Fundamentals of Traffic Flow

From single vehicle data a number of new empirical results concerning the density-dependence of the velocity distribution and its moments as well as the characteristics of their temporal fluctuations have been determined. These are utilized for the specification of some fundamental relations of traffic flow and compared with existing traffic theories.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Two-lane traffic rules for cellular automata: A systematic approach

Microscopic modeling of multi-lane traffic is usually done by applying heuristic lane changing rules, and often with unsatisfying results. Recently, a cellular automaton model for two-lane traffic was able to overcome some of these problems and to produce a correct density inversion at densities somewhat below the maximum flow density. In this paper, we summarize different approaches to lane changing and their results, and propose a general scheme, according to which realistic lane changing rules can be developed. We test this scheme by applying it to several different lane changing rules, which, in spite of their differences, generate similar and realistic results. We thus conclude that, for producing realistic results, the logical structure of the lane changing rules, as proposed here, is at least as important as the microscopic details of the rules

Presence of Many Stable Nonhomogeneous States in an Inertial Car-Following Model

A new single lane car following model of traffic flow is presented. The model is inertial and free of collisions. It demonstrates experimentally observed features of traffic flow such as the existence of three regimes: free, fluctuative (synchronized) and congested (jammed) flow; bistability of free and fluctuative states in a certain range of densities, which causes the hysteresis in transitions between these states; jumps in the density-flux plane in the fluctuative regime and gradual spatial transition from synchronized to free flow. Our model suggests that in the fluctuative regime there exist many stable states with different wavelengths, and that the velocity fluctuations in the congested flow regime decay approximately according to a power law in time.Comment: 4 pages, 4 figure

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.Comment: Revtex, 30 pages, full postscript version (including figures) available by anonymous ftp from "fileserv1.mi.uni-koeln.de" in the directory "pub/incoming/" paper accepted for publication in Phys.Rev.

SDSS J212531.92–010745.9 : the first definite PG 1159 close binary system

Aims. The archival spectrum of SDSS J212531.92−010745.9 shows not only the typical signature of a PG 1159 star, but also indicates the presence of a companion. Our aim was the proof of the binary nature of this object and the determination of its orbital period. Methods. We performed time-series photometry of SDSS J212531.92−010745.9. We observed the object during 10 nights, spread over one month, with the Tübingen 80 cm and the Göttingen 50 cm telescopes. We fitted the observed light curve with a sine and simulated the light curve of this system with the nightfall program. Furthermore, we compared the spectrum of SDSS J212531.92−010745.9 with NLTE models, the results of which also constrain the light curve solution. Results. An orbital period of 6.95616(33) h with an amplitude of 0.354(3) mag is derived from our observations. A pulsation period could not be detected. For the PG 1159 star we found, as preliminary results from comparison with our NLTE models, T eff ∼ 90 000 K, log g ∼ 7.60, and the abundance ratio C/He ∼ 0.05 by number fraction. For the companion we obtained with a mean radius of 0.4 ± 0.1 R, a mass of 0.4 ± 0.1 M, and a temperature of 8200 K on the irradiated side, good agreement between the observed light curve and the nightfall simulation, but we do not regard those values as final

Far-infrared spectroscopy of spin excitations and Dzyaloshinskii-Moriya interactions in a Shastry-Sutherland compound SrCu2_2(BO3_3)$_2

We have studied spin excitation spectra in the Shastry-Sutherland model compound SrCu$_2$(BO$_3$)$_2$ in magnetic fields using far-infrared Fourier spectroscopy. The transitions from the ground singlet state to the triplet state at 24 cm$^{-1}$ and to several bound triplet states are induced by the electric field component of the far-infrared light. To explain the light absorption in the spin system we invoke a dynamic Dzyaloshinskii-Moriya (DM) mechanism where light couples to a phonon mode, allowing the DM interaction. Two optical phonons couple light to the singlet to triplet transition in SrCu$_2$(BO$_3$)$_2$. One is $a$-polarized and creates an intra-dimer dynamic DM along the c axis. The other is $c$-polarized and creates an intra-dimer dynamic DM interaction, it is in the $(ab)$ plane and perpendicular to the dimer axis. Singlet levels at 21.5 and 28.6 cm$^{-1}$ anti-cross with the first triplet as is seen in far-infrared spectra. We used a cluster of two dimers with a periodic boundary condition to perform a model calculation with scaled intra- and inter-dimer exchange interactions. Two static DM interactions are sufficient to describe the observed triplet state spectra. The static inter-dimer DM in the c-direction $d_1=0.7$ cm$^{-1}$ splits the triplet state sub-levels in zero field [C\'{e}pas et al., Phys. Rev. Lett. \textbf{87}, 167205 (2001)]. The static intra-dimer DM in the $(ab)$ plane (perpendicular to the dimer axis) $d_2=1.8$ cm$^{-1}$, allowed by the buckling of CuBO$_3$ planes, couples the triplet state to the 28.6 cm$^{-1}$ singlet as is seen from the avoided crossing.Comment: 12 pages with 7 figures, some references correcte

