Mathematics%20for%20innovative%20technology%20development

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Mathematics for innovative technology development

• M. Kleiber
• President of the Polish Academy of Sciences
• Member of the European Research Council
• Warsaw, 21.02.2008

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1. Math as backbone of applied science and
   technology
2. Applied math in ERC programme
3. Examples of advanced modelling and simulations in
   developing new technologies (J. Rojek
   International Center for Numerical Methods in
   Engineering CIMNE, Barcelona)

Mathematics as a key to new technologies
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• Applied mathematics is a part of mathematics used
  to model and solve real world problems
• Applied mathematics is used everywhere
• historically applied analysis (differential
  equations, approximation theory, applied
  probability, ) all largely tied to Newtonian
  physics
• today truly ubiquitous, used in a very broad
  context

Mathematics as a key to new technologies
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Real Problem
modelling
validation of model
Mathematical Model
verification of results
Computer Simulation
algorithm design and implementation
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• Applied math for innovative technologies
• used at every level
• product analysis and design
• process planning
• quality assessment
• life cycle analysis including environmental
  issues
• distribution and promotional techniques

Mathematics as a key to new technologies
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Members of the ERC Scientific Council

• Dr. Claudio BORDIGNON (IT) medicine
  (hematology, gene therapy)
• Prof. Manuel CASTELLS (ES) information society,
  urban sociology
• Prof. Paul J. CRUTZEN (NL) atmospheric
  chemistry, climatology
• Prof. Mathias DEWATRIPONT (BE) economics,
  science policy
• Dr. Daniel ESTEVE (FR) physics (quantum
  electronics, nanoscience)
• Prof. Pavel EXNER (CZ) mathematical physics
• Prof. Hans-Joachim FREUND (DE) physical
  chemistry, surface physics
• Prof. Wendy HALL (UK) electronics, computer
  science
• Prof. Carl-Henrik HELDIN (SE) medicine (cancer
  research, biochemistry)
• Prof. Michal KLEIBER (PL) computational science
  and engineering, solid and fluid mechanics,
  applied mathematics
• Prof. Maria Teresa V.T. LAGO (PT) astrophysics
• Prof. Fotis C. KAFATOS (GR) molecular biology,
  biotechnology
• Prof. Norbert KROO (HU) solid-state physics,
  optics
• Dr. Oscar MARIN PARRA (ES) biology, biomedicine
  
• Lord MAY (UK) zoology, ecology
• Prof. Helga NOWOTNY (AT) sociology, science
  policy
• Prof. Christiane NÜSSLEIN-VOLHARD (DE)
  biochemistry, genetics
• Prof. Leena PELTONEN-PALOTIE (FI) medicine
  (molecular biology)
• Prof. Alain PEYRAUBE (FR) linguistics, asian
  studies

Mathematics as a key to new technologies
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ERC panel structureSocial Sciences and
Humanities

• SH1 INDIVIDUALS, INSTITUTIONS AND MARKETS
  economics, finance and management.
• SH2 INSTITUTIONS, VALUES AND BELIEFS AND
  BEHAVIOUR sociology, social anthropology,
  political science, law, communication, social
  studies of science and technology.
• SH3 ENVIRONMENT AND SOCIETY environmental
  studies, demography, social geography, urban and
  regional studies.
• SH4 THE HUMAN MIND AND ITS COMPLEXITY cognition,
  psychology, linguistics, philosophy and
  education.
• SH5 CULTURES AND CULTURAL PRODUCTION literature,
  visual and performing arts, music, cultural and
  comparative studies.
• SH6 THE STUDY OF THE HUMAN PAST archaeology,
  history and memory.

