École Nationale Supérieure de
Techniques Avancées

Abstract

The inspiration behind the topic lies in an article by Togashi and Kaneko which describes the following chemical system with species A1; A2; A3; A4 and the following possible reactions Xi + Xi+1 = 2Xi+1 (modulo 4). While the classical scaling yields an easy (constant) solution for the number of molecules of each species as the initial number of molecules N tends to infinity, we get a more interesting behaviour with a certain choice of kinetics for these reactions. Due to the discreteness, even for a relatively large N, two couples of two species quickly settle to a state where they have alternatively zero and large concentrations for the same time (1 and 3, 2 and 4)