Uncertainty in Soft Temporal Constraint Problems:A General Framework and Controllability Algorithms forThe Fuzzy Case

In real-life temporal scenarios, uncertainty and preferences are often essential and coexisting aspects. We present a formalism where quantitative temporal constraints with both preferences and uncertainty can be defined. We show how three classical notions of controllability (that is, strong, weak, and dynamic), which have been developed for uncertain temporal problems, can be generalized to handle preferences as well. After defining this general framework, we focus on problems where preferences follow the fuzzy approach, and with properties that assure tractability. For such problems, we propose algorithms to check the presence of the controllability properties. In particular, we show that in such a setting dealing simultaneously with preferences and uncertainty does not increase the complexity of controllability testing. We also develop a dynamic execution algorithm, of polynomial complexity, that produces temporal plans under uncertainty that are optimal with respect to fuzzy preferences

Turbulence transition and the edge of chaos in pipe flow

The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the \emph{edge of chaos} which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in (Skufca et al, Phys. Rev. Lett. {\bf 96}, 174101 (2006)) we show that superimposed on an overall $1/\Re$-scaling predicted and studied previously there are small, non-monotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics.Comment: 4 pages, 5 figure

An implicit method for radiative transfer with the diffusion approximation in SPH

An implicit method for radiative transfer in SPH is described. The diffusion approximation is used, and the hydrodynamic calculations are performed by a fully three--dimensional SPH code. Instead of the energy equation of state for an ideal gas, various energy states and the dissociation of hydrogen molecules are considered in the energy calculation for a more realistic temperature and pressure determination. In order to test the implicit code, we have performed non--isothermal collapse simulations of a centrally condensed cloud, and have compared our results with those of finite difference calculations performed by MB93. The results produced by the two completely different numerical methods agree well with each other.Comment: 25 pages, 9 figure

Resolving the Formation of Protogalaxies. III. Feedback from the First Stars

The first stars form in dark matter halos of masses ~10^6 M_sun as suggested by an increasing number of numerical simulations. Radiation feedback from these stars expels most of the gas from their shallow potential well of their surrounding dark matter halos. We use cosmological adaptive mesh refinement simulations that include self-consistent Population III star formation and feedback to examine the properties of assembling early dwarf galaxies. Accurate radiative transport is modeled with adaptive ray tracing. We include supernova explosions and follow the metal enrichment of the intergalactic medium. The calculations focus on the formation of several dwarf galaxies and their progenitors. In these halos, baryon fractions in 10^8 solar mass halos decrease by a factor of 2 with stellar feedback and by a factor of 3 with supernova explosions. We find that radiation feedback and supernova explosions increase gaseous spin parameters up to a factor of 4 and vary with time. Stellar feedback, supernova explosions, and H_2 cooling create a complex, multi-phase interstellar medium whose densities and temperatures can span up to 6 orders of magnitude at a given radius. The pair-instability supernovae of Population III stars alone enrich the halos with virial temperatures of 10^4 K to approximately 10^{-3} of solar metallicity. We find that 40% of the heavy elements resides in the intergalactic medium (IGM) at the end of our calculations. The highest metallicity gas exists in supernova remnants and very dilute regions of the IGM.Comment: 15 pages, 16 figures, accepted to ApJ. Many changes, including estimates of metal line cooling. High resolution images and movies available at http://www.slac.stanford.edu/~jwise/research/PGalaxies3

The HII Region KR 140: Spontaneous Formation of a High Mass Star

We have used a multiwavelength data set from the Canadian Galactic Plane Survey (CGPS) to study the Galactic HII region KR 140, both on the scale of the nebula itself and in the context of the star forming activity in the nearby W3/W4/W5 complex of molecular clouds and HII regions. From both radio and infrared data we have found a covering factor of about 0.5 for KR 140 and we interpret the nebula as a bowl-shaped region viewed close to face on. Extinction measurements place the region on the near side of its parent molecular cloud. The nebula is kept ionized by one O8.5 V(e) star, VES 735, which is less than a few million years old. CO data show that VES 735 has disrupted much of the original molecular cloud for which the estimated mass and density are about 5000 $M_{\odot}$ and 100 cm$^{-3}$, respectively. KR 140 is isolated from the nearest star forming activity, in W3. Our data suggest that KR 140 is an example of spontaneous (i.e., non-triggered) formation of, unusually, a high mass star.Comment: 46 pages; includes 15 figures; accepted by the Ap

Massive stars and the energy balance of the interstellar medium. II. The 35 solar mass star and a solution to the "missing wind problem"

We continue our numerical analysis of the morphological and energetic influence of massive stars on their ambient interstellar medium for a 35 solar mass star that evolves from the main sequence through red supergiant and Wolf-Rayet phases, until it ultimately explodes as a supernova. We find that structure formation in the circumstellar gas during the early main-sequence evolution occurs as in the 60 solar mass case but is much less pronounced because of the lower mechanical wind luminosity of the star. Since on the other hand the shell-like structure of the HII region is largely preserved, effects that rely on this symmetry become more important. At the end of the stellar lifetime 1% of the energy released as Lyman continuum radiation and stellar wind has been transferred to the circumstellar gas. From this fraction 10% is kinetic energy of bulk motion, 36% is thermal energy, and the remaining 54% is ionization energy of hydrogen. The sweeping up of the slow red supergiant wind by the fast Wolf-Rayet wind produces remarkable morphological structures and emission signatures, which are compared with existing observations of the Wolf-Rayet bubble S308. Our model reproduces the correct order of magnitude of observed X-ray luminosity, the temperature of the emitting plasma as well as the limb brightening of the intensity profile. This is remarkable, because current analytical and numerical models of Wolf-Rayet bubbles fail to consistently explain these features. A key result is that almost the entire X-ray emission in this stage comes from the shell of red supergiant wind swept up by the shocked Wolf-Rayet wind rather than from the shocked Wolf-Rayet wind itself as hitherto assumed and modeled. This offers a possible solution to what is called the ``missing wind problem'' of Wolf-Rayet bubbles.Comment: 52 pages, 20 figures, 2 tables, accepted for publication in the Astrophysical Journa

