Fast Rotation Research Articles

Process simulation and development for laser beam welding with rotating bifocal optics

Laser welding has been an established technology in industrial production. Nevertheless, there are many unsolved problems with cracks and pores when welding certain materials. New process or exposure strategies are therefore being developed to enable a controlled temperature field within the welding zone and thus deliver better welding results.The aim of this study is to investigate a new type of processing optic that uses bifocal optics to split the laser beam into two partial beams and a fast rotation of these two partial beams. Optimum welding parameters for stainless steel were determined while varying the rotational speed and laser power. the same time, simulations were created with the FLOW 3D software, which agree very well with the experimental results.

A theoretical view on the stereochemistry of 1,3-benzoxazol-2-(3H)-ylidenes obtained from double vinylic substitution.

2-(1,3-Benzoxazol-2(3H)-ylidene)-3-oxo-3-phenylpropanenitrile (1) and methyl-2-(1,3-benzoxazol-2(3H)-ylidene)(cyano)acetate (2) are observed as single isomers by NMR spectroscopy. A theoretical study was carried out to investigate if this is due to the exclusive presence of the most stable diastereoisomer or if the ene moiety undergoes fast rotation, thereby allowing for the observation of an average conformer. Indeed, the pronounced stabilization of the E stereoisomer, attributed to intramolecular hydrogen bonding, makes it the single obtained product.

Влияние приливных сил на движение космических аппаратов. Модель тороидального спутника

The model of a toroidal satellite is considered in the limiting case when the major radius of the torus (the distance from the center of the tube to the center of the torus) is much larger than its minor radius (the radius of the tube). Based on the Lagrange method, the equations of motion are derived. It is shown that the obtained mathematical equations describing the rotational motion do not contain small parameters, which implies that tidal forces have a significant effect on the rotational motion of the satellite. Numerical solutions of the obtained equations can be studied by students based on the use of differential equation solving procedures available in MATLAB and Octave environments. Numerical experiment in combination with analytical methods for studying these equations shows that with a sufficiently fast rotation of the satellite around the axis of symmetry, its orientation motion stabilizes and becomes quasi-periodic.

When the horseshoe fits: Characterizing 2023 FY3 with the 10.4 m Gran Telescopio Canarias and the Two-meter Twin Telescope

Context. The Arjuna asteroid belt is loosely defined as a diverse group of small asteroids that follow dynamically cold, Earth-like orbits. Most of them are not actively engaged in resonant, co-orbital behavior with Earth. Some of them experience temporary but recurrent horseshoe episodes. Objects in horseshoe paths tend to approach Earth at a low velocity, leading to captures as Earth’s temporary satellites or mini-moons. Four such objects have already been identified: 1991 VG, 2006 RH120, 2020 CD3, and 2022 NX1. Here, we focus on 2023 FY3, a recent finding, the trajectory of which might have a co-orbital status and perhaps lead to temporary captures. Aims. We want to determine the physical properties of 2023 FY3 and explore its dynamical evolution. Methods. We carried out an observational study of 2023 FY3 using the OSIRIS camera spectrograph at the 10.4 m Gran Telescopio Canarias, to derive its spectral class, and time-series photometry obtained with QHY411M cameras and two units of the Two-meter Twin Telescope to investigate its rotational state. N-body simulations were also performed to examine its possible resonant behavior. Results. The visible reflectance spectrum of 2023 FY3 is consistent with that of an S-type asteroid; its light curve gives a rotation period of 9.3±0.6 min, with an amplitude of 0.48±0.13 mag. We confirm that 2023 FY3 roams the edge of Earth’s co-orbital space. Conclusions. Arjuna 2023 FY3, an S-type asteroid and fast rotator, currently exhibits horseshoe-like resonant behavior and in the past experienced mini-moon engagements of the temporarily captured flyby type that may repeat in the future. The spectral type result further confirms that mini-moons are a diverse population in terms of surface composition.

Concurrent Validity of Cervical Movement Tests Using VR Technology-Taking the Lab to the Clinic.

