Some new results on one-dimensional outflow dynamics

Abstract

In this paper we introduce modified version of one-dimensional outflow dynamics (known as a Sznajd model) which simplifies the analytical treatment. We show that simulations results of the original and modified rules are exactly the same for various initial conditions. We obtain the analytical formula for exit probability using Kirkwood approximation and we show that it agrees perfectly with computer simulations in case of random initial conditions. Moreover, we compare our results with earlier analytical calculations obtained from renormalization group and from general sequential probabilistic frame introduced by Galam. Using computer simulations we investigate the time evolution of several correlation functions to show if Kirkwood approximation can be justified. Surprisingly, it occurs that Kirkwood approximation gives correct results even for these initial conditions for which it cannot be easily justified.Comment: 6 pages, 7 figure