Internal Rotation Rate Research Articles

Association and impact of patellofemoral dysplasia on patellofemoral arthropathy and arthroplasty

BackgroundThe association of patellar and trochlear anomalies resulting in isolated patellofemoral osteoarthritis has often been postulated but rarely studied. The purpose of this study was to examine the association of patellofemoral dysplasia, specifically trochlear anomalies, which are a cause for degenerative disease and may result in a worse outcome after arthroplasty for isolated patellofemoral arthritis. MethodsEighteen consecutive patients who underwent robotic image-based patellofemoral arthroplasty were compared with an age and sex-matched group of patients who underwent medial unicompartmental arthroplasty using the same image-based navigation system and had no patellofemoral, lateral disease or malalignment.The compared parameters were the patellofemoral–trochlear angle and Dejour score in the preoperative radiographs and patellofemoral–trochlear angle and internal rotation of the trochlea compared to the intercondylar line in the proximal, middle and distal trochlea. ResultsSignificantly higher rates of patella alta (T=5, P=0.0001) and trochlear dysplasia (6% vs. 55%) were found, as manifested by an increase in the trochlear angle and Dejour score. Furthermore, the trochlea was found to have a higher degree of internal rotation in patients with isolated patellofemoral arthritis compared to the control group. ConclusionsIn conclusion, patellofemoral anomalies such as patella alta and trochlear dysplasia are present in association with isolated patellofemoral arthritis. Isolated patellofemoral arthritis is also associated with higher rates of trochlear internal rotation. Correction of this internal rotation is essential in the success of arthroplasty in patients with patellofemoral disease. Level of evidenceLevel III study, It is a case control study.

Misleading variations in estimated rotational frequency splittings of solar p modes: consequences for helioseismology and asteroseismology

The aim of this paper is to investigate whether there are any 11-yr or quasi-biennial solar cycle-related variations in solar rotational splitting frequencies of low-degree solar p modes. Although no 11-yr signals were observed, variations on a shorter timescale (~2yrs) were apparent. We show that the variations arose from complications/artifacts associated with the realization noise in the data and the process by which the data were analyzed. More specifically, the realization noise was observed to have a larger effect on the rotational splittings than accounted for by the formal uncertainties. When used to infer the rotation profile of the Sun these variations are not important. The outer regions of the solar interior can be constrained using higher-degree modes. While the variations in the low-l splittings do make large differences to the inferred rotation rate of the core, the core rotation rate is so poorly constrained, even by low-l modes, that the different inferred rotation profiles still agree within their respective 1sigma uncertainties. By contrast, in asteroseismology, only low-l modes are visible and so higher-l modes cannot be used to constrain the rotation profile of stars. Furthermore, we usually only have one data set from which to measure the observed low-l splitting. In such circumstances the inferred internal rotation rate of a main sequence star could differ significantly from estimates of the surface rotation rate, hence leading to spurious conclusions. Therefore, extreme care must be taken when using only the splittings of low-l modes to draw conclusions about the average internal rotation rate of a star.

The rotation rate and its evolution derived from improved mode fitting and inversion methodology

We present inferences of the internal solar rotation rate and its evolution during solar cycle 23. A full solar cycle of MDI observations have been analyzed using an improved fitting methodology and using time series of various lengths, up to a single 4,608 day long epoch (64 times 72 days or 12.6 yr). We used time series of spherical harmonic coefficients computed by the MDI group, including those resulting from using their improved spatial decomposition. This decomposition includes our best estimate of the image plate scale and of the MDI instrumental image distortion. The leakage matrix used in the fitting includes the effect of the distortion of the eigenfunctions by the solar differential rotation, while the undistorted leakage matrix was itself carefully reviewed and independently recomputed. Rotation inversions were carried out for all available mode sets, fitted for that epoch, including the MDI and GONG "pipe-line" values. The improved inversion method uses an iterative methodology based on a least-squares regularization, but with an optimal model grid determined by the actual information in the input set. This method also allows us to use an optimized irregular grid, with a variable number of latitudes at different depths.

