Exact results for one dimensional stochastic cellular automata for different types of updates

We study two common types of time-noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions. We first construct the stationary states using the matrix product formalism. This construction then allows to prove a general connection between the stationary states which are produced by the two different types of updates. Using this connection, we derive explicit relations between the densities and correlation functions for these different stationary states.Comment: 7 pages, Late

Density fluctuations and phase separation in a traffic flow model

Within the Nagel-Schreckenberg traffic flow model we consider the transition from the free flow regime to the jammed regime. We introduce a method of analyzing the data which is based on the local density distribution. This analyzes allows us to determine the phase diagram and to examine the separation of the system into a coexisting free flow phase and a jammed phase above the transition. The investigation of the steady state structure factor yields that the decomposition in this phase coexistence regime is driven by density fluctuations, provided they exceed a critical wavelength.Comment: in 'Traffic and Granular Flow 97', edited by D.E. Wolf and M. Schreckenberg, Springer, Singapore (1998

The asymmetric exclusion process: Comparison of update procedures

The asymmetric exclusion process (ASEP) has attracted a lot of interest not only because its many applications, e.g. in the context of the kinetics of biopolymerization and traffic flow theory, but also because it is a paradigmatic model for nonequilibrium systems. Here we study the ASEP for different types of updates, namely random-sequential, sequential, sublattice-parallel and parallel. In order to compare the effects of the different update procedures on the properties of the stationary state, we use large-scale Monte Carlo simulations and analytical methods, especially the so-called matrix-product Ansatz (MPA). We present in detail the exact solution for the model with sublattice-parallel and sequential updates using the MPA. For the case of parallel update, which is important for applications like traffic flow theory, we determine the phase diagram, the current, and density profiles based on Monte Carlo simulations. We furthermore suggest a MPA for that case and derive the corresponding matrix algebra.Comment: 47 pages (11 PostScript figures included), LATEX, Two misprints in equations correcte