Reduced cervical range of motion (ROM) and movement velocity are often seen in people with neck pain. Objective assessment of movement characteristics is important to identify dysfunction, to inform tailored interventions, and for the evaluation of the treatment effect. The purpose of this study was to investigate the concurrent validity of a newly developed VR technology for the assessment of cervical ROM and movement velocity. VR technology was compared against a gold-standard three-dimensional optical motion capture system. Consequently, 20 people, 13 without and 7 with neck pain, participated in this quantitative cross-sectional study. ROM was assessed according to right/left rotation, flexion, extension, right/left lateral flexion, and four diagonal directions. Velocity was assessed according to fast cervical rotation to the right and left. The correlations between VR and the optical system for cervical ROM and velocity were excellent, with intraclass correlation coefficient (ICC) values > 0.95. The mean biases between VR and the optical system were ≤ 2.1° for the ROM variables, <12°/s for maximum velocity, and ≤3.0°/s for mean velocity. In conclusion, VR is a useful assessment device for ROM and velocity measurements with clinically acceptable biases. It is a feasible tool for the objective measurement of cervical kinematics in the clinic.

Organic acid fractionation of hardwoods planted in social forestry

Abstract Trema orientalis and Trewia nudiflora are the fastest rotation trees (3–4 years’ rotation) in Bangladesh, and experimentally planted in social forestry in Gazipur district. Biorefinery is the most cited topic in research recent era in order to established circular bioeconomy. In established a biorefinery initiative, both species were fractionated into pulp, lignin and hemicellulose by formic acid (FA) treatment at atmospheric conditions. After alkaline peroxide bleaching of FA treated pulp, the yield was 47.0 % and 41.0 % with α-cellulose of 82.39 % and 81.61 %, and residual pentosan content of 9.26 % and 11.13 % for T. orientalis and T. nudiflora, respectively. The brightness of the pulps was 84.5 % and 85.0 %. Cold alkali extraction of the bleached pulp increased α-cellulose to 92.36 % and 91.29 % which was suitable for cellulose derivatives. Lignin was separated from the spent liquor by adding water. The FA lignin from hardwood replaced 20 % phenol in phenol-formaldehyde resin preparation without sacrifice of shear strength. The lignin separated FA liquor contains mainly pentose sugars, which was subsequently converted to furfural with a yield of 41.39 % and 41.72 % at 170 °C using 0.1 % H2SO4 catalyst from T. orientalis and T. nudiflora, respectively.

Determining the effects of AR/VR HMD design parameters (mass and inertia) on cervical spine joint torques

This study aimed to determine gravitational and dynamic torques and muscle activity of the neck across a series of design parameters of head mounted displays (mass, center of mass, and counterweights) associated with virtual and augmented reality (VR/AR). Twenty young adult participants completed five movement types (Slow and Fast Flexion/Extension and Rotation, and Search) while wearing a custom-designed prototype headset that varied the three design parameters: display mass (0, 200, 500, and 750 g), distance of the display's center of mass in front of the eyes (approximately 1, 3, and 5 cm anteriorly), and counterweights of 0, 166, 332, and 500 g to balance the display mass of 500 g at 7 cm. Inverse dynamics of a link segment model of the head and headset provided estimates of the torques about the joint between the skull and the occiput-first cervical vertebrae (OC1) and joint between the C7 and T1 vertebrae (C7). Surface electromyography (EMG) measured bilateral muscle activity of the splenius and upper trapezius muscles. Adding 750 g of display mass nearly doubled root mean square joint torques across all movement types. Increasing the distance of the display mass in front of the eyes by 4 cm increased torques about OC1 for the Slow and Fast Rotation and Search movements by approximately 20%. Adding a counterweight decreased torques about OC1 during the rotation and search tasks but did not decrease the torques experienced in the lower cervical spine (C7). For the flexion/extension axis, the magnitude of the dynamic torque component was 20% or less of the total torque experienced whereas for the rotation axis the magnitude of the dynamic torque component was greater than 50% of the total torque. Surface EMG root mean square values significantly varied across movement types with the fast rotation having the largest values; however, they did not vary significantly across the headset configurations.

Continuous fiber reinforced meta-composites with tailorable Poisson’s ratio and effective elastic modulus: Design and experiment

