Angular Velocity Research Articles

EXPLORATION OF THE INVERSE AND FORWARD KINEMATICS OF A TWO-LINK ROBOT ARM USING MATLAB

This contribution focuses on solving the inverse and forward kinematics in the kinematic analysis of a two-link manipulator model. It involves determining the trajectory of the end effector through fifth-degree polynomial interpolation. Furthermore, given initial and final arm angle values, it computes not only the end effector trajectory but also the angular parameters of individual actuators in both arms. Additionally, it calculates the variations of angular parameters such as rotation angle, angular velocity, and angular acceleration in each kinematic pair. The direct kinematics task is utilized to define the manipulator's workspace. The task is carried out using Matlab software, and the results are presented in the form of graphs and tables.

Dynamics of a bouncing capsule: An impulse model vs a Hertzian model

A capsule-shaped object, unlike a sphere, can rebound to a higher height than it is dropped from if it has an initial spin. In this paper, we compare two quantitative models of this phenomenon: an impulse-based analytic model and a force-based Hertzian model. We experimentally studied the effects of impact angular velocity and contact angle on the capsule's rebounding velocity and angular velocity. Our experimental findings showed successful agreement with our Hertzian model but not with our impulse model. We attribute the comparative success of the Hertzian model to its intricate treatment of the slip–stick behavior of friction during the collision.

A Bionic Localization Memristive Circuit Based on Spatial Cognitive Mechanisms of Hippocampus and Entorhinal Cortex.

In this article, a bionic localization memristive circuit is proposed, which mainly consists of head direction cell module, grid cell module, place cell module and decoding module. This work modifies the two-dimensional Continuous Attractor Network (CAN) model of grid cells into two one-dimensional models in X and Y directions. The head direction cell module utilizes memristors to integrate angular velocity and represents the real orientation of an agent. The grid cell module uses memristors to sense linear velocity and orientation signals, which are both self-motion cues, and encodes the position in space by firing in a periodic mode. The place cell module receives the grid cell module's output and fires in a specific position. The decoding module decodes the angle or place information and transfers the neuron state to a 'one-hot' code. This proposed circuit completes the localizing task in space and realizes in-memory computing due to the use of memristors, which can shorten the execution time. The functions mentioned above are implemented in LTSPICE. The simulation results show that the proposed circuit can realize path integration and localization. Moreover, it is shown that the proposed circuit has good robustness and low area overhead. This work provides a possible application idea in a prospective robot platform to help the robot localize and build maps.

Kinematic modelling of three link robot manipulator and joint torque optimization using genetic algorithm in MATLAB

This research article presents the non-linear dynamic of a three-link robotic manipulator formulated by the Newton-Euler method. The planar manipulator is composed of three links and three revolute joints rotating about the z-axis. The three nonlinear non-homogeneous dynamic equations have been solved graphically with the help of MATLAB by phase variable method. The work represents the graphical solution of the transient response of angular position, and angular velocity of each link member for a predetermined interval of time. With the help of simulated value from MATLAB, torque characteristics have been determined for different torque ratios and optimum torque has been derived using a genetic algorithm to move the manipulator in a proper direction.

The tri-band high spectral resolution spectrometer with gratings in tandem for the charge-exchange recombination spectroscopy diagnostic system on HL-2A tokamak

Charge-exchange (CX) recombination spectroscopy is a powerful tool monitoring ion temperature and plasma rotation with good temporal and spatial resolutions. A compact, new design for a high-throughput, tri-band high spectral resolution spectrometer has been developed for the charge-exchange recombination spectroscopy measurement on the HL-2A tokamak. The simultaneous measurements of He II (468.57 nm), C VI (529.1 nm), and Dα (656.1 nm accompanied by beam emission spectra) with an acquisition frequency up to 400 Hz are achieved by vertically binning the spectrum from each fiber in experiments. Initial results indicate that the system can provide radial profiles of not only ion temperature and rotation velocity, but also concentration of carbon. For the case of helium, the measurements for the ion temperature and rotation velocity are straightforward but the apparent concentration associated with the observed CX intensity is obviously too high. Modeling of the active He II CX feature including plume contributions needs to be carried out to extract the true helium concentration. The spectrometer could become a prototype for the ITER charge-exchange recombination spectroscopy diagnostic and the pilot experiments, as presented here, demonstrate the possibility of impurity concentrations measurements based on the combined measurement of local beam emission and charge-exchange recombination spectroscopy spectra.

