arXiv subjects

M. Schreckenberg

Publications and source records attributed to M. Schreckenberg.

26 records · Page 2Linked to original sources

arXiv1995

The Kasteleyn model and a cellular automaton approach to traffic flow

We propose a bridge between the theory of exactly solvable models and the investigation of traffic flow. By choosing the activities in an apropriate way the dimer configurations of the Kasteleyn model on a hexagonal lattice can be interpreted as space-time trajectories of cars. This then allows for a calculation of the flow-density relationship (fundamental diagram). We further introduce a closely-related cellular automaton model. This model can be viewed as a variant of the Nagel-Schreckenberg model in which the cars do not have a velocity memory. It is also exactly solvable and the fundamental diagram is calculated.

cond-mat↗

arXiv1995

Off-Equilibrium Dynamics in Finite-Dimensional Spin Glass Models

The low temperature dynamics of the two- and three-dimensional Ising spin glass model with Gaussian couplings is investigated via extensive Monte Carlo simulations. We find an algebraic decay of the remanent magnetization. For the autocorrelation function $C(t,t_w)=[< S_i(t+t_w)S_i(t_w)>]_{av}$ a typical aging scenario with a $t/t_w$ scaling is established. Investigating spatial correlations we find an algebraic growth law $ξ(t_w)\sim t_w^{α(T)}$ of the average domain size. The spatial correlation function $G(r,t_w)=[< S_i(t_w)S_{i+r}(t_w)>^2]_{av}$ scales with $r/ξ(t_w)$. The sensitivity of the correlations in the spin glass phase with respect to temperature changes is examined by calculating a time dependent overlap length. In the two dimensional model we examine domain growth with a new method: First we determine the exact ground states of the various samples (of system sizes up to $100\times 100$) and then we calculate the correlations between this state and the states generated during a Monte Carlo simulation.

cond-mat↗

arXiv1994

Discrete stochastic models for traffic flow

We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow vs.\ density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with maximum velocity 1 the simplest non-trivial approximation gives the exact result. For higher velocities the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations.

cond-mat↗

arXiv1994

Escape from Metastability via Aging: Non-Equilibrium Dynamics in a One- Dimensional Ising Model

The non-equilibrium dynamics of a one-dimensional Ising model with uniform, short-ranged three-spin interactions is investigated. It is shown that this model possesses an exponentially large number of metastable configurations that are stable against single spin flips. This glass-like situation results in a complete freezing of the system at low temperatures for times smaller than an intrinsic time-scale, which diverges exponentially with inverse temperature. Via thermal activation the system eventually escapes from this frozen state, which is signals the onset of aging by domain growth.

cond-mat↗

arXiv1994

Non-equilibrium dynamics in the random bond Ising chain: A reminiscence of aging in spin glasses

Results of extensive Monte-Carlo simulations that investigate the out-of-equilibrium dynamics of the one-dimensional Ising spin glass model with a Gaussian bond-distribution are presented. At low enough temperatures a typical (interrupted) aging scenario is established as in two- and similar to three-dimensional spin glass models. Since the underlying mechanism is a slow domain-growth we study in detail spatial correlations and the time-dependence of the domain- as well as kink-statistics. We find that all correlation functions in time and in space as well as the domain-size probability distribution function obey simple scaling laws.

cond-mat↗

arXiv1994

Aging and domain growth in the two--dimensional Ising spin glass model

Interrupted aging in the two-dimensional Ising spin glass model with Gaussian couplings is established and investigated via extensive Monte-Carlo simulations. The spin autocorrelation function scales with $t/τ(t_w)$, where $t_w$ is the waiting time and $τ$ is equal to $t_w$ for waiting times smaller than the equilibration time $τ_{\rm eq}$. The spatial correlations scale with $r/ξ(t_w)$, where the correlation length $ξ$ gives information about the averaged domain size in the system. Our results are better compatible with an algebraic growth law for $ξ(t_w)$, although it can also nicely be fitted to $(\log t_w)^{1/ψ}$ with $ψ\approx0.63$.

cond-mat↗

arXiv1994

Reentrant Behavior in the Domany-Kinzel Cellular Automaton

We present numerical and analytical results for a special kind of one-dimensional probabilistic cellular automaton, the so called Domany-Kinzel automaton. It is shown that the phase boundary separating the active and the recently found chaotic phase exhibits reentrant behavior. Furthermore exact results for the $p_2$=0-line are discussed.

hep-lat↗

arXiv1993

Cellular automaton models and traffic flow

A recently introduced cellular automaton model for the description of traffic flow is investigated. It generalises asymmetric exclusion models which have attracted a lot of interest in the past. We calculate the so-called fundamental diagram (flow vs.\ density) for parallel dynamics using an improved mean-field approximation which takes into account short-range correlations. For maximum velocity 1 we find that the simplest non-trivial of these approximations gives already the exact result. For higher velocities our results are in excellent agreement with numerical data.

cond-mat↗