Depinning exponents of the driven long-range elastic string

Abstract

We perform a high-precision calculation of the critical exponents for the long-range elastic string driven through quenched disorder at the depinning transition, at zero temperature. Large-scale simulations are used to avoid finite-size effects and to enable high precision. The roughness, growth, and velocity exponents are calculated independently, and the dynamic and correlation length exponents are derived. The critical exponents satisfy known scaling relations and agree well with analytical predictions.

6 pages, 5 figures

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Cited by in corpus (22)

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• Avalanches and clusters in planar crack front propagation
• Non-steady relaxation and critical exponents at the depinning transition
• Inter-event correlations from avalanches hiding below the detection threshold
• Intermittency and roughening in the failure of brittle heterogeneous materials
• Crackling vs. continuum-like dynamics in brittle failure
• Atomic-scale avalanche along a dislocation in a random alloy
• Universal scaling of the velocity field in crack front propagation
• Universal Critical Exponents of the Magnetic Domain Wall Depinning Transition
• Seismic-like organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks
• Anisotropic Avalanches and Critical Depinning of Three-Dimensional Magnetic Domain Walls
• Effect of disorder geometry on the critical force in disordered elastic systems
• On the critical region of long-range depinning transitions
• Scaling theory for the statistics of slip at frictional interfaces
• Roughness and multiscaling of planar crack fronts
• Asymmetric Roughness of Elastic Interfaces at the Depinning Threshold
• Droplet spreading and pinning on heterogeneous substrates
• Depinning and flow of a vortex line in an uniaxial random medium
• Depinning free of the elastic approximation
• Height distribution of elastic interfaces in quenched random media
• Pinning-depinning transitions in two classes of discrete elastic-string models in (2+1)-dimensions