Nonsteady relaxation and critical exponents at the depinning transition

Abstract

We study the nonsteady relaxation of a driven one-dimensional elastic interface at the depinning transition by extensive numerical simulations concurrently implemented on graphics processing units. We compute the timedependent velocity and roughness as the interface relaxes from a flat initial configuration at the thermodynamic random-manifold critical force. Above a first, nonuniversal microscopic time regime, we find a nontrivial long crossover towards the nonsteady macroscopic critical regime. This "mesoscopic" time regime is robust under changes of the microscopic disorder, including its random-bond or random-field character, and can be fairly described as power-law corrections to the asymptotic scaling forms, yielding the true critical exponents. In order to avoid fitting effective exponents with a systematic bias we implement a practical criterion of consistency and perform large-scale (L 2 25 ) simulations for the nonsteady dynamics of the continuum displacement quenched Edwards-Wilkinson equation, getting accurate and consistent depinning exponents for this class: β = 0.245 ± 0.006, z = 1.433 ± 0.007, ζ = 1.250 ± 0.005, and ν = 1.333 ± 0.007. Our study may explain numerical discrepancies (as large as 30% for the velocity exponent β) found in the literature. It might also be relevant for the analysis of experimental protocols with driven interfaces keeping a long-term memory of the initial condition.

Spatiotemporal Patterns in Ultraslow Domain Wall Creep Dynamics

“…This geometrical crossover is compatible with the exponent crossover in the clusters' size distribution and supports the idea of these objects being depinning-like above a scale L opt . The robustness of this conclusion is confirmed by the study of the random field (RF) disorder case, which belongs to a different universality class at equilibrium but shares the same exponents as RB at the depinning transition [19,37,45] (see Supplemental Material [29]). …”

“…The figure clearly shows a crossover length scale 1=q c ∼ L opt ∼ f −ν eq that separates short scales (large q) displaying an equilibrium roughness exponent ζ eq ¼ 2=3 from large scales (small q) displaying a depinning roughness ζ dep ≈ 1.25, in agreement with Refs. [43] and [44,45], respectively. This geometrical crossover is compatible with the exponent crossover in the clusters' size distribution and supports the idea of these objects being depinning-like above a scale L opt .…”

Scaling description of the yielding transition in soft amorphous solids at zero temperature

“…Much more is known about the depinning transition: it is a dynamical critical point characterized by two independent exponents related to avalanche extension and duration (26,27). These exponents have been computed perturbatively with the functional renormalization group (28)(29)(30) and evaluated numerically with high precision (31,32). The comparison between these two phenomena has led to the proposition that the yielding transition is in the universality class of mean-field depinning (33,34).…”

Dynamic depinning phase transition in magnetic thin film with anisotropy

“…There have been theoretical efforts with the quenched Edwards-Wilkinson (QEW) equation and the Monte Carlo simulation, to understand the depinning phase transition of the domain-wall motion [15][16][17][18][19][20][21]. The QEW equation is a simple phenomenological model, where a domain wall is considered to be an elastic string, and detailed microscopic structures and interactions of the materials are not concerned.…”

“…Recently, the transition point in a magnetic thin film was estimated, with the static exponent β as input [23]. On the other hand, the non-stationary dynamic approach looks efficient in tackling the dynamic phase transitions, since the measurements are carried out in the short-time regime of the dynamic evolution [18,19]. The domain-wall motion in a magnetic nanowire was analyzed based on the LLG equation, and a dynamic scaling behavior was observed [24].…”