Staticity and regularity for zero rest-mass fields near spatial infinity on flat spacetime

Linear zero-rest-mass fields generically develop logarithmic singularities at the critical sets where spatial infinity meets null infinity. Friedrich's representation of spatial infinity is ideally suited to study this phenomenon. These logarithmic singularities are an obstruction to the smoothness of the zero-rest-mass field at null infinity and, in particular, to peeling. In the case of the spin-2 field it has been shown that these logarithmic singularities can be precluded if the initial data for the field satisfies a certain regularity condition involving the vanishing, at spatial infinity, of a certain spinor (the linearised Cotton spinor) and its totally symmetrised derivatives. In this article we investigate the relation between this regularity condition and the staticity of the spin-2 field. It is shown that while any static spin-2 field satisfies the regularity condition, not every solution satisfying the regularity condition is static. This result is in contrast with what happens in the case of General Relativity where staticity in a neighbourhood of spatial infinity and the smoothness of the field at future and past null infinities are much more closely related.

Differentiating lightning in winter and summer with characteristics of wind-field and mass-field

Lightning in winter (December, January, February, DJF) is rare compared to lightning in summer (June, July, August, JJA) in central Europe. The conventional explanation attributes the scarcity of winter lightning to seasonally low values of variables that create favorable conditions in summer. Here we systematically examine whether different meteorological processes are at play in winter. We use cluster analysis and principal component analysis and find physically meaningful groups in ERA5 atmospheric reanalysis data and lightning data for northern Germany. Two sets of conditions emerged: Wind-field-dominated and mass-field (temperature) dominated lightning conditions. Wind-field type lightning is characterized by increased wind speeds, high cloud shear, large dissipation of kinetic energy in the boundary layer, and moderate temperatures. Clouds are close to the ground and a relatively large fraction of the clouds is warmer than −10 °C. Mass-field type lightning is characterized by increased convective available potential energy (CAPE), the presence of convective inhibition (CIN), high temperatures, and accompanying large amounts of water vapor. Large amounts of cloud-physics variables related to charge separation such as ice particles and solid hydrometeors further differentiate both mass-field and wind-field lightning. Winter lightning is wind-field driven whereas in summer lightning is mostly mass-field driven with a small fraction of cases being wind-field driven. Consequently, typical weather situations for wind-field lightning in the study area in northern Germany are strong westerlies with embedded cyclones. For mass-field lightning, the area is typically on the anticyclonic side of a southwesterly jet.

Validation of a Prototype Global 4D-Var Data Assimilation System for the MPAS-Atmosphere Model

A four-dimensional variational (4D-Var) data assimilation (DA) system is developed for the global nonhydrostatic atmospheric dynamical core of the Model for Prediction Across Scales (MPAS). The nonlinear forward and adjoint models of the MPAS-Atmosphere dynamic core are included in a Python-driven structure to formulate a continuous 4D-Var DA system, shown to effectively minimize the cost function that measures the distances between the nonlinear model simulations and observations. In this study, three idealized experiments with a six-hour assimilation window are conducted to validate and demonstrate the numerical feasibilities of the 4D-Var DA system for both uniform- and variable-resolution meshes. In the first experiment, only a single point observation is assimilated. The resulting solution shows that the analysis increments have highly flow-dependent features. The observations in the second experiment are all model prognostic variables that span the entire global domain, the purpose of which is to check how well the initial conditions six hours prior to the observations can be reversely inferred. The differences between the analysis and the referenced "truth" are significantly smaller than those calculated with the first guess. The third experiment assimilates the mass field only, i.e., potential temperatures in the case of MPAS-Atmosphere, and examines the impacts on the wind field and the mass field under initial conditions. Both the wind vectors and potential temperatures in the analysis agree more with the referenced "truth" than the first guess because the adjustments made to the initial conditions are dynamically consistent in the 4D-Var system.

Probability distribution function of the aperture mass field with large deviation theory

ABSTRACT In the context of tomographic cosmic shear surveys, a theoretical model for the one-point statistics of the aperture mass (Map) is developed. This formalism is based on the application of the large deviation principle to the projected matter density field and more specifically to the angular aperture masses. The latter holds the advantage of being an observable that can be directly extracted from the observed shear field and to be, by construction, independent from the long wave modes. Furthermore, we show that, with the help of a nulling procedure based on the so-called BNT transform, it is possible to build observables that depend only on a finite range of redshifts making them also independent from the small-scale modes. This procedure makes predictions for the shape of the one-point probability distribution function of such an observable very accurate, comparable to what had been previously obtained for 3D observables. Comparisons with specific simulations reveal however inconsistent results showing that synthetic lensing maps were not accurate enough for such refined observables. It points to the need for more precise dedicated numerical developments whose performances could be benchmarked with such observables. We furthermore review the possible systematics that could affect such a formalism in future weak-lensing surveys like Euclid, notably the impact of shape noise as well as leading corrections coming from lend–lens couplings, geodesic deviation, reduced shear and magnification bias.

