Mathematics with industry: driving innovation

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ECMIMissionMathematics, as the universal language of the sciences,plays a decisive role in technology, economics and the lifesciences. European industry is increasingly dependent onmathematical expertise in both research and developmentto maintain its position as a world leader for hightechnology and to comply with the EU 2020 agenda forsmart, sustainable and inclusive growth. ECMI initiatives inresponse to these needs may be summarized as follows:

ECMI advocates the use of mathematical modelling,simulation, and optimization in industry

ECMI stimulates the education of young scientists andengineers to meet the growing demands of industry

ECMI promotes European collaboration, interaction andexchange within academia and industry

Mathematics with industry:driving innovation

Annual Report 2017

Imprint

Editor: Andreas Münch

Guest editors: Adérito Araújo,Cláudia Nunes

ECMI Secretariat:Prof Poul G. HjorthTechnical University of DenmarkMatematiktorvet 303-BDK-2800 Kgs. Lyngby, DenmarkEmail: [email protected]

Guideline for author & templates:https://ecmiindmath.org/annual-reports/.

For more informations pleasevisit the ECMI website:https://ecmiindmath.org

Print ISSN: 2616-7867Online ISSN: 2616-7875

ECMI EUROPEAN CONSORTIUM FORMATHEMATICS IN INDUSTRY ECMI EUROPEAN CONSORTIUM FOR

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Contents

5 1 Editorial

7 2 Welcome from the President

9 3 Activities and Initiatives

10 131st ESGI

15 4 Featured People

16 Interview: Peregrina Quintela

19 Interview: Milana Pavi�-�oli�

23 5 Projects and Case Studies

24 Universality

34 Optimization of buckling for textiles

39 Dynamics of the capillary rise

43 Mathematical Algorithms for MICADO

49 6 Educational Committee

50 Experience as an Instructor during aModelling week

51 University of Verona

53 7 ECMI Special Interest Groups (SIGs)

54 Math for the Digital Factory

55 Sustainable Energies

57 Computational Finance

60 Mathematics for Big Data

62 Liquid Crystals, Elastomers and BiologicalApplications

65 Shape and Size in Medicine, Biotechnologyand Materials Science

67 Advancing the Design of Medical Stents

70 Net Campus for Modeling Edu-cation and Industrial Mathematics

73 8 About ECMI

75 9 Institutional members

1EditorialDear Colleagues!

When this issue leaves the printers shortly, many ECMImembers will already have their eyesset on this year’s ECMI conference in Budapest. The biannual series e�ectively started 35 yearsago, in 1983, in one of the epicenters of mathematics, Oberwolfach, followed by Amsterdamand then Oberwolfach again for the third conference in 1987. These conferences did not yetcontain the name of ECMI and ECMI did not exist as an institution; its �rst president only tooko�ce in 1987. After that, the series acquired its current name. Conference sites moved aroundEurope, to the North, South and West - but not yet to the East: This year’s 20th Europeanconference on Mathematics is the �rst one to be in an East European city!

This comes at a time when Industrial Mathematics (or Maths in Industry) is gaining a strongerfoothold in the Eastern European countries – only this year, Romania joined the ranks of ECMI.Hence the idea that it is worthwhile for mathematics to engage with industry - and vice versa! -continues to spread since 1983, when the concept of a study group and “Maths in Industry” asa discipline were new and needed to be explained to the many uninitiated. Today, the additionof new members and the ongoing Modelling Weeks and European Study Groups demonstratesthat ECMI and its view on mathematics and the interaction with industry are alive and thriving.It still continues to bring together Mathematicians and practitioneers of the various branches ofindustry – do take a look at the 2017 report, or come to Budapest, if you need any reassurance.

See you all in Budapest!

Andreas Münch, University of Oxford, May 2018

Collaborate and Cooperate Annual Report 2017 5

2Welcome fromthe PresidentDear colleagues,

This is already my second and last welcome letter as president before Adérito Araújo takesover and I would like to thank him and the other board members (Poul Hjorth, Jan ter Maten,Stephen o’Brien, Cláudia Nunes, Wil Schilders) for their support during the last two years.

Recently, a number of activities in industrial mathematics haven been initiated supported byECMI. EU-MATHS-IN, the European Service Network of Mathematics for Industry and Innovation is atop-down network of networks striving to emphasise the importance of mathematics forinnovations in key technologies on a European scale. The COST action TD1409, Maths forIndustry Network, aims at increasing the interaction between industry and academia by runningindustry workshops, training weeks, and short-term scienti�c missions to both academic andindustrial hosts.

But besides of all these important activities, ECMI remains a cornerstone for the collaborationbetween academia and industry in Europe. As a bottom-up network of more than 100institutional members in 24 European countries and Israel, ECMI’s Educational Committeetoday overseas more than 20 high-standard master programmes in industrial andecono-mathematics, it organises modeling weeks and summer schools. We support theEuropean collaboration, interaction and exchange within academia and industry in SpecialInterest Groups. Moreover, ECMI now overseas the European Study Groups with Industry, a bynow 50 years old success story in fostering math and industry collaboration. The third pillar ofECMI’s work is outreach: we have a Springer bookseries and a journal in IndustrialMathematics. As a service to the community, ECMI has established a new blog providingup-to-date information on workshops, projects, positions and opportunities in industrial andapplied mathematics. Last but not least the outreach events with highest visibility are thebiennial European Conferences on Mathematics for Industry. This summer we will have the


20th ECMI conference in Budapest. All in all it is fair to say that ECMI is a truly Europeansuccess story proving the bene�t of international collaboration and I am very grateful that I hadthe chance to contribute to its development as president during the last two years.

Now, presidents come and go every other year but before I come to an end it is my pleasure toexpress my great appreciation to Jan ter Maten for eight years of dedicated and invaluableservice to ECMI. Since 2008, Jan served ECMI in dual role both as treasurer and secretary. Hehas been a pillar of trust and a steadfast guardian of ECMI’s funds, he was the primary contactfor all ECMImembers and supported four presidents in preparing and holding numerouscouncil and board meetings!

From 2018, the duties as secretary will be taken over by our executive director, Poul Hjorth.Moreover, I’m happy to announce that Thomas Götz from the University of Koblenz–Landauhas accepted to be the treasurer for the next four years. Together with our new presidentAdérito Araújo and our new vice president Nata�a Kreji� I am sure they will do an excellent jobin shaping ECMI’s future in the coming years.

Dietmar HömbergWeierstraß-Institut and Technische Universität BerlinMay 2018

8 Collaborate and Cooperate Annual Report 2017

3Activities and

Initiatives

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Ongi etorri ESGI!The 131st European Study Group with Industry took place in Bilbao, Spain,from 15th to 19th May 2017 at BCAM - the Basque Center for AppliedMathematics. This was the �rst time an ESGI was held in the BasqueCountry.

BCAM (www.bcamath.org) is the researchcenter on Applied Mathematics which aimsto strengthen the Basque science andtechnology system, by performinginterdisciplinary research in the frontiers ofmathematics, excellence scienti�c research,talented scientists’ training, and attraction.

Figure 1. Poster of the 131st ESGI.

BCAM’s motto say “Mathematics, a world ofpossibilities at the service of Basqueindustry”.

“Mathematics, a world ofpossibilities at theservice of Basqueindustry”

During an exciting week, companies andacademic participants with expertise inMathematical �elds joined their e�orts tocreate new mathematical solutions for theneeds of the Basque industry.

Challenges

At the 131st ESGI, the participants workedon four challenges:

1. Parametric Design by Computational FluidDynamics Simulation.

2. Improvement of the Contact CenterPerformance.

3. Self-Organized Networks.

4. Big Data in Sports: Predictive Models forBasketball Player’s’ Performance.

The 4th Challenge was of particular interestfor many participants and a success storywhich encompasses data analysis and avariety of mathematical techniques fromstatistical learning, regression techniques

“Ongi etorri” means “Welcome” in Basque language

10 Collaborate and Cooperate Annual Report 2017 Activities and Initiatives

and predictive modelling of Basketballplayer’s performance from a historicaldatabase of professional Basketball leagues.

Data Science in professionalBasketball

Data analytics in professional sports hasexperienced such rapid growth in recentyears that the way professional sports aremanaged is changing. The world ofprofessional sports is only just starting toexplore this world of applying Data Scienceto gain a competitive advantage.

“The world ofprofessional sports isonly just starting toexplore this world ofapplying Data Science togain a competitiveadvantage”

Aryuna c� is a platform that allowsperforming advanced data analytics ofmen’s professional basketball statistics ofthe last 16 seasons in more than 25professional leagues and 71 FIBAtournaments. The challenge consisted ofthe next four goals:

1. Study the performance curve, peak andoptimal age of a basketball player in topEuropean leagues.

2. Player’s performance and their in�uencein the game.

3. Rating correction factor for di�erentbasketball leagues.

4. Which factors predict a successfulprofessional career?

Sports metrics

Sports metrics is the term for the empiricalanalysis of Statistics in sports that measurein-game productivity and e�ciency. Inbasketball, player’s statistics are usuallyproduced by the player per 100 Team’spossessions. Some important metrics are:

OE (O�ensive E�ciency): measures thequality of o�ensive production. OE is thetotal number of successful o�ensivepossessions the player was directlyinvolved in divided by that player’s totalnumber of potential ends of possessions

EOP(E�cient O�ensive Production): isde�ned as

EOP= (0,76⇤Assists+Points)⇤OE

Data and Methods

A database containing a total of 44 variablesof 5227 professional basketball playersduring seasons 2000-2015, and sixcompetitions (Euroliga, Eurocup, ACB,Argentina, ABA, ProA) was provided for thechallenge. The participants of this challengeworked in small groups and used the OpenSource Software R to perform the Statisticalanalysis and �t statistical models.

In order to address the 1st goal and studythe performance curves, the EOPx40M (EOPper 40 minutes) for each player in allseasons and competitions was consideredin a linear mixed-e�ects model withvariables “Position” (center, forward andguard) and “Age”, a quadratic term for “Age”and interaction terms between “Position”and “Age”. The variability of the player’s wasaccounted by a random e�ect term, i.e.uPlayer ⇠ N (0,s2

Player). The quadratic term ofthe model is intrinsically assuming thatprofessional athletes performance isunimodal (i.e., it reaches a maximum). Themodel was �tted with the function lme fromthe R library for linear mixed-e�ects modelsnlme.

Activities and Initiatives Collaborate and Cooperate Annual Report 2017 11

Figure 2, shows the �tted curves, where thepeak of performance for “Ages“ (and their95% con�dence intervals) by “Position” areCenter: 27.23 (26.48, 27.98) years; Forward:27.46 (27.00, 27.92) years and Guard:28.08 (27.57, 28.59) years. These peaks andtheir statistical uncertainties are between 26and 29, which are similar to those for theNBA, 27-30.

15 20 25 30 35 40

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Age (y)

EO

P p

er

40 M

in

Figure 2: Performance curves by “Age” for centers,

forwards and guards. Their respective maxima are

represented by dots.

However, one might be interested in thepeak performance of a player’s EOPx40Mbased on his experience as a professionalbasketball player. Therefore, the samelinear mixed-e�ects model was �tted,including a new variable we named as“Years of experience” instead of “Age”. Thisnew variable was created assuming thatthose players from the 2001 seasonyounger than 20 were playing their �rstseason. This new variable may account forthe fact that the peak performance reachesa di�erent maximum depending on theplayer’s position. Peak performance for“Experience” (and their 95% con�denceintervals) by position are Center: 10.63 (2.37,18.88) years; Forward: 7.35 (5.76, 8.93) yearsand Guard: 9.46 (6.38, 12.55) years.

Figure 3, shows the performance peaksbased on “years of experience”. They arebetween 7 and 11 years, which are similar tothose for the NBA (6-8 years). The 95%con�dence intervals are much larger

(especially for the center players) due to thelack of players that met the condition wede�ned as “Years of experience”. Analternative de�nition of “Experience” couldhave been considering the number ofgames played or the numbers of seasonssince professional debut.

0 2 4 6 8 10 12 14

05

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Experience (y)

EO

P p

er

40 M

inFigure 3: Performance curves by “years of experience” for

centers, forwards and guards. Their respective maxima are

represented by dots.

For the 2nd goal (“Player’s performance andtheir in�uence in the game”) we startedconsidering the player’s shot precision (i.e.:Free-throws, 2-Points and 3-Points shoots).Thus, we consider the performance by“100xPossesions” or “x40 Minutes”. Theresults for this goal were not conclusive tocon�rm any evidence of player’sperformance in the game. We consider theplayer’s performance based on theteammates on the court might be importantinformation to be considered in furtheranalysis.

For the 3rd goal (“Rating correction factorfor di�erent basketball leagues”). Weconsider basketball competitions may bedi�erent depending on the level of theteams/players, the number of games, thelevel of competitiveness, o�ensive ordefensive game-play, etc. The Euroleague isthe most prestigious basketball competitionaround the world besides NBA, and it isplayed by top teams in Europe. During theregular season, the teams in the Euroleaguealso compete in their local competition.


Argentina league was also considered forthe analysis because many players of thatleague end up playing in Europe andviceversa. All those aspects were modelledusing Analysis-Of-Variance (ANOVA) modelsfor some particular variables such as“Points” (scored/attempted), “Fouls”, “Blocks”,“O�ensive” and “Defensive rebounds”, “Steals”,“Turnovers” or “Assists” per 100 possessions.

Table 1. Summary of ANOVA models for each of the basic

game variables. Darker colors imply smaller p-values

ranking from <0.001 to <0.01, to <0.05 and to <0.1.

Table 1, present some evidence about thedi�erence among the leagues.

Finally, the 4th goal (“Which factors predictsa successful professional career?”) was themost challenging task. As a measure ofsuccess, we considered the variableEOPx40M converted to a binary variable(0=Fail and 1=Success), where above the10th quantile of EOPx40M among all playersis equal to 1, otherwise 0.

Figure 4: Correlation matrix of selected features using

Random forests and Cross-validation.

A random forest algorithm was performed

for the most important game-relatedfeatures for prediction using R softwarelibraries randomForest and caret. Figure 4shows the correlation matrix for the 13 outof 44 selected variables by the randomforest algorithm.

Figure 5: Plot of highest correlated odds-ratios.

The odds-ratios (OR) of the most highlycorrelated variables (9 out-of 13) predictedwith the random forest algorithm are shownin Figure 5. A OR’s greater than 1, indicatethe variables more likely the event ofsuccess. Variables such as “Steals” and“O�ensiveRebounds” (not included in the EOPformula) have an estimated OR close to 2.

Conclusions

The data analysis of this challenge providedstatistical evidence from a large historicalprofessional basketball sport metrics. TheESGI team provided new insights that mayhelp to provide new perspectives tobasketball management and sports dataanalytics via statistical modelling. The groupmade lots of interesting suggestions to thecompany specialists, particularly on thedesign of data acquisition tool andcodi�cation of some of the variables. Thereare some open questions suggested by theESGI team, such as the subjective nature ofsome metrics (as it is not easy to �nd aoverall global measure), since most of them,favours the o�ensive game play rather thandefensive game play. For the successfulcareer, the interest of the professionalbasketball managers is to know whichvariables can help them to identify a

Activities and Initiatives Collaborate and Cooperate Annual Report 2017 13

potential top player. i.e., a successful careercan be considered as, winning an MVP (mostvaluable player) trophy or signing along-term contract with an NBA team.Unfortunately, the database did not containsuch information in order to measuresuccess.

Summary of the 131st ESGI

For the Basque Center for AppliedMathematics, the ESGI was a greatopportunity to attract companies and morethan 30 academic participants includingMaster and PhD students, Postdoctoralfellows with expertise in Mathematical �eldsincluding Computer Science, Statistics andEngineering to create new mathematicalsolutions for the Basque industry.Laster arte ESGI ! (see you soon ESGI !).

Visit the event webpage athttps://wp.bcamath.org/esgi131

Ainara GonzálezDae-Jin Lee

Basque Center for Applied Mathematics


4FeaturedPeople

15

Interview:Peregrina Quintela

Today we are interviewing ProfessorPeregrina Quintela from the Universidadede Santiago de Compostela, known mainlyfor her incessant activity in the promotion ofIndustrial Mathematics. She was Presidentof the 2016 ECMI Conference OrganizingCommittee, which was held in Santiago deCompostela in June 2016, and a leading�gure in the creation and support ofnational networks of IndustrialMathematics.

You have been a promoter and �rstpresident of the Spanish Network forMathematics & Industry in 2011.What led you to promote thisinitiative?Actually the creation of the “math-in”network was something natural: in Spainthere are numerous research groups with a

special inclination to developing newtechnologies applicable to the industry. Atsome point, with all the accumulatedexperience, it was clear that an e�ort had tobe made to make companies aware of thegreat potential of Mathematics, somethingthat many of them did not know. Thisbecame a challenge for all of us, Spanishmathematicians. We were looking for a wayto show with practical cases and simplelanguage the ability of Mathematics toprovide solutions adapted to each industrydemand. We needed to establish a structurethat was broad and coordinated so we couldquickly connect a company with the mostexperienced researcher in their area. Andobviously, being such a heterogeneousgroup of researchers scattered throughoutSpain does not help. It was necessary toestablish synergies among us, quicklyconnect supply and demand and, above all,to sensitize companies to generate newdemands. That is how the “math-in”network was launched, completely �tted torespond to these needs.

