Department of Physics, Kyung Hee University

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Presentation transcript:

Department of Physics, Kyung Hee University 제13차 열 및 통계물리 워크샵 Drift와 결함이 있는 계의 표면 거칠기 Sooyeon Yoon & Yup Kim Department of Physics, Kyung Hee University

Background of this study • Edward-Wilkinson Eq. • G. Pruessner (PRL 92, 246101 (2004)) v : drift velocity with Fixed Boundary Condition (FBC)  Surface roughness L : system size h : the height of surface  Family-Vicsek Scaling behavior EW universality class Anomalous exponents

Motivation 1. What is the simple stochastic discrete surface growth model to describe the EW equaiton with drift and FBC ? • Numerical Integration • Toy models : Family model, Equilibrium Restricted Solid-On-Solid (RSOS) model …  Stochastic analysis for the Langevin equation ( S.Y. Yoon & Yup Kim, JKPS 44, 538 (2004) ) 2. Application The effect of the defect and drift for the surface growth ?

A stochastic analysis of continuum Langevin equation for surface growths S.Y. Yoon & Yup Kim, JKPS 44, 538 (2004)) • Continuum Langevin Equation : • Fokker-Planck Equation : is the transition rate from H′ to H. • Master Equation : If we consider the deposition(evaporation) of only one particle at the unit evolution step. ( a is the lattice constant. ) (deposition) (evaporation)

Model • Evolution rate on the site For the Edward-Wilkinson equation with drift, • Determine the evolution of the center point (x0=L/2) by the defect strength. x0=L/2 p x d (e ) d (e ) or

Simulation Results  Scaling Properties of the Surface Width (FBC, p=0) (PBC, p=1)

 Analysis of the Interface Profile ~

Crossover (EWanomalous roughening) according to the defect strength

Phase transition of RSOS model with a defect site : H.S.Song & J.M.Kim (Sae Mulli, 50, 221 (2005)) r : the distance from the center point P : defect strength P=0, facet Pc P=1, RSOS EW p=0 p=1

G  Application of the surface growth by the defect (Queuing problem) . . ( a : lattice constant ) . (  : particle density )   G slowly go out ! fast get in !

EW (p0)  Anomalous roughening (p=0) Conclusion We studied the phase transition of the stochastic model which satisfies the Edward-Wilkinson equation with a drift and a defect on the 1-dimensional system. 1. The scaling exponents are changed by the drift and the perfect defect. Anomalous exponents 2. Crossover EW (p0)  Anomalous roughening (p=0) 3. Application to the queuing phenomena ( at p=0 : perfect defect ).