Heike Emmerich

An improved cellular automaton model for traffic flow simulation

Starting from a basic cellular automaton model (CA) for traffic flow on a freeway we study various modifications to its update procedure aiming at a quantitative improvement of the fundamental diagram obtained. The investigation results in the suggestion of an improved automaton, showing qualitative and quantitative coincidence of maximum flux with values taken from real traffic measurements.

PHASE TRANSITION IN A DIFFERENCE EQUATION MODEL OF TRAFFIC FLOW

A difference equation is presented to describe traffic flow on a highway. The difference equation model is derived from the optimal velocity models formulated in terms of the differential equations. It is compared with the differential equation models. We investigate phase transitions among the freely moving phase, the coexisting phase in which jams appear, and the uniform congested phase. The linear stability theory is applied and the neutral stability line is obtained. We find the critical point below which no jams appear. To derive the modified Korteweg-de Vries equation near the critical point we apply the reductive perturbation method. We also compare the nonlinear analysis result with that of the optimal velocity model. It is shown that the critical point and the amplitude of the jam are different from those of the optimal velocity model.

INVESTIGATING TRAFFIC FLOW IN THE PRESENCE OF HINDRANCES BY CELLULAR AUTOMATA

Starting from a cellular automaton model (CA) for general conditions on a freeway we come up with a formulation of an automaton to include the case of hindrances on a road. Investigation of our model results in a phase diagram introducing a new phase between laminar and jammed traffic. This phase is characterized by the spatial coexistence of behaviour known from the original model.

Burgers equation for kinetic clustering in traffic flow

A kinetic clustering of cars is analyzed using a limiting procedure and a reductive perturbation method. By using the limiting procedure, the difference–difference equation to describe the clustering is obtained. We derive the coarse-grained equation describing the hydrodynamic mode, using the reductive perturbation method. It is shown that this hydrodynamic equation is given by the Burgers equation and that the typical headway and velocity scale as t1/2 and t−1/2 in time for the initial random velocity distribution.

Vicinal surfaces: growth structures close to the instability threshold and far beyond

We introduce a new numerical approach to step flow growth, making use of its analogies to dendritic growth. Concentrating on the situation close to the instability threshold of step growth, nonlinear evolutionary equations for the steps on a vicinal surface can be derived in a multiple-scale analysis. This approach retains the relevant nonlinearities sufficiently close to the threshold. Our simulations recover and visualize these findings. However, on the basis of our simulations we further report results on the behaviour far from the threshold. Step propagation is treated as a moving-boundary problem based on the Burton-Cabrera-Frank (Burton W K, Cabrera N and Frank F C 1951 Phil. Trans. R. Soc. A 243 299) model. Our method handles the problem in a fully dynamical manner without any quasistatic approximations. Furthermore, it allows for overhangs.

Confinement effects in dendritic growth

We study the interplay between crystal orientation and confinement in diffusion-limited growth. Growth of the overall morphology in the direction of minimal surface stiffness has been investigated in some detail by various authors, the most recent advances being summarized by Brener et al (Brener E, Muller-Krumbhaar H and Temkin D 1996 Phys. Rev. E 54 2714). Here, we consider competing influences, each trying to impose a different growth direction. The simplest possible situation giving rise to such a competition is growth in a channel with a mismatch between the orientation of the channel walls and surface tension anisotropy. Analysing this situation, we find a new structure and gain further insight into the problem of morphological stability. Another case is that of periodic boundary conditions, where the same angle of misorientation can be used to describe growth of a tilted array of finger-shaped crystals. It is found that the transition between dendritic and doublonic structures is affected by the tilt.

From modified KdV-equation to a second-order cellular automaton for traffic flow

We propose a cellular automaton (CA) model for traffic flow which is second order in time. The model is derived from the modified Korteweg–de Vries (MKdV) equation by use of the ‘ultra-discretization method’ (UDM) proposed by Tokihiro et al. (Phys. Rev. Lett. 76, (1996) 3247). This result can be seen as an analogue of the derivation of nonlinear evolution equations from differential- and differential-difference-equation traffic models. It is the intention of this paper to draw attention to exactly this analogy. We show that the model exhibits a crossover from a freely moving regime to a jammed regime with increasing density.

A random cellular automaton related to the noisy Burgers equation

We derive a random cellular automaton (CA) model from the noisy Burgers equation. The method for that derivation is a nonanalytic limiting procedure called ‘ultra-discretization method’ (UDM) proposed by Tokihiro et al. (Phys. Rev. Lett. 76 (1996) 3247). Special attention is paid to the noise term. It is the intention of this paper to propose a random CA model which could be used as a starting point to understand on a CA basis the precise mechanism leading from deterministic evolutionary equations which trigger chaos such as the Kuramoto–Shivashinsky (KS) equation to equivalent stochastic large-scale descriptions. We investigate our CA model to ensure that it belongs to the same universality class as the noisy Burgers (and thereby also KS) equation itself.

Dynamic simulations of interface morphologies in free dendritic growth

We study the evaluation of interface morphologies in free dendritic growth with heat or mass transport by either diffusion alone or by both diffusion and convection. This is done by quantitative numerical simulations; in particular, we try to capture the effects of crystalline anisotropy accurately, avoiding artefacts of the numerical grid. Tracking the interface dynamically, we find oscillating structures that can be related to transient behaviour in extended systems. The set-up of our program allows us to directly compare the effects of diffusion on the evolving patterns versus those of convection. Our aim is to study how the morphology diagram suggested by Brener et al. (Phys. Rev. E 54 (1996) 2714) is to be extended as a function of parameters describing convention.

Nuclear quadrupole moment of the {sup 99}Tc ground state

By combining first-principles calculations and existing nuclear magnetic resonance (NMR) experiments, we determine the quadrupole moment of the 9/2{sup +} ground state of {sup 99}Tc to be (-)0.14(3)b. This confirms the value of -0.129(20)b, which is currently believed to be the most reliable experimental determination, and disagrees with two earlier experimental values. We supply ab initio calculated electric-field gradients for Tc in YTc{sub 2} and ZrTc{sub 2}. If this calculated information would be combined with yet to be performed Tc-NMR experiments in these compounds, the error bar on the {sup 99}Tc ground state quadrupole moment could be further reduced.