Rotation Profile Research Articles

Coronal Plane Rotation of the Medial Column in Hallux Valgus (HV), Progressive Collapsing Foot Deformity (PCFD), and Combined PCFD HV: A Retrospective Case Control Study

Category: Bunion; Hindfoot; Midfoot/Forefoot Introduction/Purpose: The presence of hyperpronation of the first metatarsal (M1) seems to have a clinically significant role in Hallux Valgus (HV). Some authors reported a decrease in recurrence rates after M1 hyperpronation correction in HV. However, when measuring the M1 head pronation relative to the ground, we are assessing and quantifying the aggregate coronal rotational profile of each bone and joint throughout the medial column. Therefore, we do not know the location of this hyperpronation. Moreover, studies showed a strong influence of the hindfoot alignment on coronal rotational measurements and Progressive Collapsing Foot Deformity (PCFD) is a condition frequently associated with HV. Our study aimed to assess and compare coronal plane alignment of medial column bones in HV, PCFD, PCFD HV and controls. Methods: We performed a retrospective IRB approved study. We collected 33 feet who consulted our center with combinations of symptomatic PCFD and HV. We then matched 33 HV, 33 PCFD, and 33 controls for BMI, Gender, and Age to this group. We assessed the coronal plane rotation of the navicular, medial cuneiform, M1 at its base and head, the Sesamoid Rotation Angle (SRA) with respect to the ground, and the hallux valgus angle (HVA) using Weight-Bearing CT images (Figure).The positions of the different joints (first naviculocuneiform (NC1), first tarsometatarsal (TMT1) and metatarsosesamoid rotation angle (MSRA)) were found by subtracting the adjacent angles. Intrinsic torsion of M1 was calculated by subtracting the M1 base angle from the M1 head angle.Normality of different variables was assessed using the Shapiro-Wilk test. Groups were compared using t test or ANOVA for normal and Mann Whitney or Kruskal Wallis for nonnormal variables. Results: HV, PCFD and PCFD HV presented higher M1 intrinsic torsion when compared to controls (respectively 7.3°[CI95%:2.9-11.7], p<0.001; 7.5°[CI95%:2.5-12.6], p<0.001; 7.5°[CI95%: 2.9-12],p<0.001).The navicular was more pronated in PCFD HV compared to controls (respectively 20+/-5.2° vs 12.5+/-3.9°,p<0.001) whereas it was not for PCFD and HV.NC1 was 6.8° significantly more supinated in HV (p<0.001) and 5.7° in PCFD HV (p<0.001) compared to controls whereas there was no significant difference between PCFD HV and Controls.TMT1 was 7.3° significantly more pronated in HV (p<0.001) and 4.9° in PCFD HV (p<0.001) compared to controls whereas there was no significant difference between PCFD HV and Controls. MSRA was significantly higher in HV (p<0.001) and PCFD HV (p<0.001) compared to controls whereas there was no significant difference between PCFD and Controls. In multivariate analysis, MSRA (β=0.95,[0.83;1.07], p <0.0001) were associated with higher values of HVA whereas NC1 (β=-0.24,[-0.42;-0.06], p= 0.0076) were associated with lower values of HVA. Conclusion: The intrinsic increase in M1 pronation appears to be a shared developmental abnormality in PCFD and HV. Combination of PCFD and HV seems to originate from the presence of a paradoxical supinatory malposition of the NC1 which was not present in PCFD without HV in our study. The presence of this compensatory supination malposition might explain the presence of HV by causing a metatarsosesamoid dislocation in HV and PCFD HV. In contrast, hyperpronation compensation in PCFD without HV might be proximal to the navicular because there was no difference between PCFD and control regarding the navicular position in our study.

Development and Validation of a Mobile Application for Measuring Tibial Torsion.

