Cellular Automata Approach to Reaction-Diffusion Systems (original) (raw)
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Iranian Journal of Chemistry & Chemical Engineering-international English Edition, 2011
The Cellular Automata method has been used to simulate the pattern formation of the Schlogl model as a bistable Reaction-Diffusion System. Both microscopic and macroscopic Cellular Automata approaches have been considered and two different methods for obtaining the probabilities in the microscopic approach have been mentioned. The results show the tendency of the system towards the more stable phase in both microscopic and macroscopic cases. It is shown that the fluctuation effect plays an important rule in the microscopic approach while it is negligible in the macroscopic case.
Simulation of diffusion controlled reaction kinetics using cellular automata
Physics Letters A, 1989
Cellular automata techniques are employed to simulate the irreversible bimolecular reaction kinetics of particles diffusing in two dimensions. The reaction induces a marked short-range anticorrelation between the reacting species. The simulation results are compared with the predictions of a discrete stochastic model which ignores interparticle correlations,
Cellular automata approach to pattern formation in reaction-diffusion systems
Physica A: Statistical Mechanics and its Applications, 1997
The dynamics of reaction~zliffusion systems in low dimensions is often driven by fluctuations and a simple-minded description in terms of rate equations is not sufficient. Moreover, the emergence of complex patterns in such systems can involve simultaneously several new mechanisms as, for example, aggregation and precipitation. We shall show that the properties of these complex systems can be well understood in the framework of a mesoscopic description based on cellular automata models.
New class of cellular automata for reaction-diffusion systems applied to the CIMA reaction
1998
We present a class of cellular automata (CAs) for modelling reaction-di usion systems. The construction of the CA is general enough to be applicable to a large class of reactiondi usion equations. The automata are based on a running average procedure to implement di usion, and on a probabilistic table-lookup to implement the reaction. As an example application we present the Brandeisator (Lengyl-Epstein model for the chlorite-iodide-malonic acid reaction CIMA), which exhibits a rich set of behaviors: oscillations, hexagonal structures, stripes, and spirals. We investigate cases showing mixed states, in which di erent structures coexist in space: isolated spots, isolated regions of hexagons in a surrounding homogeneous region, coexistence between stripes and oscillations, and hexagons and stripes. The cellular automaton approach has the following advantages: fast simulations of large systems, easy implementation of noise in the system, and connections to other, more phenomenologically constructed CAs.
Seck-Tuoh-Mora: Phenomenology of reactiondiffusion binary-state cellular automata
2006
We study a binary-cell-states eight-cell neighborhood two-dimensional cellular automaton model of a quasi-chemical system with a substrate and a reagent. Reactions are represented by semi-totalistic transitions rules: every cell switches from state 0 to state 1 depending on if sum of neighbors in state 1 belongs to some specified interval, cell remains in state 1 if sum of neighbors in state 1 belong to another specified interval. We investigate space-time dynamics of 1296 automata, establish morphology-bases classification of the rules, explore precipitating and excitatory cases and scrutinize collisions between mobile and stationary localizations (gliders, cycle life and still life compact patterns). We explore reaction-diffusion like patterns produced in result of collisions between localizations. Also, we propose a set of rules with complex behavior called Life 2c22.
Phenomenology of Reaction–Diffusion Binary-State Cellular Automata
International Journal of Bifurcation and Chaos, 2006
We study a binary-cell-states eight-cell neighborhood two-dimensional cellular automaton model of a quasi-chemical system with a substrate and a reagent. Reactions are represented by semi-totalistic transitions rules: every cell switches from state 0 to state 1 depending on if sum of neighbors in state 1 belongs to some specified interval, cell remains in state 1 if sum of neighbors in state 1 belong to another specified interval. We investigate space-time dynamics of 1296 automata, establish morphology-bases classification of the rules, explore precipitating and excitatory cases and scrutinize collisions between mobile and stationary localizations (gliders, cycle life and still life compact patterns). We explore reaction-diffusion like patterns produced in result of collisions between localizations. Also, we propose a set of rules with complex behavior called Life 2c22.
Mesoscopic model for diffusion-influenced reaction dynamics
The Journal of Chemical Physics, 2004
A hybrid mesoscopic multi-particle collision model is used to study diffusion-influenced reaction kinetics. The mesoscopic particle dynamics conserves mass, momentum and energy so that hydrodynamic effects are fully taken into account. Reactive and non-reactive interactions with catalytic solute particles are described by full molecular dynamics. Results are presented for largescale, three-dimensional simulations to study the influence of diffusion on the rate constants of the A + C ⇋ B + C reaction. In the limit of a dilute solution of catalytic C particles, the simulation results are compared with diffusion equation approaches for both the irreversible and reversible reaction cases. Simulation results for systems where the volume fraction φ of catalytic spheres is high are also presented, and collective interactions among reactions on catalytic spheres that introduce volume fraction dependence in the rate constants are studied.
Dynamic Simulation of Mixing-Limited Pattern Formation in Homogeneous Autocatalytic Reactions
Chemical Product and Process Modeling, 2008
Interaction between transport and reaction generates a variety of complex spatio-temporal patterns in chemical reactors. These patterned states, which are typically initiated by autocatalytic effects and sustained by differences in diffusion/local mixing rates, often cause undesired effects in the reactor. In this work, we analyze the dynamic evolution of mixing-limited spatial pattern formation in fast, homogeneous autocatalytic reactions occurring in isothermal tubular reactors using two-dimensional (2-D) convection-diffusion-reaction (CDR) models that are obtained through rigorous spatial averaging of the three-dimensional (3-D) CDR model using Liapunov-Schmidt technique of bifurcation theory. We use the spatially-averaged 2-D CDR model (and its…
Ju n 20 05 Mesoscopic Multi-Particle Collision Dynamics of Reaction-Diffusion Fronts
2005
A mesoscopic multi-particle collision model for fluid dynamics is generalized to incorporate the chemical reactions among species that may diffuse at different rates. This generalization provides a means to simulate reaction-diffusion dynamics of complex reactive systems. The method is illustrated by a study of cubic autocatalytic fronts. The mesoscopic scheme is able to reproduce the results of reaction-diffusion descriptions under conditions where the mean field equations are valid. The model is also able to incorporate the effects of molecular fluctuations on the reactive dynamics.
Mesoscopic Multiparticle Collision Dynamics of Reaction−Diffusion Fronts †
The Journal of Physical Chemistry B, 2005
A mesoscopic multiparticle collision model for fluid dynamics is generalized to incorporate the chemical reactions among species that may diffuse at different rates. This generalization provides a means to simulate reaction-diffusion dynamics of complex reactive systems. The method is illustrated by a study of cubic autocatalytic fronts. The mesoscopic scheme is able to reproduce the results of reaction-diffusion descriptions under conditions where the mean field equations are valid. The model is also able to incorporate the effects of molecular fluctuations on the reactive dynamics.