Chaotic quasi-collision trajectories in the 3-centre problem

We study a particular kind of chaotic dynamics for the planar 3-centre problem on small negative energy level sets. We know that chaotic motions exist, if we make the assumption that one of the centres is far away from the other two (see Bolotin and Negrini, J. Diff. Eq. 190 (2003), 539--558): this result has been obtained by the use of the Poincar\'e-Melnikov theory. Here we change the assumption on the third centre: we do not make any hypothesis on its position, and we obtain a perturbation of the 2-centre problem by assuming its intensity to be very small. Then, for a dense subset of possible positions of the perturbing centre on the real plane, we prove the existence of uniformly hyperbolic invariant sets of periodic and chaotic almost collision orbits by the use of a general result of Bolotin and MacKay (see Cel. Mech. & Dyn. Astr. 77 (2000), 49--75). To apply it, we must preliminarily construct chains of collision arcs in a proper way. We succeed in doing that by the classical regularisation of the 2-centre problem and the use of the periodic orbits of the regularised problem passing through the third centre.Comment: 22 pages, 6 figure

Compressing the cosmological information in one-dimensional correlations of the Lyman-α\alpha forest

Observations of the Lyman-$\alpha$ (Ly$\alpha$) forest from spectroscopic surveys such as BOSS/eBOSS, or the ongoing DESI, offer a unique window to study the growth of structure on megaparsec scales. Interpretation of these measurements is a complicated task, requiring hydrodynamical simulations to model and marginalise over the thermal and ionisation state of the intergalactic medium. This complexity has limited the use of Ly$\alpha$ clustering measurements in joint cosmological analyses. In this work we show that the cosmological information content of the 1D power spectrum ($P_\mathrm{1D}$) of the Ly$\alpha$ forest can be compressed into a simple two-parameter likelihood without any significant loss of constraining power. We simulate $P_\mathrm{1D}$ measurements from DESI using hydrodynamical simulations and show that the compressed likelihood is model independent and lossless, recovering unbiased results even in the presence of massive neutrinos or running of the primordial power spectrum.Comment: Submitted to ApJ. 17 pages, 7 figure

Oracion fúnebre de Luis XVI, rey de Francia y de Navarra

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Gravitational waves from relativistic rotational core collapse

We present results from simulations of axisymmetric relativistic rotational core collapse. The general relativistic hydrodynamic equations are formulated in flux-conservative form and solved using a high-resolution shock-capturing scheme. The Einstein equations are approximated with a conformally flat 3-metric. We use the quadrupole formula to extract waveforms of the gravitational radiation emitted during the collapse. A comparison of our results with those of Newtonian simulations shows that the wave amplitudes agree within 30%. Surprisingly, in some cases, relativistic effects actually diminish the amplitude of the gravitational wave signal. We further find that the parameter range of models suffering multiple coherent bounces due to centrifugal forces is considerably smaller than in Newtonian simulations.Comment: 4 pages, 3 figure

Ethnomathematical and Mathematical Connections Activated by a Teacher in Mathematical Problems Posing and Solving

Background: Connections are essential for understanding concepts, but difficulties have been evidenced in connecting representations and meanings of concepts and creating contextualised mathematical problems by teachers and students. Objective: Therefore, ethnomathematical and mathematical connections were analysed in a teacher's mathematical activity when posing and solving mathematical problems. Design: The methodology was qualitative-ethnographic, developed in a workshop done in stages. Setting and participants: An indigenous Mokaná teacher from Sibarco was selected. Data collection and analysis: Semi-structured interviews were conducted in the workshop, and the data were analysed based on the connections; the workshop was initially designed considering previous literature on the issue, and the researchers were familiarised with the teacher. Results: For the analysis of the mathematics used by the teacher in the classroom, we considered his sociocultural context, where he set problems about the area and perimeter of lots of land and enclosures. Then, the researchers presented the ethnomathematical connections that emerged in the elaboration and commercialisation of the pigeon peas sancocho, which was the basis for the teacher to pose and solve problems involving conversions between units of measurement, volume of the totumas (ellipsoid), etc. Simultaneously, mathematical connections of different representations, procedural, meaning, and modelling were identified. Finally, the researchers gave feedback by assessing the Acta Sci. (Canoas), 25(1), 86-121, Jan./Fev. 2023 87 potential of the mathematics known and explained by the teacher. Conclusion: This research provides input for teachers to pose and solve problems contextualised through connections