What strategies have been followedto achieve these objectives that youhave highlighted?We cannot talk about a single strategy, but acombination of several. In the �rst place, aclimate of trust among the mathematiciansthemselves was generated; this allowed usde�ning a single catalogue of mathematicaltechnologies for the industry in Spain. Atthe same time, we carried out a macrosurvey to establish a demand map formathematical technology that would allowus to better understand our industry and itsneeds. Both studies were combined withmultiple informative e�orts, such as visiting

16 Collaborate and Cooperate Annual Report 2017 Featured People

representative enterprises, organization ofdissemination days and workshops,participation in technology platforms andforums in which the majority of attendantsare from the industry.

How many research groups andresearchers participate in math-in?Nowadays, about thirty research groups ofalmost 20 Spanish universities and researchcenters are membership of “math-in”; thismeans more than 450 Spanish researchers.We also have sponsor companies such asArcelor Mittal, BSH Electrodomésticos, orRepsol.

How is the involvement of theSpanish network in EU-MATHS-IN?You are also part of the BoardCommittee, right?Actually, “math-in” was one of the sixfounding networks of EU-MATHS-IN. Westarted this initiative in 2013 seeking tointensify collaboration with industry at aEuropean level. To achieve this,EU-MATHS-IN tries to connect the nationalnetworks of the di�erent countries–currently there are already 17– andharmonize a joint path. In this sense, a lot ofwork has been done using severalcomplementary strategies too. We havepushed to place Modelling, Simulation andOptimization (MSO) as an emergenttechnology in the European institutions, andin particular in the strategic lines of theH2020 Programme. We started an initiativeto implement a European technologicalplatform for which a good number of bigEuropean companies have been mobilized,all of them convinced of the essential rolethat Mathematics must play in theirprocesses improvement. I am convincedthat achievements in this area will soon beseen. Attention has also been given toindustrial doctorates, which allow fore�ective collaborations between Academiaand Industry in the training of youngresearchers. This new worker pro�le is ofgreat interest for the industry and will be

our best ambassadors in the future. Justrecently, two H2020 proposals have alsobeen submitted, targeting industry andinnovation through MSO. So since at“math-in” we are convinced thatinternational cooperation can be adetermining factor in the future of IndustrialMathematics and the society in general,“math-in” itself is collaborating, supporting,and promoting joint initiatives withEU-MATHS-IN.

In addition, you are the director ofthe Technological Institute ofIndustrial Mathematics (ITMATI) thatwas created in 2013. Why did theneed arise to create this Institute?ITMATI was the result of an agreementbetween the three Galician universities tounite around 150 researchers with a strongvocation towards the e�ective transfer ofknowledge developed in their universities.We are talking about a region innorth-western Spain that constitutes amicrocosm with a history of more thanthirty years e�ectively collaborating with theindustry. ITMATI was launched in 2013 as anew concept of the Technology TransferUnit, since it not only promotes andfacilitates the transfer but also executes itsown projects and transfer contracts. Seniorresearchers who pass a selective processcan dedicate up to 25% of their day to theinstitute, and this is our greatest asset.

How do you think the transferactivity developed in ITMATI enrichthe microcosm to which youreferred?There is no doubt that it hasprofessionalized the transfer activitytowards companies, and it provides moreagile responses. ITMATI has also created anAcademia-Industry bridge for the training ofrecent graduates, both for the completion ofMaster’s thesis and industrial doctorates. SoI think that it is indirectly improving thesocial projection of mathematicians andtheir professional outings towards

Featured People Collaborate and Cooperate Annual Report 2017 17

non-academic works, since many of ourcontracted are being successfully inserted inthe industry. Also the research groups areenriched with our activity since theymaintain a continuous renewal of their linesof research orienting them more towardsthe real demand. So this microcosmcontinues to grow with ITMATI activities.

How is �nancing found for this kindof initiatives? Are they wellsupported by universities or otherpublic institutions?Actually, these are initiatives that are theresult of the illusion and unsel�shcontribution of many researchers. In thissense I believe that we mathematicians canorganize ourselves with no strongself-interests, making it easier to drivee�orts towards a common good and abetter future for all. However, manyinstitutions just do not believe it and still donot bet on initiatives like “math-in” orITMATI. For example, math-in does not havedirect public funding; it only has �nancingfrom its partners’ fees, or indirectly throughthe contracts it promotes. In ITMATI the�nancing is being obtained mainly thanks tothe private sphere, which for example in2017 has meant a turnover of 90% of itsbudget. Of course, I would tell theinstitutions responsible for Science to beton these modern intermediateinfrastructures that agglutinate the interestsof a large group and with great potential foradvancement and smart digitization of theindustry.

You belong to the MathematicalEngineering research group of theUniversidade of Santiago deCompostela. What does your groupfundamentally work on?Our group, led by Professor AlfredoBermúdez, focuses on modelling,mathematical analysis, and the numericalsimulation of industrial problems. It is agroup with very varied �elds of interest,ranging from Solid Mechanics to Fluids, Heat

Transfer, Acoustics, Chemical Kinetics,Combustion, or Electromagnetism, and themultiple coupling of several of thesephenomena. This has allowed contributionsto the industry in very di�erent �elds andsectors. The list would be very long, so justto name a few, I would like to mention thethermoelectric simulation of aluminiumelectrolysis cells, the adaptation andoptimization of vacuum furnaces for theevaporation of impurities, the modelling andoptimization of gas transport networks, thedevelopment of e�cient silicon productionstrategies, the prediction of the quality ofwater in the recovery of coal extractionmines as lakes, or the acoustic insulation ofbuses and cars. Our research group hasmaintained stable objectives since the yearof its creation in 1986, always with a focuson applied and industrial research, and thatis what has also motivated me to acceptresponsibilities aimed at consolidating thisMathematics and Industry tandem.

Finally, what actions do you thinkshould be addressed to furtherenhance the presence ofMathematics in the industry?I believe that Mathematics are the DNA ofIndustry, they are everywhere, but manytimes, as you cannot see them, you are notaware of it. Therefore, to continue movingforward, I believe that a lot of �eldwork isnecessary. We need to relate more tocompanies, become more reliable andcompetent partners for them, and to erasethe idea from the collective subconsciousthat university researchers are dilators, whodo not come down to reality. On the otherhand, it is also necessary to end the ideathat many mathematicians have thatindustrial mathematics are interesting butnot very prestigious.

Interviewed by Elena Vázquez Cendón

Universidade de Santiago de Compostela,Spain


Interview: MilanaPavi�-�oli�

Tell us about yourself: what is yourbackground and training?My name is Milana Pavi�-�oli�. Currently, Iam assistant professor at Department ofMathematics and Informatics (DMI), Facultyof Sciences, at the University of Novi Sad inSerbia.

At bachelor and master level, I was studentof Applied Mathematics at DMI. Shortly aftermy graduation I became a PhD student incotutelle between the University of Novi Sadand the École Normale Supériure de Cachanin France, as a French Government fellow. Iworked with prof. Srboljub Simi� and prof.Laurent Desvillettes, mainly focusing oncomparisons of mathematical models forpolyatomic gases and mixtures in thecontext of kinetic theory of gases and �uidmechanics.

What is your research area?My research interests focus in the area of

collisional kinetic theory of gases thatmodels a wide range of physicalphenomena, from rare�ed gas �owmixtures in the upper atmosphere, plasmadynamics to charged hot electron transportin semiconductor devices or the formationof Bose-Einstein condensation. This �eldbelongs to non-equilibrium statisticalphysics, where models of continuummechanics fail to accurately describe timedynamics or quantum or molecular systemsare not suitable due to the size of thesystem. I would stress that this areaenriches many �elds of mathematicalresearch closely connected to physics whereprobability theory and functional analysisprovide the natural framework.

The area of kinetic transport theory isrelatively young. Its basic concepts wereintroduced by Boltzmann at the end of XIXcentury, marking the birth of statisticalmechanics, where �ows can be describedprobabilistically. Mathematiciansintertwined their �ngers from late ’80 verysuccessfully, culminating with two Fieldsmedals associated to the area, for PierreLouis Lions in 1994 and Cédric Villani in2010. Nowadays, we have quite goodunderstanding in the case of monatomicgases, where the model is well described bya single equation that can be viewed asbi-linear Integro-Di�erential equation.Beyond this setting, where systems of suchequations arise, very little is known. Andhere lays my interests: the enlarging ofconcepts to tackle the problem for solvingmixtures of monatomic and polyatomicgases. This �eld of research is offundamental importance to industrialapplications from a broad engineering and


science viewpoint, enhances theunderstanding a quite broader area ofstatistical mechanics. It has, indeed, apromising future!

What are you doing now?At this moment, I am visitor at the Instituteof Computational Engineering and Sciences(ICES) at The University of Texas at Austin,USA, as a Fulbright Visiting Scholar and JTOfellow at ICES. I am currently working withProf. Irene M. Gamba on the mathematicallyrigorous theory for the Boltzmann system inthe context of mixture of monatomic gases.For instance, we are dealing with existenceand uniqueness theory, propagation andgeneration of exponential tails. I am lookingforward for important results for the theorythat also include a detailed description totime decay rate to statistical equilibrium, aquantity that usually can be compared toexperimental data. Our work also apply tothe development of new computationalmethods for gas mixtures.

Your ECMI engagement startedwhen you were a master student.Could you comment from theperspective of a student and aninstructor at Modeling Weeks?At Modeling Weeks in Milano 2010, for the�rst time Imet real a life problem where Itook part in solving it, together with othercolleagues from my group. I truly think thatModeling Weeks takes best out of you: theneed to apply all your available knowledgeto a particular problem within given timeframework, jointly with your teammembers. This was a valuable experienceand a wonderful opportunity to meetpossible future collaborators!

Later, being an instructor at ECMIModelingWeeks in So�a 2016, was very challenging aswell, from adapting the problem to its study,to �nal conclusions with students. I thinkthat, from instructor point of view, ModelingWeeks o�ers an extraordinary frameworkfor mathematicians to concentrate on aparticular problem and hear another

opinions (always very constructive!) fromstudent teams.

At �nal presentations, one can notice thelively and cheerful mood of, both studentsand instructors, arising as a positive sign ofgood communication and work.

How do you see a role of industrialmathematicians in the near future?I think that industrial mathematicians playan important role in nowadays society.Applied mathematics has becomerecognized as a necessary tool in research inall sciences. It is essential to pursue in thisdirection. When I was preparing problem onDeer population for Modelling Week, Iinitiated meeting with our local NationalPark Fru�ka gora. They kindly supported alldata that I needed, and appeared to be verysurprised by the power of mathematics.Although they provide control on deerpopulation, it is not based on any reliablemathematical model. Therefore,mathematics can help and we should say itloudly.

What are the challenges andopportunities for industrialmathematics in Serbia andSouth-East Europe as a region? Howdo you see the role of yourDepartment?I believe that the recent inclusion of our DMIas an ECMI Node is one of the most recentimportant events for industrial mathematicsin Serbia. In such a way, DMI has becamethe Serbian center of Applied Mathematics,giving great opportunities for Serbianindustrial mathematics to become morevisible, as current applied mathematicsstrength can be shown mainly throughmutual collaborations and synergy betweenindustry and academia. In this context, ECMIModeling Weeks is de�nitely a good startingpoint.

In addition, a current challenging issue allover the world is the inclusion of women inscience. I would like to point out that, as a


woman, I am proud that my Departmentpromotes and encourages women to bepart of mathematical community. And, as amatter of fact, women are very wellrepresented at our Department.

By promoting these values, I am convinced

that Serbia, and DMI, will be able to providea role model that our neighbors may bewilling to embrace.

Interviewed by Prof. Nata�a Kreji�

University of Novi Sad, Serbia


5Projects andCase Studies

23

Universality frommicroscopicstochastic dynamicsMany di�erent physical systems, when analysed from a mathematicalpoint of view, show identical patterns of growth. This slightly mysterioustendency for very di�erent things to behave in very similar ways is theessence of universality. Here we report a methodology that connects themacroscopic world with the microscopic behavior of particles and allowsto derive rigorously macroscopic universal laws from the randommotionof the underlying microscopic dynamics.

In real life situations we come across withmany di�erent episodes where we feel thatit has similarities with something we havelived before in the past. Either this is relatedto emotions or to physical reactions, thesimilarity can be present. In nature,similarities between very di�erentorganisms also occur. As an example of thispuzzling reality which somehow connects allof us, in the picture below, we see a growingpattern of ice particles which is formed in awindscreen in a very rigorous winter day.

The ice particles fall, randomly, from the skyand when they hit the windscreen they form

a growing pattern which can be seen inother, in principle, uncorrelated, situationsas: co�ee ring e�ects, bacterial growth likeE-coli, the wake of a �ame, tumor growth...

There are various di�erent physical systems,that when they are mathematicallymodelled they show identical patterns ofgrowth. This slightly mysterious tendencyfor very di�erent things to behave in verysimilar ways is the essence of universality.There are di�erent shapes for thesepatterns and their study is the core of thisproject and it is related to a very active areaof research in both mathematics andphysics known as universality. A way tomodel mathematically the falling of iceparticles is to identify them as blocks thatfall independently from each other andaccording to some random law. By this wemean that the time it takes for a block to fallis random and times between the fall of twoblocks are independent. Probabilisticallyspeaking we can assume that the law forthese times is exponential and moreover,

24 Collaborate and Cooperate Annual Report 2017 Projects and Case Studies

blocks fall in a sticky way, that is, whenever afalling block touches another block, evenonly from the side, then it immediatelysticks into place. We could have alsoassumed that blocks fall independently andin parallel above each site according toexponentially distributed waiting times. Inthis case there is no stickiness. Let us makean analogy with a game that everyoneknows: the tetris game. In the latter randomdeposition, the one without stickiness, thetypical pattern we see is like the one on theleft hand side in the picture below, this is theusual tetris game; while the typical patternfor the sticky random deposition of particlesis like the one on the right hand side in thepicture below, which would be a sticky tetris.Obviously a player looses more quickly withthe sticky tetris than with the usual tetrisgame, due to the existence of holes in thepattern.

These two di�erent types of randomdeposition give rise to two di�erentuniversality classes. Mathematicallyspeaking, this is a way to catalogue systemsthat somehow exhibit the same behavior.Above we have seen two universalityclasses: the random straight deposition isin, what is called, the Gaussian universalityclass and the sticky deposition is in, what iscalled, the KPZ universality class. In 1986,three physicists: Kardar, Parisi and Zhangproposed [1] a phenomenological model forthe evolution of a random growing interfacegiven by what is called today the Kardar,Parisi and Zhang (KPZ) equation. One of thepopular topics in research related to theclassi�cation of systems in universality

classes, is to explore the universality of thismacroscopic law, the KPZ equation, fromunderlying microscopic stochastic dynamics.Here are some of the questions that peoplelook for answers: What are the macroscopiclaws governing the evolution of theconserved quantities of a microscopicstochastic dynamics? What are theuniversality classes to which the models,with certain general features, belong to?What is the relation between these classes?Are they linked by some parameterprescribed on the underlying microscopicstochastic dynamics? How local dynamicalperturbations are "felt" at the macroscopiclevel?

Here we report a methodology [2] whichallows to rigorously prove, the emergence ofmacroscopic laws from microscopicstochastic dynamics. The goal is to obtainpartial di�erential equations (PDEs) orstochastic PDEs from microscopic systemsof random particles, depending on whetherone is looking at the law of large numbersor the central limit theorem for thosemicroscopic systems. There are severalmacroscopic laws which are obtained frommany di�erent systems. The goal is todescribe these laws by using someunderlying models which are analysed froma probabilistic point of view.

This work is being developed in theMathematics Department of InstitutoSuperior Técnico (IST) of the University ofLisbon, in the framework of the researchproject HyLEF: Hydrodynamic Limits andEquilibrium Fluctuations funded by theEuropean research council through an ERCStarting Grant leaded by Patrícia Gonçalves.This project gathers a group of externalcollaborators from IMPA (Brazil), UniversityParis Dauphine (France), University of Nice(France), INRIA (France), HU Berlin(Germany) and other institutions abroad. Itcounts with a local team of post docs andPhD students. For more information checkthe website:http://patriciamath.wixsite.com/patricia/hylef.

Projects and Case Studies Collaborate and Cooperate Annual Report 2017 25

Scienti�c background

Interacting particle systems, is a recentbranch of study in probability theory as partof a general theory known as Markovprocesses. Interacting particle systems [3]were introduced in the mathematicscommunity by Frank Spitzer in [4], but werealready known to physicists, as microscopicstochastic systems, whose dynamicsconserves a certain number ofthermodynamical quantities of interest.

A classical problem in the �eld of interactingparticle systems is to derive themacroscopic laws of the thermodynamicalquantities of a physical system byconsidering an underlying microscopicdynamics which is composed of particlesthat move according to some prescribedstochastic, or deterministic, law. Themacroscopic laws can be PDEs or stochasticPDEs depending on whether one is lookingat the convergence to the mean or to the�uctuations around that mean. The maingoals of this research �eld are related to themathematical rigorous derivation of thesemacroscopic laws.