Auxetic metamaterials, i.e., with negative Poisson’s ratio are attracting increasing attention. This study develops a novel method to design and investigate continuous fiber-reinforced meta-composites with tailorable negative Poisson’s ratio and effective elastic modulus. First, the design scheme based on parametric level set method, is proposed by combining fast marching method, filtering technology and matrix rotation for attaining the two-dimensional isotropic composites. A novel objective function considering both negative Poisson’s ratio and effective elastic modulus is introduced and the result demonstrate that it is effective to not only accelerate the numerical convergence but also achieve a larger negative Poisson’s ratio when compared with that using the currently-used objective function. By tailoring a weight ratio for balancing the negative Poisson’s ratio and effective elastic modulus, a general contradictive trend was captured. Experimentally, the specimens are accordingly fabricated via 3D printing. Then, the axial compression tests are performed with the aid of digital image correlation technology to characterize the deformation behaviors and evaluate the mechanical properties of the designed meta-composites. Experimental results show that, as the weight ratio increases from 0.02 to 1.57, the effective elastic modulus increases from 180.5 MPa to 310.3 MPa (enhanced by 71.9 %) while the negative Poisson’s ratio decreases from − 0.41 to − 0.036 (reduced by 91.4 %), proving the effectiveness of the design method. The design methods and experimental results can provide effective approaches and important information for designing novel continuous fiber reinforced meta-composites with tailorable mechanical performance.

Cellular dynamics as a marker of normal-to-cancer transition in human cells

Normal-to-cancer (NTC) transition is known to be closely associated to cell´s biomechanical properties which are dependent on the dynamics of the intracellular medium. This study probes different human cancer cells (breast, prostate and lung), concomitantly to their healthy counterparts, aiming at characterising the dynamical profile of water in distinct cellular locations, for each type of cell, and how it changes between normal and cancer states. An increased plasticity of the cytomatrix is observed upon normal-to-malignant transformation, the lung carcinoma cells displaying the highest flexibility followed by prostate and breast cancers. Also, lung cells show a distinct behaviour relative to breast and prostate, with a higher influence from hydration water motions and localised fast rotations upon NTC transformation. Quasielastic neutron scattering techniques allowed to accurately distinguish the different dynamical processes taking place within these highly heterogeneous cellular systems. The results thus obtained suggest that intracellular water dynamics may be regarded as a specific reporter of the cellular conditions—either healthy or malignant.

New mass limit of a strange star admitting a colour flavor locked equation of state

A class of strange stars is analysed in the present article in hydrostatic equilibrium, whose state is defined by a CFL phase equation of state. We have compared our results with those obtained from the MIT equation of state for strange quark matter, which is regarded as free particles. We have noted that if we consider quarks to form a cooper pair and if their description is made by the CFL equation of state, the maximum mass of strange star reaches a value as high as 3.61 M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{\\odot }$$\\end{document}. This value is well above the value of 2.03 M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{\\odot }$$\\end{document} obtained by using the MIT bag equation of state for massless free quarks. Both the maximum masses are determined by solving the TOV equation for different values of the strange quark mass ms\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_s$$\\end{document}. Thus, the inclusion of the possibility of quark pair formation in the theory permits us to accommodate a wider class of compact objects such as PSR J1614-2230, PSR J0740+6620, PSR J0952-0607 etc. and the mass of the companion star in the GW190814 event in our model. The consideration of such a high value of mass is hardly theoretically obtainable from normal strange star models in general relativity even with a fast rotation effect. The object PSR J0952-0607 is found to be the fastest and heaviest pulsar in the disk of Milky Way Galaxy, having a mass of 2.35 M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{\\odot }$$\\end{document}, which may be predicted in our model, as observational evidence supports the existence of strange quark matter in its composition.

Efficiency of orbital atherectomy for eccentric calcium in bending vessels: in-vitro vessel models

