Velocity Moments Research Articles

Single-Leg Drop Jump Biomechanics After Ankle or Knee Joint Cooling in Healthy Young Adults.

It is unclear if lower-extremity joint cooling alters biomechanics during a functional movement. To investigate the effects of unilateral lower-extremity cryotherapy on movement alterations during a single-leg drop jump. A crossover design. Laboratory. Twenty healthy subjects (10 males and 10 females; 23y, 169cm, 66kg). Subjects completed a single-leg drop jump before and after a 20-minute ankle or knee joint cooling on the right leg, or control (seated without cooling) on 3 separate days. Time to peak knee flexion, vertical ground reaction force, lower-extremity joint angular velocity (sagittal plane only), and angle and moment (sagittal and frontal planes) in the involved leg over the entire ground contact (GC; from initial contact to jump-off) during the first landing. Time to peak knee flexion was compared using an analysis of variance; the rest of the outcome measures were analyzed using functional analyses of variance (P < .05). Neither joint cooling condition changed the time to peak knee flexion (F2,95 = 0.73, P = .49). Ankle joint cooling reduced vertical ground reaction force (55N at 4% of GC), knee joint angular velocity (44°/s during 5%-9% of GC), and knee varus moment (181N·m during 18%-20% of GC). Knee joint cooling resulted in a reduction in knee joint angular velocity (24°/s during 37%-40% of GC) and hip adduction moment (151N·m during 46%-48% of GC), and an increase in hip joint angular velocity (16°/s during 49%-53% of GC) and plantarflexion angle (1.5° during 11%-29% of GC). Resuming activity immediately after lower-extremity joint cooling does not seem to predispose an individual to injury during landing because altered mechanics are neither overlapping with the injury time period nor of sufficient magnitude to lead to an injury.

Multiple stellar populations in Schwarzschild modeling and the application to the Fornax dwarf

Dwarf spheroidal (dSph) galaxies are believed to be strongly dark matter dominated and thus are considered perfect objects to study dark matter distribution and test theories of structure formation. They possess resolved, multiple stellar populations that offer new possibilities for modeling. A promising tool for the dynamical modeling of these objects is the Schwarzschild orbit superposition method. In this work we extend our previous implementation of the scheme to include more than one population of stars and a more general form of the mass-to-light ratio function. We tested the improved approach on a nearly spherical, gas-free galaxy formed in the cosmological context from the Illustris simulation. We modeled the binned velocity moments for stars split into two populations by metallicity and demonstrate that in spite of larger sampling errors the increased number of constraints leads to significantly tighter confidence regions on the recovered density and velocity anisotropy profiles. We then applied the method to the Fornax dSph galaxy with stars similarly divided into two populations. In comparison with our earlier work, we find the anisotropy parameter to be slightly increasing, rather than decreasing, with radius and more strongly constrained. We are also able to infer anisotropy for each stellar population separately and find them to be significantly different.

The velocity distribution of white dwarfs in Gaia EDR3

ABSTRACT Using a penalized maximum likelihood, we estimate, for the first time, the velocity distribution of white dwarfs in the solar neighbourhood. Our sample consists of 129 675 white dwarfs within 500 pc in Gaia Early Data Release 3. The white dwarf velocity distributions reveal a similar structure to the rest of the solar neighbourhood stars, reflecting that white dwarfs are subject to the same dynamical processes. In the velocity distribution for three magnitude-binned subsamples, we, however, find a novel structure at (U, V) = (7, −19) km s−1 in fainter samples, potentially related to the Coma Berenices stream. We also see a double-peaked feature in U − W at U ≈ −30 km s−1 and in V − W at V ≈ −20 km s−1 for fainter samples. We determine the velocity distribution and velocity moments as a function of absolute magnitude for two samples based on the bifurcation identified in Gaia Data Release 2 in the colour–magnitude diagram. The brighter, redder sequence has a larger velocity dispersion than the fainter, bluer sequence across all magnitudes. It is hard to reconcile this kinematic difference with a bifurcation caused purely by atmospheric composition, while it fits neatly with a significant age difference between the two sequences. Our results provide novel insights into the kinematic properties of white dwarfs and demonstrate the power of analytical techniques that work for the large fraction of stars that do not have measured radial velocities in the current era of large-scale astrometric surveys.

