Related papers: Dynamics of bootstrap percolation
We review some results for the dynamics of first-order phase transitions in functional materials. We especially focus on simple models of athermal evolution in driven ferromagnets that give a global picture of metastability and hysteresis,…
Crystal plasticity is mediated through dislocations, which form knotted configurations in a complex energy landscape. Once they disentangle and move, they may also be impeded by permanent obstacles with finite energy barriers or frustrating…
The dynamics of weak vs. strong first order phase transitions is investigated numerically for 2+1 dimensional scalar field models. It is argued that the change from a weak to a strong transition is itself a (second order) phase transition,…
The propagation of dislocations in random crystals is evidenced to be governed by atomic-scale avalanches whose the extension in space and the time intermittency characterizingly diverge at the critical threshold. Our work is the very first…
A self-organized branching process is introduced to describe one-dimensional ricepile model with stochastic topplings. Although the branching processes are generally supposed to describe well the systems in high dimension, our modification…
An avalanche or cascade occurs when one event causes one or more subsequent events, which in turn may cause further events in a chain reaction. Avalanching dynamics are studied in many disciplines, with a recent focus on average avalanche…
We analyze the metastable states near criticality of the bootstrap percolation on Galton-Watson trees. We find that, depending on the exact choice of the offspring distribution, it is possible to have several distinct metastable states,…
Percolation theory characterizing the robustness of a network has applications ranging from biology, to epidemic spreading, and complex infrastructures. Percolation theory, however, only concern the typical response of a infinite network to…
A salient feature of cyclically driven first-order phase transformations in crystals is their scale-free avalanche dynamics. This behavior has been linked to the presence of a classical critical point but the mechanism leading to…
The strength and stability properties of hierarchical load bearing networks and their strengthened variants have been discussed in recent work. Here, we study the avalanche time distributions on these load bearing networks. The avalanche…
Recently, Lipowski [cond-mat/0002378] investigated a stochastic lattice model which exhibits a discontinuous transition from an active phase into infinitely many absorbing states. Since the transition is accompanied by an apparent power-law…
We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of…
Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations…
Consider the first passage percolation model on ${\bf Z}^d$ for $d\geq 2$. In this model we assign independently to each edge the value zero with probability $p$ and the value one with probability $1-p$. We denote by $T({\bf 0}, v)$ the…
We study one- and two-dimensional models which undergo a transition between active and absorbing phases. The transition point in these models is of novel type: jump of the order parameter coincides with its power-law singularity. Some…
A simple one dimensional model to simulate the establishment of the Bean critical state is introduced. It is shown that the dynamics of the flux lines as they enter the superconductor are dominated by `avalanches'. The distribution of…
A damped chain of particles with harmonic nearest-neighbor interactions in a spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is studied numerically. One end of the chain is pulled slowly which acts as a weak…
Surface flows are excited by steadily adding spherical glass beads to the top of a heap. To simultaneously characterize the fast single-grain dynamics and the much slower collective intermittency of the flow, we extend photon-correlation…
$k$-Core percolation has served as a paradigmatic model of discontinuous percolation for a long time. Recently it was revealed that the order parameter of $k$-core percolation of random networks additionally exhibits critical behavior. Thus…
Disordered materials under an imposed forcing can display creep and aging effects, accompanied by intermittent, spatially heterogeneous dynamics. We propose a unifying microscopic description of these phenomena, based on the notion that as…