A Keck High Resolution Spectroscopic Study of the Orion Nebula Proplyds

We present the results of spectroscopy of four bright proplyds in the Orion Nebula obtained at a velocity resolution of 6 km/s. After careful isolation of the proplyd spectra from the confusing nebular radiation, the emission line profiles are compared with those predicted by realistic dynamic/photoionization models of the objects. The spectral line widths show a clear correlation with ionization potential, which is consistent with the free expansion of a transonic, ionization-stratified, photoevaporating flow. Fitting models of such a flow simultaneously to our spectra and HST emission line imaging provides direct measurements of the proplyd size, ionized density and outflow velocity. These measurements confirm that the ionization front in the proplyds is approximately D-critical and provide the most accurate and robust estimate to date of the proplyd mass loss rate. Values of 0.7E-6 to 1.5E-6 Msun/year are found for our spectroscopic sample, although extrapolating our results to a larger sample of proplyds implies that 0.4E-6 Msun/year is more typical of the proplyds as a whole. In view of the reported limits on the masses of the circumstellar disks within the proplyds, the length of time that they can have been exposed to ionizing radiation should not greatly exceed 10,000 years - a factor of 30 less than the mean age of the proplyd stars. We review the various mechanisms that have been proposed to explain this situation, and conclude that none can plausibly work unless the disk masses are revised upwards by a substantial amount.Comment: 23 pages, 8 figures, uses emulateapj.sty, accepted for publication in The Astronomical Journal (scheduled November 1999

HST/WFPC2 and VLT/ISAAC observations of PROPLYDS in the giant HII region NGC 3603

We report the discovery of three proplyd-like structures in the giant HII region NGC 3603. The emission nebulae are clearly resolved in narrow-band and broad-band HST/WFPC2 observations in the optical and broad-band VLT/ISAAC observations in the near-infrared. All three nebulae are tadpole shaped, with the bright ionization front at the head facing the central cluster and a fainter ionization front around the tail pointing away from the cluster. Typical sizes are 6,000 A.U. x 20,000 A.U. The nebulae share the overall morphology of the proplyds (``PROto PLanetarY DiskS'') in Orion, but are 20 to 30 times larger in size. Additional faint filaments located between the nebulae and the central ionizing cluster can be interpreted as bow shocks resulting from the interaction of the fast winds from the high-mass stars in the cluster with the evaporation flow from the proplyds. The striking similarity of the tadpole shaped emission nebulae in NGC 3603 to the proplyds in Orion suggests that the physical structure of both types of objects might be the same. We present 2D radiation hydrodynamical simulations of an externally illuminated star-disk-envelope system, which was still in its main accretion phase when first exposed to ionizing radiation from the central cluster. The simulations reproduce the overall morphology of the proplyds in NGC 3603 very well, but also indicate that mass-loss rates of up to 10^-5 Mo/yr are required in order to explain the size of the proplyds. (abbreviated)Comment: 10 pages, 4 Postscript figures, uses emulateapj.sty and psfig.tex. Astronomical Journal, in press (January 2000 issue

Radioactive Probes of the Supernova-Contaminated Solar Nebula: Evidence that the Sun was Born in a Cluster

We construct a simple model for radioisotopic enrichment of the protosolar nebula by injection from a nearby supernova, based on the inverse square law for ejecta dispersion. We find that the presolar radioisotopes abundances (i.e., in solar masses) demand a nearby supernova: its distance can be no larger than 66 times the size of the protosolar nebula, at a 90% confidence level, assuming 1 solar mass of protosolar material. The relevant size of the nebula depends on its state of evolution at the time of radioactivity injection. In one scenario, a collection of low-mass stars, including our sun, formed in a group or cluster with an intermediate- to high-mass star that ended its life as a supernova while our sun was still a protostar, a starless core, or perhaps a diffuse cloud. Using recent observations of protostars to estimate the size of the protosolar nebula constrains the distance of the supernova at 0.02 to 1.6 pc. The supernova distance limit is consistent with the scales of low-mass stars formation around one or more massive stars, but it is closer than expected were the sun formed in an isolated, solitary state. Consequently, if any presolar radioactivities originated via supernova injection, we must conclude that our sun was a member of such a group or cluster that has since dispersed, and thus that solar system formation should be understood in this context. In addition, we show that the timescale from explosion to the creation of small bodies was on the order of 1.8 Myr (formal 90% confidence range of 0 to 2.2 Myr), and thus the temporal choreography from supernova ejecta to meteorites is important. Finally, we can not distinguish between progenitor masses from 15 to 25 solar masses in the nucleosynthesis models; however, the 20 solar mass model is somewhat preferred.Comment: ApJ accepted, 19 pages, 3 figure