Solubility of nickel in slags equilibrated with Ni-S melt

To provide thermodynamic data for converting the nickel matte to liquid nickel, an experimental study was conducted in the phase equilibrium between the Ni-S melt and FeOX-SiO2, FeOX-CaO or CaO-Al2O3 based slag melted in a magnesia crucible at 1773 and 1873 K. pSO2 was controlled at 10.1 kPa while pO2 and pS2 ranged between those where NiO precipitated and Ni3S2 formed, respectively. The nickel content in the slag and the sulfur content in the metal at given pO2 and pS2 were smallest for the CaO-Al2O3 based slag. Both decreased with increasing temperature. At 1873 K, the content of nickel in the CaO-Al2O3 based slag at pO2 of 10 Pa (near the precipitation of NiO) was 4%, while the content of sulfur in alloy is 0.4 mass %. Thus, the CaO-Al2O3 base slag at 1873 K would be suitable for direct converting of Ni3S2 to metallic nickel. The distribution behavior of nickel between the slag and the Ni-S melt was discussed based on the concept of oxidic and sulfidic dissolution

Matter flows around black holes and gravitational radiation

We develop and calibrate a new method for estimating the gravitational radiation emitted by complex motions of matter sources in the vicinity of black holes. We compute numerically the linearized curvature perturbations induced by matter fields evolving in fixed black hole backgrounds, whose evolution we obtain using the equations of relativistic hydrodynamics. The current implementation of the proposal concerns non-rotating holes and axisymmetric hydrodynamical motions. As first applications we study i) dust shells falling onto the black hole isotropically from finite distance, ii) initially spherical layers of material falling onto a moving black hole, and iii) anisotropic collapse of shells. We focus on the dependence of the total gravitational wave energy emission on the flow parameters, in particular shell thickness, velocity and degree of anisotropy. The gradual excitation of the black hole quasi-normal mode frequency by sufficiently compact shells is demonstrated and discussed. A new prescription for generating physically reasonable initial data is discussed, along with a range of technical issues relevant to numerical relativity.Comment: 27 pages, 12 encapsulated figures, revtex, amsfonts, submitted to Phys. Rev.

Does M31 result from an ancient major merger?

The numerous streams in the M31 halo are currently assumed to be due to multiple minor mergers. Here we use the GADGET2 simulation code to test whether M31 could have experienced a major merger in its past history. It results that a 3+/-0.5:1 gaseous rich merger with r(per)=25+/-5 kpc and a polar orbit can explain many properties of M31 and of its halo. The interaction and the fusion may have begun 8.75+/-0.35 Gyr and 5.5 +/-0.5 Gyr ago, respectively. With an almost quiescent star formation history before the fusion we retrieve fractions of bulge, thin and thick disks as well as relative fractions of intermediate age and old stars in both the thick disk and the Giant Stream. The Giant Stream is caused by returning stars from a tidal tail previously stripped from the satellite prior to the fusion. These returning stars are trapped into elliptical orbits or loops for almost a Hubble time period. Large loops are also predicted and they scale rather well with the recently discovered features in the M31 outskirts. We demonstrate that a single merger could explain first-order (intensity and size), morphological and kinematical properties of the disk, thick disk, bulge and streams in the halo of M31, as well as the distribution of stellar ages, and perhaps metallicities. It challenges scenarios assuming one minor merger per feature in the disk (10 kpc ring) or at the outskirts (numerous streams & thick disk). Further constraints will help to properly evaluate the impact of such a major event to the Local Group.Comment: accepted in Astrophysical Journal, 29 September, 2010 ; proof-edited version; 1st column of Table 3 correcte

A Supersymmetric Model with an Extra U(1) Gauge Symmetry

In the standard model the proton is protected from decay naturally by gauge symmetries, whereas in the ordinary minimal supersymmetric standard model an ad hoc discrete symmetry is imposed for the proton stability. We present a new supersymmetric model in which the proton decay is forbidden by an extra U(1) gauge symmetry. Particle contents are necessarily increased to be free from anomalies, incorporating right-handed neutrinos. Both Dirac and Majorana masses are generated for neutrinos, yielding non-vanishing but small masses. The superpotential consists only of trilinear couplings and the mass parameter $\mu$ of the minimal model is induced by spontaneous breaking of the U(1) symmetry.Comment: 10 pages, Revte