Tibial torsion lacks a single and reliable method for its measurement. While physical examination, computed tomography (CT), and EOS imaging are used complementarily, three-dimensional (3D) CT is the most widely used method for intuitive documentation and visualization. However, concern regarding the associated radiation hazard limits its use in the evaluation of pediatric patients. Moreover, EOS machines are too expensive and too large to be placed in every clinic requiring the measurement of tibial torsion. Therefore, a new method for 3D reconstruction is needed. In the present study, we tested the validity and reliability of a novel reconstruction tool for the lower leg. A statistical shape model and Laplacian constraint were adopted for the development of a new reconstruction tool for measuring tibial torsion. Tibial torsion measurements based on a 3D reconstruction application and CT images for 36 patients were evaluated for intraobserver and interobserver reliability. Tibial torsion measurements for 75 patients were compared for validation. A 3D reconstruction system for the lower leg was developed as a mobile application and was installed in a portable device for easy access in the clinical setting. In terms of interobserver reliability, the intraclass correlation coefficient among 3 clinicians was 0.896 (95% confidence interval [CI], 0.828 to 0.941). The correlation coefficient between tibial torsion measured with use of 3D CT and that measured with the mobile application was 0.865 (p < 0.001). The mobile application showed excellent reliability and validity for measuring tibial torsion. Concurrent utilization with mobile application for the femur allows visualization of the rotational profile of the leg without the need for CT or EOS. Diagnostic Level III . See Instructions for Authors for a complete description of levels of evidence.

Prevalence of trivial zero-energy subgap states in nonuniform helical spin chains on the surface of superconductors

Helical spin chains, consisting of magnetic (ad-)atoms, on the surface of bulk superconductors are predicted to host Majorana bound states (MBSs) at the ends of the chain. Here, we investigate the prevalence of trivial zero-energy bound states in these helical spin chain systems. First, we show that the Hamiltonian of a helical spin chain on a superconductor can be mapped to an effective Hamiltonian reminiscent of a semiconductor nanowire with strong Rashba spin-orbit coupling. In particular, we show that a varying rotation rate between neighbouring magnetic moments maps to smooth non-uniform potentials in the effective nanowire Hamiltonian. Previously it has been found that trivial zero-energy states are abundant in nanowire systems with smooth potentials. Therefore, we perform an extensive search for zero-energy bound states in helical spin chain systems with varying rotation rates. Although bound states with near zero-energy do exist for certain dimensionalities and rotation profiles, we find that zero-energy bound states are far less prevalent than in semiconductor nanowire systems with equivalent non-uniformities. In particular, utilising varying rotation rates, we do not find zero-energy bound states in the most experimentally relevant setup consisting of a one-dimensional helical spin chain on the surface of a three-dimensional superconductor, even for profiles that produce near zero-energy states in equivalent one- and two- dimensional systems. Although our findings do not rule them out, the much reduced prevalence of zero-energy bound states in long non-uniform helical spin chains compared with equivalent semi-conductor nanowires, as well as the ability to measure states locally via STM, should reduce the experimental barrier to identifying MBSs in such systems.

Rotational and Gas Temperature Measurements for He-C Plasma: Application to Heterogeneous Carbon Nanotubes Synthesis

Plasmas containing carbon cover a wide range of application, either using graphite electrodes or carbon containing plasma gas. The study of the C2 molecule is an interesting way to get information on moderate temperature part of the discharge. In the case of heterogeneous carbon nanotubes (CNTs) synthesis by electric arc, reasonable yield can be achieved with substitution of boron and/or nitrogen atoms by optimizing synthesis parameters. This is based on the knowledge of the plasma and gas temperatures in the synthesis chamber. While electrodes material is vaporized through the arc, nanotubes formed in the growth zone a few centimeters away, when temperature decreases down to 1200 °C–1500 °C. Molecular temperature is particularly relevant since it corresponds to the outer part of the arc, in contact with the growth zone. In this article, Abel inversion is used on side-on integrated spectral profiles for C2(0,0) Swan band, in order to get radial rotational temperature profiles. In addition, gas temperature measurements are performed using thermocouples in the arc chamber. Results show that a strong plasma temperature gradient is associated with favorable synthesis conditions for carbon-bore-nitrogen nanotubes. Gas thermal homogeneity is reached in the chamber after about 30 s, mainly through convection processes.

