Nonlinear characterizations of stochastic completeness

We prove that conservation of probability for the free heat semigroup on a Riemannian manifold M (namely stochastic completeness), hence a linear property, is equivalent to uniqueness of positive, bounded solutions to nonlinear evolution equations of fast diffusion type on M of the form ut=Δϕ(u), ϕ being an arbitrary concave, increasing, positive function, regular outside the origin and with ϕ(0)=0. Either property is also equivalent to nonexistence of nonnegative, nontrivial, bounded solutions to the elliptic equation ΔW=ϕ−1(W), with ϕ as above. As a consequence, explicit criteria for uniqueness or nonuniqueness of bounded solutions to fast diffusion-type equations on manifolds are given, these being the first results on such issues

Cosmological parameters from strong gravitational lensing and stellar dynamics in elliptical galaxies

We show how the combination of observations related to strong gravitational lensing and stellar dynamics in ellipticals offers a new way to measure the cosmological matter and dark-energy density parameters. A gravitational lensing estimate of the mass enclosed inside the Einstein circle can be obtained by measuring the Einstein angle, once the critical density of the system is known. A model-dependent dynamical estimate of this mass can also be obtained by measuring the central velocity dispersion of the stellar component. By assuming the well-tested homologous 1/r^{2} profile for the total density distribution in the lens elliptical galaxies, these two mass measurements can be properly compared. Thus, a relation between the Einstein angle and the central stellar velocity dispersion is derived, and the cosmological matter and the dark-energy density parameters can be estimated from this. We determined the accuracy of the cosmological parameter estimates by means of simulations that include realistic measurement uncertainties on the relevant quantities. Interestingly, the expected constraints on the cosmological parameter plane are complementary to those coming from other observational techniques. Then, we applied the method to the data sets of the Sloan Lens ACS and the Lenses Structure and Dynamics Surveys, and showed that the concordance value between 0.7 and 0.8 for the dark-energy density parameter is included in our 99% confidence regions. The small number of lenses available to date prevents us from precisely determining the cosmological parameters, but it still proves the feasibility of the method. When applied to samples made of hundreds of lenses that are expected to become available from forthcoming surveys, this technique will be an important tool for measuring the geometry of the Universe.Comment: 11 pages, 9 figures, accepted by Astronomy & Astrophysic

Interdisciplinary study for knowledge and dating of the San Francesco convent in Stampace, Cagliari – Italy (XIII-XXI century)

The Franciscan monastery, situated in the historic center of Cagliari (Sardinia), was founded in the thirteenth century, and transformed during the later centuries, up to the present day. The complexity of the case and the lack of objective data about its history has led us to carry out an interdisciplinary inquiry, in order to achieve a better knowledge of the building, preliminary for the drafting of a restoration project that respects all the signs that the time left. Starting from a deep examination of the indirect sources, turned out to be incomplete, the investigation continued with the execution of a survey with laser scanner and with the characterization of materials and related diseases of degradation. For the laser scanner survey we used a Faro Focus 3D, versatile and lightweight instrument that allows to perform scans with high speed point acquisition and high accuracy. For data elaboration we used the JRC 3D Reconstructor Software by the Gexcel srl. The characterization of the materials was performed on a reasoned sampling of natural and artificial materials, referring to masonry, interstitial mortars and plasters, carried out at strategic points, representative of the various phases of the construction. The samples were studied through mineralogical-petrographic methods with instrumental techniques for the analysis of component materials (OM, X-Ray diffraction). The data obtained, crossed with the results of the reconstruction of historical maps, of the examination of masonry techniques and of the analysis of pattern elements (arches, vaults, decorative elements), have facilitated stratigraphic analysis and helped to advance chronological reasoned hypothesis referring to the building. Besides, an interdisciplinary approach for the study of cultural heritage is very important to define a proper restoration and conservation intervention

Numerical simulations challenged on the prediction of massive subhalo abundance in galaxy clusters: the case of Abell 2142

