Strategies for Multiscale Modelling
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Transcript of Strategies for Multiscale Modelling
Strategies for Multiscale Modelling
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Dimitri VvedenskyThe 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?• Methods for multiscale modelling• Coarse graining as a unifying theme• Outstanding issues
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
Nanotube with Gd–MetallofullerenesK. Suenaga et al., Science 290, 2280 (2000)
3 nm
Deformation of Carbon NanotubesYakobson et al., Phys. Rev. Lett. 76, 2511 (1996)
• axial compression
• Tersoff–Brenner potential
Multiscale Processes in Medical Implants B. Kasemo, Surf. Sci. 500, 656 (2002)
Time scale
ns
µs
ms
Moore’s LawSource: www.intel.com
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
Molecular Dynamics–Finite Element HybridE. Lidikoris et al., Phys. Rev. Lett. 87, 086104 (2001)
Basic Coarse Graining
Coarse-Graining Calculations
• Free energies for equilibrium systems
• Effective Langevin equations for nonequilibrium systems
• Scaling regimes
• Spatially–varying coarse graining
Quasicontinuum MethodR. E. Miller and E. B. Tadmor, J. Comput-Aided Mater. 9, 203 (2002)
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