New and Emerging Themes in Industrial and Applied Mathematics - Final Report of the NEST SUPPORT project NETIAM

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New and Emerging Themes in Industrial

and Applied Mathematics

Final Report of the NEST SUPPORT project NETIAM

edited by

Melvin Brown and Robert Leese

Smith Institute

This report has been produced with thanks tothe participants of the NETIAM project.

Directorate-General for Research

Structuring the European Research Area

Anticipation of Scientific and Technological Needs: Basic Research

EUROPEAN COMMISSION

2005 EUR 21797


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NETI AM Managem ent Board

Chair :

Hilary OCKENDON (University of Oxford)

Members :

Melvin BROWN (Smith Institute, UK), Project ManagerRobert LEESE (Smith Institute, UK), Partner and Project CoordinatorRobert MATTHEIJ (Technische Universiteit Eindhoven), PartnerMario PRIMICERIO (Universit degli Studi di Firenze), Partner

Andreas WIEGMANN (Fraunhofer-Institut fr Techno- undWirtschaftsm athematik ), Partner

Aivars ZEMITIS (Ventspils University College), Part ner

Sc ien t i f i c Adv isor

John OCKENDON (University of Oxford)

Rappor teurs :

David ALLWRIGHTTim BOXER

Melvin BROWNRobert LEESE

Heather TEWKESBURY(all of Smith Institute, UK)

Commiss ion :

Bernardus TUBBING (Research DG, Brussels, Belgium)


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Tab le o f con ten t s

TABLE OF CONTENTS ......................................................................................................................4

EXECUTI VE SUMMARY ....................................................................................................................5

MATHEMATI CS AND THE FORMULATION OF UNEXPLORED RESEARCH CHALLENGES ..............................5FOUR KEY THEMES .................................................................................................................................5STRATEGY: MATHEMATICS, INDUSTRY AND SOCIETY IN EUROPE ........................................................5

THE NETI AM CONSORTI UM ..........................................................................................................7

PROJECT OBJECTI VES AND MAJOR ACHI EVEMENTS.......................................................7

FOUR MULTI DI SCI PLI NARY THEMES ......................................................................................9

MATHEMATICAL MODELLING OF CRIMINALITY IN THE URBAN ENVIRONMENT ........................................9NEW MULTIDI SCIPLINARY CHALLENGES IN MODELLING THE BUSI NESS ENVI RONMENT ......................10CHALLENGES IN VISUALIZATION, SIMULATION AND DESIGN FOR VIRTUAL POROUS MATERIALS........11COMPLEXITY I N MODELLING PROTEINS AND INTERFACES AT THE MOLECULAR LEVEL .........................13

OPPORTUNI TI ES FOR MATHEMATI CS I N MULTI DI SCI PLI NARY RESEARCH .....14

STRATEGY: MATHEMATI CS, I ND USTRY AND SOCI ETY I N EUROPE........................16

PLAN FOR USI NG AND D I SSEMI NATI NG KNOWLEDGE................................................17

KNOWLEDGE DI SSEMINATION .............................................................................................................17RAISING PUBLIC PARTICI PATION AND AWARENESS ............................................................................17

NETI AM REPORTS...........................................................................................................................19

ACKNOWLEDGEMENTS.................................................................................................................20

CONTACT DETAI LS .........................................................................................................................24


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EXECUTI VE SUMM ARY

Mathem a t i cs and th e fo rm u la t i on o f u nexp lo red research cha l lenges

The NETIAM project has used mathematics as a tool to integrate the approaches of

science from m any disciplines. New theoretical and comput ing techniques, andcollaborative formulation of unexplored research challenges, enable mathematics toplay a vital part in the research process much earlier than previously. This novelproject has linked multidisciplinary teams under four themes covering complexproblems of sociology, economics, manufactur ing and natural sciences. The proj ecthas identified three underpinning mathematical methodologies and eleven diverseapplication areas for multidisciplinary research, and it has examined theinfrastru ctures that are r equired t o support such activity.

The European integration of expertise that has occurred in NETIAM has increased thepotential for dissemination and application of research results by overcoming existingintellectual and administrative fragmentation. In total, 125 researchers of many

different disciplines from 15 countries have participated in the workshops, and manyhundreds more have been reached as part of the projects dissemination initiatives.Through ongoing vision and well organised collaboration, the NETIAM project hasprovided a benchmark for the use of mathematics in the formulation of unexploredmultidisciplinary r esearch challenges in a wide r ange of areas.

Fou r k ey them es

NETIAM has five participating organisations, from five EU Member States and iscoordinated by the Smith Institute (United Kingdom). They have held thematicworkshops on the following areas:

Mathem atical m odelling of crimi nality in t he urban environment New multidisciplinary challenges in modelling the business environment Challenges in visualisation, simulation and design for virtual porous materials Complexity in modelling proteins and interfaces at the molecular level.

The themes were chosen by the partners for their challenging interdisciplinarity andtheir em erging opportunit ies for using novel math ematics. They have demonstratedhow, by working at a European level, mathematics can provide a common languagewith which to approach multidisciplinary research.

A fifth capstone workshop drew on t he work of t he them atic workshops and proposedan integrated summary of topics, methodologies and consortia for adventurousresearch activit y. New mult idisciplinary consortia have since been form ed, wit hmathematics playing a central role, and new proposals have been submitted to theNEST programm e1 to support research in the underpinning t hemes.

St r a tegy : Ma thema t i cs, i ndus t r y and socie ty i n Eu rope

Following its five thematically based workshops, the NETIAM Strategy meeting ofleading figures from mathematics communities across Europe identified the need forsustained activity to raise awareness and use of mathematics, in industry,government, academic comm unities and in society generally at all levels. Under thetitle Unleashing Mathematics, the project has established a strategic initiative to helpdeploy the power and flexibility of mathematics for exploiting opportunities for

1NEST: New and Emerging Science and Technology, Framework Six Programme of the European

Commission.


