Automata Models of Aqueous Solution Systems

Cellular Automata Models of Aqueous Solution Systems 

Lemont B. Kier, Chao-Kun Cheng,1 and Paul G. Seybold  

For the most part, experimental observations made by chemists—of phase changes, physical and chemical properties, chemical reactions, and so on—are averaged outcomes resulting from the behaviors of a very large number of interacting particles, such as molecules, ions, or rare gas atoms. To make sense of these observations, two general approaches have been pursued. 

In the second general approach to this problem, an attempt is made to examine in some manner the overall behavior of the entire ensemble of interacting units. By far, the most common approach here, and the one normally taught from textbooks, is to represent the kinetic behavior of a particular system in terms of an applicable set of coupled differential rate equations. These equations, with their associated rate constants, summarize the bulk behaviors of the ingredients involved in an averaged way. For example, the simple two-step transformation A — B — C, can be characterized by the set of rate equations  

Stochastic analysis presents an alternative avenue for dealing with the inherently probabilistic and discontinuous microscopic events that underlie macroscopic phenomena. Many processes of chemical and physical interest can be described as random Markov processes.1,2 Unfortunately, solution of a stochastic master equation can present an extremely difficult mathematical challenge for systems of even modest complexity. In response to this difficulty, Gillespie3-5 developed an approach employing numerical Monte Carlo 

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L. B. Kier, C.-K. Cheng, and R Seybold, Cellular automata models of aqueous solution systems. Rev. Comput. Chem. 2001, 17, 205-254. 

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