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

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.

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

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

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

A remarkable record of the genus Pseudolucia from Bolivia (Lepidoptera: Lycaenidae)

The occurrence of a taxon morphologically close to Pseudolucia jujuyensis Bálint, Eisele & Johnson, 2000 is recorded in dry habitats of Torotoro Dinosaurs National Park, Potosí, Bolivia. This record remarkably extends the range of Pseudolucia by almost 800 km northwards in austral South America. Five specimens were available for examinations, hence wing-pattern, genitalia and mitochondrial DNA were analysed. However, the taxonomy of the specimens could not be satisfactorily resolved in relation to P. jujuyensis, for which only the holotype exists. The females use Cuscuta for ovipositing, what is supposedly the larval host – a remarkable character of the chilensis species group of Pseudolucia, which includes P. jujuyensis. On the basis of molecular markers it was revealed that the Torotoro population is the sister to the rest of the chilensis species group, which together are the clade sister to the rest of the genus

Scalar field induced oscillations of neutron stars and gravitational collapse

We study the interaction of massless scalar fields with self-gravitating neutron stars by means of fully dynamic numerical simulations of the Einstein-Klein-Gordon perfect fluid system. Our investigation is restricted to spherical symmetry and the neutron stars are approximated by relativistic polytropes. Studying the nonlinear dynamics of isolated neutron stars is very effectively performed within the characteristic formulation of general relativity, in which the spacetime is foliated by a family of outgoing light cones. We are able to compactify the entire spacetime on a computational grid and simultaneously impose natural radiative boundary conditions and extract accurate radiative signals. We study the transfer of energy from the scalar field to the fluid star. We find, in particular, that depending on the compactness of the neutron star model, the scalar wave forces the neutron star either to oscillate in its radial modes of pulsation or to undergo gravitational collapse to a black hole on a dynamical timescale. The radiative signal, read off at future null infinity, shows quasi-normal oscillations before the setting of a late time power-law tail.Comment: 12 pages, 13 figures, submitted to Phys. Rev.