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will be a crucial element in achieving the European Unions ambition to become theworlds most dynamic knowledge-based economy.

innovation across a broad spectrum of industry and society. The use of mathematics


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The NETI AM Consor t ium

The NETIAM consort ium partners are:

Smith Inst itut e for I ndustrial Mathem atics and System Engineering, UK

Ventspils Universit y College, Latv iaFraunhofer Instit ute fr Techno- und Wirtschaftsmathem atik, GermanyTechnische Universiteit Eindhoven, NetherlandsUniversit degli Studi di Firenze, Italy

Together, the five partners represent a critical mass that has allowed the strategicplanning of interdisciplinary mathematical research on a scale never before seen inEurope. They have brought t o NETIAM a comm on comm itm ent to working on aninterdisciplinary basis and a varied expertise in mathematical modelling,demonst rated by extensive tr ack records. Existing networks such as ECMI andMACSInet had enabled the partners to become familiar with each other's particularstrengths and collaborators, and hence to fully realise the potential of the collectivestrat egic approach to new and emerging areas that NETIAM has adopted. Moreover,the NETIAM workplan was constructed so that all five partners contributed to theplanning and reporting of all workshops, with representatives of all partnerspart icipating in all workshops. These steps m inim ized any risk that the workshopsmight become disconnected and maximized the opportunity for highlighting commonmathematical frameworks across different work shop t hemes.

The strategic and management leadership was provided by the NETIAM ManagementBoard which comprised:

Dr Hilary Ockendon (Universit y of Oxford), Chair Dr Melvin Brown (Sm ith Instit ute), Project Manager Dr Robert Leese (Sm ith Inst itut e), Partner and Project Coordinator

Prof Robert Matt heij (Technische Universiteit Eindhoven) , Partner Prof Mario Prim icerio (Universit degli Studi di Firenze) , Part ner Dr Andreas Wiegmann (Fraunhofer- I nstit ut fr Techno-

und Wirtschaftsm athematik) , Partner Prof Aivars Zemit is (Ventspils University College), Partner

Pro j ect ob j ect i ves and m a jo r ach ievem en ts

The overall objectives of NETIAM are:

Objective: to raise the role of mathematics by identifying areas of highadventure and opportunity that are prime future topics for NEST, other partsof FP6 and other research programmes, and to provide advice to managers ofresearch programm es on behalf of the mathematical comm unity.

Objective: to assemble teams of researchers that are in a position togenerate proposals into NEST, other parts of FP6 and other researchprogrammes.

These over-arching objectives are comprised of several more focused objectives,which have been achieved with input to each from all five of the NETIAM consortiumpartners.

Objective: to bring together European researchers around four cross-disciplinary themes, so as to identify potential research breakthroughs, withmathematics at their core, that will be prime motivators for interdisciplinary


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efforts in new science and technology, and hence help to define the nextgeneration of innovat ion in t he European Research Area.Sum m ary of w ork and achievem ent : four thematic workshops have beenheld as planned and a summary of the final reports from each is given in thisreport. Success has been demonstrated in both the num ber of workshopparticipants (125 in total from 15 different countries) and the quality of theirscientific contributions, as demonstrated by the wealth of material in theworkshop reports. I t is intended that dissem ination of the NETIAM reports toall participants and to the wider communities from which they are drawn, willstimulate still furt her ideas for m ultidisciplinary research.

Objective: to demonstrate how, through careful modelling and analysis,mathematics provides a common language with which to describeinterdisciplinary research challenges in the chosen themes, leading to thenecessary cross-disciplinary cohesion.Summary of work and achievement: a l l o f the thematic workshops havebeen successful in demonstrating the use and potential use of mathematics ina multidisciplinary context, and have had a strong multidisciplinary

part icipation. Each work shop report is rich source of ideas and collaborativepartners for researchers wishing to embark research programmes relating tothe areas covered by the four thematic workshops.

Objective: to define gaps in the research knowledge base that need to beaddressed if innovative thinking is to shed light on the chosen themes.Summary of work and achievement: the format of each workshop wasdesigned to allow ample time for facilitated discussion aimed at identifyinggaps in current knowledge and research. The gaps identif ied have been thebasis for identifying the 11 application areas, the mathematical methodologiesand the potential consortia that have emerged for novel multidisciplinaryresearch. They are presented in detail in the Capstone Workshop report and

are summ arised in this report.

Objective: to identify the barriers, in terms of organisation and scientificculture, to the research that will fill these gaps in knowledge.Sum m ar y o f w or k a nd achi evem ent : t hese issues were discussed in thethematic workshops. More particularly, prior to the Capstone Workshop,NETIAM participants were invited to assess the novelty and importance of theresearch areas highlighted by the thematic workshops. The need to fill theidentified gaps was then further explored during the Capstone workshop. Foreach of the 11 proposed research areas, barriers and specific enablers for thepursuit of the proposed m ult idisciplinary research were discussed. Theconclusions are included in the report of the Capstone Workshop.

Objective: to recommend process enablers, for the formation ofmultidisciplinary collaborations, that will enable exciting and potentially high-benefit proposals to be brought forward and to provide generic guidance onhow to conduct multidisciplinary research programmes.Sum m ary of w or k a nd achi evem ent : The process of invited part icipation,proposed by individual workshop coordinators and overseen by the NETIAMManagement Board, has proved highly successful in achieving the required mixof skills and disciplines to explore the work shop themes. Equally import anthas been the use of dedicated workshop facilitators and rapporteurs (in thiscase prov ide by Technology Translator s of the Smit h Inst itu te) . The workshopprogramme and largely common format is reported in each of the fiveworkshop reports: briefly, each consisted of presentations on the workshopthem e(s) followed by plenary and breakout working sessions. The workshopshave provided a model for the form ation of mult idisciplinary collaborations. As


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of the publication date of this report, the NETIAM-proposed multidisciplinaryresearch programmes remain to be established, so it is not yet possible toreport complete experience and guidance on conducting such activity.

