Dynamics of surface roughening in disordered media

Kinetic roughening of magnetic flux fronts in Bi2Sr2CaCu2OBarness1, Efraim2, Taitelbaum3 et al. 2012Phys. Rev. B

“…However, as the system approaches 40 K, the exponents tend to the set of exponents (β = 0.6, α = 0.75), which, as mentioned above, associates the front dynamics with the QKPZ equation for nonlinear front evolution in quenched disorder. 12,25,28 The fact that the gross features of the front morphology are reproducible supports the argument that the front roughening is governed by the quenched noise, as expected by the QKPZ description. This description is consistent with that found in some experiments involving fronts moving in the critical state for type-II thin superconducting films.…”

“…The QKPZ model leads to β = (4 − d)/(4 + d) and α = (4 − d)/4, where d is the dimension of the interface. 12 In the one-dimensional case, this leads to β = 3/5 and α = 3/4. Another model of a growing interface in quenched disorder is the directed percolation by depinning (DPD) model, in which an interface is propagating on a square lattice with a certain fraction of forbidden sites.…”

Anisotropic percolation and the d-dimensional surface roughening problem

“…Together with J. Kertesz [25], we have been exploring the relation of this universality class to [26,27]. The numerical data for the continuum models in d = 1 + 1 strongly support the argument that these models belong to the same universality class as discrete models described below.…”

“…Numerical results are in good agreement with anomalously large values of the critical exponents, obtained in many experiments in d = 1 + 1 and d = 2 + 1. The importance of quenched noise and pinning as a mechanism of surface roughening was suggested by several authors [26,27,31,32] which studied the continuum Langevin equations with quenched noise as models of surface growth. Our numerical results are in rather good agreement with the numerical results of those authors in d = 1 + 1.…”

“…The numerical data for the continuum models in d = 1 + 1 strongly support the argument that these models belong to the same universality class as discrete models described below. However, according to [26,27] …”