An analytical connection between temporal and spatio-temporal growth rates in linear stability analysis

We derive an exact formula for the complex frequency in spatio-temporal stability analysis that is valid for arbitrary complex wave numbers. The usefulness of the formula lies in the fact that it depends only on purely temporal quantities, which are easily calculated. We apply the formula to two model dispersion relations: the linearized complex Ginzburg--Landau equation, and a model of wake instability. In the first case, a quadratic truncation of the exact formula applies; in the second, the same quadratic truncation yields an estimate of the parameter values at which the transition to absolute instability occurs; the error in the estimate decreases upon increasing the order of the truncation. We outline ways in which the formula can be used to characterize stability results obtained from purely numerical calculations, and point to a further application in global stability analyses.Comment: 36 pages, 16 figures; Article has been tweaked and reduced in size but essential features remain the same; Supplementary material (16 pages) is also include

Absolute linear instability in laminar and turbulent gas/liquid two-layer channel flow

We study two-phase stratified flow where the bottom layer is a thin laminar liquid and the upper layer is a fully-developed gas flow. The gas flow can be laminar or turbulent. To determine the boundary between convective and absolute instability, we use Orr--Sommerfeld stability theory, and a combination of linear modal analysis and ray analysis. For turbulent gas flow, and for the density ratio r=1000, we find large regions of parameter space that produce absolute instability. These parameter regimes involve viscosity ratios of direct relevance to oil/gas flows. If, instead, the gas layer is laminar, absolute instability persists for the density ratio r=1000, although the convective/absolute stability boundary occurs at a viscosity ratio that is an order of magnitude smaller than in the turbulent case. Two further unstable temporal modes exist in both the laminar and the turbulent cases, one of which can exclude absolute instability. We compare our results with an experimentally-determined flow-regime map, and discuss the potential application of the present method to non-linear analyses.Comment: 33 pages, 20 figure

Nonlinear dynamics of phase separation in thin films

We present a long-wavelength approximation to the Navier-Stokes Cahn-Hilliard equations to describe phase separation in thin films. The equations we derive underscore the coupled behaviour of free-surface variations and phase separation. We introduce a repulsive substrate-film interaction potential and analyse the resulting fourth-order equations by constructing a Lyapunov functional, which, combined with the regularizing repulsive potential, gives rise to a positive lower bound for the free-surface height. The value of this lower bound depends on the parameters of the problem, a result which we compare with numerical simulations. While the theoretical lower bound is an obstacle to the rupture of a film that initially is everywhere of finite height, it is not sufficiently sharp to represent accurately the parametric dependence of the observed dips or `valleys' in free-surface height. We observe these valleys across zones where the concentration of the binary mixture changes sharply, indicating the formation of bubbles. Finally, we carry out numerical simulations without the repulsive interaction, and find that the film ruptures in finite time, while the gradient of the Cahn--Hilliard concentration develops a singularity.Comment: 26 pages, 20 figures, PDFLaTeX with RevTeX4 macros. A thorough analysis of the equations is presented in arXiv:0805.103

The Pain in Spain: Examining Andalusia\u27s Youth Unemployment Crisis

This paper examines the youth unemployment crisis in the autonomous community of Andalusia by assessing employment policies that are currently in place. Since the economic crisis nearly a decade ago, there has been very little change in the high rates of Andalusian youth unemployment, which as a whole, has left the region, the country and the European Union at risk due to a lack of inefficient policies. By utilizing anecdotal evidence paired with facts and figures released by the European Union, recommendations to adjust employment policies such as the Youth Guarantee and PRAEM are given in order to shine a light on the areas that are lacking effectiveness when it comes to solving the problem at hand rather than allowing it to continue

The VLT-FLAMES Survey of Massive Stars: Observations centered on the Magellanic Cloud clusters NGC 330, NGC 346, NGC 2004, and the N11 region

