Thermally activated intermittent dynamics of creeping crack fronts along disordered interfaces

Vincent-Dospital, Tom; Cochard, Alain; Santucci, Stéphane; Måløy, Knut Jørgen; Toussaint, Renaud

doi:10.48550/arxiv.2010.06865

Cited by 2 publications

(3 citation statements)

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“…The agreement, especially after proper resummation, is quite good. Note however, that the functions (361), (366) and (370) are close, so that the expansion might not be enough to discriminate between them.…”

Section: Behavior At the Upper Critical Dimensionmentioning

confidence: 99%

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Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles

Wiese

2021

Preprint

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Domain walls in magnets, vortex lattices in superconductors, contact lines at depinning, and many other systems can be modelled as an elastic system subject to quenched disorder. Its field theory possesses a well-controlled perturbative expansion around its upper critical dimension. Contrary to standard field theory, the renormalization group flow involves a function, the disorder correlator ∆(w), therefore termed the functional renormalization group (FRG). ∆(w) is a physical observable, the auto-correlation function of the centre of mass of the elastic manifold. In this review, we give a pedagogical introduction into its phenomenology and techniques. This allows us to treat both equilibrium (statics), and depinning (dynamics). Building on these techniques, avalanche observables are accessible: distributions of size, duration, and velocity, as well as the spatial and temporal shape. Various equivalences between disordered elastic manifolds, and sandpile models exist: an elastic string driven at a point and the Oslo model; disordered elastic manifolds and Manna sandpiles; charge density waves and Abelian sandpiles or loop-erased random walks. Each of these mappings requires specific techniques, which we develop, including modelling of discrete stochastic systems via coarsegrained stochastic equations of motion, super-symmetry techniques, and cellular automata. Stronger than quadratic nearest-neighbor interactions lead to directed percolation, and nonlinear surface growth with additional KPZ terms. On the other hand, KPZ without disorder can be mapped back to disordered elastic manifolds, either on the directed polymer for its steady state, or a single particle for its decay. Other topics covered are the relation between functional RG and replica symmetry breaking, and random field magnets. Emphasis is given to numerical and experimental tests of the theory.

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Section: Behavior At the Upper Critical Dimensionmentioning

confidence: 99%

“…Creep motion was in less depth also studied in vortex lattices [364], fracture experiments [365,366], and quantum systems [187,367,368].…”

Section: Creep Depinning and Flow Regimementioning

confidence: 99%

Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles

Wiese

2021

Preprint

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“…Creep in experiments. The exponent μ RB eq = 1/4 was first found experimentally in [84], see figure 39, and later con- Creep motion was in less depth studied in vortex lattices [385], fracture experiments [386,387], and quantum systems [198,388,389].…”

Section: Creep Depinning and Flow Regimementioning

confidence: 90%

Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpiles

Wiese

2022

Rep. Prog. Phys.

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Domain walls in magnets, vortex lattices in superconductors, contact lines at depinning, and many other systems can be modeled as an elastic system subject to quenched disorder. The ensuing field theory possesses a well-controlled perturbative expansion around its upper critical dimension. Contrary to standard field theory, the renormalization group (RG) flow involves a function, the disorder correlator Δ(w), and is therefore termed the functional RG. Δ(w) is a physical observable, the auto-correlation function of the center of mass of the elastic manifold. In this review, we give a pedagogical introduction into its phenomenology and techniques. This allows us to treat both equilibrium (statics), and depinning (dynamics). Building on these techniques, avalanche observables are accessible: distributions of size, duration, and velocity, as well as the spatial and temporal shape. Various equivalences between disordered elastic manifolds, and sandpile models exist: an elastic string driven at a point and the Oslo model; disordered elastic manifolds and Manna sandpiles; charge density waves and Abelian sandpiles or loop-erased random walks. Each of the mappings between these systems requires specific techniques, which we develop, including modeling of discrete stochastic systems via coarse-grained stochastic equations of motion, super-symmetry techniques, and cellular automata. Stronger than quadratic nearest-neighbor interactions lead to directed percolation, and non-linear surface growth with additional Kardar–Parisi–Zhang (KPZ) terms. On the other hand, KPZ without disorder can be mapped back to disordered elastic manifolds, either on the directed polymer for its steady state, or a single particle for its decay. Other topics covered are the relation between functional RG and replica symmetry breaking, and random-field magnets. Emphasis is given to numerical and experimental tests of the theory.

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Thermally activated intermittent dynamics of creeping crack fronts along disordered interfaces

Abstract: FIG. 2. Illustration of the discretization principles and of the solver and observation grids. Three crack fronts at three successive times are shown, over which the parameters discussed in section II B are defined.

Cited by 2 publications

References 39 publications

Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles

Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles

Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpiles

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