Trajectories of vector fields asymptotic to formal invariant curves

We prove that a formal curve $\Gamma$ that is invariant by a $C^\infty$ vector field $\xi$ of $\mathbb{R}^m$ has a geometrical realization, as soon as the Taylor expansion of $\xi$ is not identically zero along $\Gamma$. This means that there is a trajectory $\gamma$ of $\xi$ which is asymptotic to $\Gamma$. This result solves a natural question proposed by Bonckaert nearly forty years ago. We also construct an invariant $C^0$ manifold $S$ in some open horn around $\Gamma$ which is composed entirely of trajectories asymptotic to $\Gamma$, and contains the germ of any such trajectory. If $\xi$ is analytic, we prove that there exists a trajectory asymptotic to $\Gamma$ which is, moreover, non-oscillating with respect to subanalytic sets

Stratification of three-dimensional real flows II: A generalization of Poincar\'e's planar sectorial decomposition

Let $\xi$ be an analytic vector field in $\mathbb{R}^3$ with an isolated singularity at the origin and having only hyperbolic singular points after a reduction of singularities $\pi:M\to\mathbb{R}^3$. Assuming certain conditions to be specified throughout the work at hand, we establish a theorem of stratification of the dynamics of $\xi$ that generalizes to dimension three the classical one, coming from Poincar\'{e}, about the decomposition of the dynamics of an analytic planar vector field into {\em parabolic}, {\em elliptic} or {\em hyperbolic} invariant sectors

Thermoacoustic analysis of lean premixed hydrogen flames in narrow vertical channels

Thermoacoustic instabilities arise for lean hydrogen-air flames propagating in narrow channels. We provide here a detailed experimental analysis of such phenomena in a semi-confined vessel, analyzing the effect of the mixture composition, geometry and gravity on the onset of acoustic-driven flame vibrations. Downward-propagating flames leaner than a critical value vibrate smoothly and transit to the secondary oscillating instability, which develops strong variations of pressure that couple with the propagation dynamics. The transition threshold changes during the propagation along very narrow channels, where heat losses are no longer negligible. The parametric region of equivalence ratio for the secondary thermoacoustic instability diminishes, showing an additional transition for very lean flames. There, the front breaks into several structures and the flame-wave feedback becomes weaker. The influence of gravity is studied by comparing upward and downward propagating flames, where the Rayleigh–Taylor instability arises for sufficiently small values of the Froude number in slow-propagating lean flames. For a constant mixture, buoyancy-driven upward-propagating flames develop less wrinkled fronts than those propagating downwards, and remain unresponsive to acoustic-front interaction. We show here a direct relation between front shape and thermoacoustics. In agreement with previous studies [1], [2], [3], curvature and strain effects on conduction and diffusion characterize the response of the flame to pressure perturbations, with the Markstein number controlling the aforementioned transition. Nevertheless, the theoretical analyses found in the literature can only be used on nearly equidiffusional mixtures, and are not accurate enough to describe the highly diffusive fuel mixtures (i.e. lean hydrogen-air flames) considered in our experiments.This work was supported by projects ENE2015-65852-C2-1-R (MINECO/ FEDER, UE), BYNV-ua37crdy (Fundación Iberdrola España) and KIT. The authors want to thank the technical support of ProScience GmbH. in the construction and operation of the experimental setup. D. Martnez-Ruiz would like to acknowledge F. Higuera for fruitful discussions.Publicad

How Can Be Lotic Ecosystem Size More Precisely Estimated? Comparing Different Approximations in Pre-Pyrenean and Pyrenean Mountains

Rivers are among the most biodiverse and endangered ecosystems on earth. In Europe, concern over their conservation promoted the development of legal instruments for habitat and species conservation, the Habitats Directive, and water resource management, the Water Framework Directive. This legal protection demanded the estimate of river ecosystem surface for different purposes. Different approaches allow river surface to be measured at a low cost. Some accurate techniques like satellite images or LiDAR (Light Detection and Ranging) do not always work at a large scale or for streams and small rivers. We discuss here the use of the traditional hydraulics relationship between drainage area and bankfull width as a good approach to river surface estimation. We confirm that the use of this cheap and simple method could be a good approach to estimate river surface. However, we also proved that the development of regional curves, i.e., to establish the empirical relationship based on study area data, constitutes an essential improvement to estimation.This research was funded by the Ministry of Ecological Transition and Demographic Challenge, project number 3081147. This research was supported by the Government of Catalonia (CERCA Program)

In vitro effect of different implant decontamination methods in three intraosseous defect configurations

