1. Coarse-Grained Theory of Surface Nanostructure Formation Dimitri D. Vvedensky The Blackett Laboratory, Imperial College London Christoph A. Haselwandter Department of Applied Physics, Caltech

2. Imperial College London

3. Outline Systems with many scales The coarse-graining road map Renormalization-group trajectories Transient effects and crossover Experimental realizations Extension to the submonolayer regime

4. Outline Systems with many scales The coarse-graining road map Renormalization-group trajectories Transient effects and crossover Experimental realizations Extension to the submonolayer regime

5. Multiscale Physics: Turbulence C. H. K. Williamson, Cornell (Source: http://www.efluids.com) Free gliding of delta-wing in water Fluorescent dye illuminated by laser Vortices in near field Turbulence in far field Both panels have same scale Energy cascades from large to small scales

6. Multiscale Physics: Fracture F. F. Abraham, D. Brodbeck, R. A. Rafey, and W. E. Rudge, Phys. Rev. Lett. 73, 272 (1994). 2D simulation of 10 6 - atom system Bond-breaking at crack tip Dislocation emission blunts crack tip Feed-back between atomic and continuum modes

7. Multiscale Physics: Critical Phenomena 2D Ising Model J. D. Noh, Chungham National University, Korea

8. Multiscale “Physics”: Medical Implants B. Kasemo, Surface Science 500, 656 (2002) Time Scale ns µm ms

9. Outline Systems with many scales The coarse-graining road map Renormalization-group trajectories Transient effects and crossover Experimental realizations Extension to the submonolayer regime

10. formulation Master & Chapman- Kolmogorov equations Lattice Langevin equation Hierarchy of equations KMC simulations Lattice model Macroscopic equation continuum variables renormalization-group (crossover, scaling, self-organization) analytic stable fixed point Chua et al., PRE 72, 051103 (2005), C. A. H. & D. D. V., PRE 76, 041115 (2007) Direct analysis/solution C. A. H. & D. D. V. PRL, EPL, PRE (2007, 2008) Coarse-Graining Road Map Continuum equation

11. Lattice-to-Continuum Method “Atomistic” Continuum Equation

12. Compare atomistic equation directly to computer simulations? Extract qualitative multiscale surface features via RG analysis… Continuum Equation for Random Deposition/Diffusion

13. The Multiscale Paradigm M. Scheffler, FHI–Berlin

14. Outline The coarse-graining road map Renormalization-group trajectories Transient effects and crossover Experimental realizations Extension to the submonolayer regime

15. Renormalization Group Transformations Real Space Momentum Space Original SystemCoarse GrainingRescaling

16. Renormalization-Group Equations Points along RG trajectory constitute a hierarchy of equations. RG “weeds out” terms that become irrelevant as the scale is increased, and absorbs their contributions into other terms.

17. Outline The coarse-graining road map Renormalization-group trajectories Transient effects and crossover Experimental realizations Extension to the submonolayer regime

18. Stable & Unstable Fixed Points

19. Initial Conditions & Crossover

20. Outline The coarse-graining road map Renormalization-group trajectories Transient effects and crossover Experimental realizations Extension to the submonolayer regime

21. Regimes of Growth D/F>>1. Typical MBE conditions. Initially, conserved Mullins-Herring. Submonolayer regime. D/F ≈ 1. Diffusion noise diminished in importance. Initially, Mullins-Herring. Al on silicone oil (Fang et al., Thin Solid Films 517, 3408 (2009)). D/F<<1. Growth dominated by shot noise.

22. Growth on Patterned Substrates. 1. H.-C. Kan et al., Phys. Rev. Lett. 92, 146101 (2004). KPZ cVLDS VLDS Moun d

23. Growth on Patterned Substrates. 2. H.-C. Kan et al., Phys. Rev. Lett. 92, 146101 (2004). ExperimentKPZcVLDS

24. Analysis from Initial Conditions

25. Outline The coarse-graining road map Renormalization-group trajectories Transient effects and crossover Experimental realizations Extension to the submonolayer regime

26. The Submonolayer Regime

27. Summary Continuum formulation that retains connection to atomistic processes Unifies a wide range of experimental scenarios Extension to submonolayer regime Large-scale morphologies on patterned substrates

28. Ongoing and Future Work Coarse-graining magnetohydrodynamics Coarse-grained molecular dynamics