Disordered elastic interfaces display avalanche dynamics at the depinning transition. For short-range interactions, avalanches correspond to compact reorganizations of the interface well described by the depinning theory. For long-range elasticity, an avalanche is a collection of spatially disconnected clusters. In this paper we determine the scaling properties of the clusters and relate them to the roughness exponent of the interface. The key observation of our analysis is the identification of a Bienaym{é}-Galton-Watson process describing the statistics of the cluster number. Our work has a concrete importance for experimental applications where the cluster statistics is a key probe of avalanche dynamics.
In this chapter, we discuss avalanches in glasses and disordered systems, and the macroscopic dynamical behavior that they mediate. We briefly review three classes of systems where avalanches are observed: depinning transition of disordered interfaces, yielding of amorphous materials, and the jamming transition. Without extensive formalism, we discuss results gleaned from theoretical approaches -- mean-field theory, scaling and exponent relations, the renormalization group, and a few results from replica theory. We focus both on the remarkably sophisticated physics of avalanches and on relativ…
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 $Δ(w)$, therefore termed the functional renormalization group (FRG). $Δ(w)$ is a physical observable, the auto-correlation function of the centre of mass of the elastic manifold. In this review, we give a …
Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect
研究了在外加磁场作用下，无序介质中铁磁畴壁的动力学行为。钉扎结构之间的畴壁的雪崩式运动产生了称为巴克豪森效应的噪声。我们讨论了软铁磁材料的实验结果，参考畴结构和样品的几何形状，并报告巴克豪森噪声测量Fe $_{21}$ Co $_{64}$ B $_{15}$非晶合金。我们建立了一个柔性畴壁的运动方程，随着电场的增加，畴壁呈现出退钉扎的转变。长程偶极相互作用被示出设置上临界尺寸为$d_c=3$，这意味着平均场指数（可能的对数校正），预计描述巴克豪森效应。我们介绍了一个平均场的无限范围模型，并表明它是等效于以前介绍的单自由度模型，已知重现几个实验结果。我们在$d=3$中数值模拟了方程，证实了理论预测。我们计算的雪崩分布的磁场驱动率和退磁场的强度的函数。标度指数与驱动率成线性关系，而分布的截止点由退磁场决定，与实验结果非常吻合。
Global Oscillations in Depinning Models with Aging
Centro Atómico Bariloche, Instituto Balseiro, Comisión Nacional de Energía Atómica CNEA, CONICET, UNCUYO（巴里洛切原子中心、巴尔塞罗研究所、阿根廷国家原子能委员会、阿根廷国家科学技术研究委员会、门多萨国立大学）
We consider the amount of energy dissipated during individual avalanches at the depinning transition of disordered and athermal elastic systems. Analytical progress is possible in the case of the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model for Barkhausen noise, due to an exact mapping between the energy released in an avalanche and the area below a Brownian path until its first zero-crossing. Scaling arguments and examination of an extended mean-field model with internal structure show that dissipation relates to a critical exponent recently found in a study of the rounding of the depin…
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 statisti…
We consider a one-dimensional sandpile model which mimics an elastic string of particles driven through a strongly pinning periodic environment with phase disorder. The evolution towards depinning occurs by the triggering of avalanches in regions of activity which are at first isolated but later grow and merge. For large system sizes the dynamically critical behavior is dominated by the coagulation of these active regions. Our analysis of the evolution and numerical simulations show that the observed sizes of active regions is well-described by a Smoluchowski coagulation equation, allowing us …
In presence of impurities, ferromagnetic and ferroelectric domain walls slide only above a finite external field. Close to this depinning threshold, they proceed by large and abrupt jumps, called avalanches, while, at much smaller field, these interfaces creep by thermal activation. In this work we develop a novel numerical technique that captures the ultra-slow creep regime over huge time scales. We point out the existence of activated events that involve collective reorganizations similar to avalanches, but, at variance with them, display correlated spatio-temporal patterns that resemble the…
Quantifying the universality of avalanche observables beyond critical exponents is of current great interest in theory and experiments. Here, we improve the characterization of the spatio-temporal process inside avalanches in the universality class of the depinning of elastic interfaces in random media. Surprisingly, at variance with the temporal shape, the spatial shape of avalanches has not yet been predicted. In part this is due to a lack of an analytically tractable definition: how should the shapes be centered? Here we introduce such a definition, accessible in experiments, and study the …
Domain-wall dynamics and spatial fluctuations are closely related to each other and to universal features of disordered systems. Experimentally measured roughness exponents characterizing spatial fluctuations have been reported for magnetic thin films, with values generally different from those predicted by the equilibrium, depinning and thermal reference states. Here, we study the roughness of domain walls in GdFeCo thin films over a large range of magnetic field and temperature. Our analysis is performed in the framework of a model considering length-scale crossovers between the reference st…
