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

A deterministic sandpile automaton revisited

The Bak-Tang-Wiesenfeld (BTW) sandpile model is a cellular automaton which has been intensively studied during the last years as a paradigm for self-organized criticality. In this paper, we reconsider a deterministic version of the BTW model introduced by Wiesenfeld, Theiler and McNamara, where sand grains are added always to one fixed site on the square lattice. Using the Abelian sandpile formalism we discuss the static properties of the system. We present numerical evidence that the deterministic model is only in the BTW universality class if the initial conditions and the geometric form of the boundaries do not respect the full symmetry of the square lattice.Comment: 7 pages, 8 figures, EPJ style, accepted for publication in European Physical Journal

The asymmetric exclusion model with sequential update

We present a solution for the stationary state of an asymmetric exclusion model with sequential update and open boundary conditions. We solve the model exactly for random hopping in both directions by applying a matrix-product formalism which was recently used to solve the model with sublattice-parallel update[1]. It is shown that the matrix-algebra describing the sequential update and sublattice-parallel update are identical and can be mapped onto the random sequential case treated by Derrida et al[2].Comment: 7 pages, Late

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

Exact density profiles for fully asymmetric exclusion process with discrete-time dynamics

Exact density profiles in the steady state of the one-dimensional fully asymmetric simple exclusion process on semi-infinite chains are obtained in the case of forward-ordered sequential dynamics by taking the thermodynamic limit in our recent exact results for a finite chain with open boundaries. The corresponding results for sublattice parallel dynamics follow from the relationship obtained by Rajewsky and Schreckenberg [Physica A 245, 139 (1997)] and for parallel dynamics from the mapping found by Evans, Rajewsky and Speer [J. Stat. Phys. 95, 45 (1999)]. By comparing the asymptotic results appropriate for parallel update with those published in the latter paper, we correct some technical errors in the final results given there.Comment: About 10 pages and 3 figures, new references are added and a comparison is made with the results by de Gier and Nienhuis [Phys. Rev. E 59, 4899(1999)

Phase Transition in a Three-States Reaction-Diffusion System

A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and annihilation of particles. It has been shown that the model undergoes a continuous phase transition from a phase where the currents of different species of particles are equal to another phase in which they are different. The total density of particles and also their currents in each phase are calculated exactly.Comment: 6 page

Mixed messages: re-initiation factors regulate translation of animal mRNAs

When ribosomes encounter upstream open reading frames (uORFs) during scanning of the 5' untranslated region (5' UTR), translation of the downstream ORF requires re-initiation. In a recent paper in Nature, Schleich et al. describe metazoan factors which specifically promote re-initiation