The physical motivation for the study ofinteracting particle systems is the following.Suppose that we are interested in analysingthe evolution of some physical system as,for example, a �uid or a gas. Due to thelarge number of molecules, it becomes quitehard to analyse the microscopic evolution ofthe system, so it is more relevant to analysethe macroscopic evolution of its structure.

According to Ludwig Eduard Boltzmann(1844-1906) who was an Austrian physicistand philosopher; and whose greatestachievement was in the development ofstatistical mechanics, "Statistical mechanicsexplains and predicts how the properties ofatoms determine the physical properties ofmatter."

Boltzmann proposed an approach whichconsists in �nding �rst the equilibriumstates of that system and thencharacterizing them through macroscopicquantities, namely, the thermodynamicalquantities, such as: pressure, temperature,density, energy... The natural question thatarises then is to analyse the macroscopicbehaviour of that system out of equilibrium.

“Statistical mechanicsexplains and predictshow the properties ofatoms determine thephysical properties ofmatter.”

The characterization and study ofphenomena out of equilibrium is one of thebiggest challenges of Statistical Physics anddespite its long history, a satisfactoryanswer to this kind of problems has not yetbeen found, see [5].

From this approach, some PDEs arise thatprovide information about the macroscopicevolution of the thermodynamicalquantities of the system. Due to the hugecomplexity of the analysis of these systems,


some simpli�cations need to be introduced.For this purpose, we assume that theunderlying microscopic dynamics, that is thedynamics between the molecules, isstochastic. As a consequence, a probabilisticanalysis of the system can be done.Assuming that particles (or molecules)behave as interacting random walks, subjectto some random local restrictions, arise theinteracting particle systems [3].

“Assuming that particles(or molecules) behave asinteracting randomwalks, subject to somerandom localrestrictions, arise theinteracting particlesystems [3].”

Probabilistically speaking, these systems arecontinuous time Markov processes, beingthe time between consecutive jumps givenby an exponential law which has thewell-known property of memory loss,therefore, the future of the system,conditioned to its past, depends only on itspresent state.

By considering these microscopic randomsystems one can, by a space-time scalinglimit, deduce (in a rigorous way) themacroscopic laws governing the evolution ofthese quantities. These laws give thespace/time evolution of thethermodynamical quantities of the systemand they are composed of one, or a system,of PDEs. In the literature, this procedure isknown as Hydrodynamic Limit.

The scaling limit is done by means of ascaling parameter, that we denote by n,

which allows us to identify relevantunknowns of the macroscopic space withthe respective microscopic space. Thereforeif the macroscopic space is, for example, theone-dimensional interval [0,1], one candivide this space into n subintervals of size1/n, in such a way that each element u 2 [0,1]

such that u 2h

jn ,

j+1

n

⌘, is identi�ed with j,

namely with the closest integer number lessor equal to un, so that the microscopic space(a discrete space where the randomdynamics is de�ned) is the set of points{0,1, ...,n�1}.

To summarize, on the underlying scenariowe are interested in analysing the physicalevolution of, for example, a gas evolving in acertain volume V. Two scales are considered:the macroscopic one, that describes theglobal motion of the gas; and a microscopicone, that describes the movement of themolecules, or particles, of the gas. We canthink of these two scales in the followingway. If we put a gas in a certain volume Vand with our eyes, we look at the evolutionof the dispersion of the gas, this would bethe macroscopic picture, while if we have aloupe to see how the molecules interactwith each other, this would be themicroscopic scale.

Due to the large number of molecules, weassume that its motion is not deterministicbut stochastic, in the sense that, eachparticle performs a random walk, that is, itmoves, after some speci�ed time, to aposition of the discretized volume V . Thediscretization of the volume V is done bymeans of the scaling parameter n. Underthe assumption of the random movementof the molecules of the gas, a probabilisticanalysis of the system can be performed.

Initially, on the volume V , we can consider apoint u and a neighbourhood around thatpoint, let us call it Vu, and since the numberof particles is big, we can assume thatlocally the microscopic model is equilibrium.


The equilibrium is characterized by thethermodynamical quantity of interest thatwe denote by r(u). Now we can let thesystem evolve in time, and for a time t, wecan pick the same point u in Vu, and assumeagain the local equilibrium, which is nowdepending also on time and we denote it byr(t,u), see the picture below. The importantquestions to answer are:

How is the space-time evolution of rt(u)? Is itdescribed by some law? Which law is this?

So, the picture behind our interpretation isthe following. First, we suppose to have twoscales: one for space and another one fortime and to have a physical system evolvingin a certain volume V . The evolution of itsparticles is random and is Markovian. In thenext step, we discretize the volume V ,according to the scaling parameter n, andwe divide it into a certain number of cells. Ineach cell, we put a random number ofparticles, being this number given as theresult of some random experiment. At eachcell, particles wait a random time after whichone of them decides to jump to someposition of the discretized volume Vaccording to a probability transition rate.The random times are assumed to beindependent and exponentially distributedso that interacting particle systems fall intothe class of Markov processes, for whichthere is a very developed theory.

The goal in the hydrodynamic limit theoryconsists in obtaining the macroscopic laws,which, mathematically speaking, are PDEs,that govern the space-time evolution ofeach conserved quantity of the system.These macroscopic laws are calledhydrodynamic equations.

A prototype example: exclusionprocess in contact with reservoirs

To explain the hydrodynamic limit let uspresent a concrete example. For thatpurpose, let us consider now the prototypeexample of an interacting particle system:the exclusion process denoted by ht , with trunning in a compact set [0,T ], with T �xed.To make the presentation as simple aspossible we consider the process evolvingon, for example, {1, ...,n�1} which we callthe bulk.

The dynamics of the simplest example ofexclusion process in contact with reservoirsis de�ned as follows. Each particle in thebulk waits an exponential time of parameter1 and then it jumps to a site according to acertain probability transition rate. Due tothe exclusion rule, the jump is performed if,and only if, the destination site is empty,otherwise nothing happens and particleswait a new random time. The space state ofthis process is {0,1}{1,...,n�1}. Let us denotethe jump rate from x to y by p(x,y).

Here we assume that p(x,y) = p(y� x), thatis, the jump rate from x to y, depends onlyon the distance between x and y and we alsoassume that jumps are allowed only tonearest neighbours. In last case, the processis said to be simple, so that p(z) = 0 if |z|> 1.In this situation two cases can occur, eitherthe process is symmetric or asymmetric, sothat

p(1) = p(�1) =1

2,

or

p(1) = 1� p(�1) =1

2+

ang ,

In the former case the process is thesymmetric simple exclusion process (SSEP),while in the latter for a 6= 0 and g > 0, theprocess is the weakly asymmetric simpleexclusion process (g-WASEP). Note that theparameter g rules the strength of theasymmetry: the higher the value of g theweaker is the asymmetry.


Now we explain the boundary mechanism.At boundary points x = 1 and x = n�1,particles can either be created orannihilated according to the following rates:

at site x = 1:

– creation rate akn�q ,– annihilation rate (1�a)kn�q ,

at site x = n�1:

– creation rate bkn�q ,– annihilation rate (1�b )kn�q .

Above the parameters are such thata,b 2 (0,1), q 2R and k > 0. Note that in anycase, the exclusion rule has to be respected.At most one particle is allowed at each siteof the bulk so that particles can only becreated (resp. removed) at the sites x = 1 orx = n�1 if the corresponding site is empty(resp. occupied), otherwise nothinghappens.

In the �gure below we represent a possiblecon�guration with the description of thedynamics.

kb/nq

k(1�b )/nq

k(1�a)/nq

ka/nq1

2

1

2

If reservoirs are not present, the exclusiondynamics just de�ned does not destroy thenumber of particles, since particles move ina discrete space according to someprescribed rule and they are not created norannihilated, therefore, the density ofparticles is a conserved quantity of thesystem.

Since we added reservoirs, the density is nolonger conserved and it will be constrainedto boundary conditions which depend onthe value q that rules the strength of thereservoirs.

Hydrodynamic limits:

Now, we explain in which sense we derivemacroscopic laws, that is PDEs, from theprevious microscopic stochastic dynamics.Taking into account that the density ofparticles, is the thermodynamical quantityof interest in the exclusion process, wede�ne a density empirical process. It consistson a process of random measures, suchthat, for a �xed time t, each measure is asum of Dirac measures supported at eachsite of {1, ...,n�1} that gives weight 1

n�1to

each particle, namely:

pnt (h ,du) = 1

n�1

n�1

Âx=1

htq(n)(x)d xn(du).

Above dA(du) is the Dirac measure of the setA. Note that above since a re-scaling inspace is done, we also need to speed up theprocess in a time scale that we denote bytq(n) and which will depend on the choice ofthe transition probability p(·). The goal inthe hydrodynamic limit consists in showingthat:

1. if starting the process {htq(n)}t from acollection of measures µn for which theLaw of Large Numbers holds: thesequence of random measures pn

0(h ,du)

converges, in probability with respect toµn and when n is taken to in�nity, to thedeterministic measure r0(u)du, wherer0(u) is a function de�ned in [0,1] which ismeasurable;

2. then, the same holds at later times t, thatis, the random measure pn

t (h ,du)converges, in probability with respect toµn(t), the distribution of htq(n) and when nis taken to in�nity, to the deterministicmeasure rt(u)du, where rt(u) is thesolution (usually in the weak sense) of aPDE, namely, the hydrodynamic equationof the system.

Note that assumption 1. above can betranslated by saying that for any continuousfunction g : [0,1]! R it holds that

limn

µn

⇣��Z

g(u)pn0(h ,du)�

Z1

0

g(u)r0(u)du��> d

⌘= 0.


For exclusion processes de�ned above, by ascaling limit procedure, one can get ashydrodynamic equations:

1. for the SSEP and re-scaling timedi�usively tq(n) = tn2- the heat equationgiven by

∂trt(u) = 1

2Drt(u), [Heat equation]

starting from r0(u) and with the followingboundary conditions [6, 7].

For q < 1, Dirichlet boundaryconditions:– rt(0) = a , rt(1) = b .

For q = 1, linear Robin boundaryconditions:– ∂urt(0) =

k2(rt(0)�a),

– ∂urt(1) =k2(b �rt(1)).

For q > 1, Neumann boundaryconditions:– ∂urt(0) = 0 = ∂urt(1).

2. for q = 0 and for the 1-WASEP and byre-scaling time di�usively tq(n) = tn2, theviscous Burgers equation, namely,

∂trt(u) = 1

2Drt(u)+(1�2a)— f (rt(u))

with Dirichlet boundary conditions.Above f (r) = r(1�r), D is the laplacianand — is the spatial derivative.

“The hydrodynamic limitis then a Law of LargeNumbers for theempirical measure. ”

We also note that we can get to fractionalPDEs from exclusion processes [8, 9]. Forexample, if we allow the dynamics to havelong jumps but still given by a symmetrictransition probability p(·) with the rates

given by p(z) = cg|z|1+g , where cg is a

normalizing constant and g 2 (1,2), see the�gure below:

kb p(5)

k(1�b )p(1)k(1�a)p(2)

ka p(8)

By re-scaling time as tq(n) = tng we can getin the hydrodynamic limit, the fractionalreaction-di�usion equation given by

∂trkt (u) = (L�kV 1,1

0)rk

t (u)+kV a,b0

(u)

starting from r0(u) and with Dirichletboundary conditions: rt(0) = a , rt(1) = b .Above L is the regional fractional laplacianand its action on functions g 2C•

c (0,1), isgiven on u 2 (0,1) by

(Lg)(u) = cg lime!0

Z1

0

1|u�v|�eg(v)�g(u)|u� v|1+g dv

and˜V a,b

0(u) = cg

⇣ au1+g +

b(1�u)1+g

⌘.

The hydrodynamic limit is then a Law ofLarge Numbers for the empirical measure.The natural questions that arise aftersolving this issue are related to the CentralLimit theorem. In that case, the macroscopiclaw that we want to obtain is, in fact, astochastic PDE which describes the�uctuations around the mean pro�le.Typically the questions are the ones below:

What are the �uctuations around the mean foreach one of these models? Is there somepattern of the macroscopic equationsdepending on the microscopic jump rates? Arethere universality classes so that all the models(with general features) belong to? If so, what isthe relation between these universality classes?Are these equations linked by some parameterthat depends on the underlying dynamics?


Fluctuations:

In order to study the �uctuations of theexclusion processes de�ned above, we canconsider that the process starts from aninvariant measure. This measure has noevolution in time by the dynamics, that is ifh0 has law µ then the law of ht is again µ forany time t > 0.

To simplify the exposition we can suppose inthe exclusion dynamics de�ned above thata = b = r and in this case, the invariantmeasures for those processes are theBernoulli product measures which areparametrized by a constant r (that wedenote here by nr ) and that are de�ned by:

nr{h(x) = 1}= r.

Then we de�ne, what is called the density�uctuation �eld, which is a linear functionalde�ned on a function f , living in someproper space of test functions, as, forexample, the Schwartz space, in thefollowing way: �rst we integrate f withrespect to the density empirical measurepn

t (h ,du), then we remove its mean (withrespect to the invariant state) and then wemultiply it by

pn (so that we are in the

Central Limit Theorem scaling), to get

Yn

t ( f ) =1p

n�1

n�1

Âx=1

f ( xn )[htq(n)(x)�r].

Note that above r is the mean of htq(n)(x)with respect to nr .

At this level, the goal consists in obtainingthe stochastic PDEs ruling the evolution ofthe limiting process of the sequence {Y n

t }n,denoted by Yt (which is obtained from{Y n

t }n in a proper topology by sending n toin�nity).

Depending on the prescribed dynamics wecan derive, from di�erent underlyingstochastic dynamics, di�erent stochastic

PDEs using this procedure. This brings aphysical motivation for the study of thestochastic PDEs that will emerge frommicroscopic dynamics.

For the exclusion processes introducedabove, we can get for:

1. the SSEP and re-scaling time di�usivelytq(n) = tn2 - the Ornstein-Uhlenbeckequation (OUE) given by

∂tYt = DYt +p

r(1�r)—Wt

with the same boundary conditions as inthe hydrodynamics level, see [10].

2. For g > 1/2 and q = 0, the g-WASEP andby re-scaling time di�usively tq(n) = tn2

the same OUE as in the previous item.This means that the asymmetry is notthat strong in order to have some impactat the macroscopic level, so that thelimiting equations are the same as in thesymmetric case [11].

3. For g = 1/2 and q = 0, the 1

2-WASEP and

by re-scaling time di�usively tq(n) = tn2,the Kardar-Parisi-Zhang equation(introduced in [1])

∂tht = Dht �2(—ht)2 +

pr(1�r)Wt

or its companion, namely the stochasticBurgers equation

∂tYt = DYt �2—Y2

t +p

r(1�r)—Wt

depending whether one is looking at theheight �uctuation �eld or the density�uctuation �eld, see [12, 11]. Above Wt isa space-time white noise.

“This brings a physicalmotivation for the studyof the stochastic PDEsthat will emerge frommicroscopic dynamics. ”


In [13, 14] it was proved that for a large classof weakly asymmetric simple exclusionprocesses without reservoirs, depending onthe range of the parameter g , the density�uctuations cross from the OUE to thestochastic Burgers equation. More precisely,in a phase of weak asymmetry (g > 1/2), thedensity �uctuations are given by an OUE(the same OUE as in the SSEP). This meansthat in this regime, the asymmetry is notseen at the macroscopic level. Nevertheless,in a phase of strong asymmetry (g = 1/2),the density �uctuations are given by energysolutions of the stochastic Burgers equation.Therefore the g-WASEP crosses from, what iscalled, the Edward-Wilkinson universalityclass to the KPZ universality class, bychanging the value of the parameter g ,which rules the strength of the asymmetry.

Making the connection with the tetris gamethat we have seen in the beginning of thisreport, the exclusion process is an exampleof microscopic stochastic model for whichby tuning the parameter g , that rules thestrength of the asymmetry, it crosses forg > 1/2 from the universality class of theOrnstein-Uhlenbeck process, which isrelated to the usual tetris game, to the caseg = 1/2 and to the KPZ universality class withis related to the sticky tetris game.Moreover, by tuning the strength of thereservoirs it also provides a transitionbetween macrosocopic laws (either PDEs orstochastic PDEs) with di�erent boundaryconditions.

Further Issues

One of the main open problems related tothe issues presented above concerning theexclusion process is to obtain the limitingprocess when the asymmetry of the modelis stronger than the symmetry.

Other important issue for other types ofdynamics is to derive other universalityclasses and other stochastic PDEs thatconnect them, as happens for the stochasticBurgers equation connecting theEdward-Wilkinson universality class and theKPZ universality class.

“The expected results willcontribute towards abetter understanding oflong standing problemsin mathematicalphysics.”

Along these lines we have mentioned onetype of dynamics, the exclusion process,which conserves one quantity, the density,but there are more complicated dynamicswhich can conserve more than one quantityof interest. In that case we can obtainsystems of PDEs or systems of stochasticPDEs which can be coupled and di�erentuniversality classes than those mentionedabove. The Kardar-Parisi-Zhang and theStochastic Burgers equation are thereforeone example of equations connecting twodi�erent universality classes but many otherare still to be explored.