Mathematics as a key to new technologies
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ERC panel structureLife Sciences

• LS1 MOLECULAR AND STRUCTURAL BIOLOGY AND
  BIOCHEMISTRY molecular biology, biochemistry,
  biophysics, structural biology, biochemistry of
  signal transduction.
• LS2 GENETICS, GENOMICS, BIOINFORMATICS AND
  SYSTEMS BIOLOGY genetics, population genetics,
  molecular genetics, genomics, transcriptomics,
  proteomics, metabolomics, bioinformatics,
  computational biology, biostatistics, biological
  modelling and simulation, systems biology,
  genetic epidemiology.
• LS3 CELLULAR AND DEVELOPMENTAL BIOLOGY cell
  biology, cell physiology, signal transduction,
  organogenesis, evolution and development,
  developmental genetics, pattern formation in
  plants and animals.
• LS4 PHYSIOLOGY, PATHOPHYSIOLOGY, ENDOCRINOLOGY
  organ physiology, pathophysiology,
  endocrinology, metabolism, ageing, regeneration,
  tumorygenesis, cardiovascular disease, metabolic
  syndrome.
• LS5 NEUROSCIENCES AND NEURAL DISORDERS
  neurobiology, neuroanatomy, neurophysiology,
  neurochemistry, neuropharmacology, neuroimaging,
  systems neuroscience, neurological disorders,
  psychiatry.

Mathematics as a key to new technologies
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ERC panel structureLife Sciences

• LS6 IMMUNITY AND INFECTION immunobiology,
  aetiology of immune disorders, microbiology,
  virology, parasitology, global and other
  infectious diseases, population dynamics of
  infectious diseases, veterinary medicine.
• LS7 DIAGNOSTIC TOOLS, THERAPIES AND PUBLIC
  HEALTH aetiology, diagnosis and treatment of
  disease, public health, epidemiology,
  pharmacology, clinical medicine, regenerative
  medicine, medical ethics.
• LS8 EVOLUTIONARY POPULATION AND ENVIRONMENTAL
  BIOLOGY evolution, ecology, animal behaviour,
  population biology, biodiversity, biogeography,
  marine biology, ecotoxycology, prokaryotic
  biology.
• LS 9 APPLIED LIFE SCIENCES AND BIOTECHNOLOGY
  agricultural, animal, fishery, forestry and food
  sciences, biotechnology, chemical biology,
  genetic engineering, synthetic biology,
  industrial biosciences, environmental
  biotechnology and remediation.

Mathematics as a key to new technologies
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ERC panel structurePhysical Sciences and
Engineering

• PE1 MATHEMATICAL FOUNDATIONS all areas of
  mathematics, pure and applied, plus mathematical
  foundations of computer science, mathematical
  physics and statistics.
• PE2 FUNDAMENTAL CONSTITUENTS OF MATTER
  particle, nuclear, plasma, atomic, molecular,
  gas and optical physics.
• PE3 CONDENSED MATTER PHYSICS structure,
  electronic properties, fluids, nanosciences.
• PE4 PHYSICAL AND ANALYTICAL CHEMICAL SCIENCES
  analytical chemistry, chemical theory, physical
  chemistry/chemical physics.
• PE5 MATERIALS AND SYNTHESIS materials
  synthesis, structure properties relations,
  functional and advanced materials, molecular
  architecture, organic chemistry.
• PE6 COMPUTER SCIENCE AND INFORMATICS
  informatics and information systems, computer
  science, scientific computing, intelligent
  systems.

Mathematics as a key to new technologies
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ERC panel structurePhysical Sciences and
Engineering

• PE7 SYSTEMS AND COMMUNICATION ENGINEERING
  electronic, communication, optical and systems
  engineering.
• PE8 PRODUCTS AND PROCESSES ENGINEERING product
  design, process design and control, construction
  methods, civil engineering, energy systems,
  material engineering.
• PE9 UNIVERSE SCIENCES astro-physics/chemistry/bio
  logy solar system stellar, galactic and
  extragalactic astronomy, planetary systems,
  cosmology, space science, instrumentation.
• PE10 EARTH SYSTEM SCIENCE physical geography,
  geology, geophysics, meteorology, oceanography,
  climatology, ecology, global environmental
  change, biogeochemical cycles, natural resources
  management.

