1. A New Scaling Theory for the Damage Spreading in Surface Growth Models C.K. Lee, Yup Kim 초청 강연이 절대 아님 10 분 Talk 로 투고 된 논문임 제도나 분과 위원장의 실수 (?)

2. Kyung-Hee Univ. DSRG I Introduction F Damage Spreading Dynamics 1. 초기에 작은 차이 ( 결함 ) 가 있는 2 개의 동일한 dynamical system 을 동일한 random number 와 동일한 dynamic rule 로 전개시키면서 결함이 얼마나 퍼지는가를 봄. F Damage Spreading in Ising Model Dynamics 1. Ising phase transition & Damage spreadings(DSs) (Stanley et al.,1987) 0.00 1.00 1.04 1.08 0.5 0.4 0.3 0.2 0.1 0.00 1.00 1.04 1.08 1.0 0.0 2. Correlated-nonlinear system 들의 dynamical property 를 연구하는데 powerful 한 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). m=magnetization 1

3. Kyung-Hee Univ. Surface width Height-Height Correlation Function I Scaling relations DSRG ln (W / L   ln (t / L z ) scaling L1L1 L2L2 L3L3 tt ln W ln t 2

4. I Damage Spreading 1. Consider two systems A and B 2. Start from two different initial conditions, which are the same except one point at r 0 3. Evolve under the same growth rules and under the same sequence of random numbers 4. The surface configurations of them evolve differently due to the different initial conditions 5. A damage site is defined as the point where the surface heights h A (r,t) and h B (r,t) are not the same Kyung-Hee Univ. DSRG 3 t  r0 r0 Damaged Site t  A d d d || r0 r0 B

5. DSRG 4 I RSOS Model  = 0.52  Kyung-Hee Univ. 1/z = 0.69 기울기 = 1.0

6. I Real Physics of the Damage Spreadings in Surface Growth Models L L : no damaged site No Informations for physics :dynamical self-affine property 를 만족함. : = the time at which the damage first touch the site at Kyung-Hee Univ. DSRG I A New Scaling Theory (self-affine property) 5

7. Kyung-Hee Univ. DSRG 6

8. Kyung-Hee Univ. DSRG 7 A는A는 로 부터 얻음 c는c는 로부터 얻음.

9. Kyung-Hee Univ. DSRG 8

10. Kyung-Hee Univ. DSRG 9

11. Kyung-Hee Univ. I Super Roughening Models I Das Sarma-Tamborenea(DT) Model DSRG 1)  >1, W sat /L diverges in the thermodynamic limit 2) Height-Height Correlation Function in Super Roughening 10 (DT, LC, RC, CRSOS,…)

12. Kyung-Hee Univ. DSRG 11 예상보다 훨씬 빨리 damage 의 전파가 일어남. 그러나 dynamical self-affinity 는 만족함. A는A는로 부터 얻음 I DT Model

13. Kyung-Hee Univ. DSRG 12

14. Kyung-Hee Univ. DSRG 13