arXiv subjects
Publications and source records attributed to J. Navarro.
We prove that the only natural operations between differential forms are those obtained using linear combinations, the exterior product and the exterior differential. Our result generalises work by Palais and Freed-Hopkins. As an application, we also deduce a theorem, originally due to Kolar, that determines those natural differential forms that can be associated to a connection on a principal bundle.
We study the impact of three-body forces on the response functions of cold neutron matter. These response functions are determined in the random phase approximation (RPA) from a residual interaction expressed in terms of Landau parameters. Special attention is paid to the non-central part, including all terms allowed by the relevant symmetries. Using Landau parameters derived from realistic nuclear two- and three-body forces grounded in chiral effective field theory, we find that the three-body term has a strong impact on the excited states of the system and in the static and long-wavelength limit of the response functions for which a new exact formula is established.
Stellar population studies of globular clusters have suggested that the brightest clusters in the Galaxy might actually be the remnant nuclei of dwarf spheroidal galaxies. If the present Galactic globular clusters formed within larger stellar systems, they are likely surrounded by extra-tidal halos and/or tails made up of stars that were tidally stripped from their parent systems. The stellar surroundings around globular clusters are therefore one of the best places to look for the remnants of an ancient dwarf galaxy. Here an attempt is made to search for tidal debris around the supernovae enriched globular clusters M22 and NGC 1851 as well as the kinematically unique cluster NGC 3201. The stellar parameters from the Radial Velocity Experiment (RAVE) are used to identify stars with RAVE metallicities, radial velocities and elemental-abundances consistent with the abundance patterns and properties of the stars in M22, NGC 1851 and NGC 3201. The discovery of RAVE stars that may be associated with M22 and NGC 1851 are reported, some of which are at projected distances of ~10 degrees away from the core of these clusters. Numerous RAVE stars associated with NGC 3201 suggest that either the tidal radius of this cluster is underestimated, or that there are some unbound stars extending a few arc minutes from the edge of the cluster's radius. No further extra-tidal stars associated with NGC 3201 could be identified. The bright magnitudes of the RAVE stars make them easy targets for high resolution follow-up observations, allowing an eventual further chemical tagging to solidify (or exclude) stars outside the tidal radius of the cluster as tidal debris. In both our radial velocity histograms of the regions surrounding NGC 1851 and NGC 3201, a peak of stars at 230 km/s is seen, consistent with extended tidal debris from omega Centauri.
The Brussels-Montreal Skyrme functionals have been successful to describe properties of both finite nuclei and infinite homogeneous nuclear matter. In their latest version, these functionals have been equipped with two extra density-dependent terms in order to reproduce simultaneously ground state properties of nuclei and infinite nuclear matter properties while avoiding at the same time the arising of ferromagnetic instabilities. In the present article, we extend our previous results of the linear response theory to include such extra terms at both zero and finite temperature in pure neutron matter. The resulting formalism is then applied to derive the neutrino mean free path. The predictions from the Brussels-Montreal Skyrme functionals are compared with ab-initio methods.
The possibility of adding a D-wave term to the standard Skyrme effective interaction has been widely considered in the past. Such a term has been shown to appear in the next-to-next-to-leading order of the Skyrme pseudo-potential. The aim of the present article is to provide the necessary tools to incorporate this term in a fitting procedure: first, a mean-field equation written in spherical symmetry in order to describe spherical nuclei and second, the response function to detect unphysical instabilities. With these tools it will be possible to build a new fitting procedure to determine the coupling constants of the new functional.
The present work discusses the pertinence of a 'sociotype' construct, both theoretically and empirically oriented. The term, based on the conceptual chain genotype-phenotype-sociotype, suggests an evolutionary preference in the human species for some determined averages of social relationships. This core pattern or 'sociotype' has been explored herein for the networking relationships of young people--165 university students filling in a 20-items questionnaire on their social interactions. In spite that this is a preliminary study, interesting results have been obtained on gender conversation time, mental health, sociability level, and satisfaction with personal relationships. This sociotype hypothesis could be a timely enterprise for mental health and quality of life policies.
