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고체상 고체모형에서의 결함 퍼짐과 상전이

고체상 고체모형에서의 결함 퍼짐과 상전이. C.K.Lee and Yup Kim. 0.5 0.4 0.3 0.2 0.1. 0.00 1.00 1.04 1.08. 1.0 0.0. 0.00 1.00 1.04 1.08. Kyung-Hee Univ. DSRG. DSRG. C Introduction. F Damage Spreading Dynamics.

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고체상 고체모형에서의 결함 퍼짐과 상전이

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  1. 고체상 고체모형에서의 결함 퍼짐과 상전이 C.K.Lee and Yup Kim

  2. 0.5 0.4 0.3 0.2 0.1 0.00 1.00 1.04 1.08 1.0 0.0 0.00 1.00 1.04 1.08 Kyung-Hee Univ. DSRG DSRG C Introduction F Damage Spreading Dynamics 1. 초기에 작은 차이(결함)가 있는 2개의 동일한 dynamical system을 동일한 random number와 동일한 dynamic rule로 전개시키면서 결함이 얼마나 퍼지는가를 봄. 2. Correlated-nonlinear system들의 dynamical property를연구하는데 powerful한 이론적 방법으로 알려져있음. 3. Biological system (Kauffman, 1969), cellular automata ( Jan and Arcangelis, 1994), spin glass (Derrida and Weisbuch, 1987),Ising model (Derrida,1987…. Thomas, 1998). F Damage Spreading in Ising Model Dynamics 1. Ising phase transition & Damage spreadings(DSs) (Stanley et al. ,1987) m=magnetization 1

  3. 2.Ising Dynamics & DSs (Derrida and Weisbuch, 1987... Thomas, 1998) standard Heat bath (HB) ; 결함이 퍼지지 않음 Glauber, Swendsen-Wang(SW) , Metropolis , uncorrelated HB, Q2R 3. Updating rule &DSs (Vojta & Schreiber,1998; Nobre, Mariz & Sousa,1992) Kyung-Hee Univ. DSRG DSRG F Roughening Transition Interface width (W)의 경우 (L ; substrate size) W ê Rough phase L ê Smooth phase Dynamics for Roughening Phase F DSs Transition in Roughening Phenomena 1. order parameter (?) 2. Dynamics (?) 3. Updating rule (?) 2

  4. - -spin +spin 새로운 -spin 새로운 +spin - - - - + - - - - - - - + - - - - - - - - - - - - - + + + + + + - + + - - + + + - + + + + + + + + + + + + + + + + + + + + + + Kyung-Hee Univ. DSRG DSRG F Our Model Ising Model Interface ê Smooth Phase Rough Phase bubble이 생길 수 있다. SOS Model (n=1) ê bubble이 생기지 않음 알려진 결과 1. 1d : Roughening phase transition이 없다. 2. 2d : Roughening phase transition이 있다. 3. Dynamics for Roughening Phase Edwards-Wilkinson(EW) universality class 3

  5. r0 r0 Damage Site Kyung-Hee Univ. DSRG DSRG F Theoretical basis B A t = 0 d|| d^ t ¹ 0 F Ansatz for DSs Phase Transition ê DS Phase ê Damage Pinning Phase Dynamics for DS Phase (?) 4

  6. s-cluster Kyung-Hee Univ. DSRG DSRG F Dynamics s-custer-flip dynamics (Glauber dynamics ; s=1) 1. Random하게 s-cluster를 선택한다. 5

  7. s 1 1.10 1 0.74 2 1.10 2 0.74 5 1.10 5 0.74 Kyung-Hee Univ. DSRG DSRG Simulation Results F 1d (¥) (t) (t) (¥) 6

  8. W D^ D|| a=0.5 a=0.5 1/z=0.5 b=0.25 b=0.25 Kyung-Hee Univ. DSRG DSRG (¥) (t) F 1d summary 7

  9. 1.09 1.05 0.95 0.90 Kyung-Hee Univ. DSRG DSRG F 2d (s=1) (t) (¥) (¥) (¥) (t) 8

  10. 1. 1d와 2d에서 D^으로 W를 잘 설명할 수 있다. 2. 2d에서 D^으로 roughening phase transition을 잘 설명할 수 있다. 3. 임을 알 수 있다. Kyung-Hee Univ. DSRG DSRG (¥) (¥) (t) F 2d summary DS Phase F결론 9

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