Related papers: Relaxation Oscillations in Model Sandpiles
The theory of SOC, and related avalanche dynamics, is proposed as the origin of the ubiquitous nonexponential relaxation observed in complex systems. Introducing some scaling laws and relations we have obtained that the normalized…
We investigate the sandpile model with Yukawa-type interactions, whose effective range is tuned by an external parameter $R$. Our results reveal that at specific values of $R$, the system exhibits giant avalanches that span the system,…
The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time…
This paper considers a sandpile model subjected to a sinusoidal external drive with the time period $T$. We develop a theoretical model for the Green function in a large $T$ limit, which predicts that the avalanches are anisotropic and…
A sandpile model with stochastic toppling rule is studied. The control parameters and the phase diagram are determined through a MF approach, the subcritical and critical regions are analyzed. The model is found to have some similarities…
We introduce a simple model for the size distribution of avalanches based on the idea that the front of an avalanche can be described by a directed random walk. The model captures some of the qualitative features of earthquakes, avalanches…
We introduce a theoretical model for the compaction of granular materials by discrete vibrations which is expected to hold when the intensity of vibration is low. The dynamical unit is taken to be clusters of granules that belong to the…
Similar evolutionary variational inequalities appear as convenient formulations for continuous models for sandpile growth, magnetization of type-II superconductors, and evolution of some other dissipative systems characterized by the…
Under an applied external load the global load-sharing fiber bundle model, with individual fiber strength thresholds sampled randomly from a probability distribution, will relax to an equilibrium state, or to complete bundle breakdown. The…
A simple lattice model is used to study compaction in granular media. As in real experiments, we consider a series of taps separated by large enough waiting times. The relaxation of the density exhibits the characteristic inverse…
A simple (2+1) dimensional discrete model is introduced to study the evolution of solid surface morphologies during ion-beam sputtering. The model is based on the same assumptions about the erosion process as the existing analytic theories.…
We study experimentally the relaxation towards mechanical equilibrium of a granular pile which has just experienced an avalanche and discuss it in the more general context of the granular jamming transition. Two coexisting dynamics are…
We study a restricted-height version of the one-dimensional Oslo sandpile with conserved density, using periodic boundary conditions. Each site has a limiting height which can be either two or three. When a site reaches its limiting height…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
The Bak-Tang-Wiesenfeld sandpile model provdes a simple and elegant system with which to demonstate self-organized criticality. This model has rather remarkable mathematical properties first elucidated by Dhar. I demonstrate some of these…
We elucidate a long-standing puzzle about the non-equilibrium universality classes describing self-organized criticality in sandpile models. We show that depinning transitions of linear interfaces in random media and absorbing phase…
A two-dimensional earthquake model that consists of a single block resting upon a slowly moving rough surface and connected by two springs to rigid supports is studied. Depending on the elastic anisotropy and the friction force three…
Computer simulations of first-order relaxation processes show that the spatial configurations of the system acquire an invariant shape once the stationary regime is attained. Inspired by them we find that, in any first-order relaxation…
In the single-source sandpile model, a number $N$ grains of sand are positioned at a central vertex on the 2-dimensional grid $\mathbb{Z}^2$. We study the stabilisation of this configuration for a stochastic sandpile model based on a…
We study well-posedness for the relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. In contrast to classical micromorphic models…