arXiv subjects

L. Santen

Publications and source records attributed to L. Santen.

23 records · Page 2Linked to original sources

arXiv1997

Jamming Transition in CA Models for Traffic Flow

The cellular automaton model for traffic flow exhibits a jamming transition from a free-flow phase to a congested phase. In the deterministic case this transition corresponds to a critical point with diverging correlation length. We present data from numerical simulations which suggest the absence of critical behavior in the presence of noise. The transition of the deterministic case is smeared out and one only observes the remnants of the critical point.

cond-mat.stat-mech↗

arXiv1997

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.

cond-mat.stat-mech↗

arXiv1997

Jamming transition in a cellular automaton model for traffic flow

The cellular automaton model for traffic flow exhibits a jamming transition from a free-flow phase to a congested phase. In the deterministic case this transition corresponds to a critical point with diverging correlation length. In the presence of noise, however, no consistent picture has emerged up to now. We present data from numerical simulations which suggest the absence of critical behavior. The transition of the deterministic case is smeared out and one only observes the remnants of the critical point.

cond-mat.stat-mech↗

arXiv1996

The critical exponents of the two-dimensional Ising spin glass revisited: Exact Ground State Calculations and Monte Carlo Simulations

The critical exponents for $T\to0$ of the two-dimensional Ising spin glass model with Gaussian couplings are determined with the help of exact ground states for system sizes up to $L=50$ and by a Monte Carlo study of a pseudo-ferromagnetic order parameter. We obtain: for the stiffness exponent $y(=θ)=-0.281\pm0.002$, for the magnetic exponent $δ=1.48 \pm 0.01$ and for the chaos exponent $ζ=1.05\pm0.05$. From Monte Carlo simulations we get the thermal exponent $ν=3.6\pm0.2$. The scaling prediction $y=-1/ν$ is fulfilled within the error bars, whereas there is a disagreement with the relation $y=1-δ$.

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↗