On a functional satisfying a weak Palais-Smale condition

In this paper we study a quasilinear elliptic problem whose functional satisfies a weak version of the well known Palais-Smale condition. An existence result is proved under general assumptions on the nonlinearities.Comment: 18 page

Nonlinear Klein-Gordon-Maxwell systems with Neumann boundary conditions on a Riemannian manifold with boundary

Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 with smooth n-1 dimensional boundary. We search the positive solutions of the singularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumann boundary conditions or for the singularly perturbed Klein Gordon Maxwell system with mixed Dirichlet Neumann homogeneous boundary conditions. We prove that stable critical points of the mean curvature of the boundary generates solutions when the perturbation parameter is sufficiently small.Comment: arXiv admin note: text overlap with arXiv:1410.884

Cosmic Evolution of Stellar Disk Truncations: From z~1 to the Local Universe

We have conducted the largest systematic search so far for stellar disk truncations in disk-like galaxies at intermediate redshift (z<1.1), using the Great Observatories Origins Deep Survey South (GOODS-S) data from the Hubble Space Telescope - ACS. Focusing on Type II galaxies (i.e. downbending profiles) we explore whether the position of the break in the rest-frame B-band radial surface brightness profile (a direct estimator of the extent of the disk where most of the massive star formation is taking place), evolves with time. The number of galaxies under analysis (238 of a total of 505) is an order of magnitude larger than in previous studies. For the first time, we probe the evolution of the break radius for a given stellar mass (a parameter well suited to address evolutionary studies). Our results suggest that, for a given stellar mass, the radial position of the break has increased with cosmic time by a factor 1.3+/-0.1 between z~1 and z~0. This is in agreement with a moderate inside-out growth of the disk galaxies in the last ~8 Gyr. In the same period of time, the surface brightness level in the rest-frame B-band at which the break takes place has increased by 3.3+/-0.2 mag/arcsec^2 (a decrease in brightness by a factor of 20.9+/-4.2). We have explored the distribution of the scale lengths of the disks in the region inside the break, and how this parameter relates to the break radius. We also present results of the statistical analysis of profiles of artificial galaxies, to assess the reliability of our results.Comment: 22 pages, 14 figures, accepted for publication in ApJ. Figures 1, 3 and 6 have somehow downgraded resolution to match uploading requirement

Radial Distribution of Near-UV Flux in Disc Galaxies in the range 0<z<1

(Abridged) The goal of this paper is to quantify the changes on the SF distribution within the disc galaxies in the last ~8 Gyr. We use as a proxy for the SF radial profile the Near-UV surface brightness distributions, allowing suitably for extinction. We compare the effective radii (R_eff) and concentration of the flux distribution in the rest-frame Near-UV for a sample of 270 galaxies in the range 0<z<1. This radial distribution is compared to that measured in the rest-frame B-band, which traces older stellar populations. The analysis is performed using deep, high resolution, multi-band images from GALEX, SDSS, and HST/ACS - GOODS-South. The relation R_eff(NUV)- M* suffers a moderate change between z~1 and z~0: at a fixed stellar mass of 1E10 M_sun, galaxies increase their effective radii by a factor 1.18+/-0.06. Median profiles in NUV show signs of truncation at R~R_eff, and median colour profiles (NUV-B) show a minimum (a "bluest" point) also around R~1-1.5 R_eff. The distributions of NUV flux are more compact at z~1 than nowadays, in terms of the fraction of flux enclosed in a specific radius (in kpc). Our results indicate that the SF surface density has decreased dramatically in discs since z~1, and this decline has been more intense in the central parts (<~R_eff) of the galaxies. In addition, our data suggest that the bulges/pseudo-bulges have grown in surface brightness with regard to the discs since z~1.Comment: 26 pages, 21 figures, accepted for publication in Astronomy & Astrophysics on March 21s

Anti-truncated stellar light profiles in the outer regions of STAGES spiral galaxies: bulge or disc related?

