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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. Math as backbone of applied science and technology Applied math in ERC programme

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mathematics for innovative technology development

Mathematics for innovative technology development

M. Kleiber

President of the Polish Academy of Sciences

Member of the European Research Council

Warsaw, 21.02.2008

slide2
Math as backbone of applied science and technology
  • Applied math in ERC programme
  • 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

slide3
Applied mathematics is apart 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

slide4
Real Problem

validation of model

modelling

verification of results

Mathematical Model

Computer Simulation

algorithm design and implementation

Mathematics as a key to new technologies

slide5
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

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) – molecularbiology, 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

Dr. Jens R. ROSTRUP-NIELSEN (DK) – chemical and process engineering, materials research

Prof. Salvatore SETTIS (IT) – history of art, archeology

Prof. Rolf M. ZINKERNAGEL (CH) – medicine (immunology)

Members of the ERC Scientific Council

Mathematics as a key to new technologies

erc p anel structure social sciences and humanities
ERC panel structure:Social Sciences and Humanities

SH1 INDIVIDUALS, INSTITUTIONS AND MARKETS: economics, finance andmanagement.

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.

SH6THE STUDY OF THE HUMAN PAST: archaeology, history and memory.

Mathematics as a key to new technologies

erc p anel structure life sciences
ERC panel structure:Life Sciences

LS1MOLECULAR 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: organphysiology, 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

erc p anel structure life sciences9
ERC panel structure:Life 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 andtreatment 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

erc p anel structure physical sciences and engineering
ERC panel structure:Physical 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

erc p anel structure physical sciences and engineering11
ERC panel structure:Physical 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/biology; 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

slide12
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
  • Application of mathematics in sciences

Mathematics as a key to new technologies

slide13
PE4 PHYSICAL AND ANALYTICAL CHEMICAL SCIENCES: analytical chemistry, chemicaltheory, 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
  • Photochemistry

Mathematics as a key to new technologies

slide14
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

Mathematics as a key to new technologies

slide15
PE7 SYSTEMS AND COMMUNICATION ENGINEERING: electronic, communication, opticaland 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

Mathematics as a key to new technologies

slide16
PE8 PRODUCTS AND PROCESS ENGINEERING: product design, process design andcontrol, 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

Mathematics as a key to new technologies

slide17
PE9 UNIVERSE SCIENCES: astro-physics/chemistry/biology; 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
  • Solar planetology

Mathematics as a key to new technologies

slide18
Further Information

Website of the ERC Scientific Council athttp://erc.europa.eu

Mathematics as a key to new technologies

disc rete e lement m ethod main assumptions
Discreteelement 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. Cundall´s 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

m icro macro relationships
s

e

e

s

Micro-macro 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)

micro-macro relationships

inverse analysis

Micromechanical constitutive laws

Macroscopic stress-strain relationships

Mathematics as a key to new technologies

simulation of the unconfined compression test
Simulation of the unconfined compression test

Distribution of axial stresses Force−strain curve

Mathematics as a key to new technologies

numerical simulation of the brazilian test
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

numerical simulation of the rock cutting test
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

rock cutting in dredging
Rock cutting in dredging

Mathematics as a key to new technologies

slide25
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

slide26
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)

Mathematics as a key to new technologies

dem fem simulation of dredging example of multiscale modelling
DEM/FEM simulation of dredging – example of multiscale modelling

Map of equivalent stresses

Mathematics as a key to new technologies

methods of reliability computation
Methods of reliability computation

Monte CarloAdaptive Monte CarloImportance Sampling

Simulation

methods

FORM SORM Response Surface Method

Approximation

methods

Mathematics as a key to new technologies

slide29
Failure in metal sheet forming processes

Real part (kitchen sink) with breakage

Deformed shape with thickness distribution

Forming Limit Diagram

Results of simulation

Mathematics as a key to new technologies

slide30
Deep drawing of a square cup (Numisheet’93)

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

Mathematics as a key to new technologies

slide31
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)

Mathematics as a key to new technologies

results of reliability analysis
Results of reliability analysis

Probability of failure in function of the safety margin for two different hardening coefficients

p roces t oczenia blach przyk ad numeryczny wyniki
Proces tłoczenia blach - przykład numeryczny, wyniki

Odchylenie standardowe współczynnika wzmocnienia2 = 0.020

  • Porównanie z metodami symulacyjnymi potwierdza dobrą dokładność wyników otrzymanych metodą powierzchni odpowiedzi
  • Metoda powierzchni odpowiedzi wymaga znacznie mniejszej liczby symulacji (jest znacznie efektywniejsza obliczeniowo)
  • Dla małych wartości Pf metoda adaptacyjna jest efektywniejsza niż klasyczna metoda Monte Carlo

Mathematics as a key to new technologies

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