Decay of the remanent magnetization in the asymmetric spin chain

The dynamics of the one-dimensional spin glass with asymmetric interactions between neighboring spins is considered. We confine ourselves to discrete couplings with values ±J. We show that the algebraic decay of the remanent magnetization of the infinite ±J-spin chain at zero temperature is only valid for symmetric couplings. Our analytical investigations as well as computer simulations show stretched exponential decay for any finite concentration of antisymmetric bonds. Thus, the asymmetric ±J-spin chain shows an asymmetry-induced phase transition at zero temperature.     

The Asymmetric Exclusion Process: Comparison of Update Procedures

The asymmetric exclusion process (ASEP) has attracted a lot of interest not only because of 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 an MPA for that case and derive the corresponding matrix algebra.     

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.     

Traffic flow models with ‘slow-to-start’ rules

We investigate two models for traffic flow with modified acceleration (‘slow-to-start’) rules. Even in the simplest case v_max = 1 these rules break the ‘particle-hole’ symmetry of the model. We determine the fundamental diagram (flow-density relationship) using the so-called car-oriented mean-field approach (COMF) which yields the exact solution of the basic model with v_max = 1. Here we find that this is no longer true for the models with modified acceleration rules, but the results are still in good agreement with simulations. We also compare the effects of the two different slow-to-start rules and discuss their relevance for real traffic. In addition, in one of these models we find a new phase transition to a completely jammed state.     

Remanence effects in symmetric and asymmetric spin glass models

A new method is introduced which yields exact results for the zero temperature (sequential) dynamics of 1d spin glasses with field and for Cayley trees with arbitrary branching numbers. The remanent magnetization and energy are calculated explicitly. For asymmetric interactionsJ _ij J _ij numerical simulations are performed which show cyclic behavior of the remanent magnetization.     

Attractors in the fully asymmetric SK-model

The mean number of attractors of arbitrary lengthl is calculated explicitly in the fully asymmetric SK-model (<J _ij J _ij >=0) for parallel dynamics and at zero temperature. Forl=2 large finite size effects are observed with a broad maximum around a system size ofN=53 (Gaussian interactions). The basin of attraction of the metastable states for one time step increases exponentially with the system size and the exponent is 0.16.     

Mechanical restriction versus human overreaction triggering congested traffic states

A new cellular automaton traffic model is presented. The focus is on mechanical restrictions of vehicles realized by limited acceleration and deceleration capabilities. These features are incorporated into the model in order to construct the condition of collision-free movement. The strict collision-free criterion imposed by the mechanical restrictions is softened in certain traffic situations, reflecting human overreaction. It is shown that the present model reliably reproduces most empirical findings including synchronized flow, the so-called pinch effect, and the time-headway distribution of free flow. The findings suggest that many free flow phenomena can be attributed to the platoon formation of vehicles (platoon effect).