Two-region model for positive and negative plasma sheaths and its application to Hall thruster metallic anodes.

An asymptotic presheath/sheath model for positive and negative sheaths in front of a conducting electrode, with a continuous parametric transition at the no-sheath case, is presented. Key aspects of the model are as follows: full hydrodynamics of both species in the presheath; a kinetic formulation with a truncated distribution function for the repelled species within the sheath; and the fulfillment of the marginal Bohm condition at the sheath edge, in order to match the two formulations of the repelled species. The sheath regime depends on the ratios of particle fluxes and sound speeds between the two species. The presheath model includes the effect of a magnetic field parallel to the wall on electrons. An asymptotic, parametric study of the anode presheath is carried out in terms of the local ion-to-electron flux ratio and Hall parameter. The drift-diffusive model of magnetized electrons fails in a parametric region that includes parts of the negative sheath regime. In the case of the Hall parameter vanishing near the electrode and a weakly collisional plasma, a quasisonic, quasineutral plateau forms next to the sheath edge

Highly collimated microquasar jets as efficient cosmic-ray sources

Supernova remnants are believed to be the main sites where Galactic cosmic rays originate. This scenario, however, fails to explain some of the features observed in the cosmic-ray spectrum. Microquasars have been proposed as additional candidates, because their non-thermal emission indicates the existence of efficient particle acceleration mechanisms in their jets. A promising scenario envisages the production of relativistic neutrons in the jets, that decay outside the system injecting relativistic protons to the surroundings. The first investigations of this scenario suggest that microquasars might be fairly alternative cosmic-ray sources. We aim at assessing the role played by the degree of collimation of the jet on the cosmic-ray energetics in the neutron-carrier scenario, as well as the properties of the emission region. Our goals are to explain the Galactic component of the observed proton cosmic-ray spectrum at energies higher than $\sim 10$ GeV and to relate the mentioned jet properties with the power and spectral index of the produced cosmic rays. We find that collimated jets, with compact acceleration regions close to the jet base, are very efficient sources that could deliver a fraction of up to $\sim 0.01$ of their relativistic proton luminosity into cosmic rays. Collimation is the most significant feature regarding efficiency; a well collimated jet might be $\sim 4$ orders of magnitude more efficient than a poorly collimated one. The main feature of the presented mechanism is the production of a spectrum with a steeper spectral index ($\sim 2.3$ at energies up to $\sim 10$ TeV) than in the supernova scenario, and closer to what is observed. The predictions of our model may be used to infer the total contribution of the population of Galactic microquasars to the cosmic ray population, and therefore to quantitatively assess their significance as cosmic-ray sources.Comment: 11 pages, 14 figure

Quantum open systems and turbulence

We show that the problem of non conservation of energy found in the spontaneous localization model developed by Ghirardi, Rimini and Weber is very similar to the inconsistency between the stochastic models for turbulence and the Navier-Stokes equation. This sort of analogy may be useful in the development of both areas.Comment: to appear in Physical Review

Photocatalytic activity of nitrogen-doped and undoped titanium dioxide sputtered thin films

In the present work titanium dioxide (TiO2) thin films were grown by d.c. reactive magnetron sputtering process, systematically varying the Ar/O2 ratio in the gas mixture, in order to study the influence of the oxygen partial pressure on the crystallographic structure and photocatalytic activity of the TiO2 thin films. After the sputtering process the TiO2 coatings were nitrided in a microwave (f= 2.45 GHz) Electron Cyclotron Resonance (ECR) plasma discharge in pure nitrogen, to compare the photocatalytic activity of undoped and nitrogen-doped TiO2 thin films. The crystal structure of the TiO2 grown samples was studied by x-ray diffraction (XRD) and the presence of the anatase phase in these films were corroborated by Raman spectroscopy. On the other hand, X-ray photoelectron spectroscopy (XPS) measurements carried out in the nitrogen-doped TiO2 samples, showed that the nitrogen was incorporated to the films with an average concentration of 18 at% of N. The UV-Vis optical spectroscopy allowed calculating the band gap. A narrowing of the optical band gap from 3.2 eV for the undoped films to 2.5 eV for the N-doped films was observed. Photocatalytic activity tests were done using a methylene blue (MB) dye solution. The irradiation of the films in the MB dye solution was carried out with an emission lamp in the UV and in the visible range for undoped and N-doped TiO2 films, respectively. The results showed that the N-doped TiO2 films had a higher photocalytic activity in the visible range, reaching a greater MB degradation in comparison with undoped samples, which were subjected to a higher energy radiation.Fil: Franco Arias, Lina Maria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad del Valle; ColombiaFil: Zambrano, G.. Universidad del Valle; ColombiaFil: Gómez, M. E.. Universidad del Valle; ColombiaFil: Camps, E.. Instituto Nacional de Investigaciones Nucleares; MéxicoFil: Escobar Alarcón, L.. Instituto Nacional de Investigaciones Nucleares; Méxic

Sharp constants in weighted trace inequalities on Riemannian manifolds

We establish some sharp weighted trace inequalities W^{1,2}(\rho^{1-2\sigma}, M)\hookrightarrow L^{\frac{2n}{n-2\sigma}}(\pa M) on $n+1$ dimensional compact smooth manifolds with smooth boundaries, where $\rho$ is a defining function of $M$ and $\sigma\in (0,1)$. This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin.Comment: 34 page

A compactness theorem for scalar-flat metrics on manifolds with boundary

Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential Equation