Probabilistic cellular automata

Iebo90a] Lebowitz, J.L., C.Maes and E.R.Speer, Probabilistic cellular automata some statistical mechanical considerations, pages 401- 414 in [jen90a],... 

The main characteristic of cellulcir automata is that each cell, which corresponds to a grid point in our model of the surface, is updated simultaneously. This allows for an efl cient implementation on massive parallel computers. It also facilitates the simulation of pattern formation, which is much harder to simulate with some asynchronous updating scheme as in dynamic Monte Carlo. [42] The question is how realistic a simultaneous update is, as a reaction seems to be a stochastic process. One has tried to incorporate this randomness by using so-called probabilistic cellular automata, in which updates are done with some probability. These cellular... 

Since we will also discuss in later chapters (Chapter 8 and 9) the use of cellular automata to study surface reactions, it is important to compare kinetic Monte Carlo with cellular automata methods. The main characteristic of cellular automata is that each cell, which corresponds to a grid point of a surface model, is updated simultaneously. The realism of such an assumption is questionable since reaction appears to be a random process. Randomness can be incorporated by using probabilistic cellular automata, in which updates are done with some probability. Probabilistic cellular automata simulations can be developed that are equivalent to the Random Selection Method. 

Two other approaches treat a spatially distributed system as consisting of a grid or lattice. The cellular automaton technique looks at the numbers of particles, or values of some other variables, in small regions of space that interact by set rules that specify the chemistry. It is a deterministic and essentially macroscopic approach that is especially useful for studying excitable media. Lattice gas automata are mesoscopic (between microscopic and macroscopic). Like their cousins, the cellular automata, they use a fixed grid, but differ in that individual particles can move and react through probabilistic rules, making it possible to study fluctuations. 

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