Acceleration and rotation rate profile comparison from inertial sensors mounted on the service arm between tennis players of different skill level

Two inertial measurement units were placed on the distal and proximal forearms of tennis players of varying skill levels to determine what type of information it is possible to obtain from such sensors and investigate the difference skill level had on the sensor readings. Players of better skill had higher rotation rate on the proximal sensor (elite 2040°/s, rec 1650°/s and beginner 700°/s), which seems similar to previously reported information on shoulder internal rotation rate.1 Shoulder internal rotation rate is a key factor for an effective service. Two players previously had formal technique coaching for their serve; these players acceleration profiles suggest that they contact the ball with less forearm supination than the nontechnique trained group (z-y acceleration ratios were 3.388 and 4.184 in technique-trained compared to 0.206 and 1.226 in nontrained). A system like this could be developed over time to quickly give coaches quantification of a player's performance without the need to use a complex biomechanics laboratory.

Rotation period of Jupiter from the observation of its magnetic field

To determine the Jovian internal rotation rate, historically one has used the repetition period (periodicity) of decametric and decimetric radio waves. The period with which decametric and decimetric radio waves recur on Jupiter (the System III period) was defined by the IAU in 1965 to be 9h 55m 29.71s, based on early radio astronomical data. A more direct way to determine this period is to examine the rotation rate of the dipole field. We have done this using Galileo, Pioneer 10 and 11, Voyager 1 and 2, and Ulysses data over a 25‐year period. We find a small drift in the apparent longitude of the dipole axis that is statistically significant, consistent with there being a small error in the original IAU period, one within the error expected in the defined period. The newly derived period is 9h 55m 29.704 ± 0.003s, 6ms shorter than the 1965 IAU definition, and inconsistent with the value of 9h 55m 29.685s proposed by Higgins et al. (1997).

Helioseismology and the solar cycle: Past, present and future

A major goal of helioseismology is to understand the mechanism of the solar cycle. In this paper, some results of helioseismic observations relevant to the cycle are briefly reviewed, the current state-of-the-art is discussed, and near-term future directions are sketched out. Topics covered include the internal rotation rate; activity-related parameter variations; the tachocline; far-side imaging; the torsional oscillation; and meridional flows.

Modulation of Saturn’s radio clock by solar wind speed

The internal rotation rates of the giant planets can be estimated by cloud motions, but such an approach is not very precise because absolute wind speeds are not known a priori and depend on latitude: periodicities in the radio emissions, thought to be tied to the internal planetary magnetic field, are used instead. Saturn, despite an apparently axisymmetric magnetic field, emits kilometre-wavelength (radio) photons from auroral sources. This emission is modulated at a period initially identified as 10 h 39 min 24 +/- 7 s, and this has been adopted as Saturn's rotation period. Subsequent observations, however, revealed that this period varies by +/-6 min on a timescale of several months to years. Here we report that the kilometric radiation period varies systematically by +/-1% with a characteristic timescale of 20-30 days. Here we show that these fluctuations are correlated with solar wind speed at Saturn, meaning that Saturn's radio clock is controlled, at least in part, by conditions external to the planet's magnetosphere. No correlation is found with the solar wind density, dynamic pressure or magnetic field; the solar wind speed therefore has a special function. We also show that the long-term fluctuations are simply an average of the short-term ones, and therefore the long-term variations are probably also driven by changes in the solar wind.

The Alpha Effect and the Observed Twist and Current Helicity of Solar Magnetic Fields

We present a straightforward comparison of model calculations for the α-effect, helicities, and magnetic field line twist in the solar convection zone with magnetic field observations at atmospheric levels. The model calculations are carried out in a mixing-length approximation for the turbulence with a profile of the solar internal rotation rate obtained from helioseismic inversions. The magnetic field data consist of photospheric vector magnetograms of 422 active regions for which spatially-averaged values of the force-free twist parameter and of the current helicity density are calculated, which are then used to determine latitudinal profiles of these quantities. The comparison of the model calculations with the observations suggests that the observed twist and helicity are generated in the bulk of the convection zone, rather than in a layer close to the bottom. This supports two-layer dynamo models where the large-scale toroidal field is generated by differential rotation in a thin layer at the bottom while the α-effect is operating in the bulk of the convection zone. Our previous observational finding was that the moduli of the twist factor and of the current helicity density increase rather steeply from zero at the equator towards higher latitudes and attain a certain saturation at about 12 – 15∘. In our dynamo model with algebraic nonlinearity, the increase continues, however, to higher latitudes and is more gradual. This could be due to the neglect of the coupling between small-scale and large-scale current and magnetic helicities and of the latitudinal drift of the activity belts in the model.