The formalism of linear response theory for a Skyrme functional including spin-orbit and tensor terms is generalized to the case of infinite nuclear matter with arbitrary isospin asymmetry. Response functions are obtained by solving an algebraic system of equations, which is explicitly given. Spin-isospin strength functions are analyzed varying the conditions of density, momentum transfer, asymmetry and temperature. The presence of instabilities, including the spinodal one, is studied by means of the static susceptibility.
Landau parameters determined from phenomenological finite-range interactions are used to get an estimation of N$^3$LO pseudopotentials parameters. The parameter sets obtained in this way are shown to lead to consistent results concerning saturation properties. The uniqueness of this procedure is discussed, and an estimate of the error induced by the truncation at N$^3$LO is given.
Non-axisymmetries in the Galactic potential (spiral arms and bar) induce kinematic groups such as the Hercules stream. Assuming that Hercules is caused by the effects of the Outer Lindblad Resonance of the Galactic bar, we model analytically its properties as a function of position in the Galaxy and its dependence on the bar's pattern speed and orientation. Using data from the RAVE survey we find that the azimuthal velocity of the Hercules structure decreases as a function of Galactocentric radius, in a manner consistent with our analytical model. This allows us to obtain new estimates of the parameters of the Milky Way's bar. The combined likelihood function of the bar's pattern speed and angle has its maximum for a pattern speed of $Ω_b=(1.89 \pm 0.08) \times Ω_0$ where $Ω_0$ is the local circular frequency. Assuming a Solar radius of 8.05 kpc and a local circular velocity of 238 km/s, this corresponds to $Ω_b=56\pm 2$ km/s/kpc. On the other hand, the bar's orientation $ϕ_b$ cannot be constrained with the available data. In fact, the likelihood function shows that a tight correlation exists between the pattern speed and the orientation, implying that a better description of our best fit results is given by the linear relation $Ω_b/Ω_0=1.91 + 0.0044[ϕ_b(°)-48]$, with standard deviation of 0.02. For example, for an angle of $ϕ_b=30°$ the pattern speed is $54.0\pm0.5$ km/s/kpc. These results are not very sensitive to the other Galactic parameters such as the circular velocity curve or the peculiar motion of the Sun, and are robust to biases in distance.
We present a method to obtain response functions in the random phase approximation (RPA) based on a residual interaction described in terms of Landau parameters with central plus tensor contributions. The response functions keep the explicit momentum dependence of the RPA, in contrast with the traditional Landau approximation. Results for symmetric nuclear matter and pure neutron matter are presented using Landau parameters derived from finite-range interactions, both phenomenological and microscopic. We study the convergence of response functions as the number of Landau parameters is increased.
Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many properties of reflexive functors.
We analyse the kinematics of disc stars observed by the RAVE survey in and beyond the Solar neighbourhood.We detect significant overdensities in the velocity distributions using a technique based on the wavelet transform.We find that the main local kinematic groups are large scale features, surviving at least up to ~1 kpc from the Sun in the direction of anti-rotation, and also at ~700 pc below the Galactic plane.We also find that for regions located at different radii than the Sun, the known groups appear shifted in the velocity plane. For example, the Hercules group has a larger azimuthal velocity for regions inside the Solar circle and a lower value outside. We have also discovered a new group at (U, V) = (92,-22) km/s in the Solar neighbourhood and confirmed the significance of other previously found groups. Some of these trends detected for the first time are consistent with dynamical models of the effects of the bar and the spiral arms. More modelling is required to definitively characterise the non-axisymmetric components of our Galaxy using these groups.
The explicit form of the next-to-next-to-leading order (N2LO) of the Skyrme effective pseudopotential compatible with all required symmetries and especially with gauge invariance is presented in Cartesian basis. It is shown in particular that for such a particular pseudopotential there is no spin-orbit contribution and that the D-wave term suggested in the original Skyrme's formulation does not satisfy the invariance properties. The six new N2LO terms contribute to both the equation of state and Landau parameters. These contributions to symmetric nuclear matter are explicitly given and discussed.
