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Strategies for Multiscale Modelling

Strategies for Multiscale Modelling. Dimitri Vvedensky The Blackett Laboratory, Imperial College, London, UK. DDV, J. Phys.: Condens. Matter 16 , R1537–R1576 (2004). Outline. What is multiscale modelling? (cf. Russ’s talk) Why multiscale modelling?

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Strategies for Multiscale Modelling

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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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