System overstrength factor induced by interaction between structural reinforced concrete walls, floors and gravity frames: Analytical formulation

In multi-storey structural wall buildings, the structural walls are required to resist additional shear force due to their interactions with the floors and gravity-resisting system, which is not fully catered for in current seismic design provisions and assessment guidelines. This paper scrutinizes the mechanics of the interaction between structural reinforced concrete (RC) structural walls, floors and gravity frames in multi-storey RC structural wall buildings during elastic and nonlinear response phases. It also investigates the implications of this interaction on design of multi-story RC wall buildings. Generic expressions are derived to predict the drift and rotation profiles of multi-storey RC wall buildings. Then, a simple hand calculation method is developed to estimate the system (moment) overstrength of multi-storey RC wall buildings due to system (wall-floor-frames) interaction. The proposed method is applied to a prototype building with different slab dimensions and stiffness, and verified by comparing with the system overstrength factor obtained using finite element analysis. The simplified method estimates, and the nonlinear finite element analyses results agree, that a system overstrength factor of 1.7 can be used to account for the 3D interaction between the structural walls, floors and gravity frames in design and assessment of typical ductile RC wall buildings.

The role of rotation on the formation of second generation stars in globular clusters

ABSTRACT By means of 3D hydrodynamic simulations, we explore the effects of rotation in the formation of second-generation (SG) stars in globular clusters (GC). Our simulations follow the SG formation in a first-generation (FG) internally rotating GC; SG stars form out of FG asymptotic giant branch (AGB) ejecta and external pristine gas accreted by the system. We have explored two different initial rotational velocity profiles for the FG cluster and two different inclinations of the rotational axis with respect to the direction of motion of the external infalling gas, whose density has also been varied. For a low (10−24 g cm−3) external gas density, a disc of SG helium-enhanced stars is formed. The SG is characterized by distinct chemo-dynamical phase space patterns: it shows a more rapid rotation than the FG with the helium-enhanced SG subsystem rotating more rapidly than the moderate helium-enhanced one. In models with high external gas density ($10^{-23}\, {\rm g\ cm^{-3}}$), the inner SG disc is disrupted by the early arrival of external gas and only a small fraction of highly enhanced helium stars preserves the rotation acquired at birth. Variations in the inclination angle between the rotation axis and the direction of the infalling gas and the velocity profile can slightly alter the extent of the stellar disc and the rotational amplitude. The results of our simulations illustrate the complex link between dynamical and chemical properties of multiple populations and provide new elements for the interpretation of observational studies and future investigations of the dynamics of multiple-population GCs.

Backtracing the internal rotation history of the β Cep star HD 129929

Context. HD 129929 is a slowly rotating β Cephei pulsator with a rich spectrum of detected oscillations, including two rotational multiplets. The asteroseismic interpretation revealed the presence of radial differential rotation in this massive star of ∼9.35 M⊙. The stellar core is indeed estimated to spin ∼3.6 times faster than the surface. The surface rotation was consequently derived as v ∼ 2 km s−1. This massive star represents an ideal counterpart to the wealth of space-based photometry results for main-sequence and evolved low-mass stars. Those latter stars have revealed a new, and often unexpected, picture of the angular momentum transport processes acting in stellar interiors. Aims. We investigate in a new way the constraints on the internal rotation of HD 129929, as a marker of the evolution of the internal rotation during the main sequence of a massive star. We test both hydrodynamic and magnetic instability transport processes of angular momentum. Methods. We used the best asteroseismic model obtained in an earlier work. We calibrated stellar models including rotation, with different transport processes, to reproduce that reference model. We then looked to determine whether one process is favoured to reproduce the rotation profile of HD 129929, based on the fit of the asteroseismic multiplets. Results. The impact of the Tayler magnetic instability on the angular momentum transport predicts a ratio of the core-to-surface rotation rate of only 1.6, while the recently revised prescription of this mechanism predicts solid-body rotation. Both are too low in comparison with the asteroseismic inference. The models with only hydrodynamic processes are in good agreement with the asteroseismic measurements. Strikingly, we can also get a constraint on the profile of rotation on the zero age main sequence: likely, the ratio between the core and surface rotation was at least ∼1.7. Conclusions. Transport of angular momentum by the Tayler magnetic instability is discarded for this star. The models with pure hydrodynamical processes reproduce the asteroseismic constraints. This result is specific to a slow rotator and has to be verified more generally in other massive main-sequence stars. Constraints on the rotation in earlier stages of this star also offer a new opportunity to test the impact of accretion during the pre-main sequence evolution.

