Related papers: Predictability of the large relaxations in a cellu…
A two-dimensional lattice system of non-interacting electrons in a homogeneous magnetic field with half a flux quantum per plaquette and a random potential is considered. For the large scale behavior a supersymmetric theory with collective…
We study a simple deterministic map that leads a fully connected network to Heider balance. The map is realized by an algorithm that updates all links synchronously in a way depending on the state of the entire network. We observe that the…
We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined…
We develop a systematic extension of mode-coupling theory (MCT) that incorporates critical dynamical fluctuations. Starting from a microscopic diagrammatic theory, we identify dominant classes of divergent diagrams near the mode-coupling…
The cellular automaton model of Piegari, Di Maio, Scandone and Milano, J. Volc. Geoth. Res., 202, 22-28 (2011) is extended to include magma-induced stress (i.e. a local magma-related augmentation of the stress field). This constitutes a…
In this work a three-states cellular automaton proposed to describe part of a biological immune system is revisited. We obtain the dynamic critical exponent $z$ of the model by means of a recent technique that mixes different initial…
Dynamic relaxation of the XY model and fully frustrated XY model quenched from an initial ordered state to the critical temperature or below is investigated with Monte Carlo methods. Universal power law scaling behaviour is observed. The…
We give a characterization of the relaxation time up to an absolute constant factor, in terms of stationary expected hitting times of large sets. This resolves a conjecture of Aldous and Fill. We give a similar characterization for the…
The probabilistic cellular automaton (PCA) method is highlighted for its relatively simple numerical algorithm and low computational cost in the simulation of microstructural evolution. In this method, probabilistic state change rules are…
Avalanche statistics of various threshold activated dynamical systems are known to depend on the magnitude of the drive, or stress, on the system. Such dependencies exist for earthquake size distributions, in sheared granular avalanches,…
Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph…
The presence of both critical behavior and oscillating patterns in brain dynamics is a very interesting issue. In this paper, we consider a model for a neuron population, where each neuron is modeled by an over-damped rotator. We find that…
Each cell of a two-dimensional lattice is painted one of k colors, arranged in a "color wheel." The colors advance (0 to k-1 mod k) either automatically or by contact with at least a threshold number of successor colors in a prescribed…
Periodicity and relaxation are investigated for the trajectories of the states in cylindrical linear cellular automata. The time evolutions are described with matrices. The eigenvalue analysis is applied to obtain the maximum values of…
The driving concept behind one of the most successful statistical forecasting models, the ETAS model, has been that the seismicity is driven by spontaneously occurring background earthquakes that cascade into multitudes of triggered…
We consider an agent-based model in which two types of agents interact locally over a graph and have a common intolerance threshold $\tau$ for changing their types with exponentially distributed waiting times. The model is equivalent to an…
We investigate the predictability aspects of rotating turbulent flows through extensive numerical simulations of a shell model of rotating turbulence. In particular, we measure the large-scale predictability time and find that it increases…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired…
Commonly studied cellular automata are memoryless and have fixed topology of connections between cells. However by allowing updates of links and short-term memory in cells we may potentially discover novel complex regimes of spatio-temporal…