Dynamic exponent in Extremal models of Pinning

Details Dynamic exponent in Extremal models of Pinning Dynamic exponent in Extremal models of Pinning

1999-08-27

arxiv.org/abs/cond-mat/9908413v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

RevTex, 3 figures .eps

Scientific paper

10.1007/s100510051109

The depinning transition of a front moving in a time-independent random potential is studied. The temporal development of the overall roughness w(L,t) of an initially flat front, $w(t)\propto t^\beta$, is the classical means to have access to the dynamic exponent. However, in the case of front propagation in quenched disorder via extremal dynamics, we show that the initial increase in front roughness implies an extra dependence over the system size which comes from the fact that the activity is essentially localized in a narrow region of space. We propose an analytic expression for the $\beta$ exponent and confirm this for different models (crack front propagation, Edwards-Wilkinson model in a quenched noise, ...).

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