Universal fluctuations and extreme statistics of avalanches near the depinning transtition
arXiv:1303.1781 · doi:10.1103/PhysRevE.87.022126
Abstract
We derive exact predictions for universal scaling exponents and scaling functions associated with the statistics of maximum velocities vm during avalanches described by the mean field theory of the interface depinning transition. In particular, we find a robust power-law regime in the statistics of maximum events that can explain the observed distribution of the peak amplitudes in acoustic emission experiments of crystal plasticity. Our results are expected to be broadly applicable to a broad range of systems in the mean-field interface depinning universality class, ranging from magnets to earthquakes.
14 pages
References in corpus (32)
- Crackling Noise
- Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations
- Intermittent dislocation flow in viscoplastic deformation
- Collective Transport: From Superconductors to Earthquakes
- Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect
- Universality Classes for Extreme Value Statistics
- Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes and human birth
- Beyond power laws: Universality in the average avalanche shape
- Scaling exponents for Barkhausen avalanches in polycrystals and amorphous ferromagnets
- Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
- Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces
- Noise in disordered systems: The power spectrum and dynamic exponents in avalanche models
- Pinning and Sliding of Driven Elastic Systems: from Domain Walls to Charge Density Waves
- Exact Maximal Height Distribution of Fluctuating Interfaces
- 1/f Noise and Extreme Value Statistics
- Avalanches in Breakdown and Fracture Processes
- Exactly solvable model of avalanches dynamics for Barkhausen crackling noise
- Driven particle in a random landscape: disorder correlator, avalanche distribution and extreme value statistics of records
- Maximal Height Scaling of Kinetically Growing Surfaces
- Universal mean moment rate profiles of earthquake ruptures
- Depinning transition of dislocation assemblies: pileup and low-angle grain boundary
- Maximal height statistics for 1/f^alpha signals
- Traveling Waves, Front Selection, and Exact Nontrivial Exponents in a Random Fragmentation Problem
- Modeling scaled processes and 1/f^b noise by the nonlinear stochastic differential equations
- Extreme statistics for time series: Distribution of the maximum relative to the initial value
- Global fluctuations in physical systems: a subtle interplay between sum and extreme value statistics
- Numerical schemes for continuum models of reaction-diffusion systems subject to internal noise
- Level Density of a Bose Gas and Extreme Value Statistics
- Dislocations Jam At Any Density
- Distribution of maximum velocities in avalanches near the depinning transition
- Maximum relative height of elastic interfaces in random media
- Maximum relative height of one-dimensional interfaces : from Rayleigh to Airy distribution
Cited by in corpus (10)
- Bulk Metallic Glasses Deform via Slip Avalanches
- Compressive failure as a critical transition: Experimental evidences and mapping onto the universality class of depinning
- Statistics of Avalanches with Relaxation, and Barkhausen Noise: A Solvable Model
- Asymmetric damage avalanche shape in quasi-brittle materials and sub-avalanches (aftershocks) clusters
- Rate-dependent Stick-slips in Steady Shearing: Signature of Transition between Granular Solid and Fluid
- Field theory of disordered systems -- Avalanches of an elastic interface in a random medium
- Large-scale Monte Carlo simulations for the depinning transition in Ising-type lattice models
- Micro-plasticity and recent insights from intermittent and small-scale plasticity
- Analytical Methods and Field Theory for Disordered Systems
- Shapes and velocity relaxation of dislocation avalanches in Au and Nb single crystals