Sunspot Rotation in High- and Low-Flaring Active Regions

Sunspot rotations are closely linked with flaring activity. They are thought to contribute to the accumulation of helicity in magnetic flux tubes and to triggering magnetic reconnection in large solar flares. This link to solar flares has led to sunspot rotations being used as a parameter in solar flare prediction methods, but analysis for long-period observations of rotations in the literature is scarce. In this study, the rotation profiles of sunspots in a selection of six active regions are studied over time periods of 5 – 10 days to measure how sunspot rotation varies as active regions develop. The active regions are divided into two categories: high-flaring groups, which produced at least one X-class flare, and low-flaring regions that had little flaring activity. Comparison of the rotation profiles in these regions showed that young complex sunspot groups exhibit faster angular velocities and more frequent changes in rotation than older single-spot groups and, although the most rotating groups were also the most flare-productive, sudden changes in rotation were found to not definitively indicate an imminent eruption.

Effects of ICRF waves to EAST LHCD discharges on intrinsic rotations

Ion cyclotron range of frequencies (ICRFs) have proven to efficiently serve as a toroidal rotation source in tokamak plasmas. Recent experiments on the experimental advanced superconducting tokamak show that the rotation profiles are remarkably modified when the internal inductance (l i) changed. The comparisons of the ion and electron temperature profiles among ICRF-heated plasmas suggest that the change in l i can remarkably affect the toroidal rotation velocity. The scaling of rotation velocity increments as a function of the change in l i also suggests that ICRF would serve as a reliable rotation source in plasmas with larger l i decrements.

Four bright eclipsing binaries with γ Doradus pulsating components: CM Lac, MZ Lac, RX Dra, and V2077 Cyg

ABSTRACT The study of pulsating stars in eclipsing binaries holds the promise of combining two different ways of measuring the physical properties of a star to obtain improved constraints on stellar theory. Gravity (g) mode pulsations such as those found in γ Doradus stars can be used to probe rotational profiles, mixing, and magnetic fields. Until recently few γ Doradus stars in eclipsing binaries were known. We have discovered g-mode pulsations in four detached eclipsing binary systems from light curves obtained by the Transiting Exoplanet Survey Satellite (TESS) and present an analysis of their eclipses and pulsational characteristics. We find unresolved g-mode pulsations at frequencies 1–1.5 d−1 in CM Lac, and measure the masses and radii of the component stars from the TESS data and published radial velocities. MZ Lac shows a much richer frequency spectrum, including pressure modes and tidally excited g-modes. RX Dra is in the northern continuous viewing zone of TESS so has a light-curve covering a full year, but shows relatively few pulsation frequencies. For V2077 Cyg we formally measure four pulsation frequencies, but the available data are inadequate to properly resolve the g-mode pulsations. V2077 Cyg also shows total eclipses, with which we obtain the first measurement of the surface gravity of the faint secondary star. All four systems are bright and good candidates for detailed study. Further TESS observations are scheduled for all four systems, with much improved temporal baselines in the cases of RX Dra and V2077 Cyg.