Avalanches are often defined as signals higher than some detection level in bursty systems. The choice of the detection threshold affects the number of avalanches, but it can also affect their temporal correlations. We simulated the depinning of a long-range elastic interface and applied different thresholds including a zero one on the data to see how the sizes and durations of events change and how this affects temporal avalanche clustering. Higher thresholds result in steeper size and duration distributions and cause the avalanches to cluster temporally. Using methods from seismology, the fr…
Very often damage and fracture in heterogeneous materials exhibit bursty dynamics made of successive impulse-like events which form characteristic aftershock sequences obeying specific scaling laws initially derived in seismology: Gutenberg-Richter law, productivity law, Båth's law and Omori-Utsu law. We show here how these laws naturally arise in the model of the long-range elastic depinning interface used as a paradigm to model crack propagation in heterogeneous media. We unravel the specific conditions required to observe this seismic-like organization in the crack propagation problem. Beyo…
The thermally activated creep motion of an elastic interface weakly driven on a disordered landscape is one of the best examples of glassy universal dynamics. Its understanding has evolved over the last 30 years thanks to a fruitful interplay between elegant scaling arguments, sophisticated analytical calculations, efficient optimization algorithms and creative experiments. In this article, starting from the pioneer arguments, we review the main theoretical and experimental results that lead to the current physical picture of the creep regime. In particular, we discuss recent works unveiling t…
We revisit the phenomenon of spinodals in the presence of quenched disorder and develop a complete theory for it. We focus on the spinodal of an Ising model in a quenched random field (RFIM), which has applications in many areas from materials to social science. By working at zero temperature in the quasi-statically driven RFIM, thermal fluctuations are eliminated and one can give a rigorous content to the notion of spinodal. We show that the latter is due to the depinning and the subsequent expansion of rare droplets. We work out the associated critical behavior, which, in any finite dimensio…
Mechanical deformation of nanopillars displays features that are distinctly different from the bulk behavior of single crystals: Yield strength increases with decreasing size and plastic deformation comes together with strain bursts or/and stress drops (depending on loading conditions) with a very strong sensitivity of the stochasticity character on material preparation and conditions. The character of the phenomenon is standing as a paradox: While these bursts resemble the universal, widely independent of material conditions, noise heard in bulk crystals using acoustic emission (AE) technique…
In presence of long range dispersal, epidemics spread in spatially disconnected regions known as clusters. Here, we characterize exactly their statistical properties in a solvable model, in both the supercritical (outbreak) and critical regimes. We identify two diverging length scales, corresponding to the bulk and the outskirt of the epidemic. We reveal a nontrivial critical exponent that governs the cluster number, the distribution of their sizes and of the distances between them. We also discuss applications to depinning avalanches with long range elasticity.
Using numerical simulations, we examine the dynamics of active matter run-and-tumble disks moving in a disordered array of obstacles. As a function of increasing active disk density and activity, we find a transition from a completely clogged state to a continuous flowing phase, and in the large activity limit, we observe an intermittent state where the motion occurs in avalanches that are power law distributed in size with an exponent of $β= 1.46$. In contrast, in the thermal or low activity limit we find bursts of motion that are not broadly distributed in size. We argue that in the highly a…
Alloying metals with other elements is often done to improve the material strength or hardness. A key microscopic mechanism is precipitation hardening, where precipitates impede dislocation motion, but the role of such obstacles in determining the nature of collective dislocation dynamics remains to be understood. Here, three-dimensional discrete dislocation dynamics simulations of FCC single crystals are performed with fully coherent spherical precipitates from zero precipitate density upto $ρ_p = 10^{21}\,\text{m}^{-3}$ and at various dislocation-precipitate interaction strengths. When the d…