We present a comparison of azimuthally averaged radial surface brightness mu(r) profiles and analytical bulge-disc decompositions (de Vaucouleurs, r^(1/4) bulge plus exponential disc) for spiral galaxies using Hubble Space Telescope/Advanced Camera for Surveys V-band imaging from the Space Telescope A901/2 Galaxy Evolution Survey (STAGES). In the established classification scheme, antitruncated mu(r) profiles (Type III) have a broken exponential disc with a shallower region beyond the break radius r_brk. The excess light at large radii (r > r_brk) can either be caused by an outer exponential disc (Type III-d) or an extended spheroidal component (Type III-s). Using our comparisons, we determine the contribution of bulge light at r > r_brk for a large sample of 78 (barred/unbarred, Sa-Sd) spiral galaxies with outer disc antitruncations (mu_brk > 24 mag arcsec^-2). In the majority of cases (~85 per cent), evidence indicates that excess light at r > r_brk is related to an outer shallow disc (Type III-d). Here, the contribution of bulge light at r > r_brk is either negligible (~70 per cent) or too little to explain the antitruncation (~15 per cent). However in the latter cases, bulge light can affect the measured disc properties (e.g. mu_brk, outer scalelength). In the remaining cases (~15 per cent), light at r > r_brk is dominated by the bulge (Type III-s). Here, for most cases the bulge profile dominates at all radii and only occasionally (3 galaxies, ~5 per cent) extends beyond that of a dominant disc and explains the excess light at r > r_brk. We thus conclude that in the vast majority of cases antitruncated outer discs cannot be explained by bulge light and thus remain a pure disc phenomenon.Comment: Accepted to MNRA

Hybrid fibroin/polyurethane small-diameter vascular grafts: from fabrication to in vivo preliminary assessment

To address the need of alternatives to autologous vessels for small-calibre vascular applications (e.g. cardiac surgery), a bio-hybrid semi-degradable material composed of silk fibroin (SF) and polyurethane (Silkothane (R)) was herein used to fabricate very small-calibre grafts (o(in) = 1.5 mm) via electrospinning. Bio-hybrid grafts were in vitro characterized in terms of morphology and mechanical behaviour, and compared to similar grafts of pure SF. Similarly, two native vessels from a rodent model (abdominal aorta and vena cava) were harvested and characterized. Preliminary implants were performed on Lewis rats to confirm the suitability of Silkothane (R) grafts for small-calibre applications, specifically as aortic insertion and femoral shunt. The manufacturing process generated pliable grafts consisting of a randomized fibrous mesh and exhibiting similar geometrical features to rat aortas. Both Silkothane (R) and pure SF grafts showed radial compliances in the range from 1.37 +/- 0.86 to 1.88 +/- 1.01% 10(-2) mmHg(-1), lower than that of native vessels. The Silkothane (R) small-calibre devices were also implanted in rats demonstrating to be adequate for vascular applications; all the treated rats survived the surgery for three months after implantation, and 16 rats out of 17 (94%) still showed blood flow inside the graft at sacrifice. The obtained results lay the basis for a deeper investigation of the interaction between the Silkothane (R) graft and the implant site, which may deal with further analysis on the potentialities in terms of degradability and tissue formation, on longer time-points

On the stability of standing waves of Klein-Gordon equations in a semiclassical regime

We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.Comment: 9 page

The environmental dependence of the structure of outer galactic discs in STAGES spiral galaxies

We present an analysis of V-band radial surface brightness profiles for spiral galaxies from the field and cluster environments using Hubble Space Telescope/Advanced Camera for Surveys imaging and data from the Space Telescope A901/2 Galaxy Evolution Survey (STAGES). We use a large sample of ~330 face-on to intermediately inclined spiral galaxies and assess the effect of the galaxy environment on the azimuthally averaged radial surface brightness mu profiles for each galaxy in the outer stellar disc (24 < mu < 26.5 mag per sq arcsec). For galaxies with a purely exponential outer disc (~50 per cent), we determine the significance of an environmental dependence on the outer disc scalelength h_out. For galaxies with a broken exponential in their outer disc, either down-bending (truncation, ~10 per cent) or up-bending (anti-truncation, ~40 per cent), we measure the strength T (outer-to-inner scalelength ratio, log_10(h_out/h_in) of the mu breaks and determine the significance of an environmental dependence on break strength T. Surprisingly, we find no evidence to suggest any such environmental dependence on either outer disc scalelength h_out or break strength T, implying that the galaxy environment is not affecting the stellar distribution in the outer stellar disc. We also find that for galaxies with small effective radii (r_e < 3 kpc) there is a lack of outer disc truncations in both the field and cluster environments. Our results suggest that the stellar distribution in the outer disc of spiral galaxies is not significantly affected by the galaxy environment.Comment: Accepted to MNRAS. Appendix A available at http://www.nottingham.ac.uk/~ppxdtm/STAGES_profiles_appendix.pd