Mathematics in Industry 33 The European Consortium for Mathematics in Industry Ewald Lindner Alessandra Micheletti Cláudia Nunes  Editors Mathematical Modelling in Real Life Problems Case Studies from ECMI-Modelling Weeks Mathematics in Industry The European Consortium for Mathematics in Industry Volume 33 ManagingEditor MichaelGünther,UniversityofWuppertal,Wuppertal,Germany SeriesEditors LuisL.Bonilla,UniversityCarlosIIIMadrid,Escuela,Leganes,Spain OtmarScherzer,UniversityofVienna,Vienna,Austria WilSchilders,EindhovenUniversityofTechnology,Eindhoven,TheNetherlands The ECMI subseries of the Mathematics in Industry series is a project of The European Consortium for Mathematics in Industry. Mathematics in Industry focusesontheresearchandeducationalaspectsofmathematicsusedinindustryand otherbusinessenterprises.BooksforMathematicsinIndustryareinthefollowing categories: research monographs, problem-oriented multi-author collections, textbookswithaproblem-orientedapproach,conferenceproceedings.Relevanceto the actualpracticaluse of mathematicsin industry is the distinguishingfeatureof thebooksintheMathematicsinIndustryseries. Moreinformationaboutthissubseriesathttp://www.springer.com/series/4651 Ewald Lindner (cid:129) Alessandra Micheletti (cid:129) Cláudia Nunes Editors Mathematical Modelling in Real Life Problems Case Studies from ECMI-Modelling Weeks Editors EwaldLindner AlessandraMicheletti InstituteofComputationalMathematics DepartmentofEnvironmentalSciencesand JohannesKeplerUniversityofLinz PolicyandDataScienceResearchCenter Linz,Austria Milano Universita`degliStudidiMilano Milano,Italy CláudiaNunes CenterforComputationalandStochastic Mathematics InstitutoSuperiorTécnico(IST), UniversidadedeLisboa Lisboa,Portugal ISSN1612-3956 ISSN2198-3283 (electronic) MathematicsinIndustry TheEuropeanConsortiumforMathematicsinIndustry ISBN978-3-030-50387-1 ISBN978-3-030-50388-8 (eBook) https://doi.org/10.1007/978-3-030-50388-8 MathematicsSubjectClassification:97Mxx,97M10,00A69 ©SpringerNatureSwitzerlandAG2020 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface In recent years, numerous reports and studies have demonstrated that Mathemat- ics is an essential tool to improve industrial innovation, and mixed academic– industrial consortia and networks, like ECMI (European Consortium for Mathe- maticsinIndustry—http://ecmi-indmath.org)andMI-Net(MathematicsinIndustry Network—https://mi-network.org/)areworkingtofostertherecognitionofMathe- maticsasanenablingtechnology. In this framework, an increasing need of mathematicians trained to work in an industrial environmenthas been observed and has pushed the academic world to provide novel training formats, able to respond to industrial needs. ECMI in particular has established an educational programme, offered by the ECMI EducationalCentres,whichisaimedtoprovidesuchtraining.Itsmainingredients are mathematical modelling activities, in particular the International Modelling Weeksandthemodellingseminars. The InternationalModelling Weeks formatis an internationalworkshop where master students and/or early-career investigators (PhD students and postdocs) receivehands-ontraininginproblem-solving,teamwork,andinlearningtoexploit their different skills to model efficiently non-mathematical problems. During modelling Weeks are training workshops where students from different countries spendaweekworkinginsmallmultinationalgroupsonprojectswhicharebasedon real-lifeproblems.Eachgroupisledbyaninstructorwhointroducestheproblem, usually formulated in non-mathematical terms, on the first day and then helps to guide the students to a solution during the week. The students present their resultstotheothergroupsonthelastdayandthenwriteuptheirworkasareport. This format allows to train students in mathematical modelling and stimulate their collaborationand communicationskills, in a multinationalenvironment.The instructors “emulate” the figures of real industrial delegates, thus pushing the studentstostartworkinginanon-academicenvironment. Modelling seminarsare