Table Of ContentMathematics 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.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor
theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany
errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional
claimsinpublishedmapsandinstitutionalaffiliations.
ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG.
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
