A formal introduction to Horndeski and Galileon theories and their generalizations

We review different constructions of Galileon theories in both flat and curved space, and for both single scalar field models as well as multi-field models. Our main emphasis is on the formal mathematical properties of these theories and their construction.Comment: 19 page

CCOs and the hidden magnetic field scenario

CCOs are X-ray sources lying close the center of supernova remnants, with inferred values of the surface magnetic fields significantly lower (less than about 1e11 G) than those of standard pulsars. In this paper, we revise the hidden magnetic field scenario, presenting the first 2D simulations of the submergence and reemergence of the magnetic field in the crust of a neutron star. A post-supernova accretion stage of about 1e-4-1e-3 solar masses over a vast region of the surface is required to bury the magnetic field into the inner crust. When accretion stops, the field reemerges on a typical timescale of 1-100 kyr, depending on the submergence conditions. After this stage, the surface magnetic field is restored close to its birth values. A possible observable consequence of the hidden magnetic field is the anisotropy of the surface temperature distribution, in agreement with observations of several of these sources. We conclude that the hidden magnetic field model is viable as alternative to the anti-magnetar scenario, and it could provide the missing link between CCOs and the other classes of isolated neutron stars.Comment: 7 pages, 7 figures, MNRA

Equilibrated tractions for the Hybrid High-Order method

We show how to recover equilibrated face tractions for the hybrid high-order method for linear elasticity recently introduced in [D. A. Di Pietro and A. Ern, A hybrid high-order locking-free method for linear elasticity on general meshes, Comput. Meth. Appl. Mech. Engrg., 2015, 283:1-21], and prove that these tractions are optimally convergent

A Hybrid High-Order method for Leray-Lions elliptic equations on general meshes

In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady non-linear Leray-Lions problems. The proposed method has several assets, including the support for arbitrary approximation orders and general polytopal meshes. This is achieved by combining two key ingredients devised at the local level: a gradient reconstruction and a high-order stabilization term that generalizes the one originally introduced in the linear case. The convergence analysis is carried out using a compactness technique. Extending this technique to HHO methods has prompted us to develop a set of discrete functional analysis tools whose interest goes beyond the specific problem and method addressed in this work: (direct and) reverse Lebesgue and Sobolev embeddings for local polynomial spaces, $L^{p}$-stability and $W^{s,p}$-approximation properties for $L^{2}$-projectors on such spaces, and Sobolev embeddings for hybrid polynomial spaces. Numerical tests are presented to validate the theoretical results for the original method and variants thereof

On the difference-to-sum power ratio of speech and wind noise based on the Corcos model

The difference-to-sum power ratio was proposed and used to suppress wind noise under specific acoustic conditions. In this contribution, a general formulation of the difference-to-sum power ratio associated with a mixture of speech and wind noise is proposed and analyzed. In particular, it is assumed that the complex coherence of convective turbulence can be modelled by the Corcos model. In contrast to the work in which the power ratio was first presented, the employed Corcos model holds for every possible air stream direction and takes into account the lateral coherence decay rate. The obtained expression is subsequently validated with real data for a dual microphone set-up. Finally, the difference-to- sum power ratio is exploited as a spatial feature to indicate the frame-wise presence of wind noise, obtaining improved detection performance when compared to an existing multi-channel wind noise detection approach.Comment: 5 pages, 3 figures, IEEE-ICSEE Eilat-Israel conference (special session

An advection-robust Hybrid High-Order method for the Oseen problem

In this work, we study advection-robust Hybrid High-Order discretizations of the Oseen equations. For a given integer $k\ge 0$, the discrete velocity unknowns are vector-valued polynomials of total degree $\le k$ on mesh elements and faces, while the pressure unknowns are discontinuous polynomials of total degree $\le k$ on the mesh. From the discrete unknowns, three relevant quantities are reconstructed inside each element: a velocity of total degree $\le(k+1)$, a discrete advective derivative, and a discrete divergence. These reconstructions are used to formulate the discretizations of the viscous, advective, and velocity-pressure coupling terms, respectively. Well-posedness is ensured through appropriate high-order stabilization terms. We prove energy error estimates that are advection-robust for the velocity, and show that each mesh element $T$ of diameter $h_T$ contributes to the discretization error with an $\mathcal{O}(h_T^{k+1})$-term in the diffusion-dominated regime, an $\mathcal{O}(h_T^{k+\frac12})$-term in the advection-dominated regime, and scales with intermediate powers of $h_T$ in between. Numerical results complete the exposition

Population synthesis of isolated Neutron Stars with magneto--rotational evolution

We revisit the population synthesis of isolated radio-pulsars incorporating recent advances on the evolution of the magnetic field and the angle between the magnetic and rotational axes from new simulations of the magneto-thermal evolution and magnetosphere models, respectively. An interesting novelty in our approach is that we do not assume the existence of a death line. We discuss regions in parameter space that are more consistent with the observational data. In particular, we find that any broad distribution of birth spin periods with $P_0\lesssim 0.5$ s can fit the data, and that if the alignment angle is allowed to vary consistently with the torque model, realistic magnetospheric models are favoured compared to models with classical magneto-dipolar radiation losses. Assuming that the initial magnetic field is given by a lognormal distribution, our optimal model has mean strength $\langle\log B_0{\rm [G]}\rangle \approx 13.0-13.2$ with width $\sigma (\log B_0) = 0.6-0.7$. However, there are strong correlations between parameters. This degeneracy in the parameter space can be broken by an independent estimate of the pulsar birth rate or by future studies correlating this information with the population in other observational bands (X-rays and $\gamma$-rays).Comment: 10 pages, 9 figures, submitted and accepted to MNRAS, comments welcom

Phase-and-amplitude recovery from a single phase contrast image using partially spatially coherent X-ray radiation

A simple method of phase-and-amplitude extraction is derived that corrects for image blurring induced by partially spatially coherent incident illumination using only a single intensity image as input. The method is based on Fresnel diffraction theory for the case of high Fresnel number, merged with the space-frequency description formalism used to quantify partially coherent fields and assumes the object under study is composed of a single material. A priori knowledge of the object's complex refractive index and information obtained by characterizing the spatial coherence of the source is required. The algorithm was applied to propagation-based phase contrast data measured with a laboratory-based micro-focus X-ray source. The blurring due to the finite spatial extent of the source is embedded within the algorithm as a simple correction term to the so-called Paganin algorithm and is also numerically stable in the presence of noise