Turbulence Statistics of Arbitrary Moments of Wall-Bounded Shear Flows: A Symmetry Approach.

The calculation of turbulence statistics is considered the key unsolved problem of fluid mechanics, i.e., precisely the computation of arbitrary statistical velocity moments from first principles alone. Using symmetry theory, we derive turbulent scaling laws for moments of arbitrary order in two regions of a turbulent channel flow. Besides the classical scaling symmetries of space and time, the key symmetries for the present work reflect the two well-known characteristics of turbulent flows: non-Gaussianity and intermittency. To validate the new scaling laws we made a new simulation at an unprecedented friction Reynolds number of 10 000, large enough to test the new scaling laws. Two key results appear as an application of symmetry theory, which allowed us to generate symmetry invariant solutions for arbitrary orders of moments for the underlying infinite set of moment equations. First, we show that in the sense of the generalization of the deficit law all moments of the streamwise velocity in the channel center follow a power-law scaling, with exponents depending on the first and second moments alone. Second, we show that the logarithmic law of the mean streamwise velocity in wall-bounded flows is indeed a valid solution of the moment equations, and further, all higher moments in this region follow a power law, where the scaling exponent of the second moment determines all higher moments. With this we give a first complete mathematical framework for all moments in the log region, which was first discovered about 100years ago.

Local Similarity Theory of Convective Turbulent Layer Using “Spectral” Prandtl Mixing Length and Second Moment of Vertical Velocity

Abstract Approximations of the turbulent moments of the atmospheric convective boundary layer are constructed based on a variant of the local similarity theory. As the basic parameters of this theory, the second moment of vertical velocity and the “spectral” Prandtl mixing length are used. This specific choice of the basic parameters allows us to consider the coefficient of turbulent transfer and the dissipation of kinetic energy of the Prandtl turbulence theory as the forms of the local similarity. Therefore, the obtained approximations of the turbulent moments should be considered as natural complementation to the semiempirical turbulence theory. Moreover, within the atmospheric surface layer, the approximations of the new local similarity theory are identical to the relations of the Monin–Obukhov similarity theory (MOST). Therefore, the proposed approximations should be considered as a direct generalization of the MOST under free-convection conditions. The new approximations are compared with the relations of the known local similarity theories. The advantages and limitations of the new theory are discussed. The comparison of the approximations of the new local similarity theory with the field and laboratory experimental data indicates the high effectiveness of the proposed approach.

Design Method of Diffuser in Rotodynamic Multiphase Pump Based on Fourth-order Distribution of Velocity Moment

Design Method of Diffuser in Rotodynamic Multiphase Pump Based on Fourth-order Distribution of Velocity Moment

Impact of dribbling on spatiotemporal and kinetic parameters in wheelchair basketball athletes

BackgroundWheelchair basketball is one of the most popular Paralympic sports. Dribbling a ball while propelling is a key feature of wheelchair basketball. Very few studies have investigated the biomechanical impact of dribbling. This study aims to analyze the impact of dribbling on the amplitude and symmetry of spatiotemporal and kinetic parameters of wheelchair propulsion. MethodsTen experienced wheelchair basketball athletes (31.5 ± 10.6 years old; 7 men, 3 women) with various classifications performed eight 9-m sprints along a straight line on a basketball court: four sprints using classic synchronous propulsion, and four sprints while dribbling a ball down the court. FindingsDribbling decreased velocity, mean propulsive moments and the force rate of rise, as well as increased push time, force rate of rise asymmetry and angular impulse asymmetry. All kinetic variables were asymmetric and higher on the dominant limb. InterpretationThe combination of reduced velocity and propulsive moments when dribbling indicates that wheelchair basketball athletes may deliberately preserve a safety margin of acceleration to adapt to uncontrolled ball rebounds. Dribbling was not associated with any factors associated with an increased risk of musculoskeletal disorders.