In this Letter we compare the abundance of member galaxies of a rich, nearby ($z=0.09$) galaxy cluster, Abell 2142, with that of halos of comparable virial mass extracted from sets of state-of-the-art numerical simulations, both collisionless at different resolutions and with the inclusion of baryonic physics in the form of cooling, star formation, and feedback by active galactic nuclei. We also use two semi-analytical models to account for the presence of orphan galaxies. The photometric and spectroscopic information, taken from the Sloan Digital Sky Survey Data Release 12 (SDSS DR12) database, allows us to estimate the stellar velocity dispersion of member galaxies of Abell 2142. This quantity is used as proxy for the total mass of secure cluster members and is properly compared with that of subhalos in simulations. We find that simulated halos have a statistically significant ($\gtrsim 7$ sigma confidence level) smaller amount of massive (circular velocity above $200\,{\rm km\, s^{-1}}$) subhalos, even before accounting for the possible incompleteness of observations. These results corroborate the findings from a recent strong lensing study of the Hubble Frontier Fields galaxy cluster MACS J0416 \citep{grillo2015} and suggest that the observed difference is already present at the level of dark matter (DM) subhalos and is not solved by introducing baryonic physics. A deeper understanding of this discrepancy between observations and simulations will provide valuable insights into the impact of the physical properties of DM particles and the effect of baryons on the formation and evolution of cosmological structures.Comment: 8 pages, 2 figures. Modified to match the version published in ApJ

On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-

Massive Star cluster formation under the microscope at z=6

We report on a superdense star-forming region with an effective radius (R_e) smaller than 13 pc identified at z=6.143 and showing a star-formation rate density \Sigma_SFR~1000 Msun/yr/kpc2 (or conservatively >300 Msun/yr/kpc2). Such a dense region is detected with S/N>40 hosted by a dwarf extending over 440 pc, dubbed D1 (Vanzella et al. 2017b). D1 is magnified by a factor 17.4+/-5.0 behind the Hubble Frontier Field galaxy cluster MACS~J0416 and elongated tangentially by a factor 13.2+/-4.0 (including the systematic errors). The lens model accurately reproduces the positions of the confirmed multiple images with a r.m.s. of 0.35", and the tangential stretch is well depicted by a giant multiply-imaged Lya arc. D1 is part of an interacting star-forming complex extending over 800 pc. The SED-fitting, the very blue ultraviolet slope (\beta ~ -2.5, F(\lambda) ~ \lambda^\beta) and the prominent Lya emission of the stellar complex imply that very young (< 10-100 Myr), moderately dust-attenuated (E(B-V)<0.15) stellar populations are present and organised in dense subcomponents. We argue that D1 (with a stellar mass of 2 x 10^7 Msun) might contain a young massive star cluster of M < 10^6 Msun and Muv~-15.6 (or m_uv=31.1), confined within a region of 13 pc, and not dissimilar from some local super star clusters (SSCs). The ultraviolet appearance of D1 is also consistent with a simulated local dwarf hosting a SSC placed at z=6 and lensed back to the observer. This compact system fits into some popular globular cluster formation scenarios. We show that future high spatial resolution imaging (e.g., E-ELT/MAORY-MICADO and VLT/MAVIS) will allow us to spatially resolve light profiles of 2-8 pc.Comment: 21 pages, 14 figures, 1 table, MNRAS accepte

The Mn site in Mn-doped Ga-As nanowires: an EXAFS study

We present an EXAFS study of the Mn atomic environment in Mn-doped GaAs nanowires. Mn doping has been obtained either via the diffusion of the Mn used as seed for the nanowire growth or by providing Mn during the growth of Au-induced wires. As a general finding, we observe that Mn forms chemical bonds with As but is not incorporated in a substitutional site. In Mn-induced GaAs wires, Mn is mostly found bonded to As in a rather disordered environment and with a stretched bond length, reminiscent of that exhibited by MnAs phases. In Au-seeded nanowires, along with stretched Mn-As coordination we have found the presence of Mn in a Mn-Au intermetallic compound.Comment: This is an author-created, un-copyedited version of an article accepted for publication in Semiconductor Science and Technology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version is available online at doi:10.1088/0268-1242/27/8/08500