Hydraulic resistances of suspended flows in bedrooms with a moving bottom

The results of some existing theoretical and experimental studies of hydraulic resistances of open flows in moving channels are considered. Possible reasons for the inconsistency of the results of various studies of hydraulic resistance in open channels with increased roughness are indicated. The analysis of mass field data on the Darcy (Shezi) coefficient of canals in alluvial soils and a sandy mobile bed is carried out. It was confirmed that the channels of these categories are characterized by a mixed zone of hydraulic resistance, and regularities were revealed that take into account the features of the real resistance zone of earthen channels. Based on the analysis of the smoothly varying flow of open flows and the corresponding theory of the boundary layer and the law of the logarithmic distribution of velocities, the calculated dependencies are obtained, making it possible to determine the resistance of open flows concerning natural conditions.

Predicting Cardiorespiratory Fitness in Female Soccer Players: The Basque Female Football Cohort Study

Purpose: To develop gender-specific operational equations for prediction of cardiorespiratory fitness in female footballers. Method: Forty-eight semiprofessional female footballers performed an intermittent progressive maximal running test for determination of fixed blood lactate concentration (FBLC) thresholds. Relationships between FBLC thresholds and the physiological responses to submaximal running were examined. Developed equations (n = 48) were compared with equations previously obtained in another investigation performed in males (n = 100). Results: Submaximal velocity associated with 90% maximal heart rate was related to FBLC thresholds (r = .76 to .79; P < .001). Predictive power (R2 = .82 to .94) of a single blood lactate concentration (BLC) sample measured at 10 or 11.5 km·h−1 was very high. A single BLC sample taken after a 5-minute running bout at 8.5 km·h−1 was related to FBLC thresholds (r = −.71; P < .001). No difference (P = .15) in the regression lines predicting FBLC thresholds from velocity associated with 90% maximal heart rate was observed between the female and male cohorts. However, regressions estimating FBLC thresholds by a single BLC sample were different (P = .002). Conclusions: Velocity associated with 90% maximal heart rate was robustly related to FBLC thresholds and might serve for mass field testing independently of sex. BLC equations accurately predicted FBLC thresholds. However, these equations are gender-specific. This is the first study reporting operational equations to estimate the FBLC thresholds in female footballers. The use of these equations reduces the burden associated with cardiorespiratory testing. Further cross-validation studies are warranted to validate the proposed equations and establish them for mass field testing.

What is the most ``non-point'' gravitating or electrically charged object?

In this paper we search the shape of an aspherical body and the direction in space, for which the greatest deviations from the point mass field (the difference from the inverse-square law) take place for large distances from the field source. It turns out to be a system of two equal point-like masses at the poles of a fixed sphere (giving the greatest positive deviations from the point mass field) and uniform distribution of point-like masses (discrete or continuous) around the sphere equator (giving the greatest negative deviations from the point mass field). In these cases the extremal direction of the field measurement respectively passes through point-like particles and coincides with the axis of symmetry of a ring, which is perpendicular to its plane. Our numerical estimations show that any body can be considered with reasonable accuracy (the relative error in the determination of the field strength is less than $5 \%$) as point-like mass if the distance to the observation point is more than an order of magnitude larger than its characteristic sizes. The problem considered in this paper can help readers to probe the limits of applicability of the field point source model.

CLASH-VLT: Enhancement of (O/H) in z = 0.35 RX J2248−4431 cluster galaxies

Aims. Gas-phase metallicities offer insight into the chemical evolution of galaxies as they reflect the recycling of gas through star formation and galactic inflows and outflows. Environmental effects such as star-formation quenching mechanisms play an important role in shaping the evolution of galaxies. Clusters of galaxies at z < 0.5 are expected to be the sites where environmental effects can be clearly observed with present-day telescopes. Methods. We explored the Frontier Fields cluster RX J2248−443 at z = 0.348 with VIMOS/VLT spectroscopy from CLASH-VLT, which covers a central region corresponding to almost 2 virial radii. The fluxes of [OII] λ3727, Hβ, [OIII] λ5007, Hα and [NII] λ6584 emission lines were measured allowing the derivation of (O/H) gas metallicities, star formation rates based on extinction-corrected Hα fluxes, and contamination from active galactic nuclei. We compared our sample of cluster galaxies to a population of field galaxies at similar redshifts. Results. We use the location of galaxies in projected phase-space to distinguish between cluster and field galaxies. Both populations follow the star-forming sequence in the diagnostic diagrams, which allow the ionising sources in a galaxy to be disentangled, with only a low number of galaxies classified as Seyfert II. Both field and cluster galaxies follow the “main sequence” of star-forming galaxies, with no substantial difference observed between the two populations. In the mass–metallicity (MZ) plane, both high-mass field and cluster galaxies show comparable (O/H)s to the local SDSS MZ relation, with an offset of low-mass galaxies (log(M/M⊙) < 9.2) towards higher metallicities. While both the metallicities of “accreted” (R < R500) and “infalling” (R > R500) cluster members are comparable at all masses, the cluster galaxies from the “mass complete” bin (which is the intermediate mass bin in this study: 9.2 < log(M/M⊙) < 10.2), show more enhanced metallicities than their field counterparts by a factor of 0.065 dex with a ∼1.8σ significance. The intermediate-mass field galaxies are in accordance with the expected (O/H)s from the fundamental metallicity relation, while the cluster members deviate strongly from the model predictions, namely by a factor of ∼0.12 dex. The results of this work are in accordance with studies of other clusters at z < 0.5 and favour the scenario in which the hot halo gas of low- and intermediate-mass cluster galaxies is removed due to ram pressure stripping, leading to an increase in their gas-phase metallicity.