A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense to be precised. In a first part, we generalize the Hausdorff dimension by defining a family of bi-Lipschitz invariants, called critical parameters, that measure largeness for infinite-dimensional metric spaces. Basic properties of these invariants are given, and they are estimated for a naturel set of spaces generalizing the usual Hilbert cube. In a second part, we estimate the value of these new invariants in the case of some Wasserstein spaces, as well as the dynamical complexity of push-forward maps. The lower bounds rely on several embedding results; for example we provide bi-Lipschitz embeddings of all powers of any space inside its Wasserstein space, with uniform bound and we prove that the Wasserstein space of a d-manifold has "power-exponential" critical parameter equal to d.Comment: v2 Largely expanded version, as reflected by the change of title; all part I on generalized Hausdorff dimension is new, as well as the embedding of Hilbert cubes into Wasserstein spaces. v3 modified according to the referee final remarks ; to appear in Journal of Topology and Analysi

The VLA Galactic Plane Survey

The VLA Galactic Plane Survey (VGPS) is a survey of HI and 21-cm continuum emission in the Galactic plane between longitude 18 degrees 67 degr. with latitude coverage from |b| < 1.3 degr. to |b| < 2.3 degr. The survey area was observed with the Very Large Array (VLA) in 990 pointings. Short-spacing information for the HI line emission was obtained by additional observations with the Green Bank Telescope (GBT). HI spectral line images are presented with a resolution of 1 arcmin x 1 arcmin x 1.56 km/s (FWHM) and rms noise of 2 K per 0.824 km/s channel. Continuum images made from channels without HI line emission have 1 arcmin (FWHM) resolution. VGPS images are compared with images from the Canadian Galactic Plane Survey (CGPS) and the Southern Galactic Plane Survey (SGPS). In general, the agreement between these surveys is impressive, considering the differences in instrumentation and image processing techniques used for each survey. The differences between VGPS and CGPS images are small, < 6 K (rms) in channels where the mean HI brightness temperature in the field exceeds 80 K. A similar degree of consistency is found between the VGPS and SGPS. The agreement we find between arcminute resolution surveys of the Galactic plane is a crucial step towards combining these surveys into a single uniform dataset which covers 90% of the Galactic disk: the International Galactic Plane Survey (IGPS). The VGPS data will be made available on the World Wide Web through the Canadian Astronomy Data Centre (CADC).Comment: Accepted for publication in The Astronomical Journal. 41 pages, 13 figures. For information on data release, colour images etc. see http://www.ras.ucalgary.ca/VGP

A Spitzer IRS Survey of NGC 1333: Insights into disk evolution from a very young cluster

We report on the {\lambda} = 5-36{\mu}m Spitzer Infrared Spectrograph spectra of 79 young stellar objects in the very young nearby cluster NGC 1333. NGC 1333's youth enables the study of early protoplanetary disk properties, such as the degree of settling as well as the formation of gaps and clearings. We construct spectral energy distributions (SEDs) using our IRS data as well as published photometry and classify our sample into SED classes. Using "extinction-free" spectral indices, we determine whether the disk, envelope, or photosphere dominates the spectrum. We analyze the dereddened spectra of objects which show disk dominated emission using spectral indices and properties of silicate features in order to study the vertical and radial structure of protoplanetary disks in NGC 1333. At least nine objects in our sample of NGC 1333 show signs of large (several AU) radial gaps or clearings in their inner disk. Disks with radial gaps in NGC 1333 show more-nearly pristine silicate dust than their radially continuous counterparts. We compare properties of disks in NGC 1333 to those in three other well studied regions, Taurus-Auriga, Ophiuchus and Chamaeleon I, and find no difference in their degree of sedimentation and dust processing.Comment: 67 pages, 20 figures, accepted to The Astrophysical Journal Supplement Serie

The Emergence of the Infrared transient VVV-WIT-06

We report the discovery of an enigmatic large-amplitude (ΔKs> 10.5 mag) transient event in near-IR data obtained by the VISTA Variables in the Via Lactea (VVV) ESO Public Survey. The object (designated VVV-WIT-06) is located at R.A. = 17:07:18.917, decl. = -39:06:26.45 (J2000), corresponding to Galactic coordinates l = 347.14539, b = 0.88522. It exhibits a clear eruption, peaking at Ks = 9 mag during 2013 July and fading to Ks ~ 16.5 in 2017. Our late near-IR spectra show post-outburst emission lines, including some broad emission lines (upward of {FWHM} ~ 3000 k/s). We estimate a total extinction of A_V=10--15 mag in the surrounding field, and no progenitor was observed in ZYJHKs images obtained during 2010-2012 (down to Ks> 18.5 mag). Subsequent deep near-IR imaging and spectroscopy, in concert with the available multiband photometry, indicate that VVV-WIT-06 may be either: (I) the closest Type I SN observed in about 400 years, (II) an exotic high-amplitude nova that would extend the known realm of such objects, or (III) a stellar merger. In all of these cases, VVV-WIT-06 is a fascinating and curious astrophysical target under any of the scenarios considered.Peer reviewe

