Creation and annihilation of traffic jams in a stochastic asymmetric exclusion model with open boundaries: a computer simulation

Two-species D-dimensional diffusive model and its mapping onto a growth model

In this work, we consider a diffusive two-species d-dimensional model and study it in great detail. Two types of particles, with hard core, diffuse symmetrically and cross each other. For arbitrary dimensions, we obtain the exact density, the instantaneous, as well as noninstantaneous, two-point correlation functions for various initial conditions. We study the impact of correlations in the initial state on the dynamics. Finally, we map the one-dimensional version of the model under consideration onto a restricted solid-on-solid growth model with three states and solve its dynamics.

Convergence to equilibrium in a class of interacting particle systems evolving in discrete time

We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely, conservative cellular automata with piecewise linear flow diagrams, relaxation to the limit set follows the same power law at critical points. We further describe the structure of the limit sets of such systems as unions of shifts of finite type. Relaxation to the equilibrium resembles ballistic annihilation, with "defects" propagating in opposite directions annihilating upon collision.

Asymmetric exclusion process with next-nearest-neighbor interaction: some comments on traffic flow and a nonequilibrium reentrance transition

We study the steady-state behavior of a driven nonequilibrium lattice gas of hard-core particles with next-nearest-neighbor interaction. We calculate the exact stationary distribution of the periodic system and for a particular line in the phase diagram of the system with open boundaries where particles can enter and leave the system. For repulsive interactions the dynamics can be interpreted as a two-speed model for traffic flow. The exact stationary distribution of the periodic continuous-time system turns out to coincide with that of the asymmetric exclusion process (ASEP) with discrete-time parallel update. However, unlike in the (single-speed) ASEP, the exact flow diagram for the two-speed model resembles in some important features the flow diagram of real traffic. The stationary phase diagram of the open system obtained from Monte Carlo simulations can be understood in terms of a shock moving through the system and an overfeeding effect at the boundaries, thus confirming theoretical predictions of a recently developed general theory of boundary-induced phase transitions. In the case of attractive interaction we observe an unexpected reentrance transition due to boundary effects.

Analytic approach to the critical density in cellular automata for traffic flow

The jamming transition in the stochastic traffic cellular automaton of Nagel and Schreckenberg [J. Phys. I 2, 2221 (1992)] is examined. We argue that most features of the transition found in the deterministic limit do not persist in the presence of noise, and suggest instead to define the transition to take place at that critical density rho(c) at which a large initial jam just fails to dissolve. We show that rho(c)=v(J)/(v(J)+v(F)), where v(F) is the velocity of noninteracting vehicles and v(J) is the speed of the dissolution wave moving into the jam. An approximate analytic calculation of v(J) in the framework of a simple renormalization scheme is presented, which explicitly displays the effect of the interaction between vehicles during the acceleration stage of the Nagel-Schreckenberg rules with maximum velocity v(max)>1. The analytic prediction is compared to numerical simulations. We find a remarkable correspondence between the analytic expression for v(J) and a phase diagram obtained numerically by Lübeck et al.