An additional Strategy Meeting was added to the NETIAM plan, after the thematicworkshops had been completed; it had t he following objective:

Objective: to give the mathematics community in Europe the opportunity toformulate a strategic action plan in response to the experiences of theNETIAM project.Summary of work and achievement: The Strategy Meeting of 20 leadingrepresentatives of the mathematics community in Europe and from industryhas launched a long term initiative, entitled Unleashing Mathematics - ADriving Force for Industry and Society in Europe, to construct an Action Planfor Mathematics in Industry and Society to begin in 2007.

Fo u r m u l t i d i sci p l in a r y t h e m e s

The programme of each of the four NETIAM thematic workshops was highly flexible,interactive, and responsive to emergent ideas, so distinguishing them from moretr aditional conference and seminar events. Each workshop provided insight into themechanisms and challenges in stimulating ideas for novel multidisciplinary researchtopics and collaborations; these aspects were also addressed more fully in thesubsequent Capstone Workshop. The proceedings of each workshop (see NETIAMReports section) are summarised below.

Mathema t i ca l m ode l li ng o f cr im ina l it y i n the u rban env i ronm en tThematic Workshop, Firenze, Italy, 7-8 June, 2004

In its first Thematic Workshop, the NETIAM project explored opportunities formultidisciplinary research under the title Mathematical Modelling of Criminality in theUrban Environment. The workshop was attended by some 24 researchers from 9countries, including social scientists, geographers, physicists, and mathematicians.

There were three opening presentations on challenges in crime mapping, thegeography of crime and the sociology of crim e. I n these presentations, theparticipants sought to identify the key observations that will underpin any realisticmodel of criminality within a closed urban comm unity.

The immediate result was the decision to separate into two breakout sessions chargedwith identifying the theoretical framework within which each of the following themescould be considered quantitatively:

1. Modelling Acts of Crim e2. Modelling Crim inal Behaviour

The output s were

1. Acts of crime are perpetrated over relatively short t ime and length scales, asevidenced by phenomena such as repeat victimization, burglary localization,hot spots and crime elasticity (better law enforcement in one area makesneighbouring areas vulnerable). A mathematical m odel must be able topredict these phenomena in terms of external forces such as weather, lawenforcement and ease of access. I t m ust be a spatio-temporal model, which

may be continuous or discrete and which could draw analogies with biologicalpredation under the action of foraging predators.


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2. Criminal behaviour depends on many urban indices such as poverty,education, ethnicity and housing, and criminals must be classified as, say, juvenile, adult, drug- dependent etc. Hence a population dynamics model iscalled for, similar to those that have been successful in describinghomelessness and contagion in mathem atical biology. The model could becontinuous or agent-based, it must apply over relatively long time scales and itmust be capable of being eventually incorporated into a larger social networkmodel.

When these two themes were drawn together in the closing session, it becameapparent that not only should they be developed jointly, because of the close couplingof many of the variables, but also that a third control space theme should beconstructed; this would model the interactive coupling with the effects of social andlaw enforcement policy and public opinion.

New m u l t i d i sci p l i na ry cha l lenges in m ode l li ng t he bus iness

e n v i r o n m e n tThemat ic Workshop, Ventspils, Latvia, 2-3 August, 2004

In its second Thematic Workshop, the NETIAM project explored opportunities formultidisciplinary research under the title New Multidisciplinary Challenges inModelling the Business Environment. The workshop was attended by some 69researchers from 9 countries, including social scientists, economists, physicists, andmathematicians.

There were four opening presentations, covering macroeconomic modelling andeconometric models with an input/output core, financial engineering, economicconsequences of insurance price fluctuation, and the emergence of collective states ineconomic systems. I n these presentat ions, the participants sought to identify t he keychallenges and observations that will motivate and underpin any realistic models ofthe business, socio-economic and political environment.

The immediate result was the decision to separate into four breakout sessionscharged with identifying the t heoretical frameworks within wh ich each of t he followingthemes could be considered quantitatively:

The coupling between macro-economic modelling and social networks Risk stochastics in economic modelling (time series) Modelling the transition economies Socio-political environment, labour, accessibility, corruption

The breadth and diversity of feedback from the four sessions reflected the fact thatthis is the most ambit ious of the four NETIAM them es. I t is so large andinterdisciplinary that it is a difficult challenge even to identify those topics wheremathematicians can add significant value to the methodologies used by sociologists,economists, politicians, and managers. Concerning this challenge, the social sciencefactors that were considered to be crucial to the business environment were:

tr ansport, communications, labour supply, corrupt ion, leisure activities, humanresources/education.

The corresponding economic factor s were:

tax policy, pensions policy, currency value, insurance policy.


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The mathematical methodologies that emerge as being best suited to handle this widerange of human activity fall into tw o categories:

1 Data Management and Sta t is t ica l Model l ingNew directions for this burgeoning area of mathematical science abound in therealm of business risk, where the novelty lies in modelling corruption andmismanagement and in assessing the business implications of social risks suchas gambling, health and unemployment . The most promising methodologiesare time series and stochastic analysis, but both will be plagued by insufficientdata compared to more traditional risk analysis in, say, finance or weatherforecasting. A desirable outcom e of a research program me based on thesepremises is the development of new kinds of insurance policies.