Flow characteristics of gerotor vacuum pumps with multistage designs

This paper investigates the effect of multistage designs on flow characteristics of a gerotor type vacuum pump connected in serial and parallel. The three-dimensional computational fluid dynamics (CFD) models are established based on dynamic mesh method to simulate the fluid flow. The effects of serial versus parallel designs on fluid flow rate, pressure ripple, outlet flow velocity and fluid moment are explored and described in details for 2 to 4-stage designs. The analysis results show that both serial and parallel connection designs have relatively better flow characteristics for 3 and 4-stage designs as compared to 2-stage design however the greater stage designs encounter leakage issues and power losses. For the same number of stages, the flow rate, pressure ripple and outlet flow velocity are significantly greater in the parallel connection with multistage design as compared to serial connection. Taking into consideration all the flow aspects, a 3-stage design connected in parallel can be an economical and efficient design.

Moments of Intra-Dome Velocity Distribution as Robust Predictors of Rupture Status in Cerebral Aneurysms

Wall shear stress (WSS), the spatial gradient of flow velocity at luminal surface, has been employed for aneurysmal hemodynamic analysis, but it is sensitive to surface irregularities and noise. We devised a volumetric approach to evaluate discriminant power of intra-dome flow velocity distribution and modal analysis in rupture status determination compared with previously described WSS analysis. Catheter three-dimensional rotational angiographic datasets matched for volume were segmented in 20 sidewall aneurysms (10 ruptured), computational fluid dynamics simulations were performed, and velocity distributions were extracted from mesh-independent isometric sampling followed by moment analysis (mean, variance, skewness, and kurtosis). Univariate and multivariate analysis was used to evaluate discriminant performance of velocity moments. Sensitivity of velocity moments and WSS was evaluated to bleb presence and surface irregularity using digital bleb removal and surface noise addition. Velocity moments of ruptured aneurysms showed higher skewness (2.45 ± 0.57 vs. 1.36 ± 0.82, P= 0.003) and kurtosis (11.83 ± 4.77 vs. 6.05 ± 4.65, P= 0.01) with lower mean (0.019 ± 0.01 vs. 0.038 ± 0.02, P= 0.03) compared with unruptured lesions; in multivariate modeling, skewness alone emerged as best predictor (area under the curve= 0.88). Bleb removal increased low WSS by 548%, and surface noise decreased it by 85.8% while having a smaller (<7%) effect on velocity skewness and kurtosis. High aneurysm dome flow velocity skewness and kurtosis suggest an exponential distribution in ruptured lesions, with high peaks at low velocities, consistent with areas of slow flow. In contrast to WSS-based techniques, this approach is robust against surface variations, with promising improved rupture status discriminant performance that requires further validation in expanded future studies.

Multi-beam energy moments of measured compound ion velocity distributions

Compound ion distributions, fi(v), have been measured with high-time resolution by NASA's Magnetospheric Multi-Scale Mission (MMS) and have been found in reconnection simulations. A compound distribution, fi(v), consisting, for example, of essentially disjoint pieces will be called a multi-beam distribution and modeled as a sum of “beams,” fi(v) = f1(v) + ⋯ + fN(v). Velocity moments of fi(v) are taken beam by beam and summed. Such multi-beam moments of fi(v) have advantages over the customary standard velocity moments of fi(v), for which there is only one mean flow velocity. For example, the standard thermal energy moment of a pair of equal and opposite cold particle beams is non-zero even though each beam has zero thermal energy. We therefore call this thermal energy pseudothermal. By contrast, a multi-beam moment of two or more beams has no pseudothermal energy. We develop three different ways of approximating a compound ion velocity distribution, fi(v), as a sum of beams and finding multi-beam moments for both a compound fi(v) measured by MMS in the dayside magnetosphere during reconnection and a compound fi(v) found in a particle-in-cell simulation of magnetotail reconnection. The three methods are (i) a visual method in which the velocity centroid of each beam is estimated and the beam densities are determined self-consistently, (ii) a k-means method in which particles in a particle representation of fi(v) are sorted into a minimum energy configuration of N (= k) clusters, and (iii) a nonlinear least squares method based on a fit to a sum of N kappa functions. Multi-beam energy moments are calculated and compared with standard moments for the thermal energy density, pressure tensor, thermal energy flux (heat plus enthalpy fluxes), bulk kinetic energy density, ram pressure, and bulk kinetic energy flux. Applying this new formalism to real data demonstrates in detail how multi-beam techniques provide new insights into the energetics of observed space plasmas.

