A stochastic model of congestion caused by speed differences

The authors study interaction on a two-lane road between the trips of two types of drivers who differ by their desired speeds. The difference in desired speeds causes congestion, because slow vehicles force fast vehicles to reduce their speed. Results for this type of congestion with respect to tolling are very different from those of the classic Pigou--Knight model, where the marginal external costs are an increasing function of the number of road users. In our model we find the opposite result: the marginal external costs of slow vehicles are a decreasing function of the number of slow vehicles. This leads to rather different policy recommendations

On the relationship between travel time and travel distance of commuters. Reported versus network travel data in the Netherlands

This paper gives a detailed empirical analysis of the relationships between different indicators of costs of commuting trips by car: difference as the crow flies, shortest travel time according to route planner, corresponding travel distance, and reported travel time. Reported travel times are usually rounded in multiples of five minutes. This calls for special statistical techniques. Ignoring the phenomenon of rounding leads to biased estimation results for shorter distances. Rather surprisingly, the distance as the crow flies and the network distance appear to be slightly better proxies of the reported travel time compared with the shortest network travel time as indicated by the route planner. We conclude that where actual driving times are missing in commuting research the other three indicators mentioned may be used as proxies, but that the following problems may emerge: actual travel times may be considerably higher than network times generated by route planners, and the average speed of trips increases considerably with distance, implying an overestimate of travel time for long distance commuters. The only personal feature that contributes significantly to variations in reported travel times is gender: women appear to drive at lower average speeds according to our data. As indicated in the paper this may be explained by the differences in the car types of male and female drivers (females drive older and smaller cars) as well as higher numbers of stops/trip chaining among women. A concise analysis is carried out for carpoolers. Car-pooling leads to an increase in travel time of some 17% compared with solo drivers covering the same distance. In the case of car poolers, the above mentioned measures appear to be very poor proxies for the actual commuting times

A stochastic model of congestion caused by speed differences

We study interaction between the trips of two types of drivers on a two-lane road who differ by their desired speeds. The difference in desired speeds causes congestion, because slow drivers force fast drivers to reduce their speed. An interesting aspect of this type of congestion is that results with respect to tolling are very different from those of the classical Pigou-Knight model where the marginal external costs are an increasing function of the number of road users. In our model we find the opposite result: the marginal external costs of slow drivers are a decreasing function of the number of slow drivers. This leads to rather different policy recommendations. In many situations either laissez faire (no tolling or traffic restrictions) or prohibition of slow drivers to enter the road is in practice (i.e. taking into account costs associated with tolling) the optimal policy. This conclusion hardly changes if the possibility of overtaking is introduced into the model

The initial conditions of observed star clusters - I. Method description and validation

We have coupled a fast, parametrized star cluster evolution code to a Markov Chain Monte Carlo code to determine the distribution of probable initial conditions of observed star clusters, which may serve as a starting point for future $N$-body calculations. In this paper we validate our method by applying it to a set of star clusters which have been studied in detail numerically with $N$-body simulations and Monte Carlo methods: the Galactic globular clusters M4, 47 Tucanae, NGC 6397, M22, $\omega$ Centauri, Palomar 14 and Palomar 4, the Galactic open cluster M67, and the M31 globular cluster G1. For each cluster we derive a distribution of initial conditions that, after evolution up to the cluster's current age, evolves to the currently observed conditions. We find that there is a connection between the morphology of the distribution of initial conditions and the dynamical age of a cluster and that a degeneracy in the initial half-mass radius towards small radii is present for clusters which have undergone a core collapse during their evolution. We find that the results of our method are in agreement with $N$-body and Monte Carlo studies for the majority of clusters. We conclude that our method is able to find reliable posteriors for the determined initial mass and half-mass radius for observed star clusters, and thus forms an suitable starting point for modeling an observed cluster\rq{}s evolution.Comment: 39 pages, 28 figures, accepted for publication in MNRA

The formation of the solar system

The solar system started to form about 4.56 Gyr ago and despite the long intervening time span, there still exist several clues about its formation. The three major sources for this information are meteorites, the present solar system structure and the planet-forming systems around young stars. In this introduction we give an overview of the current understanding of the solar system formation from all these different research fields. This includes the question of the lifetime of the solar protoplanetary disc, the different stages of planet formation, their duration, and their relative importance. We consider whether meteorite evidence and observations of protoplanetary discs point in the same direction. This will tell us whether our solar system had a typical formation history or an exceptional one. There are also many indications that the solar system formed as part of a star cluster. Here we examine the types of cluster the Sun could have formed in, especially whether its stellar density was at any stage high enough to influence the properties of today's solar system. The likelihood of identifying siblings of the Sun is discussed. Finally, the possible dynamical evolution of the solar system since its formation and its future are considered.Comment: 36 pages, 7 figures, invited review in Physica Script

