Depinning transition of the Mullins-Herring equation with an external driving force and quenched random disorder

Abstract

We study the depinning transition of the quenched Mullins-Herring equation by direct integration method. At critical force F-c, the average surface velocity v(t) follows a power-law behavior v(t)similar to t(-delta) as a function of time t with delta=0.160(5). The surface width has a scaling behavior with the roughness exponent alpha=1.50(6) and the growth exponent beta=0.841(5). Above the critical force, the steady state velocity v(s) follows v(s)similar to(F-F-c)(theta) with theta=0.289(8). Finite size scalings of the velocity are also discussed.