Playing surface traction influences movement strategies during a sidestep cutting task in futsal: implications for ankle performance and sprain injury risk

ABSTRACT This descriptive laboratory crossover trial study examined the intervention of high friction synthetic vs lower friction natural sport surfaces on the ankle joint biomechanics in a sidestep cutting task. Twenty-nine male futsal players performed 5 trials of sidestep cutting task in a laboratory, recorded by an 18-camera motion capture system to obtain the ankle joint orientation, velocity and moment. Utilised friction was obtained by the peak ratio of the horizontal to vertical ground reaction force during the stance. Repeated measures (MANOVA) suggested a significant effect of the playing surface and post hoc paired t-tests revealed significantly higher utilised coefficient of friction, higher peak plantarflexion angle, lower peak eversion angle, higher peak inversion velocity, lower peak inversion moment and higher peak internal rotation moment. In performing a sidestep cutting task, futsal players demonstrated higher utilised ground friction when available friction from the playing surface was higher, resulting in higher peak inversion velocity and higher peak internal rotation moment, which may make the ankle joint more prone to sprain injury. Floorings for futsal should have an adequate coefficient of friction for agility and avoidance of the risk of slipping. Increasing the coefficient of friction may not only enhance performance but also endanger the ankle joint.

Motion of NO+ ions in uniform electrostatic fields in the rare gases

The transport of NO+ ions moving through each of the rare gases under the influence of an electrostatic field has been studied using ab initio potential energy surfaces in a rigid rotor approximation, using both Monte Carlo techniques and various velocity moment approaches. The results in helium are in very good agreement with published molecular dynamics calculations and experimental results.

Vertical Structure of Galactic Disk Kinematics from LAMOST K Giants

Abstract We examine the vertical structure of Galactic disk kinematics over a Galactocentric radial distance range of R = 5–15 kpc and up to 3 kpc away from the Galactic plane, using the K-type giants surveyed by LAMOST. Based on robust measurements of three-dimensional velocity moments, a wobbly disk is detected in a phenomenological sense. An outflow dominates the radial motion of the inner disk, while in the outer disk there exist alternate outward and inward flows. The vertical bulk velocities is a combination of breathing and bending modes. A contraction-like breathing mode with amplitudes increasing with the distance to the plane and an upward bending mode dominate the vertical motion outside R 0, and there are reversed breathing and bending modes at R &lt; R 0, with amplitudes much smaller than those outside R 0. The mean azimuthal velocity decreases with the increasing distance to the plane, with gradients shallower for larger R. Stars in the south disk are rotating faster than stars in the north. The velocity ellipsoid orientation differs between different R: in the range of 5 &lt; R &lt; 9 kpc , the gradient of the tilt angle with respect to arctan ( Z / R ) decreases from ∼0.83 for the inner disk to ∼0.52 for the outer disk; within 9 &lt; R &lt; 15 kpc , the tilt of velocity ellipsoid deviates from vertical antisymmetry. A clear flaring signature is found for both north and south disks based on the observed vertical structures of velocity ellipsoid.