2 Ad hoc p red ic t i on mode ls fo r the evo lu t i on o f the bus inesse n v i r o n m e n t

It was absolutely clear that, in this wide-open area, the way ahead is via ageneralised theory of dynamic network m odelling. The basic network structur eneeds to comprise interlinked nodes, each of which may have a multi-

dimensional behaviour involving many socioeconomic variables of which only afew will be coupled to other nodes. The netw ork should be able to nucleateand evolve new nodes, and also to have a learning capability . This is anexciting new direction for the mathematical theory of differential-algebraicsystems; but it is not a completely new challenge because two traditional, butvery elaborate ad hoc network m odels are already in use. However, theyhave never been subject to serious mathematical scrutiny and their nodalparameters need to be prescribed subjectively. There is, nonetheless, onereliable paradigm in which the social modelling is represented by a very simplenetwork and utility functions at the nodes describe the econometrics. Thedevelopment of this paradigm to make it a quality control for the larger codesis an exciting challenge.

Assuming progress can be made with 1 and/or 2 above, the resulting predictions willonly be of practical value providing two other quite different challenges are met.Firstly, many social norms/indices need to be quantified before the models fromeither 1 or 2 can be used to predict optim al policies. Secondly, t he research must beexplicable in term s that are t ransparent t o policy makers. Neither of t hese challengescan be addressed by the mathematical community alone but they must both beovercome if m athemat ics is to make a genuine contribut ion to t his outcome.

Cha l l enges i n v i sua l i za t i on , s imu la t i on and des ign fo r v i r t ua l po rousm a t e r i a l s

Themat ic Workshop, Kaiserslautern, Germany, 29- 30 September 200 4

In its third Thematic Workshop, the NETIAM project explored opportunities formultidisciplinary research under the title Challenges in Visualization, Simulation andDesign for Virtual Porous Materials. The workshop was attended by some 27researchers from 8 countries, including physicists, computer scientists, andmathematicians.

There were six opening presentations: Visualisation of very large data sets,Ventilation, material transport and separation in the human lung, Numerical rocks,Material geometry: physics and shape of spatially complex matter, Parallelalgorithms for complex materials, and Textiles and nonwovens.


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There were many possible areas within this large area of basic science upon which thebreakout groups could have focused. Of the two which emerged, one covered a broadrange of applications and the other a broad area of basic mathematical methodology.

M icrom echan ics o f fu tu r e f i l t r a t i on dev i ces

The classical theory of filters classifies their mechanics according to certain keymechanical chemical and thermodynamic parameters which emerge from paradigmstudies of single particle impact on a simple filter element. The applicability of suchideas depends considerably on the ability of scientists to scale up their predictions topractical filters with all t heir complex geomet ry.

Modern methodology offers the promise of predicting filter performance far moreprecisely by using

(i) emerging visualisation t echniques (from X-ray or synchrotron data) t o representthe filter geometry faithfully,(ii) modern CFD codes to predict f luid flow through t his geometr y, even for m odern

highly irregular filter m atrices.

However, there is one basic gap in scientific understanding that needs to beaddressed before this strategy can be considered to be reliable. This gap concerns themicroscale impact mechanics of the particle (which may be minute) with the filtermatrix. It inevitably involves delicate fluid mechanics and surface adhesion mechanicsand may also involve electrostatics, coating properties and surface chemistry.

There are also theoretical challenges concerning coupling the particle motion(including coagulation) to the fluid motion, especially when there is a filter cake, orwhen clogging needs to be predicted.

If these scientific issues can be resolved, there are really exciting applications inprospect ranging from ultra-filters, tissue engineering, catalysis and fuel cells to thepreservation of our architectural heritage and t o t he tr apping of bacteria and perhapseven viruses.

From m ic rogeomet r y o f po rous med ia to macro ma te r ia l p roper t i es

This is the fundamental multiscale problem of all porous media and it is one wherethe methodologies cited above pave the way. It is axiomatic (and provable) that fluidflow through a porous medium at the pore scale averages or homogenises itself toDarcy flow in many parameter regimes. It is already possible to explore new regimesby using CFD codes that apply when the Navier-Stokes equations contain inertial

terms. However, as flow rates increase, the accuracy of the geometricalrepresentation must be increased, and new codes must be written to computemacroscopic thermodynamic or electromagnetic properties, rather than flow per se.This challenge is waiting to be met because the code predictions can immediately betested against known homogenised models (Darcy or Biot) and then used to searchfor new correlations and scaling laws between the microgeometry measures and themacroscale properties. (For Darcy flow the porosity and tortuosity are the principalones to have been identified.)

This experimental research programme should receive as much quality control aspossible from the burgeoning mathematical theories of homogenisation,computational geometry and stochastic partial differential equations, this last being

vital in the presence of uncertain tomographic data.


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It is even possible that this research could lead to fundamental advances in imageprocessing because it is clear that state-of-the-art voxel visualisations are inadequateto represent porous media with strong inhomogeneities such as fractures. There is agreat need for the discretised visualisation to contain geometrical elements that arephysically plausible for the porous media under consideration. The problem of makingsuch elements is waiting to be addressed.

It is certain that this research topic will have really strong links with one of theprincipal NETIAM themes, namely network modelling. At the moment in the oil andfiltration industries the passage from microgeometry to macroproperties can only berealised by construct ing interm ediate scale networks of elements t hat are believed toprovide a reliable stepping -stone betw een the tw o scales. The design and reliabilityof such netw orks has never been subject to m athemat ical scrutiny.

Com p lex i t y i n m ode l li ng p ro t e i ns and i n t e r faces at t he m o lecu la r l eve lThematic Workshop, Eindhoven, Netherlands, 2-3 December 2004

This fourth NETIAM thematic workshop identified two important areas of physical andbiological science where mathematical innovation could enlighten our understandingof fundam ental molecular processes. Despite the apparent disparity between theseareas, the emergence of new insights would rely in each case on bringing newmultiscale analyses to bear.