Mathematics as a key to new technologies
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• PE1 MATHEMATICAL FOUNDATIONS all areas of
  mathematics, pure and applied, plus mathematical
  foundations of computer science, mathematical
  physics and statistics.
• Logic and foundations
• Algebra
• Number theory
• Algebraic and complex geometry
• Geometry
• Topology
• Lie groups, Lie algebras
• Analysis
• Operator algebras and functional analysis
• ODE and dynamical systems
• Partial differential equations
• Mathematical physics
• Probability and statistics
• Combinatorics
• Mathematical aspects of computer science
• Numerical analysis and scientific computing
• Control theory and optimization

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• PE4 PHYSICAL AND ANALYTICAL CHEMICAL SCIENCES
  analytical chemistry, chemical theory, physical
  chemistry/chemical physics
• Physical chemistry
• Nanochemistry
• Spectroscopic and spectrometric techniques
• Molecular architecture and Structure
• Surface science
• Analytical chemistry
• Chemical physics
• Chemical instrumentation
• Electrochemistry, electrodialysis, microfluidics
• Combinatorial chemistry
• Method development in chemistry
• Catalysis
• Physical chemistry of biological systems
• Chemical reactions mechanisms, dynamics,
  kinetics and catalytic reactions
• Theoretical and computational chemistry
• Radiation chemistry
• Nuclear chemistry

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• PE6 COMPUTER SCIENCE AND INFORMATICS
  informatics and information systems, computer
  science, scientific computing, intelligent
  systems
• Computer architecture
• Database management
• Formal methods
• Graphics and image processing
• Human computer interaction and interface
• Informatics and information systems
• Theoretical computer science including quantum
  information
• Intelligent systems
• Scientific computing
• Modelling tools
• Multimedia
• Parallel and Distributed Computing
• Speech recognition
• Systems and software

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• PE7 SYSTEMS AND COMMUNICATION ENGINEERING
  electronic, communication, optical and systems
  engineering
• Control engineering
• Electrical and electronic engineering
  semiconductors, components, systems
• Simulation engineering and modelling
• Systems engineering, sensorics, actorics,
  automation
• Micro- and nanoelectronics, optoelectronics
• Communication technology, high-frequency
  technology
• Signal processing
• Networks
• Man-machine-interfaces
• Robotics

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• PE8 PRODUCTS AND PROCESS ENGINEERING product
  design, process design and control, construction
  methods, civil engineering, energy systems,
  material engineering
• Aerospace engineering
• Chemical engineering, technical chemistry
• Civil engineering, maritime/hydraulic
  engineering, geotechnics, waste treatment
• Computational engineering
• Fluid mechanics, hydraulic-, turbo-, and piston
  engines
• Energy systems (production, distribution,
  application)
• Micro(system) engineering,
• Mechanical and manufacturing engineering
  (shaping, mounting, joining, separation)
• Materials engineering (biomaterials, metals,
  ceramics, polymers, composites, )
• Production technology, process engineering
• Product design, ergonomics, man-machine
  interfaces
• Lightweight construction, textile technology
• Industrial bioengineering
• Industrial biofuel production

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• PE9 UNIVERSE SCIENCES astro-physics/chemistry/bi
  ology solar system stellar, galactic and
  extragalactic astronomy, planetary systems,
  cosmology space science, instrumentation
• Solar and interplanetary physics
• Planetary systems sciences
• Interstellar medium
• Formation of stars and planets
• Astrobiology
• Stars and stellar systems
• The Galaxy
• Formation and evolution of galaxies
• Clusters of galaxies and large scale structures
• High energy and particles astronomy X-rays,
  cosmic rays, gamma rays, neutrinos
• Relativistic astrophysics
• Dark matter, dark energy
• Gravitational astronomy
• Cosmology
• Space Sciences
• Very large data bases archiving, handling and
  analysis
• Instrumentation - telescopes, detectors and
  techniques