Abstract Background/Introduction The mode of action of orbital atherectomy (OA) consists of a fast elliptical rotation of the crown, allowing for focal treatment with slow forward and backward movements. However, reports on the efficiency of OA for eccentric calcium in bending vessels are limited. Purpose This study aimed to clarify the mechanism of action of the crown and elucidate the anatomical condition for an efficient OA on eccentric calcium in bending lesions, via in vitro experimental models. Methods In total, 40 in vitro stenotic vessel models with eccentric calcium were developed; five models with a combination of two calcium positions (inner or outer side bending), two curvature radiuses (R, 10 or 20 mm), and two bending angles (A, 100º or 60º). Each model was connected to a whole aorta model and the procedures were performed using the Diamondback 360 coronary OA system through a 6F short-tip amplatz 1.0 guiding catheter. The protocol included two 30-second low-speed ablations followed by one 30-second high-speed ablation. Micro-computed tomography analyses of the models were performed before and after ablation to evaluate the ablated calcium volume and maximum depth. Results Eccentric calcium at inner side of the bending was more ablated than at outer side (6.6 mm3 vs 2.7 mm3, P &amp;lt; 0.0001). Among the inner side, the ablated calcium volume was higher in the R20/A60 model (8.28 mm3) than in R10/A100 (6.30 mm3; P = 0.14), R10/A60 (5.62 mm3, P = 0.04), and R20/A100 (6.06 mm3, P = 0.09) models (Figure 1A). The ablated maximum depth was also higher in the R20/A60 model (0.98 mm) than in other models (R10/A100: 0.84 mm, R10/A60: 0.90 mm, R20/A100: 0.78 mm); however, there were no significant differences. Moreover, among the outer side, the ablated calcium volume was higher in the R20/A100 model (5.17 mm3) than in the R10/A100 (1.95 mm3, P &amp;lt; 0.001), R10/A60 (2.12 mm3, P = 0.002), and R20/A60 (1.73 mm3, P &amp;lt; 0.001) models (Figure 1B). The ablated maximum depth was also significantly higher in the R20/A100 model (0.47 mm) than in other models (R10/A100: 0.32 mm, P = 0.03; R10/A60: 0.33 mm, P = 0.05; R20/A60: 0.27 mm, P = 0.01). Conclusions Curvature radius and bending angles could be associated with efficiency of OA for eccentric calcium in bending vessels. Although small curvature radiuses may be unsuitable for OA in the inner or outer side, it may be effective for inner side lesions with a large curvature radius and low bending angles, and outer side lesions with a large curvature radius and high bending angles.

Nanoconfined Water in Pillared Zeolites Probed by 1H Nuclear Magnetic Resonance

Here, we report the results of our 1H nuclear magnetic resonance study of the dynamics of water molecules confined in zeolites (mordenite and ZSM-5 structures) with hierarchical porosity (micropores in zeolite lamella and mesopores formed by amorphous SiO2 in the inter-lamellar space). 1H nuclear magnetic resonance (NMR) spectra show that water experiences complex behavior within the temperature range from 173 to 298 K. The temperature dependence of 1H spin-lattice relaxation evidences the presence of three processes with different activation energies: freezing (about 30 kJ/mol), fast rotation (about 10 kJ/mol), and translational motion of water molecules (23.6 and 26.0 kJ/mol for pillared mordenite and ZSM-5, respectively). For translational motion, the activation energy is markedly lower than for water in mesoporous silica or zeolites with similar mesopore size but with disordered secondary porosity. This indicates that the process of water diffusion in zeolites with hierarchical porosity is governed not only by the presence of mesopores, but also by the mutual arrangement of meso- and micropores. The translational motion of water molecules is determined mainly by zeolite micropores.

Building a model of the compression grinding mechanism in a tumbling mill based on data visualization

The object of the study reported here is the grinding process in a tumbling mill where the mechanism of destruction by crushing is implemented, which is caused by the mechanism of compression loading. The compressive interaction in the active zone of the lower end of the granular loading chamber of the rotating drum at the transition of the shear layer to the solid zone was taken into account. The task to determine the parameters of the compressive action was solved, which was caused by the difficulties of modeling and the complexity of the hardware analysis of the behavior of the internal loading of the mill. A mathematical model was built based on data visualization for the compression grinding mechanism. The power of compressive forces was taken as an analog of grinding performance. The initial characteristic of compression was considered to be the mean speed of movement in the central averaged normal cross-section of the shear layer. The influence on the performance of the mass fraction of the shear layer and the reversibility of loading was taken into account. The effect of rotation speed on productivity was evaluated by experimental modeling at a chamber filling degree of 0.45 and a relative size of grinding bodies of 0.0104. The maximum value of energy and grinding productivity was established at a relative speed of rotation ψω=0.6–0.65. The maximum value of the share of the shear layer loading was found at ψω=0.4–0.45. The results have made it possible to establish a rational speed during crushing by compression, ψω=0.55–0.65. This value was smaller in comparison with impact crushing, ψω=0.75–0.9. The observed effect is explained by the detected activation for the shear loading layer during slow rotation, in contrast to the fast rotation for the drop zone. The model built makes it possible to predict rational technological parameters of the process of medium and fine grinding in a tumbling mill by compression.