Reduced-dimensional prediction method for the axial aerodynamic forces in the off-design operation of near-critical CO2 centrifugal compressors

In the high-load centrifugal compressor of near-critical CO2 (NcCO2) power-generation cycle, the overload of axial aerodynamic force causes significant harms to the structural safety and operational stability of turbomachinery components. Based on a transcritical CO2 compressor of a MWt-class simple recuperated cycle, we numerically studied the aero-thermodynamic characteristics of back-cavity leakage, and discussed the physical model of the axial aerodynamic forces in off-design operation of NcCO2 compressors. Finally, reduced-dimensional prediction method for the axial aerodynamic forces in the near-critical CO2 compressor was developed. Wherein, the Japikse's method was used to estimate the primary aerodynamic loads of centrifugal impeller, and a 1-D radial equilibrium equation with angular velocity ratio was derived to predict the thrust force acting on the impeller back disk. Furtherly, based on the near-wall distribution pattern of angular velocities and physical property of Rankine vortex, a semi-empirical model of angular velocity ratio was introduced and completed the model of back-disk force. In validation, the reduced-dimensional prediction method exhibited satisfactory accuracy with perfectly acceptable errors compared to the refined CFD simulations. Thereby, a reduced-dimensional prediction method for the axial aerodynamic forces was developed for the economical and agile analysis of NcCO2 compressors in engineering practices.

Kinematics analysis of planetary roller screw mechanism with misalignment

The misalignment is unavoidable for planetary roller screw mechanism (PRSM) in practical application due to many uncertainties. The misalignment has a strong effect on the kinematic characteristics of PRSM. However, the relevant research has been rarely reported in the past. In order to clearly present the motion characteristics, a novel kinematics model of PRSM with misalignment is established in this article. The rotational tensor theory is introduced to obtain the coordinate transformation equations. The position vectors of PRSM with misalignment are acquired to calculate the position of the contact point. The motion model of PRSM with misalignment is derived by analyzing the velocity of the contact point. Compared with some published literature, the kinematic model of PRSM is verified. Moreover, a relationship between the misalignment variates, which are the misalignment angle, the misalignment azimuth angle, and the offset distance of the nut's ending point, respectively, and the kinematic characteristics of PRSM are investigated. The results indicate that those misalignment variates have a great influence on the kinematics of PRSM and lead to fluctuations in the PRSM's transmission velocity and angular velocity ratio. The fluctuation amplitude of transmission velocity is positively correlated with misalignment angle.

Evaluation of Biomechanical and Mental Workload During Human-Robot Collaborative Pollination Task.

The purpose of this study is to identify the potential biomechanical and cognitive workload effects induced by human robot collaborative pollination task, how additional cues and reliability of the robot influence these effects and whether interacting with the robot influences the participant's anxiety and attitude towards robots. Human-Robot Collaboration (HRC) could be used to alleviate pollinator shortages and robot performance issues. However, the effects of HRC for this setting have not been investigated. Sixteen participants were recruited. Four HRC modes, no cue, with cue, unreliable, and manual control were included. Three categories of dependent variables were measured: (1) spine kinematics (L5/S1, L1/T12, and T1/C7), (2) pupillary activation data, and (3) subjective measures such as perceived workload, robot-related anxiety, and negative attitudes towards robotics. HRC reduced anxiety towards the cobot, decreased joint angles and angular velocity for the L5/S1 and L1/T12 joints, and reduced pupil dilation, with the "with cue" mode producing the lowest values. However, unreliability was detrimental to these gains. In addition, HRC resulted in a higher flexion angle for the neck (i.e., T1/C7). HRC reduced the physical and mental workload during the simulated pollination task. Benefits of the additional cue were minimal compared to no cues. The increased joint angle in the neck and unreliability affecting lower and mid back joint angles and workload requires further investigation. These findings could be used to inform design decisions for HRC frameworks for agricultural applications that are cognizant of the different effects induced by HRC.