High-speed non-invasive measurement of tibial rotation during the impact phase of running

Several injuries to the lower extremity in runners have been linked to excessive rates of internal rotation of the tibia just after ground impact. This study presents an improved method of capturing internal/external tibial rotation, and investigates whether estimates of rates of internal tibial rotation during the first 50 ms of contact during running are influenced by the sampling rate and processing of tibial displacement data. A lightweight plate was moulded to the shape of each subject's right anterior-medial tibia. Nine male subjects ran barefoot (3.35 m·s−1) and the landing kinematics of the right leg were recorded at 1000 Hz. The group mean value for the total range of internal rotation of the tibia for the whole stance phase was consistent with the literature (15.4°), but peak angular velocities (8.3 rad·s−1) were substantially higher than previously reported. The cut-off frequency of the low-pass filter influenced the peak angular velocity values obtained with the largest changes occurring between 15 and 40 Hz. Typically, researchers using lower sample rates have to filter around 10 Hz and consequently are likely to underestimate peak angular velocities. These findings have implications for obtaining a sound quantitative foundation for transient tibial motion before furthering our understanding of injury mechanisms.

Asteroseismology of the β Cephei star ν Eridani: interpretation and applications of the oscillation spectrum

The oscillation spectrum of v Eri is the richest known for any variable of the β Cephei type. We interpret the spectrum in terms of normal mode excitation and construct seismic models of the star. The frequency data combined with data on mean colours set the upper limit on the extent of overshooting from the convective core. We use data on rotational splitting of two dipole (l = 1) modes (g 1 and p 1 ) to infer properties of the internal rotation rate. Adopting a plausible hypothesis of nearly uniform rotation in the envelope and increasing rotation rate in the μ-gradient zone, we find that the mean rotation rate in this zone is about three times faster than in the envelope. In our standard model only the modes in the middle part of the oscillation spectrum are unstable. To account for excitation of a possible high-order g mode at v = 0.43 cd -1 as well as p modes at v > 6 cd -1 we have to invoke an overabundance of Fe in the driving zone.

Helicity and the solar dynamo

The central mechanism in traditional mean-field dynamo theory is the α-effect, and it has been found that the presence of kinetic or magnetic helicities is favourable for the effect, which corresponds to the simultaneous generation of magnetic helicities in the mean field and in the fluctuations, the generation rates being equal in magnitude and opposite in sign. Generally, the two helicities generated by the α-effect, that in the mean field and that in the fluctuations, have either to be dissipated in the generation region or to be transported out of this region. The latter presumably leads to the observed appearance of magnetic helicity in the solar atmosphere, which thus provides valuable information on dynamo processes inaccessible to in situ measurements. We have included details of two numerical dynamo studies in the present review, one for a “laminar” dynamo, where no averaging is applied, the other for a mean-field dynamo. In the first case the full nonlinear system of the incompressible MHD equations is studied in idealized rectangular geometry, with an external forcing of the Roberts type driving a flow in the form of an array of convection-like rolls. Defining mean fields by appropriate averages, it is found that there is a segregation of magnetic helicity between the mean field and the fluctuations similar to that predicted by the mean-field theory of the α-effect. The mean-field calculations are done in a quasi-linear approximation for the turbulence, for realistic spherical geometry, with compressibihy included and using a profile of the solar internal rotation rate obtained from helioseismic inversions. The results are compared with observations, concentrating on the observational finding that the moduli of the averaged values of the force-free twist parameter α ff and and the current helicity H C increase from zero at the equator towards higher latitudes and attain a certain saturation level at middle latitudes (at about 20°–30°). On the assumption that the α-effect is operating in a thin spherical shell, the best coincidence between calculated and observed quantities is found for α-effect operation close to the bottom of the convection zone.

