arXiv subjects
Publications and source records attributed to C. García.
In this paper we determine the centers of quasi-homogeneous polynomial planar vector fields of degree 0, 1, 2, 3 and 4. In addition, in every case we make a study of the reversibility and the analytical integrability of each one of the above centers.Wefind polynomial centers which are neither orbitally reversible nor analytically integrable, this is a new scenario in respect to the one of non-degenerate and nilpotent centers.
In this paper, we construct time periodic doubly connected solutions for the 3D quasi-geostrophic model in the patch setting. More specifically, we prove the existence of nontrivial $m$-fold doubly connected rotating patches bifurcating from a generic doubly connected revolution shape domain with higher symmetry $m\geq m_0$ and $m_0$ is large enough. The linearized matrix operator at the equilibrium state is with variable and singular coefficients and its spectral analysis is performed via the approach devised in [27] where a suitable symmetrization has been introduced. New difficulties emerge due to the interaction between the surfaces making the spectral problem richer and involved.
The surface quality of replicated CFRP mirrors is ideally expected to be as good as the mandrel from which they are manufactured. In practice, a number of factors produce surface imperfections in the final mirrors at different scales. To understand where this errors come from, and develop improvements to the manufacturing process accordingly, a wide range of metrology techniques and quality control methods must be adopted. Mechanical and optical instruments are employed to characterise glass mandrels and CFRP replicas at different spatial frequency ranges. Modal analysis is used to identify large scale aberrations, complemented with a spectral analysis at medium and small scales. It is seen that astigmatism is the dominant aberration in the CFRP replicas. On the medium and small scales, we have observed that fiber print-through and surface roughness can be improved significantly by an extra resin layer over the replica's surface, but still some residual irregularities are present.
Planet Formation research is blooming in an era where we are moving from speaking about "protoplanetary disks" to "planet forming disks" (Andrews et al., 2018). However, this transition is still motivated by indirect (but convincing) hints. Up to date, the direct detection of planets "in the making" remains elusive with the remarkable exception of PDS70b and c (Haffert et al., 2019; Keppler et al., 2018; Müller et al., 2018). The scarcity of detections is attributable to technical challenges, and even for the rare jewels that we can detect, characterization (resolving their hill spheres) is unachievable. The next step in this direction demands from near to mid-infrared interferometry to jump from $\sim$100 m baselines to $\sim$1 km, and from very few telescopes (two to six) to 20 or more (PFI like concepts, Monnier et al. 2018). This transition needs for more affordable near to mid-infrared telescopes to be designed. Since the driving cost for such telescopes resides on the primary mirror, in particular scaling with its diameter and weight, our approach to tackle this problem relies on the production of low-cost light mirrors.
In the manufacturing process of Carbon Fiber Reinforced Polymer (CFRP) mirrors (replicated from a mandrel) the orientation of the unidirectional carbon fiber layers (layup) has a direct influence on different aspects of the final product, like its general (large scale) shape and local deformations. In particular, optical methods used to evaluate the surface's quality, can reveal the presence of print-through, a very common issue in CFPR manufacture. In practical terms, the surface's irregularities induced, among other artifacts, by print-through, produce unwanted scattering effects, which are usually mitigated applying extra layers of different materials to the surface. Since one of the main goals of CFPR mirrors is to decrease the final weight of the whole mirror system, adding more material goes in the opposite direction of that. For this reason a different layup method is being developed with the goal of decreasing print-through and improving sphericity while maintaining mechanical qualities and without the addition of extra material in the process.
This paper deals with the existence of $N$ vortex patches located at the vertex of a regular polygon with $N$ sides that rotate around the center of the polygon at a constant angular velocity. That is done for Euler and (SQG)$_β$ equations, with $β\in(0,1)$, but may be also extended to more general models. The idea is the desingularization of the Thomsom polygon for the $N$ point vortex system, that is, $N$ point vortices located at the vertex of a regular polygon with $N$ sides. The proof is based on the study of the contour dynamics equation combined with the application of the infinite dimensional Implicit Function theorem and the well--chosen of the function spaces.
The Centro de Laseres Pulsados in Salamanca Spain has recently started operation phase and the first User access period on the 6 J 30 fs 200 TW system (VEGA 2) already started at the beginning of 2018. In this paper we report on two commissioning experiments recently performed on the VEGA 2 system in preparation for the user campaign. VEGA 2 system has been tested in different configurations depending on the focusing optics and targets used. One configuration (long focal length f=130 cm) is for under-dense laser-matter interaction where VEGA 2 is focused onto a low density gas-jet generating electron beams (via laser wake field acceleration mechanism) with maximum energy up to 500 MeV and an X-ray betatron source with a 10 keV critical energy. A second configuration (short focal length f=40 cm) is for over-dense laser-matter interaction where VEGA 2 is focused onto an 5 microns thick Al target generating a proton beam with a maximum energy of 10 MeV and average energy of 7-8 MeV and temperature of 2.5 MeV. In this paper we present preliminary experimental results.