The Evolution of Globular Clusters in the Galaxy

We investigate the evolution of globular clusters using N-body calculations and anisotropic Fokker-Planck (FP) calculations. The models include a mass spectrum, mass loss due to stellar evolution, and the tidal field of the parent galaxy. Recent N-body calculations have revealed a serious discrepancy between the results of N-body calculations and isotropic FP calculations. The main reason for the discrepancy is an oversimplified treatment of the tidal field employed in the isotropic FP models. In this paper we perform a series of calculations with anisotropic FP models with a better treatment of the tidal boundary and compare these with N-body calculations. The new tidal boundary condition in our FP model includes one free parameter. We find that a single value of this parameter gives satisfactory agreement between the N-body and FP models over a wide range of initial conditions. Using the improved FP model, we carry out an extensive survey of the evolution of globular clusters over a wide range of initial conditions varying the slope of the mass function, the central concentration, and the relaxation time. The evolution of clusters is followed up to the moment of core collapse or the disruption of the clusters in the tidal field of the parent galaxy. In general, our model clusters, calculated with the anisotropic FP model with the improved treatment for the tidal boundary, live longer than isotropic models. The difference in the lifetime between the isotropic and anisotropic models is particularly large when the effect of mass loss via stellar evolution is rather significant. On the other hand the difference is small for relaxation- dominated clusters which initially have steep mass functions and high central concentrations.Comment: 36 pages, 11 figures, LaTeX; added figures and tables; accepted by Ap

A dozen colliding wind X-ray binaries in the star cluster R136 in the 30Doradus region

We analyzed archival Chandra X-ray observations of the central portion of the 30 Doradus region in the Large Magellanic Cloud. The image contains 20 X-ray point sources with luminosities between $5 \times 10^{32}$ and $2 \times 10^{35}$ erg s$^{-1}$ (0.2 -- 3.5 keV). A dozen sources have bright WN Wolf-Rayet or spectral type O stars as optical counterparts. Nine of these are within $\sim 3.4$pc of R136, the central star cluster of NGC2070. We derive an empirical relation between the X-ray luminosity and the parameters for the stellar wind of the optical counterpart. The relation gives good agreement for known colliding wind binaries in the Milky Way Galaxy and for the identified X-ray sources in NGC2070. We conclude that probably all identified X-ray sources in NGC2070 are colliding wind binaries and that they are not associated with compact objects. This conclusion contradicts Wang (1995) who argued, using ROSAT data, that two earlier discovered X-ray sources are accreting black-hole binaries. Five of the eighteen brightest stars in R136 are not visible in our X-ray observations. These stars are either single, have low mass companions or very wide orbits. The resulting binary fraction among early type stars is then unusually high (at least 70%).Comment: 23 pages, To appear in August in Ap

Broad-band gravitational-wave pulses from binary neutron stars in eccentric orbits

Maximum gravitational wave emission from binary stars in eccentric orbits occurs near the periastron passage. We show that for a stationary distribution of binary neutron stars in the Galaxy, several high-eccentricity systems with orbital periods in the range from tens of minutes to several days should exist that emit broad gravitational-wave pulses in the frequency range 1-100 mHz. The space interferometer LISA could register the pulsed signal from these system at a signal-to-noise ratio level $S/N>5\sqrt{5}$ in the frequency range $\sim 10^{-3}-10^{-1}$ Hz during one-year observational time. Some detection algorithms for such a signal are discussed.Comment: 17 pages, LATEX, 3 figures, Astronomy Letters, 2002, in press; typos corrected, refference adde

A Neutron Star with a Massive Progenitor in Westerlund 1

We report the discovery of an X-ray pulsar in the young, massive Galactic star cluster Westerlund 1. We detected a coherent signal from the brightest X-ray source in the cluster, CXO J164710.2-455216, during two Chandra observations on 2005 May 22 and June 18. The period of the pulsar is 10.6107(1) s. We place an upper limit to the period derivative of Pdot<2e-10 s/s, which implies that the spin-down luminosity is Edot<3e33 erg/s. The X-ray luminosity of the pulsar is L_X = 3(+10,-2)e33 (D/5 kpc)^2 erg/s, and the spectrum can be described by a kT = 0.61+/-0.02 keV blackbody with a radius of R_bb = 0.27+/-0.03 (D/5 kpc}) km. Deep infrared observations reveal no counterpart with K1 Msun. Taken together, the properties of the pulsar indicate that it is a magnetar. The rarity of slow X-ray pulsars and the position of CXO J164710.2-455216 only 1.6' from the core of Westerlund 1 indicates that it is a member of the cluster with >99.97% confidence. Westerlund 1 contains 07V stars with initial masses M_i=35 Msun and >50 post-main-sequence stars that indicate the cluster is 4+/-1 Myr old. Therefore, the progenitor to this pulsar had an initial mass M_i>40 Msun. This is the most secure result among a handful of observational limits to the masses of the progenitors to neutron stars.Comment: 4 pages, 5 figures. Final version to match ApJL (added one figure since v2