Inversion of the Internal Solar Rotation Rate

Accurate determination of the rotation rate in the inner radiative zone (0.2 < r/R☉ < 0.5) of the Sun from helioseismic observations requires rotational frequency splittings of exceptional quality. Indeed, only the very low degree modes are sensitive to the dynamics of the deep interior. Low- and intermediate-degree splittings have been estimated from a variety of instruments and different data analysis procedures. Therefore, it is not surprising that these determinations present significant differences. We have attempted to build consistent data sets to constrain the dynamics of the solar core, excluding features in the data that are not common to all sets as well as excluding modes for frequencies for which such measurements are not reliable. Our inferences of the solar internal rotation profile were obtained from a full two-dimensional numerical inversion based on the optimal mesh distribution methodology, a variant of the regularized least-squares technique. Our results show that the radiative zone rotates at a rate of approximately 435 nHz, slowing down slightly in the core (r/R☉ < 0.35). We also did not find any significant angular differential rotation below the base of the convective zone (r/R☉ ≈ 0.7). We can rule out any departure of the rotation rate in the solar deep interior, 0.2 < r/R☉ < 0.4, by more than 20% of the surface rotation rate at midlatitude. This result is in clear disagreement with the theoretical hydrodynamical models that expect a much faster rotation rate in the solar core, some 10-50 times faster than the surface rate.

Comparative Analysis of GALLEX‐GNO Solar Neutrino Data andSOHO/MDI Helioseismology Data: Further Evidence for Rotational Modulation of the Solar Neutrino Flux

We carry out a comparative analysis of the GALLEX-GNO solar neutrino data and estimates of the solar internal rotation rate derived from the MDI helioseismology experiment on the SOHO spacecraft. We introduce a statistic, which we evaluate as a function of radius and latitude, that is a measure of the degree of of oscillations in the neutrino flux and the synodic solar rotation rate at that radius and latitude. A map of this statistic indicates that the probable location is deep in the convection zone near the equator. We also examine the integral of this statistic over the equatorial section of the convection zone. This provides a measure of the likelihood that the variability of the solar neutrino flux, as measured by the GALLEX-GNO data, has its origin in the equatorial section of the convection zone. We apply the shuffle test, randomly reassigning measurements among runs, to estimate the significance of the value of the statistic computed from the actual data. This test implies that the result is significant at the 0.2% level. When, for comparison, we repeat this analysis for the radiative zone, we find that the integral resonance statistic is not significant. These results support earlier evidence for rotational modulation of the solar neutrino flux.

Helioseismology—sound inside the sun

In 1960, the solar surface was found to be moving radially with a period of 5 min. The cause of this effect was found to be the trapping of acoustic waves in the solar internal thermal gradient. Since the sound fills a resonant cavity, only specific oscillatory modes are present whose characteristics depend on the plasma properties. Thus, the solar interior can be remotely sensed by observing the trapping region’s upper boundary at the surface. This led to the field of helioseismology and produced new information about the solar internal rotation rate, composition, neutrino flux, convection zone depth, and internal changes associated with the solar activity cycle. It has also generated progress in remote sensing techniques (acoustic holography, ring diagrams, inversions), observing facilities (GONG Network, MDI instrument on SOHO), and insights into the coupling of turbulent convection and sound. Presumably, other stars also contain sound and their interiors could thus be probed, but so far no conclusive observations of these vibrations have been obtained. [Work supported by NSF and NASA.]

High-pressure NMR study of cis-1,n-disubstituted[n]paracyclophanes. Effect of increased pressure on the hindered internal rotation.

The effect of hydrostatic pressure on the rate of internal rotation of title compounds has been examined by the DNMR method. Quartz pressure-resisting NMR cells were used to realize the high-pressure experiments up to 390 (line shape measurements) and 450 MPa (chemical shift measurements). Application of hydrostatic pressure was found to accelerate the rotation of the benzene ring, while pressure-induced low-frequency chemical shifts of bridge methylene protons indicated that there is a considerable shrinkage of the methylene bridge structure upon pressurization.

Pressure-Dependent NMR Spectroscopy Indicates That Internal Rotation of Gas-Phase Formamide Follows Statistical Kinetics

Pressure-dependent internal rotation rate constants for [15N]formamide in gas mixtures containing 1.3 Torr of [15N]formamide and SF6 pressures ranging from 150 to 5225 Torr were determined from ana...

