par Provata, Astero 
;Turner, J. W.;Nicolis, Grégoire
Référence Journal of Statistical Physics, 70, 5-6, page (1195-1213)
Publication Publié, 1993
;Turner, J. W.;Nicolis, Grégoire Référence Journal of Statistical Physics, 70, 5-6, page (1195-1213)
Publication Publié, 1993
Article révisé par les pairs
| Résumé : | Restricting space to low dimensions can cause deviations from the mean-field behavior in certain statistical systems. We investigate, both numerically and analytically, the behavior of the chemical reaction A+2X⇌3X in one and two dimensions. In one dimension, we produce exact results showing that the trimolecular reaction system stabilizes in a nonequilibrium, locally frozen, asymptotic state in which the ratio r of A to X particles is a constant number, r=0.38, quite different from the mean-field ratio, rMF=1. The same trimolecular model, however, reaches the mean-field limit in two dimensions. In contrast, the bimolecular chemical reaction A+X⇌2X is shown to agree with the mean-field predictions in all dimensions. For both models, we show that the adoption of certain types of transition rules in the laws of evolution can lead to oscillatory steady states. © 1993 Plenum Publishing Corporation. |