An optimal regulation of grid-connected doubly-fed induction generator angular speed and the DC-link voltage

In this work, a linear quadratic regulator controller is utilized to optimize the gains of the machine-side converter and grid-side converter controllers. The DC-link voltage and the rotational speed of the doubly-fed induction generator are optimally regulated by these controls. Additionally, the small-signal stability of the proposed system has been evaluated using the linearized model of the system. The small-signal stability analysis of the designed system has been accomplished through the application of the eigenvalues and participation factors technique. The suggested controller has been tested in a variety of operating conditions under small disturbances. MATLAB/SIMULINK simulation simulations have been used to evaluate the efficacy of the suggested optimal control system. Additionally, the generator-angular speed and DC-link voltage dynamic performances demonstrate the efficacy of the proposed controller. Finally, the robustness of the proposed controller has also been tested and validated using OPAL-RT technology under large perturbations at stator terminal voltage.

A Full Accounting of the Visible Mass in SDSS MaNGA Disk Galaxies

We present a study of the ratio of visible mass to total mass in spiral galaxies to better understand the relative amount of dark matter present in galaxies of different masses and evolutionary stages. Using the velocities of the Hα emission line measured in spectroscopic observations from the Sloan Digital Sky Survey (SDSS) MaNGA Data Release 17 (DR 17), we evaluate the rotational velocity of over 5500 disk galaxies at their 90% elliptical Petrosian radii, R 90. We compare this to the velocity expected from the total visible mass, which we compute from the stellar, H i, H2, and heavy metals and dust masses. H2 mass measurements are available for only a small subset of galaxies observed in SDSS MaNGA DR17, so we derive a parameterization of the H2 mass as a function of absolute magnitude in the r band using galaxies observed as part of SDSS DR7. With these parameterizations, we calculate the fraction of visible mass within R 90 that corresponds to the observed velocity. Based on statistically analyzing the likelihood of this fraction, we conclude that the null hypothesis (no dark matter) cannot be excluded at a confidence level better than 95% within the visible extent of the disk galaxies. We also find that when all mass components are included, the ratio of visible to total mass within the visible extent of star-forming disk galaxies increases with galaxy luminosity.

Experimental study and numerical simulation of the impact of under-sleeper pads on the dynamic and static mechanical behavior of heavy-haul railway ballast track

AbstractLaying the under-sleeper pad (USP) is one of the effective measures commonly used to delay ballast degradation and reduce maintenance workload. To explore the impact of application of the USP on the dynamic and static mechanical behavior of the ballast track in the heavy-haul railway system, numerical simulation models of the ballast bed with USP and without USP are presented in this paper by using the discrete element method (DEM)—multi-flexible body dynamic (MFBD) coupling analysis method. The ballast bed support stiffness test and dynamic displacement tests were carried out on the actual operation of a heavy-haul railway line to verify the validity of the models. The results show that using the USP results in a 43.01% reduction in the ballast bed support stiffness and achieves a more uniform distribution of track loads on the sleepers. It effectively reduces the load borne by the sleeper directly under the wheel load, with a 7.89% reduction in the pressure on the sleeper. Furthermore, the laying of the USP changes the lateral resistance sharing ratio of the ballast bed, significantly reducing the stress level of the ballast bed under train loads, with an average stress reduction of 42.19 kPa. It also reduces the plastic displacement of ballast particles and lowers the peak value of rotational angular velocity by about 50% to 70%, which is conducive to slowing down ballast bed settlement deformation and reducing maintenance costs. In summary, laying the USP has a potential value in enhancing the stability and extending the lifespan of the ballast bed in heavy-haul railway systems.

Influence of aging on the relation between head control and hip joint kinematics during crossover stepping.