This Month in Anesthesiology

This Month in Anesthesiology

Hybrid Method for Optimization of Permanent Magnet Synchronous Machine (PMSM) Rotation using FA-ANFIS

PMSM uses the principle of Faraday's experiment by rotating a magnet in a coil by utilizing another energy source. When the magnet moves in the coil or vice versa. The rotation of the machine will change the flux of magnetic force on the coil and penetrate perpendicularly to the coil so that a potential difference arises between the ends of the coil. It is caused by a change in magnetic flux. The Firefly Algorithm (FA) method has been proven successful in overcoming system optimization problems. Modifying the FA is expected to improve its performance of the FA. To get the best control method, it is necessary to vary the speed control model. This study compares the PMSM speed control without a controller, PID Control, PID-FA, and PID-FA-ANFIS. The simulation results show that the best model on the PID-FA-ANFIS controller which is closest to the Speed Reff (2980 rpm) is that PID-FA-ANFIS obtains a rotation profile with the smallest undershot, the fastest steady state, the best output current profile, the best torque profile, and the best stress profile. The results of this study will be followed by other uses of artificial intelligence.

The halo of M 105 and its group environment as traced by planetary nebula populations

Context. M 105 (NGC 3379) is an early-type galaxy in the nearby Leo I group, the closest galaxy group to contain all galaxy types and therefore an excellent environment to explore the low-mass end of intra-group light (IGL) assembly. Aims. We present a new and extended kinematic survey of planetary nebulae (PNe) in M 105 and the surrounding 30′×30′ in the Leo I group with the Planetary Nebula Spectrograph (PN.S) to investigate kinematically distinct populations of PNe in the halo and the surrounding IGL. Methods. We use PNe as kinematic tracers of the diffuse stellar light in the halo and IGL, and employ photo-kinematic Gaussian mixture models to (i) separate contributions from the companion galaxy NGC 3384, and (ii) associate PNe with structurally defined halo and IGL components around M 105. Results. We present a catalogue of 314 PNe in the surveyed area and firmly associate 93 of these with the companion galaxy NGC 3384 and 169 with M 105. The PNe in M 105 are further associated with its halo (138) and the surrounding exponential envelope (31). We also construct smooth velocity and velocity dispersion fields and calculate projected rotation, velocity dispersion, and λR profiles for the different components. PNe associated with the halo exhibit declining velocity dispersion and rotation profiles as a function of radius, while the velocity dispersion and rotation of the exponential envelope increase notably at large radii. The rotation axes of these different components are strongly misaligned. Conclusions. Based on the kinematic profiles, we identify three regimes with distinct kinematics that are also linked to distinct stellar population properties: (i) the rotating core at the centre of the galaxy (within 1Reff) formed in situ and is dominated by metal-rich ([M/H] ≈ 0) stars that also likely formed in situ, (ii) the halo from 1 to 7.5Reff consisting of a mixture of intermediate-metallicity and metal-rich stars ([M/H] &gt; −1), either formed in situ or was brought in via major mergers, and (iii) the exponential envelope reaching beyond our farthest data point at 16Reff, predominately composed of metal-poor ([M/H] &lt; −1) stars. The high velocity dispersion and moderate rotation of the latter are consistent with those measured for the dwarf satellite galaxies in the Leo I group, indicating that this exponential envelope traces the transition to the IGL.

Dark energy and extending the geodesic equations of motion: A spectrum of galactic rotation curves

A recently proposed extension of the geodesic equations of motion, where the worldline traced by a test particle now depends on the scalar curvature, is used to study the formation of galaxies and galactic rotation curves. This extension is applied to the motion of a fluid in a spherical geometry, resulting in a set of evolution equations for the fluid in the nonrelativistic and weak gravity limits. Focusing on the stationary solutions of these equations and choosing a specific class of angular momenta for the fluid in this limit, we show that dynamics under this extension can result in the formation of galaxies with rotational velocity curves (RVC) that are consistent with the Universal Rotation Curve (URC), and through previous work on the URC, the observed rotational velocity profiles of 1100 spiral galaxies. In particular, a spectrum of RVCs can form under this extension, and we find that the two extreme velocity curves predicted by it brackets the ensemble of URCs constructed from these 1100 velocity profiles. We also find that the asymptotic behavior of the URC is consistent with that of the most probable asymptotic behavior of the RVCs predicted by the extension. A stability analysis of these stationary solutions is also done, and we find them to be stable in the galactic disk, while in the galactic hub they are stable if the period of oscillations of perturbations is longer than 0.91_{pm 0.31} to 1.58_{pm 0.46} billion years.

