Lee C, Kim JM. Depinning transition of the Mullins-Herring equation with an external driving force and quenched random disorder.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006;
73:016140. [PMID:
16486249 DOI:
10.1103/physreve.73.016140]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2005] [Indexed: 05/06/2023]
Abstract
We study the depinning transition of the quenched Mullins-Herring equation by direct integration method. At critical force Fc, the average surface velocity v(t) follows a power-law behavior v(t) approximately 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 v2 follows vs approximately (F - Fc)theta with theta=0.289(8). Finite size scalings of the velocity are also discussed.
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