Effects of resistance training on gait velocity and knee adduction moment in knee osteoarthritis patients: a systematic review and meta-analysis

The systematic review aimed to analyze the effects of resistance training in knee osteoarthritis (OA) rehabilitation from a biomechanical perspective. A meta-analysis was performed to determine the potential benefits of resistance training on patients with knee OA. Relevant studies based on the inclusion and exclusion criteria were selected from CENTRAL, PubMed, Scopus, and Web of Science databases inception to August 2020. Outcome measures included gait velocity and knee adduction moment (KAM). The mean differences of the data with a 95% confidence interval were analyzed using STATA 15.1 software The search identified eight studies that satisfied all the inclusion criteria, in which 164 patients were involved in gait velocity studies and another 122 patients were part of KAM studies. Analysis of the pooled data showed that resistance training significantly improved the gait velocity in patients with knee OA (p < 0.01, z = 2.73), ES (95% CI) = 0.03 (0.01, 0.06) m/s. However, resistance training had no significant effect on improving KAM in patients with knee OA (p = 0.98, z = 0.03), ES (95% CI) = 0.00 (− 0.16, 0.16) percentage of body weight × height (%BW × Ht). Therefore, resistance training may enhance gait velocity but not KAM in knee OA patients. The protocol was registered at PROSPERO (registration number: CRD42020204897).

Wake Width: Discussion of Several Methods How to Estimate It by Using Measured Experimental Data

Several methods of defining and estimating the width of a turbulent wake are presented and tested on the experimental data obtained in the wake past an asymmetric prismatic airfoil NACA 64(3)-618, which is often used as tip profile of the wind turbines. Instantaneous velocities are measured by using the Particle Image Velocimetry (PIV) technique. All suggested methods of wake width estimation are based on the statistics of a stream-wise velocity component. First, the expansion of boundary layer (BL) thickness is tested, showing that both displacement BL thickness and momentum BL thickness do not represent the width of the wake. The equivalent of 99% BL thickness is used in the literature, but with different threshold value. It is shown that a lower threshold of 50% gives more stable results. The ensemble average velocity profile is fitted by Gauss function and its σ-parameter is used as another definition of wake width. The profiles of stream-wise velocity standard deviation display a two-peak shape; the distance of those peaks serves as wake width for Norberg, while another tested option is to include the widths of such peaks. Skewness (the third statistical moment) of stream-wise velocity displays a pair of sharp peaks in the wake boundary, but their position is heavily affected by the statistical quality of the data. Flatness (the fourth statistical moment) of the stream-wise velocity refers to the occurrence of rare events, and therefore the distance, where turbulent events ejected from the wake become rare and can be considered as another definition of wake width. The repeatability of the mentioned methods and their sensitivity to Reynolds’ number and model quality are discussed as well.

Macroscopic turbulent flow via hard sphere potential

In recent works, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential and examined the proposed mechanics of turbulence formation in a simple model of two particles for a variety of different potentials. In this work, we use the same hypothesis to develop new fluid mechanics equations that model turbulent gas flow on a macroscopic scale. The main difference between our approach and the conventional formalism is that we avoid replacing the potential interaction between particles with the Boltzmann collision integral. Due to this difference, the velocity moment closure, which we implement for the shear stress and heat flux, relies upon the high Reynolds number condition rather than the Newton law of viscosity and the Fourier law of heat conduction. The resulting system of equations of fluid mechanics differs considerably from the standard Euler and Navier–Stokes equations. A numerical simulation of our system shows that a laminar Bernoulli jet of an argon-like hard sphere gas in a straight pipe rapidly becomes a turbulent flow. The time-averaged Fourier spectra of the kinetic energy of this flow exhibit Kolmogorov’s negative five-thirds power decay rate.

Expansion series of the pairwise velocity generating function and its implications on redshift space distortion modeling

The pairwise velocity generating function G has a deep connection with both the pairwise velocity probability distribution function and modeling of redshift space distortion (RSD). Its implementation into RSD modeling is often faciliated by expansion into a series of pairwise velocity moments . Motivated by the logrithmic transformation of the cosmic density field, we investigate an alternative expansion into series of pairwise velocity cumulants . We numerically evaluate the convergence rate of the two expansions, with three 30723 particle simulations of the CosmicGrowth N-body simulation series. (1) We find that the cumulant expansion performs significantly better, for all the halo samples and redshifts investigated. (2) For modeling RSD at k ∥ < 0.1h Mpc−1, including only the n = 1,2 cumulants is sufficient. (3) But for modeling RSD at k ∥ = 0.2h Mpc−1, we need and only need the n = 1,2,3,4 cumulants. These results provide specific requirements on RSD modeling in terms of m-th order statistics of the large-scale structure.