We present new observations of 470 stars using the Fibre Large Array Multi-Element Spectrograph (FLAMES) instrument in fields centered on the clusters NGC 330 and NGC 346 in the Small Magellanic Cloud (SMC), and NGC 2004 and the N11 region in the Large Magellanic Cloud (LMC). A further 14 stars were observed in the N11 and NGC 330 fields using the Ultraviolet and Visual Echelle Spectrograph (UVES) for a separate programme. Spectral classifications and stellar radial velocities are given for each target, with careful attention to checks for binarity. In particular we have investigated previously unexplored regions around the central LH9/LH10 complex of N11, finding ~25 new O-type stars from our spectroscopy. We have observed a relatively large number of Be-type stars that display permitted Fe II emission lines. These are primarily not in the cluster cores and appear to be associated with classical Be-type stars, rather than pre main-sequence objects. The presence of the Fe II emission, as compared to the equivalent width of H$\alpha$, is not obviously dependent on metallicity. We have also explored the relative fraction of Be- to normal B-type stars in the field-regions near to NGC 330 and NGC 2004, finding no strong evidence of a trend with metallicity when compared to Galactic results. A consequence of service observations is that we have reasonable time-sampling in three of our FLAMES fields. We find lower limits to the binary fraction of O- and early B-type stars of 23 to 36%. One of our targets (NGC346-013) is especially interesting with a massive, apparently hotter, less luminous secondary component.Comment: 35 pages, 17 figures (some reduced in size). Replacement copy, includes an erratum on the final page. A copy with full res. & embedded figures is at http://www.roe.ac.uk/~cje/flamesMC.ps.g

Terminal velocities of luminous, early-type SMC stars

Ultraviolet spectra from the Space Telescope Imaging Spectrograph (STIS) are used to determine terminal velocities for 11 O and B-type giants and supergiants in the Small Magellanic Cloud (SMC) from the Si IV and C IV resonance lines. Using archival data from observations with the Goddard High-Resolution Spectrograph and the International Ultraviolet Explorer telescope, terminal velocities are obtained for a further five B-type supergiants. We discuss the metallicity dependence of stellar terminal velocities, finding no evidence for a significant scaling between Galactic and SMC metallicities for Teff < 30,000 K, consistent with the predictions of radiation driven wind theory for supergiant stars. A comparison of the $v_\infty / v_{esc}$ ratio between the SMC and Galactic samples, while consistent with the above statement, emphasizes that the uncertainties in the distances to galactic O-stars are a serious obstacle to a detailed comparison with theory. For the SMC sample there is considerable scatter in this ratio at a given effective temperature, perhaps indicative of uncertainties in stellar masses.Comment: 28 pages, 8 figures, accepted by ApJ; minor revisions prior to acceptanc

Associations between fibrin D-dimer, markers of inflammation, incident self-reported mobility limitation, and all-cause mortality in older men

Objectives&lt;p&gt;&lt;/p&gt; To examine the independent relationships between fibrin D-dimer, interleukin 6 (IL-6), C-reactive protein (CRP), and fibrinogen and incident mobility limitation and mortality.&lt;p&gt;&lt;/p&gt; Design&lt;p&gt;&lt;/p&gt; Prospective.&lt;p&gt;&lt;/p&gt; Setting&lt;p&gt;&lt;/p&gt; General practice in 24 British towns.&lt;p&gt;&lt;/p&gt; Participants&lt;p&gt;&lt;/p&gt; Men aged 60 to 79 without prevalent heart failure followed up for an average of 11.5 years (N = 3,925).&lt;p&gt;&lt;/p&gt; Measurements&lt;p&gt;&lt;/p&gt; All-cause mortality (n = 1,286) and self-reported mobility disability obtained at examination in 1998 to 2000 and in a postal questionnaire 3 to 5 years later in 2003.&lt;p&gt;&lt;/p&gt; Results&lt;p&gt;&lt;/p&gt; High D-dimer (top vs lowest tertile: adjusted odds ratio (aOR) = 1.46, 95% confidence interval = 1.02–2.05) and IL-6 (aOR = 1.43, 95% CI = 1.01–2.02) levels (but not CRP or fibrinogen) were associated with greater incident mobility limitation after adjustment for confounders and prevalent disease status. IL-6, CRP, fibrinogen, and D-dimer were significantly associated with total mortality after adjustment for confounders. Only D-dimer and IL-6 predicted total mortality independent of each other and the other biomarkers. The adjusted hazard ratio (aHR) was 1.16 (95% CI = 1.10–1.22) for a standard deviation increase in log D-dimer and 1.10 (95% CI = 1.04–1.18) for a standard deviation increase in log IL-6. D-dimer was independently related to vascular and nonvascular mortality, and IL-6 was independently related to vascular mortality. Risks of mobility limitation and mortality were greatest in those with a combination of high D-dimer and IL-6 levels.&lt;p&gt;&lt;/p&gt; Conclusion&lt;p&gt;&lt;/p&gt; D-dimer and IL-6 are associated with risk of mobility limitation and mortality in older men without heart failure. The findings suggest that coagulation leads to functional decline and mortality s that inflammation does not explain