Unde rstand ing i n te r faces at the m o lecu la r l eve l

The more physically based topic is that of the bonding of two disparate materials atan interface, and specifically that of a polym er coating a met al substr ate. Despite theimportance of such interfaces to the automotive, semiconductor, metal and foodindustries, there is still no reliable basic understanding of the atomic configurations

that are adopted even in the simplest configuration when the interface is nearly flatand the coating and substrate are infinite in extent. Here the new mathematical ideais to systemat ically use mult iscale methodologies to m atch together

(i) a classical statistical physics theory for the atoms in the relatively wide sublayerwhere energy and entropy compete in the polym er between its long chain bulk andthe nominal interface;(ii) a density functional theory for t he relatively even m ixture of at oms in a nanolayeraround the interface;(iii) an atom istic theory for metal atom s deeper into t he substrate.

These three theories have a completely different mathematical character but they all

highlight the role played by t he Gibbs free energy, and t his will be of vital im portancewhen matching the theories together. The resulting composite theory will not onlyallow cohesive forces to be predicted with confidence, but stage (ii) will reveal defectstructure in the interface itself. This is the all-important stage at which quantummechanical effects cannot be avoided and the only way this can be done for anyrealistic number of at oms is by exploiting t he dramatic reduction in t he dimensionalityof the governing differential equations that density functional theory offers.

If this methodology can be perfected on this paradigm class of problems, it should berelatively easy to generalise it to study cases of imperfect contrast (so called loopsand trains in the polymer), steps and/or ledges at the metal interface, the effect ofimpurity atoms such as oxygen and perhaps even to areas like quantum dot

fabrication.


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Understand ing p r o te in m o lecu les i n the ce ll u la r env i r onm en t

There is an urgent need to gain a better quantitative understanding of the behaviourof protein molecules in a cell. From a physico-chemical viewpoint the principalchallenge is to predict the evolution of both large and small protein molecules as theymove through the complicated pathways between each other and the deformable cellskeleton and its microtubules and lipid bilayers. This is not just a problem inmechanics because of the numerous reactions that can occur between all the kinds ofmolecules in the cell and because of the important effects of electrical, thermal andchemical gradients. However it is clear that the geometry of the protein molecule isits most important mathematical characteristic as far as its reactivity is concerned(the geometry being most conveniently defined by its van der Waals surface).Moreover, user-friendly three-dimensional visualisations of this geometry are nowbecoming readily available, and t here is much current int erest in t he apparently closerelation between geometry and biological functionality.

In this highly complex situation, it was proposed that the first requisite was tounderstand how the classical theory of immiscible multiphase flow in a porous

medium could be generalised to highlight the roles played by both the geometry ofthe dispersed phase in the pores and by the highly deformable nature of the porousmatrix. This multiscale approach will be similar in spirit to the well-developedBuckley-Leverett theory as used so successfully in the oil recovery industry.

Such a paradigm will ignore reactions in the first instance but it is anticipated thatthese reactions will ultim ately be incorporated as a body force distributed t hrough t hedisperse phase in a way that is crucially dependent on the protein molecule geometry.I t is also hoped that the m odel will provide a basis for understanding transport acrossthe bridges between the cytoplasm and the nucleus.

Oppor t un i t i es fo r m a them at i cs i n m u l t i d i sc ip l ina ry r esearchCapstone Workshop, Oxford, UK, 14-15 March 2005

In the Capstone Workshop of the series, the NETIAM project summarised and furtherexamined the opportunities for multidisciplinary research identified by the precedingfour thematic workshops. The workshop was attended by 20 researchers from 6countr ies including mathemat icians and physical, economic and social scient ists. Theproceedings of this workshop are available in a report which may be downloaded fromthe NETIAM website at www.netiam.net .

Top ics fo r m u l t i d i sc ip l i na ry r esea rch ac t i v i t y

Presentations were made by the local organisers of the earlier thematic workshops to

summ arise the findings in each of the workshop them es:

Mathem atical modelling of criminality in t he urban environment New multidisciplinary challenges in modelling the business environment Challenges in visualisation, simulation and design for virtual porous materials Complexity in modelling proteins and interfaces at the molecular level.

Three underpinning themes of importance to all these diverse areas emerged

1. Modelling phenomena over disparate tim e and length scales2. Dynamic network modelling3. Visualisation and comput ational geomet ry.


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Each of these underpinning themes was discussed in relation to the topics arising inthe preceding thematic workshops. Common areas of challenge and importantdistinctions between the areas were highlighted in the discussions.

The following eleven application areas, covering one or more of the themes, havebeen proposed for further research activity as a result of the workshop.

Bonding forces between organic and inorganic materialsFilter (porous) media designSelf- organized crime space analysisOpportunity networks in crimeTime- evolution of criminality in ur ban areasCoordination between businessesCharacterisation of protein geometryDynamic social and economic networksPricing insurance policies in high risk environmentsQuantifying economic freedomInstitut ional governance and corruption.

In the workshop report, the corresponding mathematical methodologies and otherdisciplines required have been highlighted for each application, and multidisciplinaryEuropean consortia with the skills to undertake work in each area have beenidentified. Taking each application area in turn, the structure of the relevant sciencebase has been analysed and, where possible, opportunities have been sought forinfluencing science policy to facilitate progress.

In f r as t ruc tu re and mechan ism

The Capstone meeting also addressed the issues of mechanism and structure in orderto re- visit th e last of the NETIAM objectives. A num ber of points emerged:

The NETI AM a pp r oac h is very application-oriented, not mathematics-driven, and forgood reason. It is difficult to bring people together in a multidisciplinary environmentunless there is a common point on the horizon to aim for: this is the underlyingphilosophy of the NETIAM approach, and is one of the reasons why identifying andfocusing the problem is half the work. NETIAM has laid the groundwork in identifyingand outlining areas for adventurous multidisciplinary research.

The listed applications and methodologies do not imply that the methodologies areadequate rather it m eans that they are t he starting points for t he applications. Newmathematics and new developments may be required: there is no telling what newm at h em at ics may be stimulated by the problems arising in any of these application

areas. Developments in mathematics can either be stimulated by problems arisingfrom outside mathematics itself, or from within, and NETIAM has been concerned withthe first kind of developments. It is also important to realise that NETIAM is notrepresentative of mathematics as a whole; rather, it is at the interface ofmathematics with industr ial and m ultidisciplinary applications.

