Related papers: A Cellular Automaton Model for Diffusive and Dissi…
We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…
We present an analysis of diffusion in terms of the spontaneous density fluctuations in a non-thermal two-species fluid modeled by a lattice gas automaton. The power spectrum of the density correlation function is computed with statistical…
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…
A kinetic description of lattice-gas automaton models for reaction-diffusion systems is presented. It provides corrections to the mean-field rate equations in the diffusion-limited regime. When applied to the two-species Maginu model, the…
We develop a lumped parameter model to describe and predict the mass release of (absorption from) an arbitrary shaped body of any dimension in a large environment. Through the one-to-one analogy between diffusion-dominated mass transfer…
We review some exact results for the motion of a tagged particle in simple models. Then, we study the density dependence of the self diffusion coefficient, $D_N(\rho)$, in lattice systems with simple symmetric exclusion in which the…
We introduce a stochastic cellular automaton as a model for culture and border formation. The model can be conceptualized as a game where the expansion rate of cultures is quantified in terms of their area and perimeter in such a way that…
In this article a stochastic cellular automata model is examined, which has been developed to study a "small" world, where local changes may noticeably alter global characteristics. This is applied to a climate model, where global…
In the context of fluctuation relations, we study the distribution of energy dissipated by a driven two-level system. Incorporating an energy counting field into the well known spin-boson model enables us to calculate the distribution…
We study the statistics of the dissipated energy in the two-dimensional random fuse model for fracture under different imposed strain conditions. By means of extensive numerical simulations we compare different ways to compute the…
In this article, we have proposed an epidemic model by using probability cellular automata theory. The essential mathematical features are analyzed with the help of stability theory. We have given an alternative modelling approach for the…
We investigate number conserving cellular automata with up to five inputs and two states with the goal of comparing their dynamics with diffusion. For this purpose, we introduce the concept of decompression ratio describing expansion of…
We obtain the exact full counting statistics of a cellular automaton with freely propagating vacancies and charged particles that are stochastically scattered or transmitted upon collision by identifying the problem as a colored stochastic…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
An introduction to cellular automata (both deterministic and probabilistic) with examples. Definition of deterministic automata, dynamical properties, damage spreading and Lyapunov exponents; probabilistic automata and Markov processes,…
In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and…
The stochastic discrete space-time model of an immune response on tumor spreading in a two-dimensional square lattice has been developed. The immunity-tumor interactions are described at the cellular level and then transferred into the…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We present a 2-dimensional cellular automaton model for the simulation of pedestrian dynamics. The model is extremely efficient and allows simulations of large crowds faster than real time since it includes only nearest-neighbour…