Nowadays, there is a vast and intense �eldof research on these topics, but, due to itscomplexity and di�culty, the results havebeen derived almost model by model,equation by equation with many results


given at an heuristic level and, some ofthem, obtained by computationalsimulations. Therefore, a rigorousmathematical proof of these results islacking and the expected results willcontribute towards a better understandingof long standing problems in mathematicalphysics.

Patricia Gonçalves,

Center for Mathematical Analysis, Geometryand Dynamical Systems, Instituto SuperiorTécnico, Universidade de Lisboa, Av. RoviscoPais 1, 1049-001 Lisboa, Portugal,[email protected]

References

1. M. Kardar, G. Parisi, and Y. C. Zhang.Dynamic scaling of growing interfaces.Physical Review Letters, 56(9):889–892, 1986.

2. C. Kipnis and C. Landim. Scaling limits ofinteracting particle systems. Springer-Verlag,1999.

3. T. Liggett. Interacting Particle Systems.Springer-Verlag, 1985.

4. F. Spitzer. Interaction of markov processes.Advances in Mathematics, 5:246–290, 1970.

5. H. Spohn. Large scale Dynamics of InteractingParticles. Springer-Verlag, 1991.

6. R. Baldasso, O. Menezes, A. Neumann, andR. R. Souza. Exclusion process with slowboundary, journal of statistical physics.Journal of Statistical Physics, 167(5):1112–1142, 2017.

7. C. Bernardin, P. Gonçalves, andB. Jiménez-Oviedo. Slow to fast in�nitelyextended reservoirs for the symmetricexclusion process with long jumps. In eprintarXiv:1702.07216, 2017.

8. C. Bernardin, P. Gonçalves, andB. Jiménez-Oviedo. A microscopic model fora one parameter class of fractional laplacianswith dirichlet boundary conditions. In eprintarXiv:1803.00792, 2018.

9. P. Gonçalves. Hydrodynamics for symmetricexclusion in contact with reservoirs, 2017.URL http://patriciamath.wixsite.com/patricia/publications.

10. T. Franco, P. Gonçalves, and A. Neumann.Equilibrium �uctuations for the slowboundary exclusion process. In P. Gonçalvesand A. J. Soares, editors, From Particle Systemsto Partial Di�erential Equations, pages177–197. Springer International Publishing,2017.

11. P. Gonçalves, N. Perkowski, and M. Simon.Derivation of the stochastic burgers equationwith dirichlet boundary conditions from thewasep. In eprint arXiv:1710.11011, 2017.

12. P. Gonçalves, C. Landim, and A. Milanes.Nonequilibrium �uctuations ofone-dimensional boundary driven weaklyasymmetric exclusion processes. The Annalsof Applied Probability, 27(1):140–177, 2017.

13. P. Gonçalves and M. Jara. Nonlinear�uctuations of weakly asymmetricinteracting particle systems. Archive forRational Mechanics and Analysi, 212(2):597–644, 2014.

14. P. Gonçalves and M. Jara. Crossover to thekpz equation, annals henri poincaré. Archivefor Rational Mechanics and Analysis, 13(4):813–826, 2012.


Optimization ofbuckling for textilesTextiles are structures of �bers or yarns of arbitrary complexity, whichalso gives rise to the manifold usage of textiles in nearly every situation.Especially their �exibility standing in contrast to their durability isremarkable, but in some situations also a drawback. In particular thismay result in unwanted behaviors like the buckling of a textile underspecial movements or constraints. For instance the buckling is an e�ectregularly present and possibly leading to critical e�ects, but notdescribable in an easy manner.

The following article about buckling textilesand their optimization arises from variousindustrial applications and is still underinvestigation. The research group is locatedat the Fraunhofer Institute for IndustrialMathematics in Kaiserslautern, Germany.

Problem description

Textiles are nearly everywhere present andused in many di�erent areas with verydi�erent requirements. Variousapplications, of which some arediametrically opposed with respect to itsfunctionality, imply diverse designs in both,microscopic and macroscopiccharacteristics.

The problem coming from industry is thebuckling of textiles in special processes,which might not be wanted either out ofcosmetical or productional or even safetycritical reasons. There are plenty morereasons for many other applications andalso di�erent textiles and their demands.Hereafter we restrict to the buckling of atextile strap in the lateral direction. This

buckling arises either from a tension inlongitudinal or a compression in lateraldirection. The goal of this project is thesimultaneous retardation of the bucklingand the optimization of its shape. By theshape optimization here it is meant that thebuckling-shape is close to a given pro�lesuch that no further complications arise inthe subsequent events.

Figure 1: Textile patch in canvas structure consisting of

carbon �bers.

Important to realize here is that textiles arevery complex structures consisting of �bersor yarns. This gives rise to the design spacein which the properties and also their


weaving structure can be chosen during theoptimization procedure.

Modeling

To model this problem described above weassume the textile to be a heterogeneous2D-plate and use therefore the nonlinearvon-Kármán-plate model. In fact, due to thesymmetries of the textile and the use of anuniaxial force, this model can be furtherreduced to a linear, one dimensional fourthorder equation

D(B(x)Du)�FDu = 0, (5.1)

Here F denotes the lateral compressiveforce (or the diverted tensional force), B(x) isthe heterogeneous bending sti�ness,depending on the microscopic design and uthe out-of plane displacement of the belt. Tocomplete the problem (5.1) we use theboundary conditions

u(±L) = u,x(±L) = 0, (5.2)

for the textile width of 2L.

In fact equation (5.1) has two regimes withvery di�erent results. The �rst regimeresults from F � 0, where the only solutionu ⌘ 0 to this equation is trivial. The secondregime arises from F < 0, whichcorresponds to the compressive case. Infact this is the interesting case and it furtherdivides into two regimes. The problem againis uniquely solvable for |F |< Fcr with u ⌘ 0,but as soon as the critical force |F |= Fcr isreached, the textile buckles. Since theretardation of the buckling directlycorresponds to the maximization of Fcr it isobvious that it is crucial to identify thiscritical force. Assuming B to be overallconstant, it turns out that this critical forcecorresponds to a generalized eigenvalue ofthe system and yields

lB =Bp2

4L2�F, (5.3)

wherefrom we derive the critical force

Fcr =Bp2

4L2. (5.4)

Hence, maximizing B or minimizing L leadsto a higher critical force and thereby aretardation of the buckling. By the relation(5.3) it is obvious that a maximization of lB

corresponds directly to a maximization ofFcr, but it is easier to derive. In fact, if B isnot constant this is a bit more involved butcan be handled by a generalizedRayleigh-quotient argument to compute lB

for constant F . The shape-optimization ofthe buckling mode is then rather easilyadded, since it is the correspondingeigenmode to the above Rayleigh-quotient.

Those two considerations give rise to theobjective functional

J(u) = gku�ugkL2((�L,L)) + (1� g)lB (5.5)

for the optimization, where ug is the desiredshape of the buckling mode and lB = lB(Fcr)

the generalized eigenvalue. Here we addedan additional factor g 2 [0,1], which issuitable to weight the two terms in theobjective function. For instance this factorallows to balance the terms and also givesthe possibility to manage thePareto-e�ciency.

Finally note also that the bending sti�nessdepends on the material and the inherentstructure of the textile and is obviouslyrestricted and bounded. This leads to theadditional constraint

0 < b1 B(x) b2, (5.6)

where b1 and b2 are given by themanufacturing process. Moreover, it is ofteninteresting to preserve the mean value of Bor at least only small deviations from it. Thisleads to

1

2L

Z L

�LB dx = MB, (5.7)

where MB is a prede�ned mean value toachieve.

The last constraint is the symmetry of theproduct. This means that the �nal textile is aproduct symmetric with respect to x = 0,meaning that the resulting bending sti�ness


Bopt is also symmetric with respect to thisaxis.

Results

The discussed model is implemented inMatlab and the optimization is done by aMatlab internal optimizer. The most crucialingredient to control the problem abovetowards a desired solution is the factor g . Toemphasize this, we show below twodi�erent computations where one seesdirectly what e�ects a slight modi�cation ofthis factor can have. Beside g all otherparameters maintain constant in bothsimulations. The bending sti�ness B(x) isbounded from below by b1 = MB/10, i.e. thelowest value for B(x) is 10% from the initialbending sti�ness. Furthermore, the meanbending sti�ness can di�er at most 10%from its initial constant value MB = Binit . Asfurther adaptation, the bending sti�ness isdivided into 20 piecewise constant sections,being symmetric with respect to x = 0. Thepiecewise constant character of the bendingsti�ness corresponds to one or more �berswith the same properties and thus the sameresulting bending sti�ness in such a section.

In the following example the goal-shape ug ischosen to be �at at the ends for 20% of eachside of the sample. This corresponds to ahigher overall amplitude, but a lower one atthe lateral boundaries of the sample.

Simulation 1

For the �rst simulation the factor g = 0.98 ischosen to balance both terms in theobjective functional J(u). This means thatboth the shape-optimization and theretardation are taken into account andoptimized. In Figure 2 the objectivefunctional and the two terms within aredepicted. The value lB responsible for theretardation is improved by more than 15%while the second part even achieves a morethan 45% better result than before the

optimization.

Figure 2: Simulation for g = 0.98. From top to bottom:

Development of the function value of JB(u), the eigenvalue

lB and the distance to the goal function ug during the

optimization.

Figure 3: Simulation for g = 0.98. Top: The �rst Buckling

modes for the initial and the optimized problem with the

desired buckling-shape ug.

Figure 3 shows the e�ect of the optimization.In the top �gure we see that the shape ofthe buckling transforms from an initially(blue) quite bad similarity to a more �ttingshape (red) being closer to the desiredshape ug (green) in the end. The secondgraph shows how the bending sti�ness B(x)is optimized from a constant function to astep function, which is sti�er at the endsand rather soft in its middle of the textile.


Over the whole textile the mean bendingsti�ness has reached its maximum of 110%of MB.

Simulation 2

The second simulation uses g = 0.995 andthus weights the buckling-shapeoptimization a bit more than theretardation. Although the di�erencebetween the values of gamma is not verybig, the change in the result is noticeable.Here the buckling-shape is improved byalmost 75% with the cost that lB is evenreduced by 3%.

Figure 4: Simulation for g = 0.995. From top to bottom:

Development of the function value of JB(u), the eigenvalue

lB and the distance to the goal function ug during the

optimization.

Concluding the second simulation, we seethat also the resulting optimized bendingsti�ness and shape look di�erent. Asexpected from Figure 4 we see that the �nalshape is very close to the desired one. Also,Bopt is evidently changed, e.g. the maximalsti�ness is no longer at the ends of thetextile, and the mean value is now increasedby only 6% instead of 10% in the �rstexample.

Figure 5: Simulation for g = 0.995. Top: The �rst Buckling

modes for the initial and the optimized problem with the

desired buckling-shape ug.

Conclusions

In the presented case, the buckling oftextiles, we were able to �nd aheterogeneous bending sti�ness, which canbe adapted via g to the optimal needs of thelater product. Further customizations likeother desired shapes or additional demandscan be applied.

Both simulations show the versatility ande�ciency of this optimization. Additionally,this simulative approach saves a lot of workin comparison to trail and error procedures,to obtain textiles with higher quality andbetter adaption to their demands.

Stephan Wackerle12, René Pinnau2, JuliaOrlik1

1 Fraunhofer ITWM, Germany2 Technische Universität Kaiserslautern,Germany

References

1. Eric Puntel, Luca Deseri, and Eliot Fried.Wrinkling of a stretched thin sheet. Journal ofElasticity, 105(1):137–170, 2011. ISSN1573-2681. DOI: 10.1007/s10659-010-9290-5.


2. Gero Friesecke, Richard D James, and StefanMüller. A Hierarchy of Plate Models Derivedfrom Nonlinear Elasticity byGamma-Convergence. Archive for RationalMechanics and Analysis, 180(2):183–236, 2006.ISSN 1432-0673. DOI:10.1007/s00205-005-0400-7.

3. E Cerda and L Mahadevan. Geometry andphysics of wrinkling. Physical review letters, 90

(7):074302, 2003. ISSN 0264-9381. DOI:10.1088/0264-9381/20/6/701.

4. V. Berdichevsky. Variational Principles ofContinuum Mechanics: I. Fundamentals.Interaction of Mechanics and Mathematics.Springer Berlin Heidelberg, 2009. ISBN9783540884675. URL https://books.google.de/books?id=thnVhjYHVJcC.


Dynamics of thecapillary rise: apeculiar occurrenceof oscillationsCapillary rise in a narrow vertical tube is a remarkable physicalphenomenon that can be observed in many everyday situations. One ofthe most common natural examples of capillary action is water transportin soil or plants. Moreover, its applications can readily be found in variousindustrial processes like inkjet printing. Despite of the complexity of thisphenomenon at the molecular level, the �uid-dynamical approach allowsfor a systematic and accurate analysis. For instance, we are able to provethat there exists a critical value of the fundamental dimensionlessparameters at which the capillary motion undergoes a transition frombeing monotone to oscillatory. In this article we give an exposition of thispeculiar phenomenon.

Problem description

Mathematical models describing thebehaviour of a liquid in a narrow tube wereposed and extensively studied in the lastfew decades. However, the initial steps indescribing capillary action were made muchearlier by Washburn [1]. His model wasbased on an approximate di�erentialequation describing the balance betweengravity and capillary pressure in a narrowtube. In what follows we analyse a singularsecond-order nonlinear ODE that takes intoaccount some other factors and can bethought as a generalization of Washburn’sequation.

Capillary rise is a movement of a liquid dueto upward force caused by interaction of the�uid molecules with the surroundingsurface. Parallel to the theoreticalmodelling, many experiments (see [2, 3])discovered that for certain liquids we canobserve free boundary oscillations near theequilibrium point (level of the liquid after avery long time) while for other - simplemonotone increase of their height.

Authors distinguish two dynamical regimesof the �uid �ow in a capillary riseexperiment: gravity dominated case andviscosity dominated. Those regimescorrespond to the situations where the �uidcolumn height either increases or oscillatesnear the Jurin’s height. The occurrence of


these two situations depend on the ratio oftwo dimensionless quantities, namelyOhnesorge and Bond numbers.Experiments show that there exists a criticalvalue of the dimensionless parameter whichdistinguishes those two behaviours.

It can be checked that the Reynolds’ numberat the beginning of rise is low hence the �owis laminar. Initial conditions are set byentrance e�ect only. It was experimentallyand theoretically proved that the initialvelocity is equal to zero while the heightstarts increasing from a small positive value[4]. On the other hand, it seems natural toassume that the �uid is initially at rest withzero height but physically this not the case.A more adequate choice of the initialconditions, which is con�rmed by theexperiment, is setting the height to be equalthe mass of a liquid entrained below thepipe. Additionally, in [5] it was analyticallyshown by using the energy balance that theinitial acceleration can not be in�nite.

Mathematical model

We consider a tube with small radius r of itscross-section. It is put into a contact with aliquid container. The walls of this bath are insome distance from the tube so we will notconsider any perturbation of the �owcaused by them. To �nd the governingequation describing the capillary rise in tubewe need to take into account all the forcesthat act on a volume of the liquid. Of course,the upward force that is responsible for themovement of �uid have to be strictlyassociated with the surface tension g andwith contact angle q . The other forcescaused by the gravity and viscosity inhibitthe �ow

8µr2

hh0| {z }Viscosity

+ rgh|{z}Gravity

+r ddt

�hh0

�

| {z }Inertia

=2g cosq

r| {z }Capillarity

, (5.8)

where h = h(t) is a liquid column height attime t, µ is the viscosity, and r is the density.We will say that the liquid attains the Jurin’s

height if

h(t) =2g cosq

rgr=: he, (5.9)

or in other words, when the capillary forcebalances the weight of the liquid.

As was mentioned above, the most naturalchoice of the initial conditions is based onan assumption that at the beginning of theexperiment the �uid velocity is zero and theheight of liquid has a positive value (thiscorresponds to the mass of a liquid that isinitially accelerated). For simplicity ofcalculations we are considering a slightlydi�erent initial conditions, namely

h(0) = 0, h0(0) =

s2g cosq

rr, (5.10)

These conditions arise from therequirement that h(0) = 0 and theconsistency of the governing equation. It isworth emphasizing that the other popularchoice of initial conditions (h(0) 6= 0, h0(0) = 0)does not a�ect the �nal results.

To reduce number of constants involved inthe governing equation we can cast it intothe dimensionless form. The proper scalesfor height h and time t are respectively: he,de�ned before, and t = 8µPc

r2g2r2. Therefore,

HH 0+H +w�HH 0�0 = 1, (5.11)

with the initial conditions

H(0) = 0, H 0(0) =1pw, (5.12)

and the dimensionless parameter

w =r2gr4

64µ2he. (5.13)

As it turns out the quantity w has asigni�cant in�uence on the behaviour of theliquid.

Results and discussion

Having the governing equation in thenon-dimensional form we can proceed withfurther analysis of this nonlinear secondorder di�erential equation. In [6] thetheoretical methods were applied to ensure


that the problem is well posed. We provedexistence and uniqueness of the solution to(5.11) and obtained the exact form ofenergy function

E(s) =1

2u0(s)2 �u(s)+

2

p2

3u(s)

3

2 , (5.14)

where u(s) = 1

2H(s

pw)2 and s = T/

pw . It can

be shown that E(s) is nonincreasing withE(0) = 0. This implies the fact that theenergy is dissipated outside the system.Moreover, an utilisation of the equivalentintegral equation along with the energymethod can be used to �nd the asymptoticbehaviour for small times

h(t) =he

tp

wt +O(t2) as t ! 0

+. (5.15)

Therefore, the height of liquid for smalltimes increase linearly with time.

