Analysis for time discrete approximations of blow-up solutions of semilinear parabolic equations

We prove a posteriori error estimates for time discrete approximations, for semilinear parabolic equations with solutions that might blow up in finite time. In particular we consider the backward Euler and the Crank–Nicolson methods. The main tools that are used in the analysis are the reconstruction technique and energy methods combined with appropriate fixed point arguments. The final estimates we derive are conditional and lead to error control near the blow up time

The drag coefficient of cylindrical spacecraft in orbit at altitudes greater than 150 km

The spacecraft of the Geopotential Research Mission (GRM) are cylindrical in form and designed to fly with their longitudinal axes parallel to their direction of flight. The ratio of length to diameter of these spacecraft is roughly equal to 5.0. Other spacecraft previously flown had corresponding ratios roughly equal to 1.0, and therefore the drag produced by impacts on the lateral surfaces of those spacecraft was not as large as it will be on the GRM spacecraft. Since the drag coefficient is essentially the drag force divided by the frontal area in flight, lateral impacts, when taken into account make the GRM drag coefficient significantly larger than the coefficients used before for shorter spacecraft. A simple formula is derived for the drag coefficient of a cylindrical body flying with its long axis along the direction of flight, and it is used to estimate the drag for the GRM. The formula shows that the drag due to lateral surface impacts depends on the ratio of length-to-diameter and on a coefficient C sub LS (lateral surface impact coefficient) which can be determined from previous cylindrical spacecraft flown with the same attitude, or can be obtained from laboratory measurements of momentum accommodation coefficients

Anatomy of Higgs decays into γγ\gamma \gamma and γZ\gamma Z within the EChL in the RξR_\xi gauges

In this work we study the Higgs boson decays into two photons and into one photon and one $Z$ gauge boson within the context of the non-linear Effective Field Theory called the Electroweak Chiral Lagrangian. We present a detailed computation of the corresponding amplitudes to one-loop level in the covariant $R_\xi$ gauges. We assume that the fermionic loop contributions are as in the Standard Model and focus here just in the computation of the bosonic loop contributions. Our renormalization program and the anatomy of the various contributions participating in the $R_\xi$ gauges are fully explored. With this present computation we demonstrate the gauge invariance of the EChL result, not only for the case of on-shell Higgs boson, but also for the most general and interesting case of off-shell Higgs boson. We finally analyse and conclude on the special relevance of the Goldstone boson loops, in good agreement with the expected chiral loops behaviour in Chiral Lagrangians. We perform a systematic comparison with the corresponding computation of the Standard Model in the $R_\xi$ gauges and with the previous EChL results in the unitary gauge. This work represents the first computation within the EChL of these Higgs observables to one-loop in the most general $R_\xi$ gauges and with a full renormalization program description, not yet fully explored in the previous literature and which is different to the most frequently used in the linear Effective Field Theory (SMEFT).Comment: 44 pages, 10 figures. Minor corrections to typos detected and added new references respect to the version

The IACOB project: I. Rotational velocities in Northern Galactic O and early B-type stars revisited. The impact of other sources of line-broadening

Stellar rotation is an important parameter in the evolution of massive stars. Accurate and reliable measurements of projected rotational velocities in large samples of OB stars are crucial to confront the predictions of stellar evolutionary models with observational constraints. We reassess previous determinations of projected rotational velocities (vsini) in Galactic OB stars using a large, high quality spectroscopic dataset, and a strategy which account for other sources of broadening appart from rotation affecting the diagnostic lines We present a versatile and user friendly IDL tool, based on a combined Fourier Transform (FT) + goodness of fit (GOF) methodology, for the line-broadening characterization in OB-type stars. We use this tool to (a) investigate the impact of macroturbulent and microturbulent broadenings on vsini measurements, and (b) determine vsini in a sample of 200 Galactic OB-type stars, also characterizing the amount of macroturbulent broadening (\vmacro) affecting the line profiles. We present observational evidence illustrating the strengths and limitations of the proposed FT+GOF methodology for the case of OB stars. We confirm previous statements (based on indirect arguments or smaller samples) that the macroturbulent broadening is ubiquitous in the massive star domain. We compare the newly derived vsini with previous determinations not accounting for this extra line-broadening contribution, and show that those cases with vsini< 120 km/s need to be systematically revised downwards by ~25 (+/-20) km/s. We suggest that microturbulence may impose an upper limit below which vsini and \vmacro\ could be incorrectly derived by means of the proposed methodology as presently used, and discuss the implications of this statement on the study of relatively narrow line massive stars.Comment: Accepted for publication in A&A (19 pages, 15 figures, 6 tables). Tables A1-A5 will be make available in the final edited version of the paper (or under request to SS-D