Distribution of velocities in an avalanche

Abstract

For a driven elastic object near depinning, we derive from first principles the distribution of instantaneous velocities in an avalanche. We prove that above the upper critical dimension, d >= d_uc, the n-times distribution of the center-of-mass velocity is equivalent to the prediction from the ABBM stochastic equation. Our method allows to compute space and time dependence from an instanton equation. We extend the calculation beyond mean field, to lowest order in epsilon=d_uc-d.

4 pages, 2 figures

References in corpus (3)

• Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition
• Exactly solvable model of avalanches dynamics for Barkhausen crackling noise
• Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition

Cited by in corpus (25)

• Driving rate dependence of avalanche statistics and shapes at the yielding transition
• Avalanche dynamics of elastic interfaces
• An exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media
• Quantitative scaling of magnetic avalanches
• Avalanche shape and exponents beyond mean-field theory
• First-principle derivation of static avalanche-size distribution
• Nonstationary dynamics of the Alessandro-Beatrice-Bertotti-Montorsi model
• Statistics of Avalanches with Relaxation, and Barkhausen Noise: A Solvable Model
• Distribution of maximum velocities in avalanches near the depinning transition
• Spatial shape of avalanches in the Brownian force model
• Field theory of disordered systems -- Avalanches of an elastic interface in a random medium
• Distribution of joint local and total size and of extension for avalanches in the Brownian force model
• Distribution of velocities and acceleration for a particle in Brownian correlated disorder: inertial case
• The Spatial Shape of Avalanches
• Universal Excursion and Bridge shapes in ABBM/CIR/Bessel processes
• Correlations between avalanches in the depinning dynamics of elastic interfaces
• Long-range interactions in the avalanches of elastic interfaces
• Clusters in an epidemic model with long-range dispersal
• Distribution of velocities in an avalanche, and related quantities: Theory and numerical verification
• Roughness and critical force for depinning at 3-loop order
• Equivalence of mean-field avalanches and branching diffusions: From the Brownian force model to the super-Brownian motion
• Analytical Methods and Field Theory for Disordered Systems
• Clusters in the critical branching Brownian motion
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• On dissipation in crackling noise systems