Rotationally resolved gas-phase spectrum of the [formula omitted]2Σ+–[formula omitted]2Π3/2 electronic transition for the cyanogen halide radical cation ICN+

A rotationally resolved gas-phase absorption spectrum of the A∼2Σ+–X∼2Π3/2 electronic transition of the cyanogen iodide radical cation ICN+ was observed by cavity ring-down spectroscopy for the first time. This cation was produced in a supersonic planar discharge jet through a mixture of ICN in helium. By the aid of a program for rotational, vibrational and electronic spectra PGOPHER, the rotational constants were determined to be 0.10700(12) and 0.11002(12) cm−1 for the A∼2Σ+ and X∼2Π3/2 electronic states, respectively, and the band origin to be 18262.083(3) cm−1. The rotational constant ratio β {= (B′−B″)/B″} was determined to be −2.8%. The β values for FCN+, ClCN+, BrCN+, and ICN+ were also evaluated theoretically by CAM-B3LYP/CEP-121G using Gaussian 09W. The rotational profile of the absorption band and its temperature dependence for ClCN+, one of the important candidates for Diffuse Interstellar Bands, were simulated, aiding us in the identification of this cation as in interstellar space.

Rotational abnormalities in dysplastic hips and how to predict acetabular torsion

ObjectivesThe aim of this study was to investigate the degree to which conventional radiography can represent the acetabular and femoral rotational alignment profile between dysplastic and borderline-dysplastic hips.MethodsA retrospective trial was conducted including 56 borderline-dysplastic and dysplastic hips at a mean age of 28.9 years (range from 18 to 46). Inclusion criteria consisted of symptomatic patients with hip dysplasia undergoing 2-dimensional radiography as well as computed tomography. On radiography, the lateral center edge angle, acetabular hip index, hip lateralization index, acetabular index angle, and the Sharp angle were measured, and the presence of a crossover sign was noted. In computed tomography, the full rotational profile of the lower limb was measured.ResultsSignificant correlations were observed in the overall analysis between the anteversion of the acetabulum and the hip lateralization index (mean 0.56, coefficient of regression (CoR) −32.35, p = 0.011) as well as the acetabular index angle with a mean of 11.50 (CoR 0.544, p = 0.018). Similar results were found in the subgroup of dysplastic hips with an acetabular index angle of 13.9 (p = 0.013, CoR 0.74). For the borderline-dysplastic group, no significant correlations between the pelvis radiography and rotational CT were seen.ConclusionAlthough the femoral and acetabular torsion cannot be predicted from x-rays, the anteversion of the acetabulum correlates with the acetabular index angle, the hip lateralization index, and eventually the beta angle in dysplastic hips. For borderline-dysplastic hips, such results did not show up, which strongly illustrates the need for computed tomography in these cases.Key Points• Much of the current literature focuses on rotational alignment especially with respect to the femur and tibia in healthy patients, although little is known about the acetabular, femoral, and tibial torsion in dysplastic hips.• This is the first study showing significant correlations between the anteversion of the acetabulum and the hip lateralization index as well as the acetabular inclination angle. Also, it is the first study to provide a mechanism for estimation of the torsion of the acetabulum with plain radiography in dysplastic hips.• In borderline-dysplastic hips, no significant correlation was found, which raises the question if a simple x-ray has enough validity to address the acetabular deformity with surgery.