It is easy to see that after a long time, theheight of liquid will reach the Jurin’s heightand at the same time, the velocity of the�ow will be very small (by the energyrelation (5.14)). In order to study the liquidbehaviour near the critical point(h0,h00) = (he,0) we will use the dynamicalsystems approach. Experiments conductedby others authors (for ex. [2, 3]) provide uswith a data giving the change of the heightwith time. For various values of thenondimensional parameter w theexperiments give di�erent data graphs. Forexample, for diethyl ether (see [3]) theoscillation behaviour is observed an we cancalculate that w = 11.57. On the other hand,for the experiment with the silicone oil wehave w = 1.7⇥10

�6 and observe themonotone �ow only.

The main question arises: is it possible todeduce the conditions for oscillatory ormonotone regimes from the governingequation? We will show that the answer tothis question is a�rmative and the soughttransition is determined from the physicalproperties of the liquid and the value of thecross-sectional radius of the tube.

0 2 4 6 8t0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

H

Figure 1: Numerical solution of (5.11) with (5.12) for

w = 0.15.

0 20 40 60 80t0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

H

Figure 2:Numerical solution of (5.11) with (5.12) for w = 6.

To apply the dynamical system approach letus construct a system of �rst ODEs.Introduce the new variablesx(t) = u(t) = H2(T/w) and y(t) = u0(t), then(5.11) transforms into nonlinear ODEsystem:

(x0 = y,y0 = 1� 1p

w y�p

2x,x � 0. (5.16)

After linearisation near the critical point, wecompute the eigenvalues

l1,2 =�1±

p1�4w

2p

w. (5.17)

We conclude that for w > 0.25 theeigenvalues are complex conjugate and thuswe observe oscillatory behaviour near thecritical point. Consequently, the monotonebehaviour is present for w < 0.25. Moreover,the real part of the above is always negativehence the point is always locally stable. Wealso notice that both oscillatory ormonotone regimes are independent ofchoice of initial conditions. This critical valueof w is consistent with the experimentalevidence mentioned earlier.


-1 0 1 2 3

-2

-1

0

1

2

Figure 3: Set of asymptotic stability for w = 0.1. Light grey

represents w while light grey is the level curve mentioned in

the text.

-1 0 1 2 3

-2

-1

0

1

2

Figure 4: Set of asymptotic stability for w = 2. Light grey

represents w while light grey is the level curve mentioned in

the text.

To give a stronger stability result we canestimate the size of the basin of attraction.To this end we construct the Lyapunovfunction

V (x,y) =1

2y2 + x� lnx�1, (5.18)

which is nonincreasing and positive-de�niteon the set W := {(x,y) 2 R

2: y ��ex}. To

show the asymptotic stability we have to�nd an invariant set contained in W. Then,by the LaSalle’s Invariance Principle thisassertion will hold. For example, this set canbe the interior of the level-curve of V that istangent to the line y =�ex. Some examplesare depicted on Figs. 3 and 4. We can see

that although all the trajectories that enterthe dark grey set always stay within it, thereare some others that elude thischaracterisation. This is one of the subjectsof our future work - to provide some betterestimates on the basin of attraction.

Conclusions

A classical model for capillary rise can bewritten as a singular second-order nonlinearequation. As it appears, its uniquestationary point is asymptotically stable andundergoes a change in its behaviour. As thenondimensional parameter increasesthrough its critical value, the eigenvaluesgain nonzero imaginary part what initializesoscillations. This phenomenon has beenthoroughly veri�ed by the experiment andour analysis gives the rigorous proof of it.

Mateusz �wita�a, �ukasz P�ociniczak

Faculty of Pure and Applied Mathematics,Wroc�aw University of Science andTechnology, Poland

References

1. Edward W Washburn. The dynamics of capillary�ow. Physical review, 17(3):273, 1921.

2. D Quéré. Inertial capillarity. EPL (Europhysics Letters),39(5):533, 1997.

3. BV Zhmud, F Tiberg, and K Hallstensson. Dynamicsof capillary rise. Journal of colloid and interfacescience, 228(2):263–269, 2000.

4. Élise Lorenceau, David Quéré, Jean-Yves Ollitrault,and Christophe Clanet. Gravitational oscillations ofa liquid column in a pipe. Physics of Fluids, 14(6):1985–1992, 2002.

5. J Szekely, AW Neumann, and YK Chuang. The rate ofcapillary penetration and the applicability of thewashburn equation. Journal of Colloid and InterfaceScience, 35(2):273–278, 1971.

6. �ukasz P�ociniczak and Mateusz �wita�a.Monotonicity, oscillations and stability of a solutionto a nonlinear equation modelling the capillary rise.Physica D: Nonlinear Phenomena, 362:1–8, 2018.


MathematicalAlgorithms forMICADO – First LightInstrument at theEuropean ExtremelyLarge TelescopeModern ground-based telescopes like the planned Extremely LargeTelescope (ELT) aim for better images of very faint objects on the nightsky, and therefore, use advanced techniques to correct for any imagedegradation. Adaptive Optics (AO) is a technique to compensate foratmospheric distortions of the incoming light. However, a perfect imageis still not achievable due to, e.g., time delays within these correctionprocesses. This results in a blur which can be mathematically describedby a convolution of the true image with the point spread function (PSF).The PSF associated to an astronomical observation can be reconstructedfrom data acquired during run time by the AO system. Furthermore, thereconstructed PSF can then be used for improving the image in blinddeconvolution as a post-processing step. We present the development ofalgorithms for these problems in the context of the ELT �rst lightinstrument MICADO.

In this article, we present the reasons fordeveloping mathematical algorithms inground-based astronomy, in particular forthe ELT �rst light instrument MICADO [1],which is under construction. As members inthe MICADO Consortium, the Industrial

Mathematics Institute at Johannes KeplerUniversity (JKU) and the Johann RadonInstitute for Computational and AppliedMathematics (RICAM) of the AustrianAcademy of Sciences (AAS), both based inLinz, Austria, are involved in designing new


algorithms to tackle the challenges of anextremely large telescope as part of theData�ow team led by the KapteynAstronomical Institute at the University ofGroningen in the Netherlands and theInstitute for Astrophysics at the University ofVienna. The MICADO Consortium is led bythe Max Planck Institute for ExtraterrestrialPhysics (MPE) at Garching, Germany.

What is MICADO?

The name MICADO is well-known in aslightly di�erent spelling, Mikado, as apick-up sticks game and was used to entitlethe Japanese emperor. Within the EuropeanELT, MICADO is an imaging instrumentfocusing on high presicion astrometry andspectroscopy, equipped with aSingle-Conjugate AO (SCAO) system.Optimized for imaging at the di�raction limitat wavelengths from 0.8 to 2.4 µm with highangular resolution, MICADO will allowdiscovery and study of new or unexploredphenomena, such as the detailed structureof galaxies at high redshift, the study ofindividual stars in nearby galaxies andexoplanets. The MICADO instrument shallsee �rst light in 2024.In a second step, MICADO will be coupled toMAORY, the Multi-conjugate Adaptive OpticsRelaY for the ELT, which will provide a moreuniform correction over the �eld of view andmake use of atmospheric tomography.

Mathematics in ground-basedastronomy

In ground-based astronomy, the observedimage Io can be described as a convolutionof the true image I and the so-called pointspread function (PSF), i.e.,

Io = I ⇤PS F . (5.19)

The PSF of an astronomical observationthrough a ground-based telescope dependson the one hand on the geometry of thetelescope and the atmospheric turbulenceabove the telescope and on the other handon the design of the instrument, in

particular aberrations by its opticalcomponents (see Figure 1). Modernground-based telescopes reduce the e�ectof the rapidly changing turbulentatmosphere by using Adaptive Opticssystems (cf [2]). AO systems consist of threemain parts: one or more wavefront sensors(WFS), one or more deformable mirrors(DM) and a real time computer (RTC). Thetask of the RTC is to transform indirectmeasurements made by the WFS intocommands applied to the DM. By adaptingthe shape of the DM the incoming wavefrontof the light is altered in such a way as tocounter the aberration introduced by theatmospheric turbluence. MICADO will, as amodern instrument, be equipped with suchan AO System to obtain superior imagequality to the NASA/ESA James Webb SpaceTelescope. However, the AO system can notfully correct for the e�ects caused byatmospheric turbulence, especially due to atime lag and limited resolution of the WFS inthe system, resulting in a PSF still degradedby residual atmospheric turbulence as wellas telescope and instrument intrinsic e�ects(see Figure 2). As a consequence, theobserved image appears blurred.

Figure 1: Point spread function without an AO System.

Credit: Iuliia Shatokhina.

Figure 2: Point spread function with an AO System. The

more “delta-peak-like”, the better. Credit: Iuliia Shatokhina.

To compensate for this residual blur, oneidea is to reconstruct the PSF from data


acquired by the WFS and the commandsapplied to the DM after the image has beenobtained. Availabilitiy of the PSF allows toaccess parameters which determine thequality of an observation, withoutestimating them from the science image.Additionally, the PSF can be used for imageimprovement in a post processing step,such as deconvolution.

Estimating the blur of observedimages

Throughout the past years severalalgorithms for reconstructing the PSF fromWFS data and DM commands weredeveloped [3, 4, 5, 6] and some even testedon sky [7, 8, 9, 10, 11]. The common basicingredient is the calculation of the so-calledstructure function Df , i.e., the time averagedspatial correlation of an incoming phase fafter AO correction,

Df (r) =D|f(x, t)�f(x+r, t)|2

E

t, (5.20)

where h·it indicates the time average andx,r are spatial coordinates within thetelescope aperture. The phase f is relatedto the incoming wavefront j through thewavelength l as f = 2p

l j . The structurefunction is related to the PSF as,

PS F = F

✓1

S

Z

P

P(x)P(x+r)e�1

2Df (x,r)dx

◆,

(5.21)where F denotes the Fourier transform, Sthe area of the telescope pupil and P theindicator function of the telescope aperture.However, most of the existing algorithmsare computationally demanding as theymake use of global basis functions, such asZernike polynomials. Their use seems to benot feasible for increasing sizes of thetelescopes.We adopted the algorithm of [3] by usingbilinear splines in order to decrease thecomputational costs and make animplementation feasible for the ELT [12, 13].Furthermore, we split the approach into twoparts: First from WFS data we reconstructthe incoming wavefront on our bilinear

spline basis, second we compute from thiswavefront the covariance matrix used forfurther calculation. In the original method,the covariance matrix was calculateddirectly on measurements and thentransferred to wavefront level by using aninteraction matrix (and its transpose),resulting in a computational complexity ofO(N2) for N measurements. We can use amatrix-free wavefront reconstructionalgorithm, and thus, decrease thecomputational costs to O(N).Our algorithm delivers a reconstructed PSFin the direction of a so-called guide star,which is a star being bright enough to getreliable WFS measurements. For SCAOsystems, the correction of atmosphericturbulence is only valid for this line of sight.However, the object of interest might be in asigni�cantly di�erent position in the skyimage, resulting in a di�erent atmosphericdistortion, and hence, less correctionthrough the AO system. Thus, spatiallyvarying estimates for the PSF are needed.We are investigating new algorithms toobtain accurate PSF estimates also for thesecases. For more complex AO systems, suchas MAORY, having more guide stars, a �elddependent estimate of the PSF can beprovided by using atmospheric tomographyalgorithms such as [14, 15].

Improving images in apostprocessing step

The PSF of an observation does not onlyserve as a quality measure for the AOcorrection, but it can also be used for imageimprovement in a post-observationalprocedure. Mathematically speaking, aconvolution of the true image and the PSFgives the observed image.We illustrate how an image of a star cluster(Figure 3) is blurred when observed througha ground-based telescope even with AOcorrection in Figure 4. The estimate of thePSF shall help to compensate for this blur byusing a postprocessing step.


Figure 3: True image of a star cluster (i.e., not altered by a

PSF, which corresponds to using an in�nitely large

telescope without atmospheric aberrations). Credit: Kirk

Soodhalter.

Figure 4: Blurred Image. Credit: Kirk Soodhalter.

Having an estimate for the PSF, theobserved image can be improved by using adeconvolution algorithm. Due to e�ectsrelated to the AO system and instrumentintrinsic aberrations, the estimate for thePSF might not be accurate enough fordirectly improving the observed image bydeconvolution. We are now developing blinddeconvolution algorithms (cf [16]), allowingfor changes in the PSF and taking care ofspeci�c available information on theobserved stars. This will result in improvedimages (see Figure 5) where very faintobjects can be detected.

Figure 5: The e�ect of deconvolution is clearly visible.

Credit. Kirk Soodhalter.

Conclusions

We developed algorithms for PSFreconstruction needed for new instrumentsat ELTs using astronomical adaptive opticsand tested them in an idealized simulation.As next steps, we need to adjust thesimulation step by step to real life, e.g., byincorporating the real structure of theprimary and secondary mirror of thetelescope. We also want to verify ouralgorithms on real observations of existingAO assisted instruments. Furthermore, weexpect that our algorithms will need furtherdevelopment to account for aberrations ofother parts of the optical system oftelescope and instrument oncemanufactured and assembled. Weanticipate that this requires to inventstrategies for measuring these aberrationsand devise ways to incorporate.

Roland Wagner1, Ronny Ramlau1,2, RicDavies3, João Alves4, Gijs Verdoes Kleijn5

1 Industrial Mathematics Institute, JohannesKepler University Linz, Austria2 Johann Radon Institute for Computationaland Applied Mathematics, Linz, Austria3 Max Planck Institute for ExtraterrestrialPhysics, Garching, Germany4 Institute for Astrophysics, University ofVienna, Austria5 Kapteyn Astronomical Institute, University


of Groningen, The Netherlands

References

1. R. Davies et al. MICADO: �rst light imager forthe E-ELT. In Proc. SPIE 9908, Ground-basedand Airborne Instrumentation for Astronomy VI,volume 1, page 99081Z, 2016. DOI:http://dx.doi.org/10.1117/12.2233047.

2. R. Davies and M. Kasper. Adaptive Optics forAstronomy. Annual Review of Astronomy andAstrophysics, 50:305–351, 2012. DOI:10.1146/annurev-astro-081811-125447.

3. J.-P. Véran, F. Rigaut, H. Maître, and D. Rouan.Estimation of the adaptive optics longexposure point spread function using controlloop data. J. Opt. Soc. Am. A, 14(11):3057–3069, Nov 1997. DOI:10.1364/JOSAA.14.003057.

4. E. Gendron, Y.Clénet, T.Fusco, andG. Rousset. New algorithms for adaptiveoptics point-spread function reconstruction.Astronomy & Astrophysics, 457(1):359–463, Oct2006. DOI: 10.1051/0004-6361:20065135.

5. L. Gilles, C. Correia, J.-P. Véran, L. Wang, andB. Ellerbroek. Simulation model basedapproach for long exposure atmosphericpoint spread function reconstruction forlaser guide star multiconjugate adaptiveoptics. Applied Optics, 51(31):7443–7458, Nov2012.

6. J. Exposito, D. Gratadour, G. Rousset,Y. Clénet, E. Gendron, and L. Mugnier. A newmethod for adaptive optics point spreadfunction reconstruction. In Third AO4ELTConference – Adaptive Optics for ExtremelyLarge Telescopes, May 2013. DOI:10.12839/AO4ELT3.13328.

7. L. Jolissaint, C. Neyman, J. Christou,P. Wizinowich, and L. Mugnier. FirstSuccessful Adaptive Optics PSFReconstruction at W. M. Keck Observatory. InProc. SPIE 8447, Adaptive Optics Systems III,844728, 2012. DOI: 10.1117/12.926607.

8. L. Jolissaint, J. Christou, P. Wizinowich, andE. Tolstoy. Adaptive optics point spreadfunction reconstruction: lessons learnedfrom on-sky experiment on Altair/Geminiand pathway for future systems. In Proc. SPIE7736, Adaptive Optics Systems II, 77361F, 2010.DOI: 10.1117/12.857670.

9. R.C. Flicker. PSF reconstruction for Keck AO:Phase 1 Final Report. W.M. Keck Observatory,65-1120 Mamalahoa Hwy., Kamuela, HI 96743,USA, 2008.

10. Y. Clénet, C. Lidman, E. Gendron, G. Rousset,T. Fusco, N. Kornweibel, M. Kasper, andN. Ageorges. Tests of the PSF reconstructionalgorithm for NACO/VLT. In Proc. SPIE 7015,Adaptive Optics Systems, 701529, 2008. DOI:10.1117/12.789395.

11. O. A. Martin, C. M. Correia, E. Gendron,G. Rousset, D. Gratadour, F. Vidal, T. J. Morris,A. G. Basden, R. M. Myers, B. Neichel, andT. Fusco. PSF reconstruction validated usingon-sky CANARY data in MOAO mode. In Proc.SPIE 9909, Adaptive Optics Systems V, 2016.