Mathematics is the common denominator of the NETIAM projects, but there is anurgent need for it to be more generally appreciated as the common denominator inscience, industry and society. It is necessary to communicate the NETIAMmethodology, so that others can see how they can apply the same methods. NETIAMhas demonstrated how mathematics can be used in novel areas; that message mustbe communicated at a high level, by and through the mathematics networks aroundEurope. This issue was addressed in the subsequent NETIAM Str ategy Meeting.


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St r a tegy : Ma them at i cs, I ndus t r y and Soc ie ty i n Eu ropeStrategy Meeting, Oxford, UK, 4- 5 July, 200 5

In the NETIAM Strategy Meeting, partner coordinators of the NETIAM project and 15other leading figures from the mathematics community in Europe and from industry

explored the interface between mathematics, industry and society, to determine howEurope can best reap the practical benefits of the ideas and opportunities created byits mathematical community.

The group aimed to address a wide range of issues including: the organisation ofinterdisciplinary mathematics, the mix of private and public investment, measuringthe value of interdisciplinary mathematics, creating awareness of the valuemathematics, and accomm odating different national/ regional cultures.

An almost immediate and sustained focus of the discussions was the urgent need toinc rease awareness o f the ro le and va lue o f ma thema t i cs i n soc ie ty , i nindustry and as an aspect of our culture. A wide range of chal lenges andmechanisms to address this issue were discussed, and it was agreed that a sustainedperiod of action by the mathematics community, perhaps over 10-20 years, would berequired to enable society to reap the full benefits of mathemat ics. I n the short termof 1-2 years, it was proposed that a com prehensive m arketing and publicity campaignwould be directed towards the public, industry, the mathematics community andother disciplines. To carry forward this programme, the meeting proposed that analliance of representatives from mathematics communities in Europe be formed, andthat its strategy be implemented through an executive sub-group to be drawn fromits mem bership. The meeting approved the preparation of an action plan for widedissemination across Europe.

Following the Strategy Meeting, this initiative has been outlined by the participantsunder the t i t le Un leash ing Mathemat ics - A Dr iv ing Force fo r Indust ry and

Socie ty in Europe , and it is being widely disseminated in a brochure, through theNETIAM website www.netiam.net/Unleashing, and through other channels. Drawingon the cumulative experience spread across Europe, the 'Unleashing Mathematics'initiative aims to set up a team of committed researchers and policymakers fromacademia, industry and government agencies. Its mission will be to identify the bestway of coordinating interdisciplinary mathematics in Europe and to construct anAction Plan for Mathematics in Industry and Society to begin in 2007.

The Strategy Meeting report, and further details of the Unleashing Mathematicsinitiative may be requested from the NETIAM coordinator, whose contact details areprovided at the end of t his report.


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Plan fo r us ing and d i ssem ina t ing k now ledge

Know ledge d i ssem ina t i on

A NETIAM website at www.netiam.net is maintained by the Smith Institute to

disseminate w orkshop reports and inform ation on t he projects activities. The site alsoprovides links and information to support those wishing to participate in the NESTprogramme.

Through its multidisciplinary participation, each workshop has acted as a vehicle forthe engagement w ith and disseminat ion of inform ation about activit ies in NEST. Eachworkshop participant has been provided in advance with briefing material describingthe objectives and expected outcomes of the workshop, together with explanation ofthe opportunities and mechanisms by which they can contribute to the workshop.Each participant has also been given details of the NEST activity and encouraged todisseminate their knowledge of NEST to colleagues in their home institutions.

A workshop report has been produced for each Thematic Workshop and for the

Capstone Workshop. These reports record the proceedings, participation and ideasemerging from each workshop. Each report has been disseminated to the workshopparticipants, published on the NETIAM website and delivered to the NEST ProjectOfficer at th e European Comm ission. The web links for the report s have also beendisseminated m ore widely to r esearch and press organisations across Europe.

The NETIAM Strategy Meeting, which was added to the project plan at the end ofPeriod 1, was recorded in note form for the participants, and for dissemination bythem individually. As a first step in the initiative formulated by the Strategy Meeting,a four-page brochure entitled Unleashing Mathematics has been produced and isbeing widely disseminated. It aims to garner the active support of commit tedresearchers and policymakers from academia, industry and government agencies tohelp develop and implement an Action Plan for Mathematics in Industry and Society.

Organisations to which there has been dissemination include:

Engineering and Physical Sciences Research CouncilLa RepubblicaLatvian pressNatureFP6UKUK Departm ent of Trade and IndustryEuropean Consortium for Mathematics in Industry (ECMI)European Research Consort ium for I nform atics and Mathem atics (ERCIM News)Mathem atics, Computing and Simulation for I ndustry (MACSInet)Numerical Analysis Digest ( US based e-digest)

Institute of Mathematics and its Applications (UK)CORDIS News ( web art icle)CORDIS Wire (w eb art icle)

Ra isi ng pu b l i c pa r t i c i pat i on and aw a reness

The Smith Institute, on behalf of the consortium, has prepared a brief NETIAM projectsumm ary, in th e sty le of a press release, in English, of two pages. The summ ary isaccessible to the nonspecialist at school level, university or in the general public, andalso provides a useful overview for researchers in all disciplines. The documenthighlights the key role that mathematics can play in multidisciplinary research andsummarises mechanisms for enabling the identification and conduct of such research.

The document can be found at


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http: / / europa.eu.int/ comm / research/fp6/ nest/ pdf/nest_project_factsheets2003a.pdf

and has been disseminated to all NETIAM partners for distribution.