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• Further Information
• Website of the ERC Scientific Council at
  http//erc.europa.eu

Mathematics as a key to new technologies
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Discrete element method main assumptions

• Material represented by a collectionof particles
  of different shapes,in the presented
  formulationspheres (3D) or discs (2D) are
  used(similar to P. Cundalls formulation)
• Rigid discrete elements, deformablecontact
  (deformation is localized in discontinuities)
• Adequate contact laws yield desiredmacroscopic
  material behaviour
• Contact interaction takes intoaccount friction
  and cohesion,including the possibility of
  breakage of cohesive bonds

Mathematics as a key to new technologies
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Micro-macro relationships
micro-macro relationships
inverse analysis
Micromechanical constitutive laws
Macroscopic stress-strain relationships

• Parameters of micromechanical model kn , kT , Rn
  , RT
• Macroscopic material properties
• Determination of the relationship between micro-
  and macroscopic parameters
• Homogenization, averaging procedures
• Simulation of standard laboratory tests
  (unconfined compression, Brazilian test)

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Simulation of the unconfined compression test
Distribution of axial stresses
Force-strain curve
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Numerical simulation of the Brazilian test
Distribution of stresses Syy
Force-displacement curve (perpendicular to the
direction of loading)
Mathematics as a key to new technologies
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Numerical simulation of the rock cutting test
Failure mode
Force vs. time
Average cutting force experiment 7500 N 2D
simulation 5500 N (force/20mm, 20 mm
spacing between passes of cutting tools)
Analysis details 35 000 discrete elements,
20 hours CPU (Xeon 3.4 GHz)
Mathematics as a key to new technologies
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Rock cutting in dredging
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DEM simulation of dredging

• Model details
• 92 000 discrete elements
• swing velocity 0.2 m/s, angular velocity 1.62
  rad/s

Analysis details 550 000 steps30 hrs. CPU (Xeon
3.4 GHz)
Mathematics as a key to new technologies
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DEM/FEM simulation of dredging example of
multiscale modelling

• Model details
• 48 000 discrete elements
• 340 finite elements

Analysis details 550 000 steps16 hrs. CPU (Xeon
3.4 GHz)
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DEM/FEM simulation of dredging example of
multiscale modelling
Map of equivalent stresses
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Methods of reliability computation
Monte Carlo Adaptive Monte
Carlo Importance Sampling
Simulation methods
FORM SORM
Response Surface Method
Approximation methods
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Failure in metal sheet forming processes
Real part (kitchen sink) with breakage
Deformed shape with thickness distribution
Forming Limit Diagram
Results of simulation
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Deep drawing of a square cup (Numisheet93)
Minor principal strains

• Forming Limit Diagram (FLD)

Major principal strains
Experiment - breakage at 19 mm punch stroke
Blank holding force 19.6 kN, friction
coefficient 0.162, punch stroke 20 mm
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Metal sheet forming processes reliability
analysis
Limit state surface Forming Limit Curve (FLC)
Limit state function minimum distance from FLC
safety margin (positive in
safe domain, negative in failure domain)
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Results of reliability analysis
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Results of reliability analysis
Probability of failure in function of the safety
margin for two different hardening coefficients
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Proces tloczenia blach - przyklad numeryczny,
wyniki
Odchylenie standardowe wspólczynnika wzmocnienia
?2 0.020

• Porównanie z metodami symulacyjnymi potwierdza
  dobra dokladnosc wyników otrzymanych metoda
  powierzchni odpowiedzi
• Metoda powierzchni odpowiedzi wymaga znacznie
  mniejszej liczby symulacji (jest znacznie
  efektywniejsza obliczeniowo)
• Dla malych wartosci Pf metoda adaptacyjna jest
  efektywniejsza niz klasyczna metoda Monte Carlo

Mathematics as a key to new technologies