Falls in older individuals are a serious health issue in super-aged societies. The stepping reaction is an important postural strategy for preventing falls. This study aimed to reveal the characteristics of lateral stepping in response to mechanical disturbance by means of an analysis of the hip joint kinematics in the stepping leg and head stability during crossover steps. The participants included 11 healthy older and 13 younger individuals. An electromagnet-controlled disturbance-loading device induced crossover steps due to lateral disturbance. Responses were measured using a motion capture system and force plates. The righting reaction of the head was quantified by lateral displacement (sway), neck joint kinematics (angle displacement, angular velocity), and neck joint moment during crossover stepping. Moreover, the relationship between the neck lateral bending moment and angular velocity of hip flexion/adduction of the stepping leg was examined. The lateral head sway was significantly larger in the older participants (1.13±0.7 m/s2) than in the younger individuals (0.54±0.3 m/s2); whereas, the angle displacement (older -14.1±7.1 degree, young -8.3±4.5 degree) and angular velocity (older 9.9±6.6 degree/s, 41.2±27.7 degree/s) of the head were significantly lower in the older than in the younger participants. In both groups, the moment of neck lateral bending exhibited a significant negative correlation with the hip flexion angular velocity of the stepping leg. Correlation analysis also showed a significant negative correlation between the neck lateral bending moment and hip adduction angular velocity only in the older group (r = 0.71, p<0.01). In conclusion, older individuals increased instability in the lateral direction of the head and decreased righting angle displacement and angular velocity of the head during crossover steps. The correlation between neck moment and hip flexion/adduction angular velocity suggested a decrease in step speed due to increased neck muscle tone, which could be influenced by vestibulospinal reflexes.

Proposing a physical mechanism to explain various observed sources of QPOs by simulating the dynamics of accretion disks around the black holes

We propose a mechanism to explain the low-frequency QPOs observed in X-ray binary systems and AGNs. To achieve this, we perturbed stable accretion disks around Kerr and EGB black holes at different angular velocities, revealing characteristics of shock waves and oscillations on the disk. By applying this perturbation to scenarios with varying alpha values for EGB black holes and different spin parameters for Kerr black holes, we numerically observed changes in the disk dynamic structure and its oscillations. Through various numerical models, we found that the formation of one- and two-armed spiral shock waves on the disk serves as a mechanism for generating QPOs. We compared the QPOs obtained from numerical calculations with the low-frequency QPOs observed in X-ray binary systems and AGN sources, finding high consistency with observations. We observed that the shock mechanism, leading to QPOs, explains the X-ray binaries and AGNs studied in this article. Our numerical findings indicate that QPOs are more strongly dependent on the EGB constant than on the black hole spin parameter. However, we highlighted that the primary impact on oscillations and QPOs is driven by the perturbation angular velocity. The results from the models showed that the perturbation asymptotic speed at V∞=0.2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{\\infty }=0.2$$\\end{document} independently generates QPO frequencies, regardless of the black hole spin parameter and the EGB coupling constant. Therefore, for the moderate value of V∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{\\infty }$$\\end{document}, a two-armed spiral shock wave formed around the black hole is suggested as a decisive mechanism in explaining low-frequency QPOs.

Moderately dense granular gas of inelastic rough spheres

A kinetic theory for moderately dense gases of inelastic and rough spherical molecules is developed from the Enskog equation where a macroscopic state is characterised by 29 scalar fields which correspond to the moments of the distribution function: mass density, hydrodynamic velocity, pressure tensor, absolute temperature, translational and rotational heat fluxes, hydrodynamic angular velocity and angular velocity flux. The balance equations for the 29 scalar fields are obtained from a transfer equation derived from the Enskog equation where the kinetic and potential parts of the new moments of the distribution function and production terms are calculated from Grad’s distribution function for the basic fields. The transition from the 29 field theory to an eight field theory—with mass density, hydrodynamic velocity, absolute temperature and hydrodynamic angular velocity—leads to the determination of the transport coefficients of the Navier–Stokes and Fourier laws. The transport coefficients are functions of the normal and tangential restitution coefficients and of the local equilibrium radial distribution function. The transport coefficients in the limiting case of elastic rough spheres is also determined.

Factors Associated with Return to Sport After Anterior Cruciate Ligament Reconstruction: A Focus on Athletes Who Desire Preinjury Level of Sport.

