Driven interface depinning in a disordered medium
作者:
Heiko Leschhorn,
Thomas Nattermann,
Semjon Stepanow,
Lei‐Han Tang,
期刊:
Annalen der Physik
(WILEY Available online 1997)
卷期:
Volume 509,
issue 1
页码: 1-34
ISSN:0003-3804
年代: 1997
DOI:10.1002/andp.19975090102
出版商: WILEY‐VCH Verlag
关键词: Disorder;Interfaces;Nonequilibrium phase transitions
数据来源: WILEY
摘要:
AbstractThe dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocityv, which increases asv∼(FFc)θfor driving forcesFclose to its threshold valueFc. We consider a Langevin‐type Eq. which is expected to be valid close to the depinning transition of an interface in a statistically isotropic medium. By a functional renormalization group scheme the critical exponents characterizing the depinning transition are obtained to the first order in ϵ = 4 —D>0, whereDis the interface dimension. The main results were published earlier [T. Nattermann et al., J. Phys. II France2(1992) 1483]. Here, we present details of the perturbative calculation and of the derivation of the functional flow Eq. for the random‐force correlator. The fixed point function of the correlator has a cusp singularity which is related to a finite value of the thresholdFc, similar to the mean field theory. We also present extensive numerical simulations and compare them with our analytical results for the critical exponents. For ϵ = 1 the numerical and analytical results deviate from each other by only a few percent. The deviations in lower dimensions ϵ = 2, 3 are larger and suggest that the roughness exponent is somewhat larger than the value ξ =e/3 of an interface in thermal
点击下载:
PDF
(1679KB)
返 回