https://doi.org/10.1007/s100510051109
Dynamic exponent in extremal models of pinning
1
Laboratoire de Physique et de Mécanique des Milieux Hétérogènes, École Supérieure de Physique
et Chimie Industrielles de Paris, 10 rue Vauquelin, 75231 Paris Cedex 05, France
2
Université de Lyon I, 43 boulevard du 11 Novembre 1918, 69622 Villeurbanne, France
3
Laboratoire Surface du Verre et Interfaces, Unité Mixte de Recherche CNRS/Saint-Gobain,
39 Quai Lucien
Lefranc, BP 135, 93303 Aubervilliers Cedex, France
Received:
27
August
1999
Published online: 15 May 2000
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, , 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 β exponent and confirm
this for different models (crack front propagation,
Edwards-Wilkinson model in a quenched noise etc.).
PACS: 05.40.Fb – Random walks and Levy flights / 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 64.60.Ht – Dynamic critical phenomena
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000