Effects of the Earth’s Curvature on the Dynamics of Isolated Objects. Part I: The Disk

Abstract A disk over the frictionless surface of the earth shows an interaction between the center of mass and internal motions. At low energies, the former is an “inertial oscillation” superimposed to a uniform zonal drift c and the latter is a rotation with variable vertical angular velocity ω (as measured by a terrestrial observer). The dynamics is understood best in a stereographic frame following the secular drift. The center of mass has a circular but not uniform motion; its meridional displacement induces the variations of the orbital and internal rotation rates. On the other hand, the temporal mean of the Coriolis forces due to both rotations produces the secular drift. In spherical terrestrial coordinates geometric distortion complicates the description. For instance, the zonal velocity of the center of mass U is not equal to the average zonal component of the particle velocities 〈u〉, as a result of the earth’s curvature. The drift c and the temporal means U and 〈u〉 are all three different. In ad...

Conformational Analysis of Biphenyl Derivatives. I. A Novel Steric Constant from the Internal Rotation Rate of 2,2′-Bis-(N-Substituted Carbamoylmethyl)Biphenyl by Means of Dynamic NMR

A novel scale of steric substituent constant EsD is defined from the correlation of the logarithms of the internal rotation rate (kr) at 393 K with Hancock (Esc) steric constant by means of dynamic NMR. In the inhibition of Pseudomona species lipase by 2,2′-bis-(N-substituted carbamoylmethyl)biphenyls (1-8), the logarithms of bimolecular rate constants are multiply correlated with both the Taft substituent constant σ* and EsD.

Experimental 1H NMR and Computational Studies of Internal Rotation of Solvated Formamide

Solvent effects on the C−N bond rotation process of formamide (FA) are investigated experimentally and theoretically. Temperature-dependent exchange broadened 1H NMR line shapes of [15N]FA in water, dimethyl sulfoxide-d6, and tetrachloroethane-d2, and as neat solution are consistent with ΔG⧧298 values for FA internal rotation, in kilocalories per mole, of 18.2(0.1), 17.8(0.1), 17.2(0.1), and 18.0(0.1), respectively. These values are significantly higher than the gas-phase ΔG⧧298 value, 16.0(0.1) kcal mol-1, and they correlate well with empirical spectroscopic solvent polarity scales. Self-consistent isodensity polarizable continuum model (SC-IPCM) calculations at the HF/6-311++G** level of theory for FA in a series of dielectric constants ranging from 1 to 109 predict a complete reversal of the preferred internal rotation path for hydrated FA compared to gas-phase FA. Equal contributions to the internal rotation rate constant from both possible internal rotation paths is predicted to occur at a dielectric constant of 7.08. SC-IPCM calculations predict that ΔG⧧298 for hydrated FA is 1.99 kcal mol-1 higher than ΔG⧧298 for gas-phase FA. SC-IPCM calculations for a 1:1 FA−H2O complex were performed to allow for direct inclusion of intermolecular hydrogen bonding. The predicted ΔG⧧298 for the hydrated 1:1 FA−H2O complex is ca. 2.3 kcal mol-1 higher than the predicted gas-phase ΔG⧧298, in excellent agreement with experiment.

The effect of foot orthoses on transverse tibial rotation during walking.

The purpose of this study was to determine the effectiveness of two types of foot orthoses in controlling the magnitude and rate of internal tibial rotation, measured by the tibial pointer device, during walking. Ten subjects between the ages of 23 and 43 years volunteered to participate in the study. Prior to data collection, each subject was issued two types of foot orthoses: a pair of rigid, plastic orthoses with posting in either the forefoot or the rearfoot, and a pair of soft, accommodative, premolded orthoses with no posting. All subjects wore standardized footwear. Following a controlled break-in period for both footwear and orthoses, each subject was asked to walk at a self-selected speed over a 12-m walkway while the movement of internal tibial rotation was recorded with a video camera during five trials. The results indicated that both the rigid plastic and the accommodative foot orthoses significantly reduced the magnitude and the rate of internal tibial rotation. No significant difference was noted between the soft and rigid foot orthoses conditions.