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