Related papers: A Cellular Automaton Model for Diffusive and Dissi…
A considerable fraction of the energy in a solar flare is released as suprathermal electrons; such electrons play a major role in energy deposition in the ambient atmosphere and hence the atmospheric response to flare heating. Historically…
A simple lattice gas model in one dimension is constructed in which each site can be occupied by at most one particle of any one of $D$ species. Particles interact with a randomly drawn nearest neighbor interaction. This model is capable of…
We study properties of energy spreading in a lattice of elastically colliding harmonic oscillators (Ding-Dong model). We demonstrate that in the regular lattice the spreading from a localized initial state is mediated by compactons and…
The advantage of Cellular Potts Model (CPM) is due to its ability for introducing cell-cell interaction based on the well known statistical model i.e. the Potts model. On the other hand, Lattice gas Cellular Automata (LGCA) can simulate…
We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
We extend the energetic variational approach so it can be applied to a chemical reaction system with general mass action kinetics. Our approach starts with an energy-dissipation law. We show that the chemical equilibrium is determined by…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic…
Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…
Flexible Time is a new formalism for calculations about one-dimensional cellular automata. It unifies the states of a finite number of cells into a single object, even if they occur at different times. This gives greater flexibility to…
Powering radio access networks using renewables, such as wind and solar power, promises dramatic reduction in the network operation cost and the network carbon footprints. However, the spatial variation of the energy field can lead to…
In the article a transition from pattern evolution equation of reaction-diffusion type to a cellular automaton (CA) is described. The applicability of CA is demonstrated by generating patterns of complex irregular structure on a hexagonal…
While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular…
A simple model of particle creation and annihilation in an isolated assembly of particles with conserved energy and fixed volume, the Cell Model, is formulated. With increasing time, particle number distribution, obtained by averaging over…
We study a chipping model in one dimensional periodic lattice with continuous mass, where a fixed fraction of the mass is chipped off from a site and distributed randomly among the departure site and its neighbours; the remaining mass…
We study a Life-like cellular automaton rule $B2/S2345$ where a cell in state `0' takes state `1' if it has exactly two neighbors in state `1' and the cell remains in the state `1' if it has between two and five neighbors in state `1.' This…
Evolution of a system of diffusing and proliferating mortal reactants is analyzed in the presence of randomly moving catalysts. While the continuum description of the problem predicts reactant extinction as the average growth rate becomes…
We describe various types of traveling fronts of bistable reaction-diffusion cellular automata. These dynamical systems with discrete time, space, and state spaces can be seen as fully discrete versions of widely studied bistable…