Long-range interactions in the avalanches of elastic interfaces
arXiv:2103.07701
Abstract
Disordered systems submitted to a slowly increasing external stress often reacts with a jerky dynamics characterized by bursts of activity, called avalanches, which are the manifestation of an out-of-equilibrium phase transition. This thesis focuses on the dynamics of elastic interfaces near the depinning transition, and more specially on the effect of long-range interactions. I derive the universal scaling form of the correlation functions of the local velocity field. It allows to test the universality class of the transition as well as the range of the interactions. I also study the statistics of the clusters that form in presence of long-range interactions and show how it relates to the statistics of the global avalanches. Finally I present analytical advances towards the understanding of the spatial structure of avalanches within a mean-field model, the Brownian force model.
PhD Thesis, 132 pages
References in corpus (59)
- Crackling Noise
- Creep and depinning in disordered media
- Collective Transport: From Superconductors to Earthquakes
- Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect
- Scaling description of the yielding transition in soft amorphous solids at zero temperature
- Statistics of Earthquakes in Simple Models of Heterogeneous Faults
- Beyond power laws: Universality in the average avalanche shape
- Scaling exponents for Barkhausen avalanches in polycrystals and amorphous ferromagnets
- Elastic consequences of a single plastic event : a step towards the microscopic modeling of the flow of yield stress fluids
- Renormalization of pinned elastic systems: how does it work beyond one loop ?
- Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition
- 2-loop Functional Renormalization Group Theory of the Depinning Transition
- Critical Dynamics of Contact Line Depinning
- Roughness at the depinning threshold for a long-range elastic string
- From Individual to Collective Pinning: Effect of Long-range Elastic Interactions
- Depinning of elastic manifolds
- Exactly solvable model of avalanches dynamics for Barkhausen crackling noise
- On the density of shear transformation zones in amorphous solids
- Avalanches and clusters in planar crack front propagation
- Avalanche-size distribution at the depinning transition: A numerical test of the theory
- Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
- Driven particle in a random landscape: disorder correlator, avalanche distribution and extreme value statistics of records
- Width distribution of contact lines on a disordered substrate
- Size distributions of shocks and static avalanches from the Functional Renormalization Group
- Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator
- Viscoelastic Effects in Avalanche Dynamics: A Key to Earthquake Statistics
- Statistics of static avalanches in a random pinning landscape
- Local dynamics of a randomly pinned crack front during creep and forced propagation: An experimental study
- Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition
- Non-steady relaxation and critical exponents at the depinning transition
- Fracture Roughness Scaling: a case study on planar cracks
- Inter-event correlations from avalanches hiding below the detection threshold
- Avalanche dynamics of elastic interfaces
- Critical exponents of the driven elastic string in a disordered medium
- Universal Statistics of the Critical Depinning Force of Elastic Systems in Random Media
- Quantitative scaling of magnetic avalanches
- The effect of thresholding on temporal avalanche statistics
- Measuring functional renormalization group fixed-point functions for pinned manifolds
- First-principle derivation of static avalanche-size distribution
- Universal interface width distributions at the depinning threshold
- Distribution of velocities in an avalanche
- Roughening Transition in a Moving Contact Line
- Spatial clustering of depinning avalanches in presence of long-range interactions
- Can non-linear elasticity explain contact-line roughness at depinning?
- Nonstationary dynamics of the Alessandro-Beatrice-Bertotti-Montorsi model
- Magnetic domain wall creep and depinning: a scalar field model approach
- Statistics of Avalanches with Relaxation, and Barkhausen Noise: A Solvable Model
- Universal distribution of threshold forces at the depinning transition
- Crack front dynamics: the interplay of singular geometry and crack instabilities
- Depinning dynamics of crack fronts
- Crackling vs. continuum-like dynamics in brittle failure
- Elasticity of a contact-line and avalanche-size distribution at depinning
- Equation of motion of the triple contact line along an inhomogeneous surface
- Spatial shape of avalanches in the Brownian force model
- From bulk descriptions to emergent interfaces: connecting the Ginzburg-Landau and elastic line models
- Distribution of joint local and total size and of extension for avalanches in the Brownian force model
- Correlations between avalanches in the depinning dynamics of elastic interfaces
- Viscoelastic Interfaces Driven in Disordered Media and Applications to Friction
- Universality in the mean spatial shape of avalanches
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- Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
- Stochastic and Quantum Dynamics of Repulsive Particles: from Random Matrix Theory to Trapped Fermions