Objectives This in vitro investigation was aimed to evaluate the cleaning ability of four mechanical devices designed for decontaminating implant surfaces. Material and methods Ninety-six implants were coated with permanent ink and inserted into 3D-printed resin blocks simulating three different intraosseous defect configurations (types Ib, Ic, and Ie). The four tested mechanical decontamination devices (air-polishing with glycine powder, rotating titanium brush, polyetheretherketone [PEEK]-coated ultrasonic tip, and stainless steel ultrasonic tip) were randomly applied onto the 5 mm exposed implant surface. Standardized photographs were taken from a frontal perspective and with a 30° angle coronally and apically to the implant axis. The area with remnant ink on the implant surface was calculated. Results Although none of the groups achieved complete ink removal, air-polishing with glycine and titanium brushes demonstrated a higher cleaning ability when compared with ultrasonic devices either with standard or PEEK tips for all three defect configurations. For the three tested models, the best cleaning ability in all groups was shown on implant surfaces without facing an intraosseous wall. Titanium brush was the most effective when the intraosseous walls existed. Cleaning effectiveness diminished in the threads located in the apical third, especially when using air-polishing and ultrasonic devices. Conclusions Titanium brushes and air-polishing devices were more effective in removing artificial biofilm using this in vitro model, although their effectiveness was influenced by the presence of the intrabony component

El cine como propaganda en la Italia fascista.

En el siguiente estudio de investigación bibliográfica, se pretende comprender hasta qué punto el régimen fascista italiano hizo uso del cine como medio de propaganda política, para difundir su ideario, los medios usados para ello y los resultados que obtuvo. Para ello se comparan diferentes textos de libros y artículos de revistas que tratan sobre la historia del cine de la época fascista. Se han estudiado textos y fuentes historiográficas de diferentes épocas y autores, desde la segunda mitad del siglo XX hasta los más recientes.<br /

Experimental analysis of oscillatory premixed flames in a Hele-Shaw cell propagating towards a closed end

An experimental study of methane, propane and dimethyl ether (DME) premixed flames propagating in a quasi-two-dimensional Hele-Shaw cell placed horizontally is presented in this paper. The flames are ignited at the open end of the combustion chamber and propagate towards the closed end. Our experiments revealed two distinct propagation regimes depending on the equivalence ratio of the mixture as a consequence of the coupling between the heat-release rate and the acoustic waves. The primary acoustic instability induces a small-amplitude, of around 8 mm, oscillatory motion across the chamber that is observed for lean propane, lean DME, and rich methane flames. Eventually, a secondary acoustic instability emerges for sufficiently rich (lean) propane and DME (methane) flames, inducing large-amplitude oscillations in the direction of propagation of the flame. The amplitude of these oscillations can be as large as 30 mm and drastically changes the outline of the flame. The front then forms pulsating finger-shaped structures that characterize the flame propagation under the secondary acoustic instability. The experimental setup allows the recording of the flame propagation from two different points of view. The top view is used to obtain accurate quantitative information about the flame propagation, while the lateral view offered a novel three dimensional perspective of the flame that gives relevant information on the transition between the two oscillatory regimes. The influence of the geometry of the Hele-Shaw cell and of the equivalence ratio on the transition between the two acoustic-instability regimes is analyzed. In particular, we find that the transition to the secondary instability occurs for values of the equivalence ratio phi above (below) a critical value phi(c) for propane and DME (methane) flames. In all the tested fuels, the transition to the secondary instability emerges for values of the Markstein number M below a critical value M-c. The critical MarkstPublicad

The role of conductive heat losses on the formation of isolated flame cells in Hele-Shaw chambers

The propagation of low-Lewis-number premixed flames is analyzed in a partially confined Hele-Shaw chamber formed by two parallel plates separated a distance h apart. An asymptotic-numerical study can be performed for small gaps compared to the flame thickness deltaT . In this narrow-channel limit, the prob- lem formulation simplifies to a quasi-2D description in which the velocity field is controlled by domi- nant viscous effects. After accounting for conductive heat losses through the plates in our formulation, we found that the reaction front breaks into one or several isolated flame cells where the temperature is large enough to sustain the reaction, both in absence and in presence of buoyancy effects. Under these near-limit conditions, the isolated flame cells either travel steadily or undergo a slow random walk over the chamber in which the reacting front splits successively to form a tree-like pathway, burning only a small fraction of the fuel before reaching the end of the chamber. The production of quasi-2D circular or comet-like flames under specific favorable conditions is demonstrated in this paper, with convection, conductive heat losses and differential diffusion playing an essential role in the formation of the isolated one and two-headed flame cells.This work was supported by the project ENE2015-65852-C2-1-R (FV,MSS,DMR) and ENE2015-65852-C2-2-R (DFG,VK) (MINECO/FEDER, UE). Daniel Martínez-Ruiz would like to thank Amable Liñán for fruitful discussions