In most previous studies investigating return to preinjury level of sport (RTPS) after anterior cruciate ligament reconstruction (ACLR), whether patients continue aiming for RTPS not only before but also after ACLR was unclear because environmental and social factors were not considered. Herein, we aimed to evaluate factors associated with RTPS among athletes who desired to achieve RTPS even after ACLR, excluding patients who no longer desire this goal owing to environmental and social factors. Ninety-two patients who underwent primary double-bundle ACLR with a minimum 2-year follow-up and desired to achieve RTPS before surgery were retrospectively enrolled. Twelve (13%) patients who no longer desired to achieve RTPS after ACLR owing to environmental and social factors were excluded. Sixty-nine patients were included in the final cohort. At the final follow-up, the patients were split into two groups: those who achieved (R group) or did not achieve (N group) RTPS based on patient self-assessment. The Knee Injury and Osteoarthritis Outcome Score (KOOS) and Lysholm scores were also determined. The anterior tibial translation in the Lachman test and acceleration and external rotational angular velocity (ERAV) in the pivot shift test were measured at the hardware removal operation. Significant differences were observed for preinjury level of sports between the groups (P <.05). The rate of RTPS in competitive athletes was lower than that in recreational athletes (20/46: 43%, 16/22: 73%; P =.037). Lysholm score, KOOS symptom, pain, and quality of life showed higher values in the R than in the N group (P <.050). Acceleration was significantly lower in the R than in the N group (P =.028). Competitive level of sports is a risk factor for failure to achieve RTPS. The postoperative functional outcomes in the group that achieved RTPS showed more favorable results. These results provide important information to enable the surgeons to consider the appropriate surgical plan for competitive athletes who desire to achieve RTPS after ACLR.

Influence of operating conditions in nonlinear vibration of a drill-string

In this work, the vibrational analysis of an oil drill-string is carried out concerning nonlinear and nonsmooth dynamical model with coupled axial-torsional modes. This study aims to investigate the influence of operating conditions to avoid bit-bounce and stick-slip phenomena. A discrete lumped dynamic model with two degrees of freedom is considered. Dry friction and the possibility of loss of contact between the bit and the formation introduce two nonsmooth conditions into the system. Numerical simulations are performed to obtain the dynamic responses and to evaluate critical operating conditions. A parametric analysis is carried out to determine the influence of the weight on the drill bit and the angular velocity of the rotary table on the severity of critical vibrations for different drilling depths. A map is obtained, where normal operation, stick-slip, and bit-bounce responses are defined, allowing a choice of suitable parameters so that the drill-string does not experience critical vibration issues. The results indicate that the safety region, where normal operation is realized, depends on the drilling depth. However, when the angular velocity of the rotary table is equal to 10 rad/s and the weight on the drill bit is greater than 55 kN ensures normal operation for any drilling depth.

Feature analysis of joint motion in paralyzed and non-paralyzed upper limbs while reaching the occiput: A cross-sectional study in patients with mild hemiplegia.

The reaching motion to the back of the head with the hand is an important movement for daily living. The scores of upper limb function tests used in clinical practice alone are difficult to use as a reference when planning exercises for movement improvements. This cross-sectional study aimed to clarify in patients with mild hemiplegia the kinematic characteristics of paralyzed and non-paralyzed upper limbs reaching the occiput. Ten patients with post-stroke hemiplegia who attended the Department of Rehabilitation Medicine of the Jikei University Hospital and met the eligibility criteria were included. Reaching motion to the back of the head by the participants' paralyzed and non-paralyzed upper limbs was measured using three-dimensional motion analysis, and the motor time, joint angles, and angular velocities were calculated. Repeated measures multivariate analysis of covariance was performed on these data. After confirming the fit to the binomial logistic regression model, the cutoff values were calculated using receiver operating characteristic curves. Pattern identification using random forest clustering was performed to analyze the pattern of motor time and joint angles. The cutoff values for the movement until the hand reached the back of the head were 1.6 s for the motor time, 55° for the maximum shoulder joint flexion angle, and 145° for the maximum elbow joint flexion angle. The cutoff values for the movement from the back of the head to the hand being returned to its original position were 1.6 s for the motor time, 145° for the maximum elbow joint flexion angle, 53°/s for the maximum angular velocity of shoulder joint abduction, and 62°/s for the maximum angular velocity of elbow joint flexion. The numbers of clusters were three, four, and four for the outward non-paralyzed side, outward and return paralyzed side, and return non-paralyzed side, respectively. The findings obtained by this study can be used for practice planning in patients with mild hemiplegia who aim to improve the reaching motion to the occiput.

