernedsocial,biological,medical,geological andastronomicalproblemsrelatedtoourplanet.Mathematicalmethodsforstudying complexsystemsarisinginthefieldsofsocialpreventionandsocio-economicprob- lemswerepresented withtheaim,forexample, tounderstandemergingcollective behaviours of a high number of interacting units. In particular, stochastic models canbeusedtoinvestigatecomplexsocialandbiologicalbehaviours.Inbiologyand medicine,mathematicsplaysapivotalrolethroughmodellingandsimulationsina vi Preface diverserangeofcontexts:fromthebehaviourofcellsandtissuestothedescription oftumourgrowths.Theleadingroleofmathematicsinsupportingourplanetisalso witnessedbytheauthorshipattributionofliteraturetextsandbymodelsforfuture internetinformationdissemination. Beyond the investigation of human-related aspects, mathematics allows us to studythephysicalcharacteristicsofourplanet.Mostnotably,sometalkswerede- votedtothecalibrationofthegeologicaltimescales(acrucialaspectwhichallows ustoretrievespecificeventsinEarthhistory),totheinvestigationofboundarylay- ersassociatedwithlarge-scaleoceancirculationand,fartherupintheatmosphere,to studyingtheEarth’sclimatevariabilityandchangesusingthetheoryofdynamical systems. SafeguardingtheEarthisnotlimitedtoourplanetanditsatmospherebut-aswe areonlyonepartofthesolarsystem-onereallyneedstoinvestigatetheinteraction oftheEarthwiththeotherbodiespopulatingtheneighbouringsky.Indeed,thein- vestigation of theso-called N-bodyproblem allowsustostudy thestability ofthe Earth’s dynamics as well as to identify new interplanetary trajectories. The recent impactofthemeteoriteinChelyabinsk(Russia)alertedmankindtothenecessityof protectingtheplanetfromnear-Earthasteroidhazardsandofdevelopingmitigation strategies.Finally,wearealsodefinitelyworriedbythethousandsofpiecesofspace debrisfromdefunctsatellitesandfragments,whichnowsurroundtheEarthandform adangerousenvelope:amathematicalinvestigationofthedynamicsofspacedebris hasnowbecomevital. Inadditiontothetalksdevotedtotheinvestigationoftheabovetopics,aspecial eventoftheWorkshopwasthepubliclecturebyChristianeRousseau(Universitéde Montréal), vice-president of the International Mathematical Union. Her talk dealt withthecomplexityoftheEarthasawholeandoutlinedtheroleofmathematicsin protectinganddiscoveringourplanet. Oneinterestingaspectthatcameoutofthismeetingisthattheamountofdatain- volvedinsomescientificproblemshasbecomeoverwhelminglylarge,sothatthere isanapparentlossofsimplicitybetweenmathematicsanditsapplications.Todayno onecouldsodeeplymasterasmanymathematicalargumentsasPoincaréorHilbert wereabletodoacenturyago;butallthespeakersattheworkshopclearlyshowed that mathematicians are now also challenged in the opposite direction: more and more research topics require deep mathematical knowledge, often to tackle prob- lemsinthecontextofnetworkteams.Thoughabstractioncanallowmathematicsto remainpure,mathematiciansarecalledupontomoreintensivelyworktogetherwith therestofthescientificcommunity. INdAMbelievesthatthecollaborationsandeffortsofallscientistswhopartici- patedintheworkshoppointedoutthatourplanetishometodynamicprocessesof allsorts.Thechallengesfacingourplanetandourcivilizationaremultidisciplinary andmultifaceted,andthemathematicalsciencesplayacentralroleinscientificef- fortstounderstandandeffectivelyaddressthosechallenges. INdAMsincerelybe- lievesthatMPE2013willalsohelpustomotivatestudentsandyoungresearchesby providingstimulatinganswerstoquestionslike:“Whatismathematicsgoodfor?”