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2 - Dimensional Multi-Site-Correlated Surface Growths

2 - Dimensional Multi-Site-Correlated Surface Growths with Restricted Solid-on-Solid Condition. (이차원 기판 위에서 다입자 상관 성장 모형의 축척 특성). 김 택수, 김 엽(경희대). 1. Motivation of Study. (1) Is Anomalous Roughness Really happening ?

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2 - Dimensional Multi-Site-Correlated Surface Growths

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  1. 2-Dimensional Multi-Site-Correlated Surface Growths with Restricted Solid-on-Solid Condition. (이차원 기판 위에서 다입자 상관 성장 모형의 축척 특성) 김 택수, 김 엽(경희대)

  2. 1 Motivation of Study (1) Is Anomalous Roughness Really happening ? (Deok-Sun Lee and Marcel den Nijs, Phys. Rev. E 65, 026104 (2002)) (2) The better growth patterns corresponding to mulitply-correalated 2d Membrane

  3. 2 Model  2d The growth rule for the -site correlated growth <1> Select columns { } (  2) randomly. <2-a> If then for =1,2..., with a probability p. for =1,2..., with q =1-p. With restricted solid-on-solid(RSOS)condition, <2-b> If then new selection of columns is taken. The dissociative -mer growth ▶ A special case of the -site correlated growth. Select conneted columns Dimer model : with/without monomer diffusion on terraces (Schwoebel barrier)

  4. p q p q 3 An arbitrary combination of (2, 3) sites of the same height Nonlocal topological constraint : All height levels must be occupied by an (2,3)-multiple number of sites. Mod (2,3) conservation of site number at each height level. (1) Dimer (2) 2-site p q (3) Trimer (4) 3-site p q

  5. 4 Physical Backgrounds for This Study Steady state or Saturation regime, Simple RSOS with ( equilibrium state ) Normal RSOS Model (EW Universality class)  =-1, nh=even number, Anomalous Roughening ? Normal ?

  6. 5  1d 1. p = q = 1/2 (equilibrium state)  1/3 ( k-site, 3,4-mer)  1/3 (Dimer growth model) Ergodicity problem 2. p ≠ q (growing or eroding phase)  1 k-mer (faceted) (J. D. Noh, H. Park, Doochul Kim and M. den Nijs, PRE. (2001))  1 k-site (groove formation ) L , eff ? eff eff eff

  7. Scaling Theory for Normal Roughening Case ? ( Monomer,k-site,Trimer, Dimer & Monomer Diffusion) (Dimer model) (Deok-Sun Lee and Marcel den Nijs, Phys. Rev. E 65,026104(2002)) 6  2d

  8. Dimer & 2-site & Monomer Slope a Model Monomer 0.175 Dimer 0.162 2-site 0.176 7 2d Simulation Results

  9. Slope a Model Monomer 0.175 Dimer 0.162 Dimer & Monomer- Diffusion 0.177 8 Dimer & Dimer-Monomer Diffusion &Monomer

  10. Slope a Model Monomer 0.175 3-site 0.173 9 3-site & Monomer

  11. Slope a Model Monomer 0.175 Triemr 0.174 10 Trimer & Monomer

  12. Slope a Model Monomer 0.175 Extremal 0.174 Dimer 0.162 2-site 0.175 11 Monomer & Extremal & Dimer & 2-site

  13. 12 Scaling Collapse ( 2-site model z = 2.4 )

  14. 13 Conclusion  k-site, TrimermodelSlopea 0.175 Dimer model Slope a  0.162  Dimer & Monomer-Diffusion Slope a 0.175  In d =2, Dynamic exponent z ( 2-site model )  2.4 (?) ??? =-1 = 0 = 1 Normal Random Membrane Extremal growth Multiply-Correlated Membrane

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