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The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes advection and diffusion in a simple way, and as no restriction is placed on the number of particles at a lattice site, it is also able to describe a wide variety of chemical reactions. Assuming molecular chaos and a smooth density function, we obtain the standard reaction-transport equations in the continuum limit. Simulations on one- and two-dimensional lattices show that the discrete model can be used to approximate the solutions of the continuum equations. We discuss discrepancies which arise from correlations between molecules and how these disappear as the continuum limit is approached. Of particular interest are simulations displaying long-time behaviour which depends on long-wavelength statistical fluctuations not accounted for by the standard equations. The model is applied to the reactions $a + b rightleftharpoons c$ and $a + b rightarrow c$ with homogeneous and inhomogeneous initial conditions as well as to systems subject to autocatalytic reactions and displaying spontaneous formation of spatial concentration patterns.
Precipitation/dissolution reactions coupled with solute transport are modelled as a cellular automaton in which solute molecules perform a random walk on a regular lattice and react according to a local probabilistic rule. Stationary solid particles
The state of structural balance (termed also `Heider balance) of a social network is often discussed in social psychology and sociophysics. In this state, actors at network nodes classify other individuals as enemies or friends. Hence, the network co
A cellular automaton model of pulsar glitches is described, based on the superfluid vortex unpinning paradigm. Recent analyses of pulsar glitch data suggest that glitches result from scale-invariant avalanches citep{Melatos07a}, which are consistent
Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or quasi-loca
We present theoretical arguments and simulation data indicating that the scaling of earthquake events in models of faults with long-range stress transfer is composed of at least three distinct regions. These regions correspond to three classes of ear