. WeconcludebyquotingMartaSanz-Solé,PresidentoftheEuropeanMathematical Preface vii Society; at the UNESCO Headquarters in Paris during the MPE Day on 5 March 2013, she stated that “The MPE2013 initiative will expose mathematicians to the wholeworld,byshowingtheirusefulnessandstimulatingresearch.Fromnowon, mathematics can no longer be associated with a pure intellectual exercise without connectiontothemostimportantproblemsofmankind”.WehopethattheINdAM Workshophascontributedtopursuingthosegoals. Roma,2013 AlessandraCelletti UgoLocatelli TommasoRuggeri ElisabettaStrickland Contents MathematicsofPlanetEarth...................................... 1 ChristianeRousseau TheRoleofBoundaryLayersintheLarge-scaleOceanCirculation ..... 11 LaureSaint-Raymond Noise-induced Periodicity: Some Stochastic Models for Complex BiologicalSystems............................................... 25 PaoloDaiPra,GiambattistaGiacominandDanieleRegoli KineticEquationsandStochasticGameTheoryforSocialSystems...... 37 AndreaTosin UsingMathematicalModelling asaVirtualMicroscope toSupport BiomedicalResearch............................................. 59 ChiaraGiversoandLuigiPreziosi FerromagneticModelsforCooperativeBehavior:RevisitingUniversality inComplexPhenomena .......................................... 73 ElenaAgliari,AdrianoBarra,AndreaGalluzzi,AndreaPizzoferratoand DanieleTantari TheNearEarthAsteroidHazardandMitigation ..................... 87 EttorePerozzi MathematicalModelsofTextualData:AShortReview................ 99 MirkoDegliEsposti SpaceDebrisLongTermDynamics ................................ 111 AnneLemaitreandCharlesHubaux MathematicalModelsforSocio-economicProblems................... 123 MariaLetiziaBertottiandGiovanniModanese ix x Contents ClimateasaComplexDynamicalSystem ........................... 135 AntonelloProvenzale PeriodicOrbitsoftheN-bodyProblemwiththeSymmetryofPlatonic Polyhedra...................................................... 143 GiovanniFedericoGronchi SuperprocessesasModelsforInformationDisseminationintheFuture Internet........................................................ 157 LauraSacerdote,MicheleGaretto,FedericoPolitoandMatteoSereno Appendix:PicturesfromINdAMWorkshop...........................171 Mathematics of Planet Earth ChristianeRousseau AbstractWhydidIstartMPE2013?MaybebecauseIamadreamer... Ilovena- ture, I love mathematics and I am concerned with the planet. My own research is notinappliedmathematics,butIlikepopularizingmathematicsandwhenIdoso, Iusuallypresentthemesthatarefarfrommyownresearch.Indeed,oneofmyrole as scientist is to “digest” research papers, to extract the ideas and to explain then insimpletermshowmathematicsisdevelopingwithinsciencearoundus.Fromthe beginning, thethemeofMathematics ofPlanetEarthappeared tomeasveryrich. Now, four years after I started MPE2013, the theme appears as immense and one ofmyrewardsforcoordinatingMPE2013istocontinuouslylearnnewMPEtopics. At the same time, I am becoming more militant for the planet. In this note, I will describetoyousomeoffacetsofMPEthatIhavediscoveredwiththehopethatyou will yourself get interested in the mathematics behind discovering, understanding, organizingandprotectingourplanet. To help exploring “Mathematics of Planet Earth” we often divide it into four themes: • Aplanettodiscover. • Abiologicallydiverseplanet. • Aplanetorganizedbycivilization. • Aplanetindanger. 1 A planettodiscover OneofmyfavoritethemewhenIdooutreach isthatmathematics allowstotrans- formdataandobservationsintosomevisionofanobject:weputour“mathematical C.Rousseau( ) Départementdemathématiquesetdestatistique,UniversitédeMontréal,C.P.6128,succ.Centre- ville,Montréal,Qc,H3C3J7,Canada e-mail:[email protected] A.Celletti,U.Locatelli,T.RuggeriandE.Strickland(eds.):MathematicalModelsandMeth- odsforPlanetEarth.SpringerINdAMSeries6,DOI10.1007/978-3-319-02657-2_1, ©SpringerInternationalPublishingSwitzerland2014
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