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Strategies for Effective Multiscale Modelling in Materials Science

This work by Dimitri Vvedensky from Imperial College discusses multiscale modelling, emphasizing its importance in understanding phenomena across various scales—from atomic interactions to engineering applications. It outlines methods like coarse graining, separation of time and length scales, and concurrent methods using DFT and MD. It addresses fundamental multiscale phenomena such as crack initiation, materials design, and biological applications, highlighting the need for advanced computational techniques to tackle outstanding issues in the field.

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Strategies for Effective Multiscale Modelling in Materials Science

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  1. Strategies for Multiscale Modelling Dimitri Vvedensky The Blackett Laboratory, Imperial College, London, UK DDV, J. Phys.: Condens. Matter16, R1537–R1576 (2004)

  2. Outline • What is multiscale modelling? (cf. Russ’s talk) • Why multiscale modelling? • Methods for multiscale modelling • Coarse graining as a unifying theme • Outstanding issues

  3. Why Multiscale Modelling? • Existence of fundamentally multiscale phenomena Crack initiation and propagation • Materials design Atoms to engineering • Nanostructures Nanotubes, etc New physical effects New device concepts • Biological applications Tissue engineering Interaction between H2O and biological surfaces Implants • Availability of computational power

  4. Nanotube with Gd–Metallofullerenes K. Suenaga et al., Science290, 2280 (2000) 3 nm

  5. Deformation of Carbon Nanotubes Yakobson et al., Phys. Rev. Lett.76, 2511 (1996) • axial compression • Tersoff–Brenner potential

  6. Multiscale Processes in Medical Implants B. Kasemo, Surf. Sci.500, 656 (2002) Time scale ns µs ms

  7. Moore’s Law Source: www.intel.com

  8. Methods for Multiscale Modelling • Sequential Methods • Separation of length and time scales • Parameter passing, KMC • Speakers: Kratzer • Concurrent Methods • Different length and time scales within hybrid scheme • Typically DFT, MD, continuum (FE); Level set • Speakers: Vashishta, Kaxiras, Ortiz, Ratsch • Coarse Graining • Integration over fast time scales short length scales • Speakers: Rudd, DDV, Plechac

  9. Molecular Dynamics–Finite Element Hybrid E. Lidikoris et al., Phys. Rev. Lett.87, 086104 (2001)

  10. Basic Coarse Graining

  11. Coarse-Graining Calculations • Free energies for equilibrium systems • Effective Langevin equations for nonequilibrium systems • Scaling regimes • Spatially–varying coarse graining

  12. Quasicontinuum Method R. E. Miller and E. B. Tadmor, J. Comput-Aided Mater.9, 203 (2002)

  13. Outstanding issues • Exchange–correlation potentials for DFT • Potentials for MD • Simulations at finite temperatures • Time scales accessible by molecular dynamics • Mode transmission across atomistic/continuum interfaces • Error estimation

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