Study of the energetic X-ray superflares from the active fast rotator AB doradus

ABSTRACT We present the analyses of intense X-ray flares detected on the active fast rotator AB Dor using observations from the XMM–Newton. A total of 21 flares are detected, and 13 flares are analysed in detail. The total X-ray energy of these flares is found to be in the range of 1034−36 erg, in which the peak flare flux increased up to 34 times from the pre-/post-flaring states for the strongest observed flare. The duration of these flaring events is found to be 0.7 to 5.8 h. The quiescent state X-ray spectra are found to be explained by a three-temperature plasma with average temperatures of 0.29, 0.95, and 1.9 keV, respectively. The temperatures, emission measures, and abundances are found to be varying during the flares. The peak flare temperature was found in the 31–89 MK range, whereas the peak emission measure was 1052.5–54.7 cm−3 . The abundances vary during the flares and increase by a factor of ∼3 from the quiescent value for the strongest detected flare. The variation in individual abundances follows the inverse-FIP effect in quiescent and flare phases. The X-ray light curves of AB Dor are found to exhibit rotational modulation. The semi-loop lengths of the flaring events are derived in the range of 109.9−10.7 cm, whereas the minimum magnetic field to confine the plasma in the flaring loop is estimated between 200 and 700 G.

The formation channels of multiphase gas in nearby early-type galaxies

ABSTRACT The processes responsible for the assembly of cold and warm gas in early-type galaxies (ETGs) are not well understood. We report on the multiwavelength properties of 15 non-central, nearby (z ≤ 0.008 89) ETGs primarily through Multi-Unit Spectroscopic Explorer (MUSE) and Chandra X-ray observations, to address the origin of their multiphase gas. The MUSE data reveal that 8/15 sources contain warm ionized gas traced by the H α emission line. The morphology of this gas is found to be filamentary in 3/8 sources: NGC 1266, NGC 4374, and NGC 4684, which is similar to that observed in many group and cluster-centred galaxies. All H α filamentary sources have X-ray luminosities exceeding the expected emission from the stellar population, suggesting the presence of diffuse hot gas, which likely cooled to form the cooler phases. The morphologies of the remaining 5/8 sources are rotating gas discs, not as commonly observed in higher mass systems. Chandra X-ray observations (when available) of the ETGs with rotating H α discs indicate that they are nearly void of hot gas. A mixture of stellar mass-loss and external accretion was likely the dominant channel for the cool gas in NGC 4526 and NGC 4710. These ETGs show full kinematic alignment between their stars and gas, and are fast rotators. The H α features within NGC 4191 (clumpy, potentially star-forming ring), NGC 4643, and NGC 5507 (extended structures) along with loosely overlapping stellar and gas populations allow us to attribute external accretion to be the primary formation channel of their cool gas.

Nested spheroidal figures of equilibrium − IV. On heterogeneous configurations

ABSTRACT The theory of nested figures of equilibrium, expanded in Papers I and II, is investigated in the limit where the number of layers of the rotating body is infinite, enabling to reach full heterogeneity. In the asymptotic process, the discrete set of equations becomes a differential equation for the rotation rate. In the special case of rigid rotation (from centre to surface), we are led to an integro-differential equation (IDE) linking the ellipticity of isopycnic surfaces to the equatorial mass-density profile. In contrast with most studies, these equations are not restricted to small flattenings, but are valid for fast rotators as well. We use numerical solutions obtained from the self-consistent-field method to validate this approach. At small ellipticities (slow rotation), we fully recover Clairaut’s equation. Comparisons with Chandrasekhar’s perturbative approach and with Roberts’ work based on virial equations are successful. We derive a criterion to characterize the transition from slow to fast rotators. The treatment of heterogeneous structures containing mass-density jumps is proposed through a modified IDE.

The MASSIVE survey – XVIII. Deep wide-field K-band photometry and local scaling relations for massive early-type galaxies

ABSTRACT We present wide-field, deep K-band photometry of 98 luminous early-type galaxies (ETGs) from the MASSIVE survey based on observations taken with the WIRCam instrument on the Canada–France–Hawaii Telescope. Using these images, we extract accurate total K-band luminosities (LK) and half-light radii (Re) for this sample of galaxies. We use these new values to explore the size–luminosity and Faber–Jackson relations for massive ETGs. Within this volume-limited sample, we find clear evidence for curvature in both relations, indicating that the most luminous galaxies tend to have larger sizes and smaller velocity dispersions than expected from a simple power-law fit to less luminous galaxies. Our measured relations are qualitatively consistent with the most massive elliptical galaxies forming largely through dissipationless mergers. When the sample is separated into fast and slow rotators, we find the slow rotators to exhibit similar changes in slope with increasing LK, suggesting that low-mass and high-mass slow rotators have different formation histories. The curvatures in the Re–LK and σ–LK relations cancel, leading to a relation between dynamical mass and luminosity that is well described by a single power law: Reσ2 ∝ LKb with b ≈ 1.2. This is consistent with the tilt of the fundamental plane observed in lower mass elliptical galaxies.

