Existence and conditional energetic stability of solitary gravity-capillary water waves with constant vorticity

We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove the existence of a minimiser of the wave energy $\mathcal H$ subject to the constraint $\mathcal I=2\mu$, where $\mathcal I$ is the wave momentum and $0< \mu \ll 1$. Since $\mathcal H$ and $\mathcal I$ are both conserved quantities a standard argument asserts the stability of the set $D_\mu$ of minimisers: solutions starting near $D_\mu$ remain close to $D_\mu$ in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are described by solutions of a Korteweg-deVries equation (for strong surface tension) or a nonlinear Schr\"{o}dinger equation (for weak surface tension). We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of the appropriate model equation as $\mu \downarrow 0$Comment: Corrected version. To appear in Proceedings of the Royal Society of Edinburgh: Section

A dimension-breaking phenomenon for water waves with weak surface tension

It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence theory for three-dimensional periodically modulated solitary-wave solutions which have a solitary-wave profile in the direction of propagation and are periodic in the transverse direction; they emanate from the line solitary waves in a dimension-breaking bifurcation. In addition, it is shown that the line solitary waves are linearly unstable to long-wavelength transverse perturbations. The key to these results is a formulation of the water wave problem as an evolutionary system in which the transverse horizontal variable plays the role of time, a careful study of the purely imaginary spectrum of the operator obtained by linearising the evolutionary system at a line solitary wave, and an application of an infinite-dimensional version of the classical Lyapunov centre theorem.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-015-0941-

The mass-metallicity relation of local active galaxies

We systematically measure the gas-phase metallicities and the mass-metallicity relation of a large sample of local active galaxies for the first time. Observed emission-line fluxes from the Sloan Digital Sky Survey (SDSS) are compared to a four-dimensional grid of photoionization models using the Bayesian parameter estimation code NebulaBayes. For the first time we take into account arbitrary mixing between HII region and narrow-line region (NLR) emission, and the models are also varied with metallicity, ionization parameter in the NLR, and the gas pressure. The active galactic nucleus (AGN) oxygen abundance is found to increase by $\Delta {\rm O/H} \sim 0.1$ dex as a function of host galaxy stellar mass over the range $10.1 < \log M_* / M_\odot < 11.3$. We also measure the metallicity and ionization parameter of 231000 star-forming galaxies for comparison with the sample of 7670 Seyfert 2 galaxies. A systematic offset in oxygen abundance of 0.09 dex is observed between the mass-metallicity relations of the star-forming and active galaxies. We investigate potential causes of the offset, including sample selection and the treatment in the models of diffuse ionized gas, pressure, and ionization parameter. We cannot identify the major cause(s), but suspect contributions due to deficiencies in modeling the ionizing spectra and the treatment of dust physics. Optical diagnostic diagrams are presented with the star-forming and Seyfert data colored by the inferred oxygen abundance, ionization parameter and gas pressure, clearly illustrating the trends in these quantities.Comment: 12 pages, 4 figures and 1 table; accepted for publication in Ap

Stress-Energy Tensor for the Massless Spin 1/2 Field in Static Black Hole Spacetimes

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static non-rotating black holes, corresponding to the Schwarzschild, Reissner-Nordstrom and extreme Reissner-Nordstr\"om solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress-energy differs even in sign from the analytic approximation. For the Reissner-Nordstrom and extreme Reissner-Nordstrom solutions, divergences predicted by the analytic approximations are shown not to exist.Comment: 5 pages, 4 figures, additional discussio

Interrogating Seyferts with NebulaBayes: Spatially probing the narrow-line region radiation fields and chemical abundances

NebulaBayes is a new Bayesian code that implements a general method of comparing observed emission-line fluxes to photoionization model grids. The code enables us to extract robust, spatially resolved measurements of abundances in the extended narrow line regions (ENLRs) produced by Active Galactic Nuclei (AGN). We observe near-constant ionization parameters but steeply radially-declining pressures, which together imply that radiation pressure regulates the ENLR density structure on large scales. Our sample includes four `pure Seyfert' galaxies from the S7 survey that have extensive ENLRs. NGC2992 shows steep metallicity gradients from the nucleus into the ionization cones. An {\it inverse} metallicity gradient is observed in ESO138-G01, which we attribute to a recent gas inflow or minor merger. A uniformly high metallicity and hard ionizing continuum are inferred across the ENLR of Mrk573. Our analysis of IC5063 is likely affected by contamination from shock excitation, which appears to soften the inferred ionizing spectrum. The peak of the ionizing continuum E_peak is determined by the nuclear spectrum and the absorbing column between the nucleus and the ionized nebula. We cannot separate variation in this intrinsic E_peak from the effects of shock or HII region contamination, but E_peak measurements nevertheless give insights into ENLR excitation. We demonstrate the general applicability of NebulaBayes by analyzing a nuclear spectrum from the non-active galaxy NGC4691 using a HII region grid. The NLR and HII region model grids are provided with NebulaBayes for use by the astronomical community.Comment: Accepted for publication in ApJ; 29 pages with 10 figures and 3 table

Internal Dust Correction Factors for Star Formation Rates Derived for Dusty \HII Regions and Starburst Galaxies