Magnetic field driven metal-insulator phase transition in planar systems

A theory of the magnetic field driven (semi-)metal-insulator phase transition is developed for planar systems with a low density of carriers and a linear (i.e., relativistic like) dispersion relation for low energy quasiparticles. The general structure of the phase diagram of the theory with respect to the coupling constant, the chemical potential and temperature is derived in two cases, with and without an external magnetic field. The conductivity and resistivity as functions of temperature and magnetic field are studied in detail. An exact relation for the value of the "offset" magnetic field $B_c$, determining the threshold for the realization of the phase transition at zero temperature, is established. The theory is applied to the description of a recently observed phase transition induced by a magnetic field in highly oriented pyrolytic graphite.Comment: 22 pages, REVTeX, 16 figures. The version corresponding to that published in Phys.Rev.

Field Blue Stragglers and Related Mass Transfer Issues

This chapter contains my impressions and perspectives about the current state of knowledge about field blue stragglers (FBS) stars, drawn from an extensive literature that I searched. I conclude my review of issues that attend FBS and mass transfer, by a brief enumeration of a few mildly disquieting observational facts.Comment: Chapter 4, in Ecology of Blue Straggler Stars, H.M.J. Boffin, G. Carraro & G. Beccari (Eds), Astrophysics and Space Science Library, Springe

Mass Transfer by Stellar Wind

I review the process of mass transfer in a binary system through a stellar wind, with an emphasis on systems containing a red giant. I show how wind accretion in a binary system is different from the usually assumed Bondi-Hoyle approximation, first as far as the flow's structure is concerned, but most importantly, also for the mass accretion and specific angular momentum loss. This has important implications on the evolution of the orbital parameters. I also discuss the impact of wind accretion, on the chemical pollution and change in spin of the accreting star. The last section deals with observations and covers systems that most likely went through wind mass transfer: barium and related stars, symbiotic stars and central stars of planetary nebulae (CSPN). The most recent observations of cool CSPN progenitors of barium stars, as well as of carbon-rich post-common envelope systems, are providing unique constraints on the mass transfer processes.Comment: Chapter 7, in Ecology of Blue Straggler Stars, H.M.J. Boffin, G. Carraro & G. Beccari (Eds), Astrophysics and Space Science Library, Springe

Photoproduction of Long-Lived Holes and Electronic Processes in Intrinsic Electric Fields Seen through Photoinduced Absorption and Dichroism in Ca_3Ga_{2-x}Mn_xGe_3O_{12} Garnets

Long-lived photoinduced absorption and dichroism in the Ca_3Ga_{2-x}Mn_xGe_3O_{12} garnets with x < 0.06 were examined versus temperature and pumping intensity. Unusual features of the kinetics of photoinduced phenomena are indicative of the underlying electronic processes. The comparison with the case of Ca_3Mn_2Ge_3O_{12}, explored earlier by the authors, permits one to finally establish the main common mechanisms of photoinduced absorption and dichroism caused by random electric fields of photoproduced charges (hole polarons). The rate of their diffusion and relaxation through recombination is strongly influenced by the same fields, whose large statistical straggling is responsible for a broad continuous set of relaxation components (observed in the relaxation time range from 1 to about 1000 min). For Ca_3Ga_{2-x}Mn_xGe_3O_{12}, the time and temperature dependences of photoinduced absorption and dichroism bear a strong imprint of structure imperfection increasing with x.Comment: 20 pages, 10 figure

The Multiple Origin of Blue Straggler Stars: Theory vs. Observations

In this chapter we review the various suggested channels for the formation and evolution of blue straggler stars (BSSs) in different environments and their observational predictions. These include mass transfer during binary stellar evolution - case A/B/C and D (wind Roche-lobe overflow) mass transfer, stellar collisions during single and binary encounters in dense stellar cluster, and coupled dynamical and stellar evolution of triple systems. We also explore the importance of the BSS and binary dynamics in stellar clusters. We review the various observed properties of BSSs in different environments (halo and bulge BSSs, BSSs in globular clusters and BSSs in old open clusters), and compare the current observations with the theoretical predictions for BSS formation. We try to constrain the likely progenitors and processes that play a role in the formation of BSSs and their evolution. We find that multiple channels of BSS formation are likely to take part in producing the observed BSSs, and we point out the strengths and weaknesses of each the formation channel in respect to the observational constraints. Finally we point out directions to further explore the origin of BSS, and highlight eclipsing binary BSSs as important observational tool.Comment: Chapter 11, in Ecology of Blue Straggler Stars, H.M.J. Boffin, G. Carraro & G. Beccari (Eds), Astrophysics and Space Science Library, Springe