Flat 3-webs of degree one on the projective plane

The aim of this work is to study global $3$-webs with vanishing curvature. We wish to investigate degree $3$ foliations for which their dual web is flat. The main ingredient is the Legendre transform, which is an avatar of classical projective duality in the realm of differential equations. We find a characterization of degree $3$ foliations whose Legendre transform are webs with zero curvature.Comment: 14 page

Cosmic magnetic fields and dark energy in extended electromagnetism

We discuss an extended version of electromagnetism in which the usual gauge fixing term is promoted into a physical contribution that introduces a new scalar state in the theory. This new state can be generated from vacuum quantum fluctuations during an inflationary era and, on super-Hubble scales, gives rise to an effective cosmological constant. The value of such a cosmological constant coincides with the one inferred from observations as long as inflation took place at the electroweak scale. On the other hand, the new state also generates an effective electric charge density on sub-Hubble scales that produces both vorticity and magnetic fields with coherent lengths as large as the present Hubble horizon.Comment: 4 pages, 2 figures. Contribution to the proceedings of Spanish Relativity Meeting 2010, Granada, Spain, 6-10 September 201

Spinoza: la simultaneidad de los tres géneros del conocimiento.

Sin resume

A Structural Comparison of Ordered and Non-Ordered Ion Doped Silicate Bioactive Glasses

One of the key benefits of sol-gel-derived glasses is the presence of a mesoporous structure and the resulting increase in surface area. This enhancement in textural properties has a significant e ect on the physicochemical properties of the materials. In this context the aim of this study was to investigate how sol-gel synthesis parameters can influence the textural and structural properties of mesoporous silicate glasses. We report the synthesis and characterization of metal ion doped sol-gel derived glasses with di erent dopants in the presence or absence of a surfactant (Pluronic P123) used as structure-directing templating agent. Characterization was done by several methods. Using a structure directing agent led to larger surface areas and highly ordered mesoporous structures. The chemical structure of the non-ordered glasses was modified to a larger extent than the one of the ordered glasses due to increased incorporation of dopant ions into the glass network. The results will help to further understand how the properties of sol-gel glasses can be controlled by incorporation of metal dopants, in conjunction with control over the textural properties, and will be important to optimize the properties of sol-gel glasses for specific applications, e.g., drug delivery, bone regeneration, wound healing, and antibacterial materials.European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 643050, project “HyMedPoly

Metastability of non-reversible mean-field Potts model with three spins

We examine a non-reversible, mean-field Potts model with three spins on a set with $N\uparrow\infty$ points. Without an external field, there are three critical temperatures and five different metastable regimes. The analysis can be extended by a perturbative argument to the case of small external fields. We illustrate the case of large external fields with some phenomena which are not present in the absence of external field.Comment: 34 pages, 12 figure

Dissecting a hot molecular core: The case of G31.41+0.31

We made a detailed observational analysis of a well known hot molecular core lying in the high-mass star-forming region G31.41+0.31. This core is believed to contain deeply embedded massive stars and presents a velocity gradient that has been interpreted either as rotation or as expansion, depending on the authors. Our aim was to shed light on this question and possibly prepare the ground for higher resolution ALMA observations which could directly detect circumstellar disks around the embedded massive stars. Observations at sub-arcsecond resolution were performed with the Submillimeter Array in methyl cyanide, a typical hot molecular core tracer, and 12CO and 13CO, well known outflow tracers. We also obtained sensitive continuum maps at 1.3 mm. Our findings confirm the existence of a sharp velocity gradient across the core, but cannot confirm the existence of a bipolar outflow perpendicular to it. The improved angular resolution and sampling of the uv plane allow us to attain higher quality channel maps of the CH3CN lines with respect to previous studies and thus significantly improve our knowledge of the structure and kinematics of the hot molecular core. While no conclusive argument can rule out any of the two interpretations (rotation or expansion) proposed to explain the velocity gradient observed in the core, in our opinion the observational evidence collected so far indicates the rotating toroid as the most likely scenario. The outflow hypothesis appears less plausible, because the dynamical time scale is too short compared to that needed to form species such as CH3CN, and the mass loss and momentum rates estimated from our measurements appear too high.Comment: Astronomy and Astrophysics, in pres

Cosmology with moving dark energy and the CMB quadrupole

We study the consequences of a homogeneous dark energy fluid having a non-vanishing velocity with respect to the matter and radiation large-scale rest frames. We consider homogeneous anisotropic cosmological models with four fluids (baryons, radiation, dark matter and dark energy) whose velocities can differ from each other. Performing a perturbative calculation up to second order in the velocities, we obtain the contribution of the anisotropies generated by the fluids motion to the CMB quadrupole and compare with observations. We also consider the exact problem for arbitrary velocities and solve the corresponding equations numerically for different dark energy models. We find that models whose equation of state is initially stiffer than radiation, as for instance some tracking models, are unstable against velocity perturbations, thus spoiling the late-time predictions for the energy densities. In the case of scaling models, the contributions to the quadrupole can be non-negligible for a wide range of initial conditions. We also consider fluids moving at the speed of light (null fluids) with positive energy and show that, without assuming any particular equation of state, they generically act as a cosmological constant at late times. We find the parameter region for which the models considered could be compatible with the measured (low) quadrupole.Comment: 23 pages, 6 figures. Confidence intervals calculated from WMAP data, new references and comments included. Final version to appear in PR