Related papers: Continuum Theory with Memory for Avalanches in Sel…
Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary…
We study propagation of avalanches in a certain excitable network. The model is a particular case of the one introduced in [23], and is mathematically equivalent to an endemic variation of the Reed-Frost epidemic model introduced in [27].…
We report avalanche criticality of thermal relaxation in glassy systems after a rapid quench by molecular simulation. Our analysis of the energy landscape and the scaling reveals that particle rearrangement is critical. The critical…
We explore in the mean-field approximation the robustness with respect to dissipation of self-organized criticality in sandpile models. To this end, we generalize a recently introduced self-organized branching process, and show that the…
Dynamical processes exhibiting absorbing states are essential in the modeling of a large variety of situations from material science to epidemiology and social sciences. Such processes exhibit the possibility of avalanching behavior upon…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
The mechanism of self-organized criticality is based on a steady slow loading and a quick huge stress-release. We add the clustering of the events in space and time to the Bak-Tang-Wiesenfeld cellular automaton and obtain the truncated…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
Self-organized criticality (SOC) refers to the ability of complex systems to evolve towards a 2nd-order phase transition at which interactions between system components lead to scale-invariant events beneficial for system performance. For…
This paper applies the theory of continuous phase transitions of statistical mechanics to a slider-block model. The slider-block model is chosen as a representative of systems with avalanches. Similar behavior can be observed in a…
A propagator for the one dimensional time-dependent Schr\"odinger equation with an asymmetric rectangular potential is obtained using the multiple-scattering theory approach. It allows for the consideration of the reflection and…
The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting…
A self-organising model is proposed to explain the criticality in cortical networks deduced from recent observations of neuronal avalanches. Prevailing understanding of self-organised criticality (SOC) dictates that conservation of energy…
The hypothesis of critical failure relates the presence of an ultimate stability point in the structural constitutive equation of materials to a divergence of characteristic scales in the microscopic dynamics responsible for deformation.…
The hypothesis of self-organized criticality explains the existence of long-range `space-time' correlations, observed inseparably in many natural dynamical systems. A simple link between these correlations is yet unclear, particularly in…
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
We discuss sensitivity to initial conditions in a model for avalanches in granular media displaying self-organized criticality. We show that damage, due to a small perturbation in initial conditions, does not spread. The damage persists in…
Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling $p$) and deterministic critical…
Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (non-conservative) local dynamics on the…