Computational study of patterns in simple nonequilibrium systems

We present computational studies of a two component reaction diffusion system of the Grey and Scott type. The calculation involves a discrete treatment of the diffusion equation and some details of that problem are explained. As the simulation calculation runs over a 200{times}200 square spatial field ridge like patterns develop if one diffusion coefficient is about twice the size of the other and if the rate parameters are in a narrow range. Pattern development is faster when the reaction rates are larger, within this range. It is shown that for an advancing wave, the lead component has a wider front than the other although in steady state the two components obey a ridge/valley or valley/ridge equilibrium. We investigate ways in which a more complex time dependence could be introduced to the system and display one example of such a possible expansion of the study. A correlation coefficient study shows a modest but distinct difference between our pattern development and a random field. {copyright} {ital 1997 American Institute of Physics.}