Influence of the Hall current on the convective and magnetorotational instability in a thin layer of an electrically conductive nanofluid

This study investigates the combined influence of the Hall current and the axial magnetic field on the criterion for the onset of convection in a nonuniformly rotating layer of electrically conductive nanofluids taking into account the effects of Brownian diffusion and thermophoresis. The analytical and numerical computations are presented for water-based nanofluids with alumina nanoparticles. In the absence of a temperature gradient, a new type of magnetorotational instability in an axial magnetic field in a thin layer of a nanofluid is considered. The growth rate and regions of development of this instability are numerically obtained depending on the angular velocity profile (the Rossby number Ro) and the radial wavenumber k. In the presence of temperature and nanoparticle concentration gradients, the stationary regime of nonuniformly rotating magnetoconvection is studied. The exact analytical expression for critical Rayleigh number Rast is obtained in terms of various nondimensional parameters. The results indicate that the increase in the Lewis number, the modified diffusivity ratio, and the concentration Rayleigh number is to accelerate the onset of convection. The increase in the Hall current parameter can delay or enhance the onset of convective instability. Rotation profiles with negative Rossby numbers lower the threshold for the development of thermal instability and stimulate the onset of convection. The conditions for stabilization and destabilization of stationary convection in an axial magnetic field are determined. The results are represented graphically and verified numerically.

On the toroidal‐velocity antidynamo theorem under the presence of nonuniform electric conductivity

AbstractLaminar electrically conducting Couette flows with the hydrodynamically stable quasi‐Keplerian rotation profile and nonuniform conductivity are probed for dynamo instability. In spherical geometry, the equations for the poloidal and the toroidal field components completely decouple, resulting in free decay, regardless of the spatial distribution of the electric conductivity. In cylindrical geometry the poloidal and toroidal components do not decouple, but here also we do not find dynamo excitations for the cases that the electric conductivity only depends on the radius or – much more complex– that it only depends on the azimuthal or the axial coordinate. The transformation of the plane‐flow dynamo model of Busse and Wicht (1992) to cylindrical or spherical geometry therefore fails. It is also shown that even the inclusion of axial flows of both directions does not support the dynamo mechanism. The Elsasser toroidal‐velocity antidynamo theorem, according to which dynamos without any radial velocity component cannot work, is thus not softened by nonuniform conductivity distributions.

Ray Tracing of MHD Rossby Waves in the Solar Tachocline: Meridional Propagation and Implications for the Solar Magnetic Activity

Rossby waves have been recently recognised for their role in the large-scale spatio-temporal organisation of the solar magnetic activity. Here, we study the propagation of magnetohydrodynamic Rossby waves in a thin layer, representing the solar tachocline. We consider the waves embedded in a meridionally varying background state characterised by a mean zonal flow, which mimics the differential rotation profile of the Sun, and a toroidal magnetic field. Two anti-symmetric toroidal magnetic fields are utilised: one having a global structure with the maximum at around 50o and the other characterised by a narrow band centered at around 20o. We show that for a global structure toroidal magnetic field, the MHD Rossby modes undergo significant meridional propagation, either equatorward or poleward. In addition, the latitude where the waves exhibit a stationary behaviour is sensitive to the strength of the background magnetic field. On the other hand, a narrow band toroidal magnetic field is shown to work as a waveguide for the fast branch of MHD Rossby waves.

Translation and rotation of particles in different flow pattern areas of a silo

The present paper reports the results obtained for translational and rotational velocity profiles of spherical particles for the mixed flow in a conical silo. The discrete element method (DEM) based on Hertz-Mindlin (no slip) with RVD rolling friction contact model is used for simulations. Opposite correlations are found between translational and rotational velocities in different flow areas of the silo. In particular, the abrasion caused by rotation is dominant in the funnel flow area. In addition, increase of the mass flow rate of silo can effectively reduce the abrasion induced by rotation. This highlights that understanding of dynamic characteristics of particles is helpful for optimization of silos and reduction of granular material abrasion.