Investigating the Influence of High-Speed Gantry Rotation in Cardiac CT on Motion Artifacts in Aortic Stenosis Patients Not Premedicated with β-Blockers: The FAST-CCT Randomized Trial Protocol.

Coronary CT angiography (CCTA) is increasingly used as a non-invasive tool to assess coronary artery disease (CAD). However, CCTA is subject to motion artifacts, potentially limiting its clinical utility. Despite faster (0.35 and 0.28 s/rot) gantry rotation times, low (60-65 bpm) heartbeat is recommended, and the use of β-blockers is often needed. Technological advancements have resulted in the development of faster rotation speeds (0.23 s/rot). However, their added value in patients not premedicated with β-blockers remains unclear. This prospective single-center, two-arm, randomized, controlled trial aims to assess the influence of fast rotation on coronary motion artifacts, diagnostic accuracy of CCTA for CAD, and patient safety. We will randomize a total of 142 patients aged ≥ 50 scheduled for an aortic stenosis work-up to receive CCTA with either a fast (0.23) or standard (0.28 s/rot) gantry speed. rate of CCTAs with coronary motion artifacts hindering interpretation. assessable coronary segments rate, diagnostic accuracy against invasive coronary angiography (ICA), motion artifact magnitude per segment, contrast-to-noise ratio (CNR), and patient ionizing radiation dose. The local ethics committee has approved the protocol. Potential significance: FAST-CCT may improve motion artifact reduction and diagnosis quality, thus eliminating the need for rate control and β-blocker administration. gov identifier: NCT05709652.

Main-sequence companions to white dwarfs – II. The age–activity–rotation relation from a sample of Gaia common proper motion pairs

ABSTRACT Magnetic activity and rotation are related to the age of low-mass main-sequence stars. To further constrain these relations, we study a sample of 574 main-sequence stars members of common proper motion pairs with white dwarfs, identified thanks to Gaia astrometry. We use the white dwarfs as age indicators, while the activity indexes and rotational velocities are obtained from the main-sequence companions using standard procedures. We find that stars older than 5 Gyr do not display H α nor Ca ii H&amp;K emission unless they are fast rotators due to tidal locking from the presence of unseen companions and that the rotational velocities tend to decrease over time, thus supporting the so-called gyrochronology. However, we also find moderately old stars (≃2–6 Gyr) that are active presumably because they rotate faster than they should for their given ages. This indicates that they may be suffering from weakened magnetic braking or that they possibly evolved through wind accretion processes in the past. The activity fractions that we measure for all stars younger than 5 Gyr range between ≃10 and 40 per cent. This is line with the expectations, since our sample is composed of F, G, K, and early M stars, which are thought to have short (&amp;lt;2 Gyr) activity lifetimes. Finally, we observe that the H α fractional luminosities and the $R^{\prime }_\mathrm{HK}$ indexes for our sample of (slowly rotating) stars show a spread (−4 &amp;gt;log(LH α/Lbol); log($R^{\prime }_\mathrm{HK}$) &amp;gt; −5) typically found in inactive M stars or weakly active/inactive F, G, K stars.

Fast Rotating Non-homogeneous Fluids in Thin Domains and the Ekman Pumping Effect

In this paper, we perform the fast rotation limit varepsilon rightarrow 0^+ of the density-dependent incompressible Navier–Stokes–Coriolis system in a thin strip Omega _varepsilon :=,{mathbb {R}}^2times , left. right] -ell _varepsilon ,ell _varepsilon left[ right. ,, where varepsilon in ,left. right] 0,1left. right] is the size of the Rossby number and ell _varepsilon >0 for any varepsilon >0. By letting ell _varepsilon longrightarrow 0^+ for varepsilon rightarrow 0^+ and considering Navier-slip boundary conditions at the boundary of Omega _varepsilon , we give a rigorous justification of the phenomenon of the Ekman pumping in the context of non-homogeneous fluids. With respect to previous studies (performed for flows of contant density and for compressible fluids), our approach has the advantage of circumventing the complicated analysis of boundary layers. To the best of our knowledge, this is the first study dealing with the asymptotic analysis of fast rotating incompressible fluids with variable density in a 3-D setting. In this respect, we remark that the case ell _varepsilon geqslant ell >0 for all varepsilon >0 remains largely open at present.