12. R. Wagner. From Adaptive Optics systems toPoint Spread Function Reconstruction and BlindDeconvolution for Extremely Large Telescopes.PhD thesis, Johannes Kepler University Linz,2017.

13. R. Wagner, C. Hofer, and R. Ramlau. Pointspread function reconstruction forSingle-conjugate Adaptive Optics on ELTs.RICAM Report, 2017-46, 2017.

14. D. Saxenhuber and R. Ramlau. Agradient-based method for atmospherictomography. Inverse Problems and Imaging,10(3):781–805, 2016. DOI:http://dx.doi.org/10.3934/ipi.2016022.

15. T. Helin and M. Yudytskiy. Wavelet methodsin multi-conjugate adaptive optics. InverseProblems, 29(8):085003, 2013. URL http://stacks.iop.org/0266-5611/29/i=8/a=085003.

16. L. Dykes, R. Ramlau, L. Reichel, K.M.Soodhalter, and R. Wagner. Lanczos-basedfast blind deconvolution methods. RICAMReport, 2017-27, 2017.


6EducationalCommittee

49

An instructorexperience feedbackI am an associate professor in appliedmathematics at University of Grenoble since2009. As such I have, I have participated indi�erent kind of teaching activities.Grenoble have been involved with ECMI fora long time and some several of mycolleagues participated to modelling weeksas instructor. Having heard of the goal andspirit of the modelling weeks, I consideredthe challenge to be interesting.

In July 2017, I had the opportunity to takepart of the modelling week in Lappeenranta.The problem I submitted to the studentsdealt with the study and determination offundamental state if matter. The objectivewas to propose di�erent computationalapproach that help to determine thepseudo-stable states in classical frustratedspins. For example, in triangle lattice of Isingspins, one third of the spins cannot gainenergy from its neighbors, hence the stablestates are computationally di�cult todiscover.

The team that work on the project consistsof third year bachelor student, �rst yearmaster students and students that wereabut to start their PhD. None of them werefamiliar wit the subject or the mathematicaltools needed to solve the problem. Hence,several session of discussions andbrainstorming were needed to getacquainted with the physics, the possiblemodels and the numerical tools to solve theproblem. It was very interesting to see theteam seize the subject and their way tomodel new computational approach. By theend ot the week, I believe the students had a

good understanding of the problem and thesolution proposed was really well thought.

Before coming to the modelling week, Ididn’t really know what to expect. Afterspending a week working with studentsfrom all over Europe, my opinion is as aninstructor the challenge is not only to posethe problem but also to guide the studentsto formulate their own solutions withoutbiased. You need to �nd a balance betweenthe time spend with the students to helpthem come up with speci�c items and thetime they need to come up with solutions.The range of scienti�c background and skillsin the students concur to make this weekrewarding.

The time spends with students and otherinstructors out of the work session was alsofruitful. I believe it helps to give a glimpseon how each educational systems work andhow to improve the teaching of appliedmathematics in our local universities.

Overall, my participation to this modellingweek was a good experience. It provides mewith some ideas on how to suggest suchmodelling weeks in France. And also, I willgladly participate to another modellingweek.

Christophe PicardUniv. Grenoble Alpes, Grenoble INP, LJKFrance

50 Collaborate and Cooperate Annual Report 2017 Educational Committee

University of Verona

Figure 1: Verona and the Arena

The University of Verona was founded in1982, has around 24,000 students and isorganized in one downtown campus hostingthe departments/faculties of the human andsocial sciences area (BusinessAdministration, Culture and Civilisation,Economics, Foreign Languages andLiteratures, Human sciences, Law) and inone suburb campus hosting the School ofMedicine (with the Departments ofMedicine, Neurosciences Biomedicine andMovement Sciences, Surgery DentistryPediatrics and Gynaecology, Diagnostics andPublic Health) and the School of Science andEngineering (with the Departments ofBiotecnology and Computer Science). Thereare around 60 Bachelor Degree, 60 MasterDegree and 17 PhD programs. Facultymembers are around 1100, administrativesta� counts 900 people. Concerninginternationalization, there are around 45cooperation agreements with EU and nonEU Universities, 250 Erasmus+ agreements,3 Double Degrees, 6-7% of internationalstudents. There are funded mobilityprograms (Short Term Mobility, World WideStudy) besides Erasmus+ and Erasmus+ forTraineeship, moreover there is a stronglyfunded Internationalization at Homeprogram, with six Master Degrees entirelytaught in English (Economics, Mathematics,Linguistics, Medical Bioinformatics,

Biotechnologies, International Economicsand Business Management), with manyinvited international teaching faculties.

Concerning research and technologicaltransfer, the University of Verona runsspeci�c funding programmes for bothprojects in Fundamental Research and jointresearch Projects with industries,supporting innovation processes and thecreation of networks in the lively SMEenvironment at a regional level also throughstart-up and spin-o� companies.

Department of Computer Science

Figure 2: the Department of Computer Science

The Department of Computer Science of theUniversity of Verona embraces a continuumof research areas in computer science,computer engineering, mathematics andphysics, ranging from discrete andcomputational mathematics, mathematicalmodelling and applications, machineintelligence, information systems, softwareengineering and security, cyber-physicalsystems, to applied and experimentalPhysics with almost 70 permanent facultyand research sta�. It has been recentlyawarded the Italian Ministry of EducationProject "Departments of Excellence" toimplement speci�c research andeducational activities oriented to theIndustry 4.0 world. The Department,

Educational Committee Collaborate and Cooperate Annual Report 2017 51

together with the School of Science andEngineering is in charge of 3 BSc degrees(Computer Science, Applied Mathematics,Bioinformatics), 3 MSc degrees (ComputerEngineering, Mathematics, MedicalBioinformatics) one PhD program inComputer Science and one PhD program inMathematics in agreement with TrentoUniversity. It hosts a Computer SciencePark, an entity for technological transferwith several spin-o� and start-up.

Math educational programme

The 3 years BSc in Applied Mathematics isarticulated in two main educational paths:one focuses on economics and �nancialmath, while the other is a modelling andcomputational one. The MSc in Mathematicsis entirely taught in english and consists intwo curricula: one is mathematics forteaching, the other one is applied andindustrial mathematics, and ful�lls therequirements of the ECMIMaster Model.Main educational paths are in mathematical�nance and data science, mathematicalmodelling in the applied sciences, numericalmethods and scienti�c computing. Everyyear several international invited facultiesthrough the Internationalisation at Homeprogram, coming also from other ECMInodes, give many interesting complimentarycourses. This motivates students to spendsemesters abroad within Erasmus+ mobility(more than 20 partner destinations andseveral ECMI nodes), even for internshipsand master thesis. Many contacts withbanking, industries and scienti�c

laboratories (biomedicine, robotics, virtualsimulations, arti�cial intelligence) at regionaland national level give students very goodopportunities for internships, industrialmaster thesis and placement. Finally, a jointPhD program with the University of Trentoon both pure and applied math topics isalso running well , with several educationalevents involving also master students, likefor instance summer schools and modellingweeks.

Figure 1: First PhD Modelling Week in Verona, Sept. 2016

Giandomenico OrlandiDipartimento di InformaticaUniversitá di Veronae-mail: [email protected]

52 Collaborate and Cooperate Annual Report 2017 Educational Committee

7ECMI Special

InterestGroups (SIGs)

Special Interest Groups (SIGs) exist to promote collaborativeresearch on speci�c topics in Mathematics for Industry within

Europe. A particular aim is to enable researchers from bothacademia and industry with similar interests to get together

and submit proposals for funding to the European Union or toother funding bodies. ECMI can act as a catalyst in theformation of such a group by o�ering advice about the

expertise available within Europe, by posting information onthe web pages and by circulating information about events to

all members.

53

Math for the DigitalFactoryPurpose

The digital factory represents a network ofdigital models and methods of simulationand 3D visualisation for the holisticplanning, realisation, control and ongoingimprovement of all factory processesrelated to a speci�c product. In the last �veor ten years all industrialised countries havelaunched initiatives to realise this vision,sometimes also referred to as Industry 4.0(in Europe) or Smart Manufacturing (in theUnited States).

Opportunities

The Special Interest Group MaDiFa (Math forthe Digital Factory brings together universitymathematicians working in modelling,simulation and optimization related tomanufacturing with practitioners frommanufacturing industry. The generalscienti�c goal is to develop a holisticmathematical view on digital manufacturing.Topics to be discussed include

coupling of multibody systems with pdemodels to describe interactions betweenmachine tool (typically a MBS) and itsmanufacturing task (typically describedby PDEs and ODEs)

multiscale models of complexmanufacturing chains including work�ow

new concepts to model the energyconsumption of machine tools and morecomplex production systems

optimization strategies for energy andmaterial e�cient production

Activities

In 2017 our main activities were focussed on�nalizing a multi-author textbook on digitalmanufacturing, which �nally was publishedin December 2017. It provides a uniquecollection of mathematical tools andindustrial case studies in digitalmanufacturing, addressing various topics,ranging from models of single productiontechnologies, production lines, logistics andwork�ows to models and optimizationstrategies for energy consumption inproduction.For 2018 we plan 3 major activities. The nextSIG workshop already took place in Limerickin March 2018. Then we will organize aminisymposium during the ECMI conferencein Budapest. Finally, we plan to submit aproposal for a European Joint Doctorate formaths in digital manufacturing in the nextITN call.

Dietmar Hömberg

Weierstraß-Institut and TechnischeUniversität Berlin

54 Collaborate and Cooperate Annual Report 2017 ECMI Special Interest Groups (SIGs)

SustainableEnergiesThe ideas for this SIG originated with the “Mathematics in Industry”workshop “Technologies of thin �lm solar cells”, held in Berlin. It wasfollowed by a series of workshops held in the UK and Germany with everincreasing scope from organic photovoltaics, supercapacitors,Lithium-Ion batteries, solar fuels and resulted in the Kick-O�meeting“Nanostructures for Photovoltaics and Energy Storage” for this SIG, whichalso included electrothermal modelling and simulation of organicmaterials and devices.

Purpose

We address the challenges posed by the wayenergy is being generated in the future, witha high demand for sources of sustainableenergy and production capabilities andwhich entails the restructuring of existing aswell as the creation of new, smart networksfor e�cient storage and transport ofdistributed energy. Mathematics plays a keyrole in understanding the complex problemsthat arise in these areas and in exploitingunderlying structures and processes.

Opportunities

Researchers and non-academics eg. fromindustry working in �elds such asthermoelectricity, nano-scale optics,organic/polymer electronics such as organicLEDs and storage systems are presently thekey stake holders to which this SIG reacheswith its activities. Contributions relating toenergy distribution and networks are alsowelcome.

Activities

Several activities have achieved success andvisible results:

At the Weierstrass Institute, ManuelLahnstorfer and Barbara Wagner(coordinating PIs) were successful withtheir proposal on second life batteries,bringing together mathematicians,engineers and four industrial partners.The background of the research is theidea to reuse Lithium batteries asstationary storage after they have been

ECMI Special Interest Groups (SIGs) Collaborate and Cooperate Annual Report 2017 55

retired from their primary use inelectrical vehicles.

For the ECMI annual conference inBudapest, the SIGs activities areshowcased in a minisymposium on“Material design and performance insustainable energies”. Contributors willspeak on solar cells, batteries, windpower, and connections to materialscience modelling.

Mathematical research plays animportant role in the development ofrenewable energies, and hence makes acontribution to addressing thechallenges raised by climate change andthe phasing out of fossil fuels. In thecontext of photovoltaics, for example,the aim is often to optimize lightmanagement and charge transport and

understand the interplay with thenano-morphology of the material, andhow to make it. These were some of thetopics which Barbara Wagner presentedwhile speaking at an invited plenarylecture on “Mathematical Opportunitiesand Challenges in Sustainable Energies”at the SIAM Annual Meeting in Pittsburghin 2017 (and coming up at the SIAMConference on Nonlinear Waves andCoherent Structure).

Coordinators: Andreas Münch1 and BarbaraWagner2,

1 Mathematical Institute, University ofOxford2 Weierstrass Institute Berlin


ComputationalFinanceThe ECMI Special Interest Group Computational Finance was launched atECMI-2014 in Taormina (June 9–13, 2014) and (together with the ITNSTRIKE Project) organized several sessions of a minisymposium inComputational Finance, e.g. at ECMI 2016 and ICCF-2017.The aim of the SIG is to extend the network and to build a framework tocontinue close cooperation in future. It also provides a long termprofessional contact option for Alumni of ITN-STRIKE. In 2018 the SIG isactive at ECMI-2018 in Budapest and organizes a minisymposium entitledComputational Methods for Finance and Energy Markets.

Purpose

At ECMI-2018 the Special Interest Group onComputational Finance organizes aminisymposium Computational Methods forFinance and Energy Markets. We will bringtogether again twelve speakers coming fromUniversitas Indonesia Depok (Jawa Barat,Indonesia), "Pázmány Péter" CatholicUniversity Budapest (Hungary), FraunhoferInstitute for Industrial Mathematics ITWM(Kaiserslautern, Germany), University ofSouthern Denmark (Odense, Denmark),Instituto Superior Técnico (Universidade deLisboa, Portugal), Bergische UniversitätWuppertal (Germany), Wroclaw University ofScience and Technology (Poland), Universityof Sussex (Great Britain), Max PlanckInstitute for Mathematics in the Sciences(Leipzig, Germany) and Uniper GlobalCommodities (Düsseldorf, Germany).The minisymposium will address topicsfrom Computational Finance,Computational Methods for Energy Marketsand Risk Analysis.

The e�cient production and use of energy,the development of new energy sources,and responsible management of theresources available to us now are critical forour future and need properly functioningmarkets. Mathematics has played a key rolein the development of modern �nancialmarkets and risk management tools. Energycommodity and environmental marketsdi�er in fundamental ways from markets forother asset classes. Some of the challengesin this research area involve the develop-ment of new stochastic models that cancapture the extreme price movements inpower markets. The tasks of asset valuationand the determination of optimal operationstrategies in this context generate complex,high dimensional valuation problems forwhich new computational techniques mustbe developed. Changes in marketmechanisms and products demand novelmathematical techniques, stochastic anddeterministic models, microscopic andmacroscopic approaches, and �exiblepricing tools, de�ning innovative researchareas in the �eld of applied mathematics.


Opportunities

The SIG will look for opportunities for newprojects in both directions, ComputationalFinance and Energy Markets, in the comingyears (ETN, EID, and EJD).The Special Interest Group is open forfurther participation.

Activities

Poster Workshop Lorentz Center, Leiden, Sep. 18–22, 2017.

Participants Workshop Lorentz Center, Leiden (NL).

Kees Oosterlee (TU Delft), Karel in ’t Hout (UAntwerp) and Matthias Ehrhardt (BUWuppertal) organized an interdisciplinaryWorkshop “Applied Mathematics Techniquesfor Energy Markets in Transition”. It tookplace in September 18–22, 2017 in the

Lorentz Center, Leiden, the Netherlands, seehttps://www.lorentzcenter.nl/lc/web/2017/907/info.php3?wsid=907&venue=Oort.Many companies from the energy sectorparticipated actively and gave presentations,e.g. EnBW Energy (Karlsruhe, Germany),Uniper Energy, (Düsseldorf, Germany), KYOS(Haarlem, the Netherlands) Energy Quants(Amsterdam, the Netherlands) and N-SIDE(Louvain-la-Neuve, Belgium).

Key points addressed were:

(A) Risk management issues related to theenergy transition,

(B) Energy derivatives facilitating the energytransition,

(C) Decisions for demand �exibilization inenergy intensive industry.

Discussions were on the economics of theenergy transition with mathematicalmodels, on research questions from andwith the industry and on in energyoperations and energy derivatives.

Banner ICCF Conference, Lisbon, Sep. 4–8, 2017.

On September 4-8, 2017, the conferenceICCF 2017 - International Conference onComputational Finance (Lisbon, Portugal)was organized by Maria do RosárioGrossinho, seehttp://cemapre.iseg.ulisboa.pt/iccf2017/.Several people from the SIG, or from theformer ITN-STRIKE project, were involved incommittees and/or as invited speaker. WithICCF we have established a new series ofconferences. The �rst one was held inGreenwich/London (2015). Nextconferences will be in 2019 (A Coruña,Spain), 2021 (Wuppertal, Germany) and


2023 (Dublin, Ireland).

Cover of the STRIKE Book, Springer, Sep. 2017.

In September the "STRIKE Book" (NovelMethods in Computational Finance), withoutcomes of the ITN-STRIKE project(2013-2016) was published in the bookseries Mathematics in Industry at Springer.This book already turned out to be a greatsuccess. Since its online publication onSeptember 20, 2017, there has been in 2017a total of 11,964 chapter downloads for thiseBook on SpringerLink. This means theSTRIKE book was one of the top 25% mostdownloaded eBooks in the relevant eBookCollection in 2017.For more details on the SIG see ourinformation on the ECMI Blog,https://ecmiindmath.org/2017/12/01/successful-outcomes-of-itn-strike/.Additionally, a STRIKE Success Story waspublished on the CORDIS Server, and apress release was published by theUniversity of Wuppertal, see

http://ec.europa.eu/research/infocentre/article_en.cfm?artid=47876.

