We study avalanche dynamics and local activity of forced-flow imbibition fronts in disordered media. We focus on the front dynamics as the mean velocity $\bar{v}$ of the interface is decreased and the pinning state is approached. Scaling arguments allow us to obtain the statistics of avalanche sizes and durations, which become power-law distributed due to the existence of a critical point at $\bar{v}= 0$. Results are compared with phase-field numerical simulations.
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 …
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…
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）
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 …
We characterize the soft modes of the dynamical matrix at the depinning transition, and compare it with the properties of the Anderson model (and long--range generalizations). The density of states at the edge of the spectrum displays a universal linear tail, different from the Lifshitz tails. The eigenvectors are instead very similar in the two matrix ensembles. We focus on the ground state (soft mode), which represents the epicenter of avalanche instabilities. We expect it to be localized in all finite dimensions, and make a clear connection between its localization length and the Larkin len…
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…