The present report, which captures the integration of outputs and ideas from theNETIAM workshops and from the NETIAM Strategy Meeting, is published for publicdissemination to a wide range of organisations across Europe, including industry,government and education.


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NETI AM Repor t s

[ 1] Mathem atical m odelling of criminality in t he urban environment , Report of theThematic Workshop held in Firenze, I taly, 7- 8 June, 2004 .

[ 2] New mult idisciplinary challenges in m odelling the business environment, Report ofthe Thematic Workshop held in Ventspils, Latvia, 2-3 August, 2004.

[3] Challenges in visualization, simulation and design for virtual porous materials,Report of the Thematic Workshop held in Kaiserslautern, Germany, 29-30 September2004.

[ 4] Complexity in m odelling proteins and interfaces at the m olecular level,Report of the Thematic Workshop held in Eindhoven, The Netherlands, 2-3 December2004.

[ 5] Opportunities for m athematics in m ultidisciplinary research, Report of t heCapstone Workshop held in Oxford, UK, 14-15 March 2005.

[6] Mathematics, Industry and Society in Europe, Notes of the NETIAM StrategyMeeting held in Oxford , UK, 4-5 July, 2005. Available on request [email protected] .

References [1-5] may be downloaded from the NETIAM website: www.netiam.net.


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ACKNOWLEDGEMENTS

The NETIAM Consortium was supported by a gr ant fr om the European Comm issionunder Contract No. NEST-CT-2003-002513. The Consortium acknowledges with warmthanks t he contributions of those who m ade time available to contribute expertise,

ideas, opinion and information:

Fi r enze w o rkshop pa r t i c i pan ts :(Mathematical modelling of criminality in t he urban environm ent)

Giacomo Alett i Universit degli Studi di Milano, I talyDaniele Amat i Scuola I nternazionale Superiore di Studi Avanzati,

Trieste, I talyFrancesco Battist i Universit degli Studi di Cassino, I talyHenri Berestycki L'cole des Hautes tudes en Sciences Sociales, FranceMelvin Brown Smith I nstitut e, UKJon Chapman University of Oxford, UK

Claire Cunty CNRS-UMR Gographie- cits, FranceOlof Dahlbck Stockholm University, SwedenMirta Gordon Laboratoir e Leibniz-I mag, Grenoble, FranceMats Gyllenberg University of Turku, FinlandMiguel Herrero Universidad Complu tense de Madrid, SpainNeil Johnson University of Oxford, UKShane Johnson University College London, UKAndrew Lacey Heriot- Watt University , UKRobert Leese Smit h I nstit ute, UKRobert Mattheij Technische Universiteit Eindhoven, The NetherlandsAndro Mikelic Universit Claude Bernard Lyon 1, FranceJuan Carlos Nuo Universidad Politcnica de Madrid, SpainHilary Ockendon University of Oxford, UKJohn Ockendon University of Oxford, UKMario Prim icerio Universit degli Studi di Firenze, I talyBeatr iz Rum bos I nstit uo Tecnolgico Autnom o de MxicoMiguel Virasoro Universit di Roma1 La SapienzaAndreas Wiegmann Fraunhofer -I TWM, Germ anyAivars Zemitis Ventspils University College, Latv ia

Ven tsp i l s w o rkshop pa r t i c i pan ts :(New multidisciplinary challenges in modelling the business environment)

Giuliano Basso Energy Solut ions, UKMart in Berzin Daugavas Vanagi, Germ anyUgis Berzin SLD Consulting, SwedenMelvin Brown Smith I nstitut e, UKAlistair Fitt University of Southam pton, UKMirta Gordon Laboratoir e Leibniz-I mag, Grenoble, FranceGunars Grizans Ventspils University College, Latv iaSergejs Hilkevics Ventspils University College, Latv iaAndrejs Jaunzems Ventspils University College, Latv iaPer Richard Johansen Norwegian Central Bureau of Statist ics, NorwayJuris Roberts Kalnin Social technology Instit ute, Latv iaValentinas Kiauleikis Kaunas University of Technology, LithuaniaUlrich Ngel Fraunhofer -I TWM, Germ anyJohn Ockendon University of Oxford, UK

Tiiu Paas University of Tart u, EstoniaMario Prim icerio Universit degli Studi di Firenze, I taly


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Fabio Rossi Universit degli Studi di Trieste, I talyJanis Stir na KTH, SwedenWilma Teness CC Consult ing, SwedenHeather Tewkesbury Smith I nstitut e, UKVincenzo Vespri University of Firenze, I talyJanis Vucans Ventspils University College, Latv iaAndreas Wiegmann Fraunhofer -I TWM, Germ anyMatt hias Winkel University of Oxford, UKAivars Zemitis Ventspils University College, Latv ia

A further 4 4 Latvian participants from government, financial and research institut ionsattended this workshop on its first day.

Ka ise rslau te rn w o rkshop pa r t i c i pan ts :(Challenges in visualization, simulation and design for virtual porous materials)

David Allwright Smith I nstitut e, UKMart ijn Anthonissen Technische Universiteit Eindhoven, The Netherlands

Iacopo Borsi University of Florence, I talyBoris Breidenbach Max- Planck-I nsitut fr Metallfor schung, GermanyMart in Dauner I nstit ute of Text ile Technology and Process Engineering,

Denkendorf, GermanyChris Farmer Schlumberger Evaluation and Production Services, UKChristoph Gart h University of Kaiserslautern, Germ anyOleg I liev Fraunhofer- ITWM, Germ anyWolfgang Koch Fraunhofer I nst. fr Toxikologie und Experim entelle

Medizin, Germ anyArnulf Latz Fraunhofer -I TWM, Kaiserslautern, GermanyBas van der Linden Technische Universiteit Eindhoven, The NetherlandsRobert Mattheij Technische Universiteit Eindhoven, The Netherlands