Star formation rates in galaxies are frequently estimated using the Balmer line fluxes. However, these can be systematically underestimated because dust competes for the absorption of Lyman continuum photons in the ionized gas. Here we present theoretical correction factors in a simple analytic form. T These factors scale as the product of the ionization parameter, ${\cal U}$, and the nebular O/H abundance ratio, both of which can now be derived from the observation of bright nebular line ratios. The correction factors are only somewhat dependent upon the photoelectron production by grains, but are very sensitive to the presence of complex PAH-like carbonaceous molecules in the ionized gas, providing that these can survive in such an environment.Comment: 13 pages, 1 figures, Accepted for publication in ApJ. (Feb 1, 2003

Spatially Resolved Spitzer-IRS Spectroscopy of the Central Region of M82

We present high spatial resolution (~ 35 parsec) 5-38 um spectra of the central region of M82, taken with the Spitzer Infrared Spectrograph. From these spectra we determined the fluxes and equivalent widths of key diagnostic features, such as the [NeII]12.8um, [NeIII]15.5um, and H_2 S(1)17.03um lines, and the broad mid-IR polycyclic aromatic hydrocarbon (PAH) emission features in six representative regions and analysed the spatial distribution of these lines and their ratios across the central region. We find a good correlation of the dust extinction with the CO 1-0 emission. The PAH emission follows closely the ionization structure along the galactic disk. The observed variations of the diagnostic PAH ratios across M82 can be explained by extinction effects, within systematic uncertainties. The 16-18um PAH complex is very prominent, and its equivalent width is enhanced outwards from the galactic plane. We interpret this as a consequence of the variation of the UV radiation field. The EWs of the 11.3um PAH feature and the H_2 S(1) line correlate closely, and we conclude that shocks in the outflow regions have no measurable influence on the H_2 emission. The [NeIII]/[NeII] ratio is on average low at ~0.18, and shows little variations across the plane, indicating that the dominant stellar population is evolved (5 - 6 Myr) and well distributed. There is a slight increase of the ratio with distance from the galactic plane of M82 which we attribute to a decrease in gas density. Our observations indicate that the star formation rate has decreased significantly in the last 5 Myr. The quantities of dust and molecular gas in the central area of the galaxy argue against starvation and for negative feedback processes, observable through the strong extra-planar outflows.Comment: 15 pages, 12 figures, 3 tables, ApJ, emulateap

Cell Lineage Determination and the Control of Neuronal Identity in the Neural Crest

The diverse cell types of complex tissues such as the blood and the brain are generated from self-renewing, multipotent progenitors called stem cells (for reviews, see Hall and Watt 1989; Potten and Loeffler 1990; Morrison et al. 1997). These stem cells must generate progeny of different phenotypes, in the correct proportions, sequence, and location. The manner in which this is accomplished is not well understood. It is clear that the local microenvironment of stem cells has an important influence on their development, as do transcription factors that act within the cells. However, the manner in which such signals and transcription factors interact to control lineage determination by multipotent stem cells is poorly understood. To address this issue, it is necessary to both alter the expression of transcription factors in stem cells and challenge the cells by altering their environment to determine their state of lineage commitment. There are relatively few experimental systems in which such combined genetic and cell biological manipulation of stern cells are feasible

Making Change: Diffusion of Technological, Relational, and Cultural Innovation in the Newsroom

Diffusion of innovations theory typically has been applied to the spread of a particular technology or practice rather than the interplay of a cluster of innovations. This case study of a news company undergoing significant change seeks to offer a deeper understanding of multifaceted industry upheaval by considering the diffusion of three interdependent yet distinct changes. Findings suggest technological change faces the fewest hurdles, as journalists recognize the need to adapt their practices to newer capabilities. Changes to audience relationships face greater resistance, while responses to changes to the professional culture of journalism remain the most tepid

The dust energy balance in the edge-on spiral galaxy NGC 4565

We combine new dust continuum observations of the edge-on spiral galaxy NGC 4565 in all Herschel/SPIRE (250, 350, 500 micron) wavebands, obtained as part of the Herschel Reference Survey, and a large set of ancillary data (Spitzer, SDSS, GALEX) to analyze its dust energy balance. We fit a radiative transfer model for the stars and dust to the optical maps with the fitting algorithm FitSKIRT. To account for the observed UV and mid-infrared emission, this initial model was supplemented with both obscured and unobscured star-forming regions. Even though these star-forming complexes provide an additional heating source for the dust, the far-infrared/submillimeter emission long wards of 100 micron is underestimated by a factor of 3-4. This inconsistency in the dust energy budget of NGC 4565 suggests that a sizable fraction (two-thirds) of the total dust reservoir (Mdust ~ 2.9e+8 Msun) consists of a clumpy distribution with no associated young stellar sources. The distribution of those dense dust clouds would be in such a way that they remain unresolved in current far-infrared/submillimeter observations and hardly comtribute to the attenuation at optical wavelengths. More than two-thirds of the dust heating in NGC 4565 is powered by the old stellar population, with localized embedded sources supplying the remaining dust heating in NGC 4565. The results from this detailed dust energy balance study in NGC 4565 is consistent with that of similar analyses of other edge-on spirals.Comment: 16 pages, 7 figures, accepted for publication in MNRA