(Planned) Activities for 2018 and beyond

Submission of EU MC proposals. InJanuary 2018 the Wuppertal groupresubmitted an ETN proposal ETN SWINGMathematical Modelling and Scienti�cComputing for Future Energy Markets andsubmitted an EID proposal CONFIRMComputational Methods for FinancialMarkets. In both proposals there is astrong engagement of European �rms.

June 11-16, 7th Conference FiniteDi�erence Methods: Theory andApplications, Lozenetz, Bulgaria. MatthiasEhrhardt is organisator of the mini-symposiums “Novel Methods in Compu-tational Finance” and invited speaker.

June 18-22, ECMI 2018 ConferenceBudapest, Hungary. Minisymposium"Computational Methods for Finance andEnergy Markets" at ECMI 2018, 12speakers, 3 sessions, on June 18.

Co-organize ICCF-2019 – InternationalConference on Computational Finance, ACoruña, Spain, July 8-12, 2019, as asatellite event to ICIAM 2019, Valencia,Spain, July 15-19, 2019. MatthiasEhrhardt is the Chair of the Scienti�cCommittee and plenary speaker.

A proposal by Michael Coulon, CarlosVázquez and Tony Ware for a BIRSworkshop in Ban� (Alberta, Canada), on"New challenges in energy markets –data analytics, modelling and numerics"has been accepted, and is scheduled forSept. 22-27, 2019.

Coordinators: Matthias Ehrhardt andE. Jan W. ter Maten,

Bergische Universität Wuppertal, Germany,http://www-amna.math.uni-wuppertal.de/ecmi-sig-cf/


Mathematics forBig DataPurpose

The availability of huge amounts of data isoften considered as the fourth industrialrevolution we are living right now. Theincrease in data accumulation allows us totackle a wide range of social, economic,industrial and scienti�c challenges. Butextracting meaningful knowledge from theavailable data is not a trivial task andrepresents a severe challenge for dataanalysts. Mathematics plays an importantrole in the existing algorithms for dataprocessing through techniques of statisticallearning, signal analysis, distributedoptimization, compress sensing etc.

The amounts of data that are available andthat are going to be available in near futurecall for signi�cant e�orts in mathematics.These e�orts are needed to make the datauseful. The main challenges we plan toconsider within this SIG are, roughlyspeaking, in the area of mathematicaloptimization and statistics.

Opportunities

Minimization of a cost function, based onlarge amount of data is a typical problem inall big data areas – from smart agriculture,energy e�ciency, computational biology,high tech industries based on simulations,material design, social networks analysis,challenge in policy decisions based on data,risk assessment in �nance, security, naturaldisasters etc. The challenges in these areas,mathematically speaking are design ofalgorithms that will be able to process hugeamounts of data within a reasonable timespan and with computer power that is

widely available today. Two importantissues are distributed optimization andprivacy issues. Several EU documents citeprivacy of data as an important questionthat is to be resolved. On the other hand,distributed optimization allows us to employoptimization techniques in parallel, atseveral di�erent computers placed innetworks of di�erent types. On anotherhand, extraction of meaningful informationfrom data is one of the main tasks ofStatistics. In presence of big data the mostpart of the usual techniques for statisticalanalysis can not easily been applied, sincethey are based on the simultaneousprocessing of the whole dataset. A big e�orthas been made during these years, mainlyby computer scientists, to �nd fast andscalable procedures that have becomepopular in presence of distributedarchitectures (like e.g. the well knownMapReduce paradigm). Unfortunately inmany situations such procedures can not beapplied to solve statistical problems in adistributed way, or they work under toomuch restrictive and thus unrealisticconditions. The deepening of themathematical insight in this context mayhelp to better understand the theoreticaland applied power of the new algorithmsand to extend them to more realistic cases.Sometimes data are “big” because of theirhigh dimensionality and space-timestructure (think e.g. to satellite images,signals registered by sensors or antennas,etc.). In such cases suitable mathematicaltechniques for dimensionality reduction areneeded both for data visualization and fortheir numerical treatment. FunctionalStatistics, that is a �eld in which a lot ofresearch is concentrating nowadays, may


help in facing this task. In other contextsdata are considered “big” because of theircomplexity or heterogeneity (e.g. dataextracted from social networks with textmining, mixed to socioeconomic data formarketing purposes; or data highlyinterrelated which may be represented bycomplex graphs, like atoms and bounds in aprotein, relationships between users of asocial network, etc.). Sentiment analysis andTopological Data Analysis are new statistical�elds of research, still under development,which may help to tackle the problem ofanalyzing such data.

The aim of this Special Interest Group is tocollect people working on the themesdescribed above, coming both fromacademy and from “industry” (to beintended in a wide sense) to favor scienti�ccollaboration and research, by organizingcommon activities.

Activities

A kicko� workshop has been held in NoviSad (Serbia) on May 31 - June 1, 2017.The workshop was attended by over 70participants, including many industrialdelegates, and 19 talks have beenpresented as well as some posters. Theworkshop was closed by a round tablewhere industrial delegates addressed themajor challenges that their work andinvolvement with Big Data is posing toacademy, both in terms of research and

training of students.

A MSC-ITN-EID European project calledBIGMATH has been submitted forevaluation in early January 2018. Theproject, coordinated by Universitá degliStudi di Milano, includes other 3academic centres (IST Lisbon,TU-Eindhoven, University of Novi Sad)and 7 SMEs, and is aimed to recruit 7PhD students who will work on Big Datarelated industrial mathematical problemsspanning many �elds of application.

Planned activities for 2018

A minisymposium of the SIG is planned totake place during the conference ECMI 2018,Budapest, June 18-22, 2018

For further information seehttps://sites.google.com/view/mathbigdata/home

Coordinators:Natasa Krejic, University of Novi SadAlessandra Micheletti, Università degli Studidi Milano


Liquid Crystals,Elastomers andBiologicalApplicationsPurpose

The ECMI Special Interest Group in LiquidCrystals, Elastomers and BiologicalApplications originated with discussions atBritish Liquid Crystal Society and ECMImeetings, and aims to focus the e�orts ofapplied mathematicians in anisotropic �uidsand solid mechanics. The SIG coordinatorshave since brought together researchersfrom various �elds, and from around theworld, by organising workshops andsessions at larger conferences. With newactivity planned for the near future,particularly linking to other networks withinEurope, the hope is to make the SIGincreasingly international andinterdisciplinary in the near future.

Opportunities

From a mathematical point of view, thisresearch area encompasses the analysis ofanisotropic materials through continuummechanics, �uid dynamics, non-equilibriumphysics and the analysis of ordinary andpartial di�erential equations.

The intrinsic anisotropy of these materialsleads to asymmetries in elasticity and stresswhich produce interesting couplingsbetween elastic deformation, �ow andorder. Since these e�ects are key to a

number of existing and burgeoningindustries and scienti�c �elds, such as liquidcrystal displays, elastomeric materials andactive �uids, there are multiple exiciting andnovel interdisciplinary opportunities formathematicians in this �eld.

Microscope image of a nematic liquid crystal as it changes

to a twisted grain boundary structure (courtesy of Dr

Stephen Cowling, University of York, UK)

Activities

The Group is small at present but plans toexpand through collaborations with theBritish and German Liquid Crystal Societyand the UK Fluids Network. The SIGmeetings to date include an Institute forPure and Applied Mathematics (UCLA)workshop on “Partial Order: Mathematics,Analysis and Simulations” 25th-29th January20161 a Centre de Recherches

1http://www.ipam.ucla.edu/programs/workshops/partial-order-mathematics-simulations-and-applications/


Mathématiques (Montreal) two-weekworkshop on “Partial Order in Materials:Analysis, Simulations and Beyond” 21st-30th June 20162 and a LondonMathematical Society South West and SouthWales Regional Workshop on PartiallyOrdered Materials, University of Bath 21stDecember 20163 and a more recentinternational research workshop on "PartialOrder in Materials: at the Triple Point ofMathematics, Physics and Applications" atthe Ban� International Research Station(https://www.birs.ca/events/2017/5-day-workshops/17w5059). New links have beenformed from the SIG to groups around theworld through a variety of methods, andlinks now exist to the University of Malaya(Malaysia), Nanyang TechnologicalUniversity (Singapore), the NationalAutonomous University of Mexico and theCentro de Investigación en Matemáticas, aswell as the Indian Institute of TechnologyDelhi (India).

Workshop participants from the SIG and Nanyang

Technological University

Future activities

We are pleased to announce a forthcomingresearch workshop on "Nematics at theMeeting Point of Solid Mechanics andFluid Dynamics: New Perspectives andChallenges" at the University of Bath on the28th and 29th June 2018. This meetings is

funded by the EPSRC UK Fluids Network andis being organized under the auspices of theUK Fluids Special Interest Group on "Fluiddynamics of liquid crystalline materials"(https://�uids.ac.uk/sig/LiquidCrystals). Themeeting brings together researchersworking in nematic liquid crystals, theirstatic and dynamic theories, opticalmodelling, numerical simulations andanalogies between nematic theories andsolid mechanics. This meeting will serve as acommon platform to discuss recent excitingdevelopments in nematic solitons, nematicmicro�uidics, the rich applications ofnematics in con�nement and nematicsunder �ow along with powerful newcomputational techniques to explore thesolution landscapes.

The seven con�rmed speakers and theirtitles are given below.

1. Halim Kusumaatmaja (Durham, UK)Tentative title: Applications of energylandscape methods to problems inelasticity and liquid crystals.

2. Noel Smyth (Edinburgh) Title: Thenonlinear optics of nematic liquidcrystals: solitary waves and undularbores

3. Oliver Henrich (Strathclyde) Title:Mesoscopic Simulation of FlowingTopological Composite Materials

4. Duvan Henao (PUC Chile) Title: Meetingpoints of cavitation and nematics

5. Nigel Mottram (Strathclyde UK) Title:Trapped! - anisotropic �uids in con�nedgeometries

6. Ian Gri�ths (University of Oxford) Title:Mathematical modelling for liquid crystalmicro�uidics

7. Lei Zhang (Peking University) Title:Numerical Methods of Finding TransitionStates and its Applications in Materials

This meeting is also partly supported by aRoyal Society Newton Advanced Fellowship

2http://www.crm.umontreal.ca/2016/Order16/index_e.php3http://people.bath.ac.uk/jlpn20/lms2016.html


awarded to Apala Majumdar (University ofBath) and Lei Zhang (Peking University). Themeeting is open to everybody and pleasesend an expression of interest to Dr ApalaMajumdar ([email protected]) if youare interested in attending. There is noregistration fees and lunch & refreshmentswill be provided to all participants on both

days. We look forward to welcoming you atBath!

Coordinators: Apala Majumdar1 and NigelMottram2

1 University of Bath2 University of Strathclyde


Shape and Size inMedicine,Biotechnology andMaterials SciencePurpose

Thanks to the development of informationtechnologies, the last decade has seen aconsiderable growth of interest in themathematical and statistical theory of shapeand its application to many and diversescienti�c areas. Often the diagnosis of apathology, or the description of a biologicalprocess mainly depend on the shapespresent in images of cells, organs, biologicalsystems, etc. However, mathematicalmodels that relate the main features ofthese shapes to the correct outcome of thediagnosis, or to the main kinetic parametersof a biological system are not yet present. Inmaterials science, optimisation for qualitycontrol, texture description and prediction,. . . require methods of mathematicalmorphology.

Opportunities

From the mathematical point of view, shapeanalysis uses a variety of mathematical toolsfrom di�erential geometry, geometricmeasure theory, stochastic geometry, etc.Quite recently, instruments from algebraictopology have been introduced for shapedescription, giving rise to a new �eld ofresearch called Topological Data Analysis. Asfar as applications are concerned, themembers of the SIG emphasize here topicswhich are relevant in medicine,

biotechnology and materials science. Wedeal with direct and inverse problems.Among direct problems, spatio-temporalpattern formation deals with the analysis ofhow patterns are created and developed inbiology, medicine and materials science.Modeling, numerical simulation andanalyses of the corresponding systems aretasks of paramount importance for directproblems. Among inverse problems, westudy various statistical techniques of shapeanalysis to measure in a quantitative waythe random variability of objects; recentmethods of image analysis include opticalimaging of objects in turbid media, whichcan be used as a non-invasive technique forthe detection of tumors in the body.

Activities

This year has seen the transition in the roleof coordinator from Alessandra Micheletti(Università degli Studi di Milano) to JesusAngulo (Ecole des Mines de Paris, Paristech)and Luis Bonilla (Universidad Carlos III deMadrid). Main activity so far:

Workshop Physics and mechanics ofrandom structures: from morphology tomaterial properties in honor ofDominique Jeulin, Peninsula of Oléron,Atlantic Coast, France, June 17-23, 2018(http://cmm.ensmp.fr/ willot/PMRM/).The activities of the SIG Shape and Size inMedicine, Biotechnology and Materials


Science are to be presented andpromoted during this Workshop sincemost of the Workshop topics arecommon to those of the SIG. Invitedspeakers in the Workshop include SIGmembers:

– Jesus Angulo, Mines ParisTech,France.

– Luis Bonilla,Universidad Carlos III deMadrid, Spain

– Vincenzo Capasso, Università degliStudi di Milano, Italy.

Planned activities for 2019

New workshops or thematicminisymposia in internationalconferences are being planned and willbe announced on the ECMI web pages.

Figure 1: Comparison of experimentally measured strain

and rotation �elds of a dislocation in graphene to di�erent

theoretical reconstructions

Figure 2: A simulation of a mathematical model for

angiogenesis

Coordinators: Jesus Angulo (MinesParisTech, France),

Luis L. Bonilla (Universidad Carlos III deMadrid, Spain)


Advancing theDesign of MedicalStentsA number of events were organsied over the past year, including theminisymposium “Applied mathematics in stent development” at ECMI2016 in Santiago de Compostela and the three day workshop “Modellingand experiments in drug delivery systems” at University of Coimbra.

These events brought together in excess of70 participants including mathematicalmodellers and experimentalists fromseveral countries including the UK, Ireland,France, Italy, Portugal, Germany, Denmark,Iceland and Spain.

SIG Purpose

Coronary artery disease is a global problemand devising e�ective treatments is thesubject of intense research activitythroughout the world. Over the pastdecade, stents have emerged as one of themost popular treatments. Acting as asupporting sca�old, these small meshdevices are now routinely inserted intoarteries where the blood �ow has becomedangerously restricted. Stents have evolvedfrom bare metal sca�olds to polymercoated drug-delivery vehicles and, morerecently, sophisticated fully biodegradabledrug delivery con�gurations. Despite theseadvances, signi�cant opportunities toimprove on arterial stent design remain. Inparticular, research is focussed on thedevelopment of stents which accelerate the

healing process to minimise thrombosis riskand which can be used in previouslyunserved patient groups and lesion types.

This SIG therefore consists of aninternational network of experts interestedin stent research, and provides a platform toco-ordinate research e�orts and helpexpedite the development of novel stentdesigns and technologies.


Modelling and experiments in drugdelivery systems

The Modelling and experiments in drugdelivery systems (MEDDS2016) workshopwas held at the University of Coimbra inJune 2016, under the auspices of the SIG.The workshop achieved its main goal ofbringing mathematicians, biologists,physicians and engineers together in anopen discussion environment. Whilst therewere several talks on stents, the scope ofthe workshop was wider and included talkson drug delivery in general as well as severalspeci�c applications including transdermaldelivery and intravitreal implants.

Applied mathematics in stentdevelopment

We organised the above titledminisymposium at the 19th EuropeanConference on Mathematics for Industry(ECMI 2016) in Spain. There were �vecontributed talks from members of the SIG.The talks covered the development ofinnovative models to help industry optimiseand improve stent design, to identify the keyparameters governing the behaviour of thesystem, to simulate the �ow of plasmaaround complex stent geometries, toidentify the drug release mechanism, and tohelp decrease the number of experimentalstudies, thereby saving time and money.The minisymposium was attended byresearchers with expertise in continuum

mechanics, physiological �ow modelling,structural and soft tissue mechanics,numerical analysis, mathematical biologyand multi-objective optimisation, to namebut a few. The talks included:

The role of mathematics in stentdevelopment, Dr Sean McGinty, Universityof Glasgow (Scotland).

Optimizing the performance of drug-elutingstents: simulations and experiments, ProfAbdul Barakat, Ecole Polytechnique(France).

Mathematical models of drug release frompolymer-free drug-eluting stents, Dr TuoiVo, University of Limerick (Ireland).

Variable porosity coatings as a means ofcontrolling drug release from stents, DrGiuseppe Pontrelli, IAC-CNR, Rome (Italy).

Numerical simulation of drug transport inarterial wall under healthy andatherosclerotic conditions, Javier Escuer,University of Zaragoza (Spain).

SIG Inaugural Committee Meeting

ECMI 2016 also provided the opportunity forus to hold our �rst SIG Committee meeting,attended by members of the SIG Committeeas well as ECMI president DietmarHoemberg. It was decided that the SIG seedmoney would be used to fund a workshopwith an Industrial presence (see below).Among the matters raised at the meetingincluded the possibility of widening the


scope of the SIG in the medium-term toinclude medical implants and/or drugdelivery devices more generally. The idea ofsubmitting a proposal for an EU PhDtraining network was discussed as well asthe possibility of writing a book related tothe themes of the SIG which could also actas a teaching resource.