also offeredlocally by the ECMI EducationalCentres. Theyhaveastructuresimilartothemodellingweeks,butareusuallyspreadoverone semester,andareattendedonlybythestudentsenrolledintheofferinguniversity. v vi Preface This book is a collection of real-world problems that have been assigned to students during the ECMI InternationalModelling Weeks. The problems are first described, and then a possible solution is proposed. The aim of this book is thus to provide a set of examples, in different fields of application, and faced with different mathematical techniques, to support teachers and instructors to organize futuremodellingactivities. Linz,Austria EwaldLindner Milano,Italy AlessandraMicheletti Lisboa,Portugal CláudiaNunes February2020 Contents 1 InverseProblemsinDiffuseOpticalTomographyApplications....... 1 PaolaCausinandRada-MariaWeishaeupl 2 1DModelsforBloodFlowinArteries.................................... 17 AlexandraBugalhodeMoura 3 UncertaintyQuantificationofChemicalKineticReactionRate Coefficients.................................................................. 35 É.ValkóandT.Turányi 4 NuclearAccidents:HowCanMathematiciansHelptoSave Lives? ........................................................................ 45 SimoneGöttlich 5 DrugDeliveryfromOphthalmicLenses ................................. 59 JoséAugustoFerreira 6 TheZombieInvasion....................................................... 71 JarosławGruszka 7 OptimalHeatingofanIndoorSwimmingPool ......................... 87 MonikaWolfmayr 8 SomeBasicEpidemicModels ............................................. 103 DanijelaRajter-C´iric´ 9 MathematicalModelfortheGameManagementPlan................. 117 MilanaPavic´-Cˇolic´ 10 EfficientParameter-DependentSimulationofInfectionsina PopulationModel........................................................... 133 FilippoTerragni vii viii Contents 11 OptimisingaCascadeofHydro-ElectricPowerStations .............. 147 MartaPascoal 12 NetworksofAntennas:PowerOptimization ............................ 155 StéphaneLabbé Chapter 1 Inverse Problems in Diffuse Optical Tomography Applications PaolaCausinandRada-MariaWeishaeupl 1.1 Introduction Aim of this material is to provide a guideline to the modeling and fast numerical solutionoftheinverseproblemarisinginthecontextofDiffuseOpticalTomography (DOT),aninnovativeimagingtechniquewhichfindsapplicationinseveralclinical settings. DOT applications extend to a wide ensemble of diagnostic/monitoring purposes, ranging from cancer screening—object of this work, and in particular forbreastcancerscreening—tomonitoringofbrainfunctioninnewbornsorstroke patients,toseizuredetectioninrealtime(see[11]foracomprehensivereview). Background In the seventeenth century, the French painter Georges de La Tour (1593–1652)portrayed in his work St. Joseph the carpenter the light of a candle transmitted throughthe thin fingersof the child Jesus (see Fig.1.1).The painter’s observationrepresentsacommonexperience,whichcanbeeasilyreproducedalso withpresentmeans:ifaflashlightisshoneontoone’shand,itisclearlyapparentthat lightcantravelthroughtissueandbedetectedontheothersidewithrespecttothe source.Thisfactmotivatestheuseoflighttoimagetheinsideofthebody,withthe benefitofanon-invasiveandnonionizingtechnique.Moreover,inabroadersense, physicians have always tried to diagnose health conditions from the appearance of a patient. However, the first attempts to use light as a quantitative diagnostic tool were impractical. The depth of penetration of light at visible frequencies is toolowtoallowforinvestigationsintissues/organsthickerthanafewmillimeters. In the context of breast screening, optical characterizationwas attempted in 1929 P.Causin((cid:2)) DepartmentofMathematics,UniversityofMilano,Milano,Italy e-mail:[email protected] R.-M.Weishaeupl DepartmentofEnvironmentalScienceandPolicy,UniversityofMilano,Milano,Italy ©SpringerNatureSwitzerlandAG2020 1 E.Lindneretal.(eds.),MathematicalModellinginRealLifeProblems, MathematicsinIndustry33,https://doi.org/10.1007/978-3-030-50388-8_1