Synchronized flow and wide moving jams from balanced vehicular traffic

Recently we proposed an extension to the traffic model of Aw, Rascle and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse $\lambda$ shape of the fundamental diagram of traffic flow. In the current work we analyze the steady state solutions of the new model and their stability properties. In addition to the equilibrium flow curve the trivial steady state solutions form two additional branches in the flow-density diagram. We show that the characteristic structure excludes parts of these branches resulting in the reverse $\lambda$ shape of the flow-density relation. The upper branch is metastable against the formation of synchronized flow for intermediate densities and unstable for high densities, whereas the lower branch is unstable for intermediate densities and metastable for high densities. Moreover, the model can reproduce the typical speed of the downstream front of wide moving jams. It further reproduces a constant outflow from wide moving jams, which is far below the maximum free flow. Applying the model to simulate traffic flow at a bottleneck we observe a general pattern with wide moving jams traveling through the bottleneck.Comment: 10 pages, 12 figure

Correlations between total cell concentration, total adenosine tri-phosphate concentration and heterotrophic plate counts during microbial monitoring of drinking water

The general microbial quality of drinking water is normally monitored by heterotrophic plate counts (HPC). This method has been used for more than 100 years and is recommended in drinking water guidelines. However, the HPC method is handicapped because it is time-consuming and restricted to culturable bacteria. Recently, rapid and accurate detection methods have emerged, such as adenosine tri-phosphate (ATP) measurements to assess microbial activity in drinking water, and flow cytometry (FCM) to determine the total cell concentration (TCC). It is necessary and important for drinking water quality control to understand the relationships among the conventional and new methods. In the current study, all three methods were applied to 200 drinking water samples obtained from two local buildings connected to the same distribution system. Samples were taken both on normal working days and weekends, and the correlations between the different microbiological parameters were determined. TCC in the samples ranged from 0.37–5.61×10<sup>5</sup> cells/ml, and two clusters, the so-called high (HNA) and low (LNA) nucleic acid bacterial groups, were clearly distinguished. The results showed that the rapid determination methods (i.e., FCM and ATP) correlated well (<i>R</i><sup>2</sup>=0.69), but only a weak correlation (<i>R</i><sup>2</sup>=0.31) was observed between the rapid methods and conventional HPC data. With respect to drinking water monitoring, both FCM and ATP measurements were confirmed to be useful and complimentary parameters for rapid assessing of drinking water microbial quality

Simulating the dynamics of relativistic stars via a light-cone approach

We present new numerical algorithms for the coupled Einstein-perfect fluid system in axisymmetry. Our framework uses a foliation based on a family of light cones, emanating from a regular center, and terminating at future null infinity. This coordinate system is well adapted to the study of the dynamical spacetimes associated with isolated relativistic compact objects such as neutron stars. In particular, the approach allows the unambiguous extraction of gravitational waves at future null infinity and avoids spurious outer boundary reflections. The code can accurately maintain long-term stability of polytropic equilibrium models of relativistic stars. We demonstrate global energy conservation in a strongly perturbed neutron star spacetime, for which the total energy radiated away by gravitational waves corresponds to a significant fraction of the Bondi mass. As a first application we present results in the study of pulsations of axisymmetric relativistic stars, extracting the frequencies of the different fluid modes in fully relativistic evolutions of the Einstein-perfect fluid system and making a first comparison between the gravitational news function and the predicted wave using the approximations of the quadrupole formula

Axisymmetric core collapse simulations using characteristic numerical relativity

We present results from axisymmetric stellar core collapse simulations in general relativity. Our hydrodynamics code has proved robust and accurate enough to allow for a detailed analysis of the global dynamics of the collapse. Contrary to traditional approaches based on the 3+1 formulation of the gravitational field equations, our framework uses a foliation based on a family of outgoing light cones, emanating from a regular center, and terminating at future null infinity. Such a coordinate system is well adapted to the study of interesting dynamical spacetimes in relativistic astrophysics such as stellar core collapse and neutron star formation. Perhaps most importantly this procedure allows for the unambiguous extraction of gravitational waves at future null infinity without any approximation, along with the commonly used quadrupole formalism for the gravitational wave extraction. Our results concerning the gravitational wave signals show noticeable disagreement when those are extracted by computing the Bondi news at future null infinity on the one hand and by using the quadrupole formula on the other hand. We have strong indication that for our setup the quadrupole formula on the null cone does not lead to physical gravitational wave signals. The Bondi gravitational wave signals extracted at infinity show typical oscillation frequencies of about 0.5 kHz.Comment: 17 pages, 18 figures, submitted to Phys. Rev.