Forthcoming Activities

The SIG intends to submit a minisymposiumproposal for the ECMI 2018 conference andadditionally plans to use the SIG seedmoney to partially fund a 3 day workshop in

Autumn 2018 in Glasgow, on the theme of“Modelling and experiments in drug deliverysystems”. A full day of the workshop will bedesignated as an Industrial workshop, andanother full day dedicated to stentsresearch. The attendance of companies,clinicians and experimentalists will onlyserve to enhance collaboration in thismulti-disciplinary area. Those interested inattending should contact Sean McGinty([email protected]) or Tuoi Vo([email protected]).

Coordinator: Sean McGinty

University of Glasgow


Net Campus forModeling Edu-cation and Indus-trial MathematicsThe ECMI Special Interest Group Net Campus for Modeling Education andIndustrial Mathematics was launched in 2017 following initiatives takenby ECMI’s Educational Committee. The aim of the SIG is to coordinate thealready ongoing activities at the various ECMI centers in the �eld of onlineand digital education and extend them towards joint ECMI online courses.

Purpose

The ECMI educational committee has takenvirtual education and web-supportedsolutions as one of its target areas tocomplement the other strategic areas likeECMI curriculum development, modelingweeks, mobility of students & sta� etc.

The cutting edge knowledge in industrialmathematics is dispersed at small nodes ofexpertise. Online environments are a viablemedia to access this knowledge and supportinnovative processes, training andeducational needs, to facilitate distributedconsultation processes, etc. The evolutionfrom textbook to interactive cross mediaenvironments means a new learningparadigm. Advantages include easy accessand portability, �exible updates, dynamicedition, multi–/hypermedia tools fromsearch facilities, quiz–structures toanimations, interactive exercises, remotelectures and videoconference etc.

We envisage to build a European digitalenvironment and web–portal for appliedand industrial mathematics. Moreimmediate goal is to share information andexperience, describe examples of webbased courses in applied mathematics andtechnologies for web publication ofinteractive documents. Such environmentare suitable for students in appliedmathematics and engineering programs inadvanced BS and MS level as well as forpersons who are already in their working lifeand are looking for continuing educationand professional development. The coursesshould be based on customized content fora special applications area.

Activities

The kick-o�meeting initiating this SIG hasbeen held at the university in Koblenz,Germany (March 23–24, 2017). Here, thestructure and participants of a �rstintroductory online course on mathematical


modeling were discussed.

At the ECMI 2018 conference in Budapest(June 18–22, 2018) we will organize aminisymposium dedicated to onlineeducational issues.

Online Course Description

In October 2017, the “ECMIModelingCourse” was hosted on the Moodle platformat Lappeenranta University. Coordinated bythe University in Koblenz, six introductoryreal-world problems were selected andpreprocessed for undergraduate student’suse. In summary, 30 students from allpartner universities participated in this �rstround. In detail, the problems included thefollowing topics (posing partner inparenthesis):

1. Indoor mobile phone positioning usingaccess point signals (Tampere, Finland),

2. Opinion dynamics on social networkgraphs (Verona, Italy),

3. Stratospheric beanstalk modeling (St.Petersburg, Russia),

4. Pursuing the sun (Koblenz, Germany),

5. Ecological forest growth modeling(Lappeenranta, Finland),

6. Indoor shortest path problems (Coimbra,Portugal).

Figure 1: Indoor positioning (Problem 1). True (olive) versus

calculated path (red) of a mobile phone user in a building

(blue). Axes are only for scale.

Figure 2: Pursuing the sun (Problem 2). Path on the earth’s

surface when following the sun using di�erent integration

methods (blue and red). Axes scaled to a normalized earth

radius of 1.

Coordinators: Dietmar Hömberg1, ThomasGötz2, Robert Rockenfeller2 and MattiHeiliö3

1 Weierstrass Institute Berlin, Germany2 University Koblenz-Landau, Germany3 Technical University Lappeenranta, Finland


8About ECMIMission

Mathematics, as the universal language of the sciences, plays a decisive role in technology,economics and the life sciences. European industry is increasingly dependent on mathematicalexpertise in both research and development to maintain its position as a world leader for hightechnology and to comply with the EU 2020 agenda for smart, sustainable and inclusivegrowth. ECMI initiatives in response to these needs may be summarized as follows:

ECMI advocates the use of mathematical modelling, simulation, and optimization in industryECMI stimulates the education of young scientists and engineers to meet the growingdemands of industryECMI promotes European collaboration, interaction and exchange within academia andindustry

Executive board

Dietmar Hömberg, PresidentWeierstrass Institute and Technische UniversitätBerlinAdérito Araújo, Vice PresidentUniversity of CoimbraPoul G. Hjorth, Executive DirectorTechnical University of Denmark, Kgs. LyngbyE. Jan W. ter Maten, Secretary and TreasurerUniversity of Wuppertal and Eindhoven Universityof TechnologyCláudia Nunes, Chair Educational CommitteeUniversity of LisbonWil Schilders, Chair Research and InnovationCommitteeEindhoven University of TechnologyStephen o’Brien, ECMI Representative inEU-MATHS-IN boardUniversity of Limerick


Countries participating in ECMI

DENMARK

ISRAEL


9InstitutionalmembersAustria

Institut für IndustriemathematikJohannes Kepler UniversitätContact Person Ronny Ramlau

Institute for Analysis and Scienti�cComputingVienna University of TechnologyContact Person Jens Markus Melenk

Computational Science Center, Faculty ofMathematicsUniversity of VienaContact Person Otmar Scherzer

Department of MathematicsLeopold-Franzens-Universität InnsbruckContact Person Richard Kowar

MathConsult GmbH

Contact Person Andreas Binder

Bulgaria

Faculty of Mathematics and InformaticsSo�a University “St. Kliment Ohridski”Contact Person Mikhail Krastanov

Institute of Mathematics and InformaticsBulgarian Academy of SciencesContact Person Neli Dimitrova

Institute of Information andCommunication TechnologiesBulgarian Academy of SciencesContact Person Svetozar Margenov

Faculty of Mathematics, Informatics andInformation TechnologyPlovdiv UniversityContact Person Anton Iliev

Faculty of Applied Mathematics andInformaticsTechical University of So�aContact Person Michail Todorov

Croatia

Department of MathematicsUniversity of OsijekContact Person Domagoj Matijevic


Denmark

Department of Applied Mathematics andComputer ScienceTechnical University of DenmarkContact Person Mads Peter Sørensen

Institute of MathematicsAarhus UniversityContact Person Hans Anton Salomonsen

Department of Mathematical SciencesAalborg UniversityContact Person Arne Jensen

Center for Energy Informatics, TheMærsk Mc-Kinney Møller InstituteUniversity of Southern DenmarkContact Person Christian T. Veje

Estonia

Institute of Mathematics and StatisticsUniversity of TartuContact Person Peep Miidla

Finland

Department of Mathematics andStatisticsUniversity of HelsinkiContact Person Mats Gyllenberg

Department of Mathematics and PhysicsLappeenranta University of TechnologyContact Person Matti Heiliö

Department of MathematicalInformation TechnologyUniversity of JyväskyläContact Person Pekka Neittaanmäki

Department of MathematicsTampere University of TechnologyContact Person Simo Ali-Löytty

Department of Mathematics andSystems AnalysisAalto UniversityContact Person Juha K. Kinnunen

France

Department Génie MathématiqueLaboratoire de Mathématiques, INSA deRouenContact Person Natalie Fortier

École des Mathématiques Appliquées,UFR IM2AGUniversitè Joseph FourierContact Person Georges-Henri Cottet

CMM - Centre de MorphologieMathèmatiqueMathématiques et Systèmes, MINESParistechContact Person Jesús Angulo

Unité de Formation Mathématiques etIntéractionsUniversité Bordeaux 1Contact Person Jean-Jacques Ruch

AMIESCNRS AMIES - UMS 3458Contact Person VéroniqueMaume-Deschamps

IRMA - Dept. of Mathematics andComputer ScienceUniversity of StrasbourgContact Person Christophe Prud’homme

Laboratoire Informatique d’AvignonUniversité d’Avignon et des Pays deVaucluseContact Person Rosa Figueiredo


Germany

Aerodynamic Institute RWTHUniversity of AachenContact Person Michael Klaas

AG TechnomathematikTU KaiserslauternContact Person Axel Klar

Department of MathematicsUniversity of TrierContact Person Volker Schulz

Institut für Mathematik IIFreie Universität BerlinContact Person Ralf Kornhuber

Institut für IndustriemathematikUniversität PaderbornContact Person Andrea Walther

Department of Mathematics, Institute ofAnalysisTechnische Universität DresdenContact Person Stefan Siegmund

Fakultät für MathematikTechnische Universität ChemnitzContact Person Kerstin Seidel

Department Vehicle System Dynamics(FAZ), Robotics and Mechatronics Center(RMC)German Aerospace Center (DLR)Contact Person Andreas Heckmann

Forschungsverbund Berlin e. V.Weierstrass Institute for Applied Analysisand Stochastics (WIAS)Contact Person Michael Hintermüller

Angewandte Mathematik undNumerische Analysis, Fakultät fürMathematik und NaturwissenschaftenBergische Universität WuppertalContact Person Michael Günther

Institut für Mathematik, Fakultät II -Mathematik und Naturwissenschaften

TU BerlinContact Person Dietmar Hömberg

Fraunhofer Institut für Techno- undWirtschaftsmathematikITWMContact Person Markus Pfe�er

Technische Universität BerlinForschungszentrum MATHEONContact Person Elisabeth Asche

Mathematical InstituteUniversity Koblenz-LandauContact Person Thomas Götz

IWRUniversität HeidelbergContact Person Hans Georg Bock

Technische Universität Darmstadt

Contact Person Sebastian Schöps

Hungary

Institute of MathematicsEötvös Loránd UniversityContact Person Andrá Bátkai

MTA SZTAKIHungarian Academy of SciencesContact Person László Gerencsér

Institute of MathematicsBudapest University of Technology andEconomicsContact Person Róbert Horváth

Bolyai InstituteUniversity of SzegedContact Person Gergely Röst

Széchenyi István University

Contact Person Zoltán Horváth


Ireland

Department of Mathematics andStatisticsUniversity of LimerickContact Person Stephen O’Brien

School of Mathematics, Statistics,Applied MathematicsNational University of Ireland, GalwayContact Person Martin Meere

School of Mathematics and StatisticsUniversity College DublinContact Person Miguel D. Bustamante

Israel

TechnionIsrael Institute of TechnologyContact Person Nir Gavish

Department of MathematicsBraude CollegeContact Person Aviv Gibali

Italy

Dipartimento di Matematica eInformatica “Ulisse Dini”Università di FirenzeContact Person Giuseppe Anichini

Dipartimento di MatematicaUniversità degli Studi di MilanoContact Person Alessandra Micheletti

Instituto per le Applicazioni del Calcolo“Mauro Picone”CNR - Consiglio Nazionale delle RicercheContact Person Roberto Natalini

Dipartimento di Matematica eInformaticaUniversità di CataniaContact Person Giovanni Russo

Dipartimento di InformaticaUniversità di VeronaContact Person Giandomenico Orlandi

MOX, Department of MathematicsPolitecnico di MilanoContact Person Luca Formaggia

Lithuania

Faculty of Mathematics and NaturalSciencesKaunas University of TechnologyContact Person Ruta Sutkute

Norway

Department of Mathematical SciencesNorwegian University of Science andTechnologyContact Person Helge Holden

SINTEF DigitalSINTEF ASContact Person Knut-Andreas Lie

Norwegian Computing Center

Contact Person Lars Holden

Poland

Institute of Applied Mathematics andMechanicsUniversity of WarsawContact Person Andrzej Palczewski

Faculty of Pure and Applied MathematicsWroclaw University of Science andTechnologyContact Person Krzysztof Burnecki

Portugal

CMUC - Centre for MathematicsUniversity of CoimbraContact Person Adérito Araújo

Mathematics DepartmentUniversidade de Lisboa (IST)Contact Person Cláudia Nunes Philippart

Centro de Matemática da Universidadedo PortoUniversidade do Porto - Faculdade deCiênciasContact Person João Nuno Tavares


Romania

Faculty of Computer Science“Alexandru Ioan Cuza” University of Ia�iContact Person Corina Forascu

Russia

Peter the Great St. PetersburgPolytechnic University

Contact Person Dmitry Arseniev

Faculty of Mathematics, Mechanics andComputer ScienceSouthern Federal UniversityContact Person Konstantin Nadolin

Faculty of ScienceRUDN UniversityContact Person Vladimir MikhailovichSavchin

Serbia

Department of Mathematics andInformatics, Faculty of Natural Sciencesand MathematicsUniversity of Novi SadContact Person Natasa Krejic

Slovenija

Department of Mathematics, Faculty ofMathematics and PhysicsUniversity of LjubljanaContact Person George Mejak

Spain

Red Española Matemática-IndustriaRed math-in.netContact Person Peregrina Quintela

Gregorio Millán Institute for Fluiddynamics, Nanoscience & IndustrialMathematicsUniversidad Carlos III de MadridContact Person Luis L. Bonilla

Department de MatemàtiquesUniversitat Autònoma de BarcelonaContact Person Susana Serna

Departamento de Matemática Aplicada,Facultade de MatemáticasUniversidade de Santiago de CompostelaContact Person Patricia Barral Rodiño

Facultad de Ciencias MatemáticasUniversidad Complutense de MadridContact Person Javier Montero

Centre de Recerca MatemáticaCRMContact Person Lluis Alsedá

Research Group Nonlinear Dynamics andStability in Aerospace EngineeringEscuelta Tecnica Superior de IngenierosAeronauticos, MadridContact Person Jose Sanchez

Department of Applied MathematicsUniversidad de ValladolidContact Person Angel Duran

Basque Center for Applied MathematicsBCAMContact Person Lorea Gómez

Sweden

Fraunhofer - Chalmers Research Centrefor Industrial MathematicsFCCContact Person Johan Carlson

Centre for Mathematical SciencesLund University of TechnologyContact Person Eskil Hansen

Department of Mathematical SciencesChalmers and Göteborg UniversityContact Person Bernt Wennberg

Department Engineering and SustainableDevelopmentMid Sweden UniversityContact Person Anders Holmbom


Switzerland

Seminar for Applied MathematicsETH ZürichContact Person Ralf Hiptmair

School of EngineeringZurich University of Applied SciencesContact Person Dirk Wilhelm

The Netherlands

Department of Mathematics andComputing ScienceTU EindhovenContact Person Martijn J.H. Anthonissen

Mathematical InstituteUtrecht UniversityContact Person Jason Frank

Department of Applied MathematicalAnalysisFaculty of Information Technology andSystemsContact Person A.W. Heemink

Center for Mathematics and ComputerScienceCWIContact Person Kees (C.W.) Oosterlee

4TU Applied Mathematics Institute(4TU.AMI)p/a Delft University of TechnologyContact Person Kees Vuik

UK

Department of MathematicsHeriot-Watt UniversityContact Person Andrew Lacey

Department of Mathematics andStatisticsUniversity of StrathclydeContact Person Anthony J. Mulholland

Mathematical SciencesUniversity of Southampton

Contact Person Chris Howls

Smith Institute

Contact Person Robert Leese

OCIAMMathematical InstituteUniversity of OxfordContact Person Andreas Muench

Division of Theoretical Mechanics, Schoolof Mathematical SciencesUniversity of NottinghamContact Person John R. King

School of MathematicsUniversity of ManchesterContact Person Geo�rey Evatt

Department of MathematicsUniversity of SurreyContact Person Philip J. Aston

Departmental Operations Manager,Department of MathematicsImperial College LondonContact Person Richard Jones

Department of Mathematical SciencesUniversity of BathContact Person Apala Majumdar

Ukraine

Faculty of Applied MathematicsNational Technical University of UkraineContact Person Oleg Chertov

(April 2018)


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ECMIMissionMathematics, as the universal language of the sciences,plays a decisive role in technology, economics and the lifesciences. European industry is increasingly dependent onmathematical expertise in both research and developmentto maintain its position as a world leader for hightechnology and to comply with the EU 2020 agenda forsmart, sustainable and inclusive growth. ECMI initiatives inresponse to these needs may be summarized as follows:

ECMI advocates the use of mathematical modelling,simulation, and optimization in industry

ECMI stimulates the education of young scientists andengineers to meet the growing demands of industry

ECMI promotes European collaboration, interaction andexchange within academia and industry


Annual Report 2017

Imprint

Editor: Andreas Münch

Guest editors: Adérito Araújo,Cláudia Nunes

ECMI Secretariat:Prof Poul G. HjorthTechnical University of DenmarkMatematiktorvet 303-BDK-2800 Kgs. Lyngby, DenmarkEmail: [email protected]

Guideline for author & templates:https://ecmiindmath.org/annual-reports/.

For more informations pleasevisit the ECMI website:https://ecmiindmath.org

Print ISSN: 2616-7867Online ISSN: 2616-7875

ECMI EUROPEAN CONSORTIUM FORMATHEMATICS IN INDUSTRY ECMI EUROPEAN CONSORTIUM FOR

MATHEMATICS IN INDUSTRY

Mathematics with industry: driving innovation

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