Some new results on one-dimensional outflow dynamics

¹  Institute of Physics, Academy of Sciences of the Czech Republic - Na Slovance 2, CZ-18221 Praha, Czech Republic, EU
²  Center for Theoretical Study - Jilská 1, Praha, Czech Republic, EU
³  Institute of Theoretical Physics, University of Wrocław - pl. Maxa Borna 9, 50-204 Wrocław, Poland, EU

Corresponding author: kweron@ift.uni.wroc.pl

Received: 12 December 2007
Accepted: 13 February 2008

Abstract

In this paper we introduce a modified version of the one-dimensional outflow dynamics in the spirit of the Sznajd model, which simplifies the analytical treatment. The equivalence between original and modified versions is demonstrated in simulations. Using the Kirkwood approximation, we obtain an analytical formula for the exit probability and we show that it agrees very well with computer simulations in the case of random initial conditions. Moreover, we compare our results with earlier analytical calculations obtained from the renormalization group method and from the general sequential probabilistic frame introduced by Galam and show that our result is superior to the others. Using computer simulations we investigate the time evolution of several correlation functions in order to check the validity of the Kirkwood approximation. Surprisingly, it turns out that the Kirkwood approximation gives correct results even for such initial conditions for which it cannot be easily justified.