Two different Variants of Leg Repositioning at maximal Sprint Speed of high Performance Junior Sprinters

ABSTRACT Two variants of leg repositioning are described biomechanically and examined for differences in step kinematics. Based on leg angle (two-point angle between radius of leg centre of gravity and a horizontal line) during air phase, 30 juniors were divided into two groups (n = 15), large leg angle (LLA, leg angle = 80 ± 4°) and small leg angle (SLA, leg angle = 69 ± 5°). Maximal flying 30-m sprints were recorded (200 fps) and group differences were analysed using a 5-point leg model. With comparable leg length, both groups differed in leg moment of inertia and leg angular velocity. Group SLA reduced knee angle under the body, the thigh of swing leg passed the support leg early, and reached a higher position during knee lift, followed by a higher vertical foot velocity during pre-support. At take-on, both groups achieved a comparable hip, knee and foot angle. Due to higher mass of thigh (66%) compared to lower leg, foot and spikes (34%), thigh movement is essential for repositioning. Despite SLA advantages, three of the six fastest sprinters (v > 10.4 m/s) were evenly divided into both groups. An influence on step length, step frequency, ground contact and flight time was not found.

A quadrature-based moment method for the evolution of the joint size-velocity number density function of a particle population

A quadrature-based moment method for the approximate solution of the generalized population balance equation (GPBE) governing the evolution of the joint size-velocity number density function (NDF) of a particle population is formulated and tested. The proposed method relies on the third-order hyperbolic conditional quadrature method of moments developed for velocity distribution transport. This approach is combined with the conditional quadrature method of moments to incorporate the dependency of the NDF on particle size, leading to an efficient, stable, quadrature method that uses an analytical solution to determine the size-conditioned velocity moments. The incorporation of source terms accounting for aggregation, breakup, and collisions, as well as acceleration terms such as gravity and drag, is performed using a realizable ODE solver. The approach is then demonstrated by considering zero-dimensional cases to verify the correct integration of the source terms. A set of one-dimensional cases involving droplet evaporation and coalescence is used to validate the velocity-dependent source terms. A two-dimensional case of crossing jets of particles with different sizes is used to demonstrate the proposed method in the case of a polydisperse flow with inertial particles. All work has been implemented in the open-source framework OpenQBMM, based on OpenFOAM®.

Discrete gas-kinetic scheme-based arbitrary Lagrangian–Eulerian method for moving boundary problems

In this work, a discrete gas-kinetic scheme (DGKS) based on the arbitrary Lagrangian–Eulerian (ALE) method is proposed for the simulation of moving boundary problems. The governing equations are the ALE-based Navier–Stokes equations, which are discretized using the finite volume method. Starting from a circular function-based Boltzmann equation, a grid motion term is introduced to obtain the Boltzmann equation in ALE form. Based on the moment relations and Chapman–Enskog analysis, the moment of particle velocity and distribution function are summed to obtain the fluxes. The DGKS expression in the ALE framework can then be derived. In this method, the flux at the cell interface can be calculated from the local solution of the Boltzmann equation, which is physically realistic and makes the algorithm more stable. As DGKS is based on a multidimensional particle velocity model, it is not necessary to use approximate values for the reconstruction process. In addition, DGKS can simultaneously handle inviscid and viscous fluxes when simulating viscous flow problems, resulting in a higher degree of consistency. Finally, several moving boundary examples are simulated to validate the ALE-DGKS method. The results show the algorithm was observed to achieve second-order accuracy and can solve moving boundary problems effectively.