Helical Gearbox Defect Detection with Machine Learning Using Regular Mesh Components and Sidebands

The current paper presents helical gearbox defect detection models built from raw vibration signals measured using a triaxial accelerometer. Gear faults, such as localized pitting, localized wear on helical pinion tooth flanks, and low lubricant level, are under observation for three rotating velocities of the actuator and three load levels at the speed reducer output. The emphasis is on the strong connection between the gear faults and the fundamental meshing frequency GMF, its harmonics, and the sidebands found in the vibration spectrum as an effect of the amplitude modulation (AM) and phase modulation (PM). Several sets of features representing powers on selected frequency bands or/and associated peak amplitudes from the vibration spectrum, and also, for comparison, time-domain and frequency-domain statistical feature sets, are proposed as predictors in the defect detection task. The best performing detection model, with a testing accuracy of 99.73%, is based on SVM (Support Vector Machine) with a cubic kernel, and the features used are the band powers associated with six GMF harmonics and two sideband pairs for all three accelerometer axes, regardless of the rotation velocities and the load levels.

Data-driven constrained reinforcement learning algorithm for path tracking control of hovercraft

This paper presents a novel Constrained Backstepping Reinforcement Learning (CBRL) approach designed for path tracking of hovercraft. The approach addresses the challenges posed by complex modeling, multiple constraints, and large sideslip angles during high-speed maneuvers of underactuated hovercraft. Initially, a unique state constraint function is formulated, incorporating constraint boundaries related to navigation speed and path curvature. Additionally, transformations are applied to the yaw angular velocity and virtual yaw control law, ensuring that the yaw angular velocity remains within safety limits. Subsequently, a data-driven backstepping reinforcement learning optimal approach, coupled with a line-of-sight guidance law, is employed to guide the hovercraft along the intended path by regulating its yaw angle. Simultaneously, the backstepping reinforcement learning optimal control scheme is used to regulate the surge speed of the hovercraft above the resistance peak speed, thereby preventing excessive sideslip angles during path tracking. Neural network observers are integrated into the design process of both the yaw and surge controllers to monitor system dynamics in the presence of interference. Through simulation, the effectiveness and feasibility of the proposed CBRL algorithm are demonstrated.

Chemical evolution of the Galactic bulge with different stellar populations

The metallicity distribution function (MDF) of the Galactic bulge is characterized by a multi-peak shape, with a metal-poor peak centered at $ Fe/H sim-0.3 $ dex and a metal-rich peak centered at $ Fe/H sim+0.3 $ dex. The bimodality of the MDF is also reflected in the alpha /Fe versus Fe/H abundance ratios, suggesting the presence of different stellar populations in the bulge. In this work we aim to reproduce the observed MDF of the Galactic bulge by testing a scenario in which the metal-poor component of the bulge is formed by stars formed in situ, during a strong burst of star formation, while the metal-rich population is formed by stars created in situ during a second burst of star formation and/or stars accreted from the innermost part of the Galactic disk as an effect of a growing bar. We adopted a chemical evolution model that is able to follow the evolution of several chemical species with detailed nucleosynthesis prescriptions. In particular, because of the importance of the production of Fe in constraining the MDF, close attention is paid to the production of this element in both Type Ia supernovae and massive stars. In particular, we included yields from rotating massive stars with different rotational velocity prescriptions. Our model also takes the infall and outflow of gas into account, as well as the effect of stellar migration. Results are compared to sim 13000 stars from the SDSS/APOGEE survey that belong to the region located at a Galactocentric distance $ R_ GC kpc We successfully reproduce the observed double-peak shape of the bulge MDF as well as the abundance trends of the alpha elements relative to Fe by assuming both (i) a multi-burst star formation history with a quenching of the first burst of $ 10^2\ Myr $ and (ii) migration of stars from the innermost part of the Milky Way disk, as an effect of a growing bar. According to our results, the fraction of the stellar mass of the bulge-bar that belongs to the inner disk is $ sim40&lt;!PCT!&gt; $. In terms of the nucleosynthesis, we conclude that models that assume either no rotation for massive stars or a distribution of rotational velocities that favors slow rotation at high metallicities best reproduce the observed MDF as well as the alpha /Fe and the Ce/Fe versus Fe/H abundance patterns.