First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations

We prescribe a choice of 18 variables in all that casts the equations of the fully nonlinear characteristic formulation of general relativity in first--order quasi-linear canonical form. At the analytical level, a formulation of this type allows us to make concrete statements about existence of solutions. In addition, it offers concrete advantages for numerical applications as it now becomes possible to incorporate advanced numerical techniques for first order systems, which had thus far not been applicable to the characteristic problem of the Einstein equations, as well as in providing a framework for a unified treatment of the vacuum and matter problems. This is of relevance to the accurate simulation of gravitational waves emitted in astrophysical scenarios such as stellar core collapse.Comment: revtex4, 7 pages, text and references added, typos corrected, to appear in Phys. Rev.

Bondian frames to couple matter with radiation

A study is presented for the non linear evolution of a self gravitating distribution of matter coupled to a massless scalar field. The characteristic formulation for numerical relativity is used to follow the evolution by a sequence of light cones open to the future. Bondian frames are used to endow physical meaning to the matter variables and to the massless scalar field. Asymptotic approaches to the origin and to infinity are achieved; at the boundary surface interior and exterior solutions are matched guaranteeing the Darmois--Lichnerowicz conditions. To show how the scheme works some numerical models are discussed. We exemplify evolving scalar waves on the following fixed backgrounds: A) an atmosphere between the boundary surface of an incompressible mixtured fluid and infinity; B) a polytropic distribution matched to a Schwarzschild exterior; C) a Schwarzschild- Schwarzschild spacetime. The conservation of energy, the Newman--Penrose constant preservation and other expected features are observed.Comment: 20 pages, 6 figures; to appear in General Relativity and Gravitatio

Gravitational waves from axisymmetrically oscillating neutron stars in general relativistic simulations

Gravitational waves from oscillating neutron stars in axial symmetry are studied performing numerical simulations in full general relativity. Neutron stars are modeled by a polytropic equation of state for simplicity. A gauge-invariant wave extraction method as well as a quadrupole formula are adopted for computation of gravitational waves. It is found that the gauge-invariant variables systematically contain numerical errors generated near the outer boundaries in the present axisymmetric computation. We clarify their origin, and illustrate it possible to eliminate the dominant part of the systematic errors. The best corrected waveforms for oscillating and rotating stars currently contain errors of magnitude $\sim 10^{-3}$ in the local wave zone. Comparing the waveforms obtained by the gauge-invariant technique with those by the quadrupole formula, it is shown that the quadrupole formula yields approximate gravitational waveforms besides a systematic underestimation of the amplitude of $O(M/R)$ where $M$ and $R$ denote the mass and the radius of neutron stars. However, the wave phase and modulation of the amplitude can be computed accurately. This indicates that the quadrupole formula is a useful tool for studying gravitational waves from rotating stellar core collapse to a neutron star in fully general relativistic simulations. Properties of the gravitational waveforms from the oscillating and rigidly rotating neutron stars are also addressed paying attention to the oscillation associated with fundamental modes

Numerical Evolution of axisymmetric vacuum spacetimes: a code based on the Galerkin method

We present the first numerical code based on the Galerkin and Collocation methods to integrate the field equations of the Bondi problem. The Galerkin method like all spectral methods provide high accuracy with moderate computational effort. Several numerical tests were performed to verify the issues of convergence, stability and accuracy with promising results. This code opens up several possibilities of applications in more general scenarios for studying the evolution of spacetimes with gravitational waves.Comment: 11 pages, 6 figures. To appear in Classical and Quantum Gravit

ATLAS Tracking Event Data Model

In this report the event data model (EDM) relevant for tracking in the ATLAS experiment is presented. The core component of the tracking EDM is a common track object which is suited to describe tracks in the innermost tracking sub-detectors and in the muon detectors in offline as well as online reconstruction. The design of the EDM was driven by a demand for modularity and extensibility while taking into account the different requirements of the clients. The structure of the track object and the representation of the tracking-relevant information are described in detail