Dynamic masses for the close PG1159 binary SDSSJ212531.92-010745.9

SDSSJ212531.92-010745.9 is the first known PG1159 star in a close binary with a late main sequence companion allowing a dynamical mass determination. The system shows flux variations with a peak-to-peak amplitude of about 0.7 mag and a period of about 6.96h. In August 2007, 13 spectra of SDSSJ212531.92-010745.9 covering the full orbital phase range were taken at the TWIN 3.5m telescope at the Calar Alto Observatory (Alm\'{e}ria, Spain). These confirm the typical PG1159 features seen in the SDSS discovery spectrum, together with the Balmer series of hydrogen in emission (plus other emission lines), interpreted as signature of the companion's irradiated side. A radial velocity curve was obtained for both components. Using co-added radial-velocity-corrected spectra, the spectral analysis of the PG1159 star is being refined. The system's lightcurve, obtained during three seasons of photometry with the G\"ottingen 50cm and T\"ubingen 80cm telescopes, was fitted with both the NIGHTFALL and PHOEBE binary simulation programs. An accurate mass determination of the PG1159 component from the radial velocity measurements requires to first derive the inclination, which requires light curve modelling and yields further constraints on radii, effective temperature and separation of the system's components. From the analysis of all data available so far, we present the possible mass range for the PG1159 component of SDSSJ212531.92-010745.9.Comment: 8 pages, in "White dwarfs", proceedings of the 16th European White Dwarf Workshop, eds. E. Garcia-Berro, M. Hernanz, J. Isern, S. Torres, to be published in J. Phys.: Conf. Se

Breakdown and recovery in traffic flow models

Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the laminar into the congested phase. In stochastic models, it may be assumed that the size of this amplitude gets translated into a waiting time, i.e.\ until fluctuations sufficiently add up to trigger the transition. A recently introduced model of traffic flow however does not show this behavior: in the density regime where the jam solution co-exists with the high-flow state, the intrinsic stochasticity of the model is not sufficient to cause a transition into the jammed regime, at least not within relevant time scales. In addition, models can be differentiated by the stability of the outflow interface. We demonstrate that this additional criterion is not related to the stability of the flow. The combination of these criteria makes it possible to characterize commonalities and differences between many existing models for traffic in a new way

Stochastic Description of a Bistable Frustrated Unit

Mixed positive and negative feedback loops are often found in biological systems which support oscillations. In this work we consider a prototype of such systems, which has been recently found at the core of many genetic circuits showing oscillatory behaviour. Our model consists of two interacting species A and B, where A activates not only its own production, but also that of its repressor B. While the self-activation of A leads already to a bistable unit, the coupling with a negative feedback loop via B makes the unit frustrated. In the deterministic limit of infinitely many molecules, such a bistable frustrated unit is known to show excitable and oscillatory dynamics, depending on the maximum production rate of A which acts as a control parameter. We study this model in its fully stochastic version and we find oscillations even for parameters which in the deterministic limit are deeply in the fixed-point regime. The deeper we go into this regime, the more irregular these oscillations are, becoming finally random excitations whenever fluctuations allow the system to overcome the barrier for a large excursion in phase space. The fluctuations can no longer be fully treated as a perturbation. The smaller the system size (the number of molecules), the more frequent are these excitations. Therefore, stochasticity caused by demographic noise makes this unit even more flexible with respect to its oscillatory behaviour.Comment: 28 pages, 17 figure