Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

Counts and Sizes of Galaxies in the Hubble Deep Field - South: Implications for the Next Generation Space Telescope

Science objectives for the Next Generation Space Telescope (NGST) include a large component of galaxy surveys, both imaging and spectroscopy. The Hubble Deep Field datasets include the deepest observations ever made in the ultraviolet, optical and near infrared, reaching depths comparable to that expected for NGST spectroscopy. We present the source counts, galaxy sizes and isophotal filling factors of the HDF-South images. The observed integrated galaxy counts reach >500 galaxies per square arcminute at AB<30. We extend these counts to faint levels in the infrared using models. The trend previously seen that fainter galaxies are smaller, continues to AB=29 in the high resolution HDF-S STIS image, where galaxies have a typical half-light radius of 0.1 arcseconds. Extensive Monte Carlo simulations show that the small measured sizes are not due to selection effects until >29mag. Using the HDF-S NICMOS image, we show that galaxies are smaller in the near infrared than they are in the optical. We analyze the isophotal filling factor of the HDF-S STIS image, and show that this image is mostly empty sky even at the limits of galaxy detection, a conclusion we expect to hold true for NGST spectroscopy. At the surface brightness limits expected for NGST imaging, however, about a quarter of the sky is occupied by the outer isophotes of AB<30 galaxies. We discuss the implications of these data on several design concepts of the NGST near-infrared spectrograph. We compare the effects of resolution and the confusion limit of various designs, as well as the multiplexing advantages of either multi-object or full-field spectroscopy. We argue that the optimal choice for NGST spectroscopy of high redshift galaxies is a multi-object spectrograph (MOS) with target selection by a micro electro mechanical system (MEMS) device.Comment: 27 pages including 10 figures, accepted for publication in the Astronomical Journal, June 2000, abridged abstrac

Synchrotron Emission from Hot Accretion Flows and the Cosmic Microwave Background Anisotropy

Current estimates of number counts of radio sources in the frequency range where the most sensitive Cosmic Microwave Background (CMB) experiments are carried out significantly under-represent sources with strongly inverted spectra. Hot accretion flows around supermassive black holes in the nuclei of nearby galaxies are expected to produce inverted radio spectra by thermal synchrotron emission. We calculate the temperature fluctuations and power spectra of these sources in the Planck Surveyor 30 GHz energy channel, where their emission is expected to peak. We find that their potential contribution is generally comparable to the instrumental noise, and approaches the CMB anisotropy level at small angular scales. Forthcoming CMB missions, which will provide a large statistical sample of inverted-spectra sources, will be crucial for determining the distribution of hot accretion flows in nearby quiescent galactic nuclei. Detection of these sources in different frequency channels will help constrain their spectral characteristics, hence their physical properties.Comment: 10 pages, 4 figures, accepted for publication in Ap

Heating the bubbly gas of galaxy clusters with weak shocks and sound waves

Using hydrodynamic simulations and a technique to extract the rotational component of the velocity field, we show how bubbles of relativistic gas inflated by AGN jets in galaxy clusters act as a catalyst, transforming the energy carried by sound and shock waves to heat. The energy is stored in a vortex field around the bubbles which can subsequently be dissipated. The efficiency of this process is set mainly by the fraction of the cluster volume filled by (sub-)kpc scale filaments and bubbles of relativistic plasma.Comment: Accepted for publication in ApJ Letters after minor wording changes, 4 figures, 4 page

Multiwavelength study of Cygnus A III. Evidence for relic lobe plasma

We study the particle energy distribution in the cocoon surrounding Cygnus A, using radio images between 151 MHz and 15 GHz and a 200 ks Chandra ACIS-I image. We show that the excess low frequency emission in the the lobe further from Earth cannot be explained by absorption or excess adiabatic expansion of the lobe or a combination of both. We show that this excess emission is consistent with emission from a relic counterlobe and a relic counterjet that are being re-energized by compression from the current lobe. We detect hints of a relic hotspot at the end of the relic X-ray jet in the more distant lobe. We do not detect relic emission in the lobe nearer to Earth as expected from light travel-time effects assuming intrinsic symmetry. We determine that the duration of the previous jet activity phase was slightly less than that of the current jet-active phase. Further, we explain some features observed at 5 and 15 GHz as due to the presence of a relic jet.Comment: Accepted for publication with MNRAS, 10 pages with 10 figure

Shocks and sonic booms in the intracluster medium: X-ray shells and radio galaxy activity

Motivated by hydrodynamic simulations, we discuss the X-ray appearance of radio galaxies embedded in the intracluster medium (ICM) of a galaxy cluster. We distinguish three regimes. In the early life of a powerful source, the entire radio cocoon is expanding supersonically and hence drives a strong shock into the ICM. Eventually, the sides of the cocoon become subsonic and the ICM is disturbed by the sonic booms of the jet's working surface. In both of these regimes, X-ray observations would find an X-ray shell. In the strong shock regime, this shell will be hot and relatively thin. However, in the weak shock (sonic-boom) regime, the shell will be approximately the same temperature as the undisturbed ICM. If a cooling flow is present, the observed shell may even be cooler than the undisturbed ICM due to the lifting of cooler material into the shell from the inner (cooler) regions of the cluster. In the third and final regime, the cocoon has collapsed and no well-defined X-ray shell will be seen. We discuss ways of estimating the power and age of the source once its regime of behavior has been determined.Comment: 4 pages, submitted for publication in Astrophysical Journal. Full paper (including figure) can be obtained from http://rocinante.Colorado.EDU/~chris/papers/xray_hydro.p