We study the effects of the tensor force, present in modern effective nucleon-nucleon interactions, in the spin instability of nuclear and neutron matter. Stability conditions of the system against certain very low energy excitation modes are expressed in terms of Landau parameters. It is shown that in the spin case, the stability conditions are equivalent to the condition derived from the spin susceptibility, which is obtained as the zero-frequency and long-wavelength limit of the spin response function calculated in the Random Phase Approximation. Zero-range forces of the Skyrme type and finite-range forces of M3Y and Gogny type are analyzed. It is shown that for the Skyrme forces considered, the tensor effects are sizeable, and tend to increase the spin instability which appears at smaller densities than in the case that the tensor is not taken into account. On the contrary, the tensor contribution of finite range forces to the spin susceptibility is small or negligible for both isospin channels of symmetric nuclear matter as well as for neutron matter. A comparison with the spin susceptibility provided by realistic interactions is also presented.
Let X be a smooth manifold of dimension 1+n endowed with a lorentzian metric g, and let T be the electromagnetic energy tensor associated to a 2-form F. In this paper we characterize this tensor T as the only 2-covariant natural tensor associated to a lorentzian metric and a 2-form that is independent of the unit of scale and satisfies certain condition on its divergence. This characterization is motivated on physical grounds, and can be used to justify the Einstein-Maxwell field equations. More generally, we characterize in a similar manner the energy tensor associated to a differential form of arbitrary order k. Finally, we develop a generalized theory of electromagnetism where charged particles are not punctual, but of an arbitrary fixed dimension p. In this theory, the electromagnetic field F is a differential form of order 2+p and its electromagnetic energy tensor is precisely the energy tensor associated to F.
A functor of sets $\mathbb X$ over the category of $K$-commutative algebras is said to be an affine functor if its functor of functions, $\mathbb A_{\mathbb X}$, is reflexive and $\mathbb X=\Spec \mathbb A_{\mathbb X}$. We prove that affine functors are equal to a direct limit of affine schemes and that affine schemes, formal schemes, the completion of affine schemes along a closed subscheme, etc., are affine functors. Endowing an affine functor $\mathbb X$ with a functor of monoids structure is equivalent to endowing $\mathbb A_{\mathbb X}$ with a functor of bialgebras structure. If $\mathbb G$ is an affine functor of monoids, then $\mathbb A_{\mathbb G}^*$ is the enveloping functor of algebras of $\mathbb G$ and the category of $\mathbb G$-modules is equivalent to the category of $\mathbb A_{\mathbb G}^*$-modules. Applications of these results include Cartier duality, neutral Tannakian duality for affine group schemes, the equivalence between formal groups and Lie algebras in characteristic zero, etc.
The RAdial Velocity Experiment (RAVE) is a medium resolution R~7500 spectroscopic survey of the Milky Way which already obtained over half a million stellar spectra. They present a randomly selected magnitude-limited sample, so it is important to use a reliable and automated classification scheme which identifies normal single stars and discovers different types of peculiar stars. To this end we present a morphological classification of 350,000 RAVE survey stellar spectra using locally linear embedding, a dimensionality reduction method which enables representing the complex spectral morphology in a low dimensional projected space while still preserving the properties of the local neighborhoods of spectra. We find that the majority of all spectra in the database ~90-95% belong to normal single stars, but there is also a significant population of several types of peculiars. Among them the most populated groups are those of various types of spectroscopic binary and chromospherically active stars. Both of them include several thousands of spectra. Particularly the latter group offers significant further investigation opportunities since activity of stars is a known proxy of stellar ages. Applying the same classification procedure to the sample of normal single stars alone shows that the shape of the projected manifold in two dimensional space correlates with stellar temperature, surface gravity and metallicity.
Within the diffusion Monte Carlo approach, we have determined the structure of isotopically pure and mixed helium droplets doped with one magnesium atom. For pure 4He clusters, our results confirm those of M. Mella et al. [J. Chem. Phys. 123, 054328 (2005)] that the impurity experiences a transition from a surface to a bulk location as the number of helium atoms in the droplet increases. Contrarily, for pure 3He clusters Mg resides in the bulk of the droplet due to the smaller surface tension of this isotope. Results for mixed droplets are presented. We have also obtained the absorption spectrum of Mg around the 3s3p 1P_1 <-- 3s2 1S_0 transition.