Cellular automata models of kinetically and thermodynamically controlled reactions

Abstract

Cellular automata simulations of the competition between kinetically controlled and thermodynamically controlled products of a reaction are described. The simulations are based on a stochastic first‐order cellular automata model described previously [20] and demonstrate an alternative to the traditional approach to such problems that relies on solution of a set of coupled differential rate equations. Unlike the traditional approach, the cellular automata models are applicable to finite numbers of elements and yield statistical information on the fluctuations to be expected in such finite cases. The usual deterministic solutions appear as limiting cases involving either very large numbers of reacting ingredients or a large number of trials for smaller sets of ingredients. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 529–534, 2000

First‐order stochastic cellular automata simulations of the lindemann mechanism

“…For the past several years we have been examining applications of cellular automata models to dynamic chemical systems 28–30, and we have recently described a general stochastic cellular automaton model for first‐order reaction kinetics 31. The latter model has served as a basis for simulations of a variety of phenomena, including molecular excited‐state dynamics 32, 33 and chemical kinetics 34. In these cellular automata models the rate constants of the traditional approach are replaced by transition probabilities, and because of the probabilistic nature of the transition rules each simulation run is, in effect, an independent “experiment.” The natural fluctuations expected in the behaviors of finite systems emerge in the simulations as variations observed between different runs.…”

Complex Modelling and Design of Catalytic Reactors Using Multiscale Approach—Part 2: Catalytic Reactions Modelling with Cellular Automata Approach

“…Currently, cellular automata are widely used for the modelling of different systems and processes, including porous structures formation and chemical reactions [13][14][15][16][17][18][19][20][21][22][23][24].…”

“…In addition to structure formation, cellular automata are successfully used to model chemical reactions of simple inorganic molecules and complex biomolecular systems [13,[20][21][22][23][31][32][33].…”

Cellular automata simulation of topological effects on the dynamics of feed-forward motifs

“…Widely applied in a variety of areas of science and technology, the cellular automata method recently showed great promise for modeling dynamics of complex biological systems [ 34 - 38 ]. In modeling biochemical processes, we followed the general method used by Kier and Cheng [ 39 , 40 ]. Specifically, this study is focused on studying the purely topological effects on motif productivity.…”