Chemical and physical properties of bulk aerosols within four sectors observed during TRACE-P

Chemical and physical aerosol data collected on the DC-8 during TRACE-P were grouped into four sectors based on back trajectories. The four sectors represent long-range transport from the west (WSW), regional circulation over the western Pacific and Southeast Asia (SE Asia), polluted transport from northern Asia with substantial sea salt at low altitudes (NNW) and a substantial amount of dust (Channel). WSW has generally low mixing ratios at both middle and high altitudes, with the bulk of the aerosol mass due to non-sea-salt water-soluble inorganic species. Low altitude SE Asia also has low mean mixing ratios in general, with the majority of the aerosol mass comprised of non-sea-salts, however, soot is also relatively important in this region. NNW had the highest mean sea salt mixing ratios, with the aerosol mass at low altitudes (\u3c2 km) evenly divided between sea salts, non-sea-salts, and dust. The highest mean mixing ratios of water-soluble ions and soot were observed at the lowest altitudes (\u3c2 km) in the Channel sector. The bulk of the aerosol mass exported from Asia emanates from Channel at both low and midaltitudes, due to the prevalence of dust compared to other sectors. Number densities show enhanced fine particles for Channel and NNW, while their volume distributions are enhanced due to sea salt and dust. Low-altitude Channel exhibits the highest condensation nuclei (CN) number densities along with enhanced scattering coefficients, compared to the other sectors. At midaltitudes (2–7 km), low mean CN number densities coupled with a high proportion of nonvolatile particles (≥65%) observed in polluted sectors (Channel and NNW) are attributed to wet scavenging which removes hygroscopic CN particles. Low single scatter albedo in SE Asia reflects enhanced soot

Warped discs and the directional stability of jets in Active Galactic Nuclei

Warped accretion discs in Active Galactic Nuclei (AGN) exert a torque on the black hole that tends to align the rotation axis with the angular momentum of the outer disc. We compute the magnitude of this torque by solving numerically for the steady state shape of the warped disc, and verify that the analytic solution of Scheuer and Feiler (1996) provides an excellent approximation. We generalise these results for discs with strong warps and arbitrary surface density profiles, and calculate the timescale on which the black hole becomes aligned with the angular momentum in the outer disc. For massive holes and accretion rates of the order of the Eddington limit the alignment timescale is always short (less than a Myr), so that jets accelerated from the inner disc region provide a prompt tracer of the angular momentum of gas at large radii in the disc. Longer timescales are predicted for low luminosity systems, depending on the degree of anisotropy in the disc's hydrodynamic response to shear and warp, and for the final decay of modest warps at large radii in the disc that are potentially observable via VLBI. We discuss the implications of this for the inferred accretion history of those Active Galactic Nuclei whose jet directions appear to be stable over long timescales. The large energy deposition rate at modest disc radii during rapid realignment episodes should make such objects transiently bright at optical and infrared wavelengths.Comment: MNRAS, in press. Revised to match accepted version, with one new figure showing alignment timescale as a function of black hole mas

High glucose exposure promotes proliferation and in vivo network formation of adipose-tissue-derived microvascular fragments

High glucose concentrations have been shown to activate endothelial cells and promote angiogenesis. In the present study, it was investigated whether high glucose concentrations could improve the vascularisation capacity of adipose-tissue-derived microvascular fragments (ad-MVF). Ad-MVF were isolated from the epididymal fat pads of donor mice and cultivated for 24 h in University of Wisconsin (UW) solution supplemented with vehicle or 30 mM glucose. Protein expression, morphology, viability and proliferation of the cultivated ad-MVF were analysed by means of proteome profiler mouse angiogenesis array, scanning electron microscopy and immunohistochemistry. Additional cultivated ad-MVF were seeded on to collagen-glycosaminoglycan scaffolds to study their in vivo vascularisation capacity in the dorsal skinfold chamber model by intravital fluorescence microscopy, histology and immunohistochemistry. In vitro, high glucose exposure changed the protein expression pattern of ad-MVF with endoglin, interleukin (IL)-1β and monocyte chemoattractant protein (MCP)-1 as the most up-regulated pro-angiogenic factors. Moreover, high glucose exposure induced the formation of nanopores in the ad-MVF wall. In addition, ad-MVF contained significantly larger numbers of proliferating endothelial and perivascular cells while exhibiting a comparable number of apoptotic cells when compared to vehicle-treated controls. In vivo, scaffolds seeded with high-glucose-exposed ad-MVF exhibited an improved vascularisation and tissue incorporation. These findings demonstrated that the exposure of cultivated ad-MVF to high glucose concentrations is a promising approach to improve their in vivo performance as vascularisation units for tissue engineering and regenerative medicine

Kinematic Age Estimates for 4 Compact Symmetric Objects from the Pearson-Readhead Survey

Based on multi-epoch observations at 15 and 43 GHz with the Very Long Baseline Array (VLBA) we detect significant angular expansions between the two hot spots of 4 Compact Symmetric Objects (CSOs). From these relative motions we derive kinematic ages of between 300 and 1200 years for the radio emission. These ages lend support to the idea that CSOs are produced in a recent phase of activity. These observations also allow us to study the evolution of the hot spots dynamically in individual sources. In all 4 sources the hot spots are separating along the source axis, but in 1031+567 the tip of one hot spot appears to be moving almost orthogonally to the source axis. Jet components, seen in 3 of the 4 sources observed, are found to be moving relativistically outward from the central engines towards the more slowly moving hot spots.Comment: in press at ApJ for v. 541 Oct. 1, 2000, 23 page LaTeX document includes 6 postscript figure