Klaus Mecke Max- Planck-I nstit ut fr Metallforschung, Germ anyMart ine Meireles CNRS and Univ. P. Sabatier , Toulouse, FranceJohn Ockendon University of Oxford, UKJulia Orlik Fraunhofer -I TWM, Kaiserslautern , GermanyGeorge Perera Perera Softw are Engineering, Stut tgar t, GermanyMario Prim icerio Universit degli Studi di Firenze, I talyEwald Quak SINTEF ICT, Oslo, NorwayKatja Schladitz Fraunhofer -I TWM, Kaiserslautern , Germ anyAdrian Sheppard Australian National UniversityMark Spivack University of Cambr idge, UKKonrad Steiner Fraunhofer -I TWM, Kaiserslautern, Germ anyHeather Tewkesbury Smith I nstitut e, UK

Andreas Wiegmann Fraunhofer ITWM, Kaiserslautern , Germ anyAinars Zemitis University of Hamburg, GermanyAivars Zemitis Ventspils University College, Latv ia

Eindhoven w o rkshop pa r t i c ipan ts :(Complexity in modelling proteins and interfaces at the molecular level)

David Allwright Smith I nstitut e, UKMart ijn Anthonissen Technische Universiteit Eindhoven, NetherlandsAlberto Bersani Universit di Roma La Sapienza, I talyEnrico Bersani DataLink I nformat ica s.r.l, It alyTim Boxer Smith I nstitut e, UKMonica Bulacu Rijk suniversiteit Groningen, NetherlandsChristopher Cox Clemson University , USAGero Friesecke University of Warwick , UK


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Christina Giannopapa Technische Universiteit Eindhoven, NetherlandsBob Matth eij Technische Universiteit Eindhoven, NetherlandsJohn Ockendon University of Oxford, UKMiguel Patr icio Technische Universiteit Eindhoven, NetherlandsMark Peletier Technische Universiteit Eindhoven, NetherlandsMario Prim icerio Universit degli Studi di Firenze, I talyJackie Schooleman Virtual Prot iens B. V., NetherlandsPaul van der Varst Technische Universiteit Eindhoven, NetherlandsWillem- Pier Vellinga Rijk suniversiteit Groningen, NetherlandsAndreas Wiegman Fraunhofer -I TWM, Germ anyBert de With Technische Universiteit Eindhoven, NetherlandsAivars Zemit is Ventspils University College, Latv ia

Capstone w o rkshop pa r t i c i pan ts :(Opportunities for mat hematics in m ultidisciplinary research)

David Allwright Smith I nstitut e, UK

Francesco Battist i Universit degli Studi di Cassino, I talyTim Boxer Smith I nstitut e, UKMelvin Brown Smith I nstitut e, UKChristina Giannopapa Technische Universiteit Eindhoven, NetherlandsMirta Gordon Laboratoir e Leibniz-I mag, Grenoble, FranceSergejs Hilkevics Ventspils University College, Latv iaShane Johnson University College London, UKJuris Roberts Kalnins Social Technology I nstit ute, Latv iaRobert Leese Smit h I nstit ute, UKRobert Mattheij Technische Universiteit Eindhoven, NetherlandsHilary Ockendon University of Oxford, UKJohn Ockendon University of Oxford, UK

Mario Prim icerio Universit degli Studi di Firenze, I talyHeather Tewkesbury Smith I nstitut e, UKBen Tubbing European Comm issionJanis Vucans Ventspi ls University College, Latv iaAndreas Wiegmann Fraunhofer -I TWM, Germ anyBert de With Technische Universiteit Eindhoven, NetherlandsAivars Zemitis Ventspils University College, Latv ia


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St ra t egy mee t ing pa r t i c i pan ts :(Mathematics, Industry and Society in Europe)

Jean-Pierre Bourguignon I nstit ut des Hautes tudes Scientif iques, FranceMelvin Brown Smith I nstitut e, UKHeinz Engl Johann Radon I nstit ute, Austrian Academy of SciencesPeter Grindrod Lawson SoftwareHelge Holden European Consortium for Mathemat ics in I ndustr yJulian Hunt University College London, UKRolf Jeltsch ETH Zr ich, Swit zerlandPhilippe Lacour-Gayet Chief Scient ist, SchlumbergerRobert Leese Smit h I nstit ute, UKRobert Mattheij Technische Universiteit Eindhoven , The NetherlandsHelmut Neunzert Fraunhofer -I TWM, Kaiserslautern , Germ anyHilary Ockendon University of Oxford, UKJohn Ockendon University of Oxford, UKMario Prim icerio Universit degli Studi di Firenze, I talyEwald Quak Tallinn University of Technology, Estonia

Mike Sheppard SchlumbergerBruce Smith Smith I nstitut e, UKMartin Taylor Physical Secretar y, Royal Society of LondonBernardus Tubbing DG Research, European Comm issionAivars Zemitis Ventspils University College, Latv ia

Particular thanks are due to Ben Tubbing (European Commission - DG RESEARCH)who, as the NETIAM Project Officer, provided valuable guidance throughout theproject.


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CONTACT DETAI LS

NETI AM Coord in a to r :

Dr Robert LeeseThe Smith I nstitut e for I ndustrial Mathematics and System EngineeringSurrey Technology CentreSurrey Research ParkGuildford GU2 7YGUnited Kingdom

Fax: + 44 (0) 1483 568710E-mail: [email protected] Web: www.smithinst.co.uk

NETI AM w ebsi te : www.netiam.net


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European Commission

EUR 21797 New and Emerging Themes in Industrial and Applied Mathematics:

Final Report of the NEST SUPPORT project NETIAM

Luxembourg: Office for Official Publications of the European Communities

2005 24 pp. 17.6 x 25.0 cm

ISBN 92-894-9700-9


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New and Emerging Themes in Industrial and Applied Mathematics - Final Report of the NEST SUPPORT project NETIAM

Documents