Symmetric Force Research Articles

Asymmetric ground reaction forces and knee kinematics during squat after anterior cruciate ligament (ACL) reconstruction

BackgroundThis bilateral squat study tests whether people with anterior cruciate ligament (ACL) reconstruction have symmetric three-dimensional ground reaction forces (GRFs) and symmetric anterior–posterior (AP) translation rates of the femur with respect to the tibia when compared with healthy control subjects. We hypothesized that there would be no long-term asymmetry in knee kinematics and kinetics in ACL reconstructed subjects following surgery and rehabilitation. MethodsPosition and GRF data were collected on eight ACL reconstructed and eight control subjects during bilateral squat. The rate of relative AP translation was determined for each subject. Principal component models were developed for each of the three GRF waveforms. Principal component scores were used to assess symmetry within the ACL reconstructed group and within the control group. ResultsACL reconstructed knees analyzed in early flexion during squat descent displayed a four-fold greater rate of change in anterior translation in the reconstructed knee relative to the contralateral side than did a similar comparison of normal knees. Differences were found between the ACL reconstructed subjects' injured and uninjured limbs for all GRFs. ConclusionsSubjects following ACL reconstruction had asymmetric GRFs and relative rates of AP translation at an average of seven years after ACL reconstructive surgery when compared with control subjects. Clinical RelevanceThese alterations in loading may lead to altered load distributions across the knee joint and may put some subjects at risk for future complications such as osteoarthritis.

Resonances in the forced turbulent wake past a 3D blunt body

We study the resonances of a forced turbulent wake past a flat-based bluff body using symmetric and antisymmetric actuation modes. The natural, unforced wake flow exhibits broadband dynamics superimposed on oscillatory motions linked to the reminiscent laminar Bénard-von Kármán instability in the turbulent flow. Harmonic and subharmonic resonances can be controlled by the phase relationship of periodic forcing and are linked to the symmetry properties of vortex shedding. Symmetric forcing leads to a strong subharmonic amplification of vortex shedding in the wake, but no harmonic excitation. The robustness of the subharmonic resonance is confirmed at different Reynolds numbers. Antisymmetric actuation, however, promotes a harmonic resonance with very similar wake and drag features.

Cover Picture: Steel Construction 2/2016

AbstractTwo frame structure tests were carried out in the Meyer‐Jens‐Halle laboratory of TU Munich to investigate the load bearing behavior and the rational anchorage length of the external reinforcement in abutments of a frame bridge. The specimen was laid on three supports and the symmetrical couple forces were applied to the ends of the cantilever beams in a horizontal direction. The loading system was placed on a rolling support that was movable in the transverse direction. Based on the force equilibrium principle, the cylinder loads on one side of the cantilever beam, the bearing reaction on the other side produces a symmetrical force, accordingly. Therefore, the symmetrical couple forces at the free end of both cantilever beams are realized by using only one cylinder (see pp. 122–131). (TU Munich)

Visual Cues of Object Properties Differentially Affect Anticipatory Planning of Digit Forces and Placement.

Studies on anticipatory planning of object manipulation showed initial task failure (i.e., object roll) when visual object shape cues are incongruent with other visual cues, such as weight distribution/density (e.g., symmetrically shaped object with an asymmetrical density). This suggests that shape cues override density cues. However, these studies typically only measured forces, with digit placement constrained. Recent evidence suggests that when digit placement is unconstrained, subjects modulate digit forces and placement. Thus, unconstrained digit placement might be modulated on initial trials (since it is an explicit process), but not forces (since it is an implicit process). We tested whether shape and density cues would differentially influence anticipatory planning of digit placement and forces during initial trials of a two-digit object manipulation task. Furthermore, we tested whether shape cues would override density cues when cues are incongruent. Subjects grasped and lifted an object with the aim of preventing roll. In Experiment 1, the object was symmetrically shaped, but with asymmetrical density (incongruent cues). In Experiment 2, the object was asymmetrical in shape and density (congruent cues). In Experiment 3, the object was asymmetrically shaped, but with symmetrical density (incongruent cues). Results showed differential modulation of digit placement and forces (modulation of load force but not placement), but only when shape and density cues were congruent. When shape and density cues were incongruent, we found collinear digit placement and symmetrical force sharing. This suggests that congruent and incongruent shape and density cues differentially influence anticipatory planning of digit forces and placement. Furthermore, shape cues do not always override density cues. A continuum of visual cues, such as those alluding to shape and density, need to be integrated.

The Response of the Lower Stratosphere to Zonally Symmetric Thermal and Mechanical Forcing

Abstract The response of the atmosphere to zonally symmetric applied heating and mechanical forcing is considered, allowing for the fact that the response may include a change in the wave force (or “wave drag”). A scaling argument shows that an applied zonally symmetric heating is effective in driving a steady meridional circulation provided that the wave force (required to satisfy angular momentum constraints) is sufficiently sensitive to changes in the mean flow in the sense that the ratio is large, where K is a measure of the sensitivity of the wave force; α, N, and f are the radiative damping rate, buoyancy frequency, and Coriolis parameter, respectively; and and are the horizontal and vertical length scales of the heating, respectively. Furthermore, in the “narrow heating” regime where this ratio is large, the structure of the meridional circulation response is only weakly dependent on the details of the wave force. The scaling arguments are verified by experiments in a dry dynamical circulation model. Consistent with the scaling prediction, the regime does not apply when the width of the imposed heating is increased. The narrow-heating regime is demonstrated to be relevant to the double peak in tropical lower-stratospheric upwelling considered in a companion paper, supporting the hypothesis that this feature is radiatively driven. Similar arguments are applied to show that a narrow zonally symmetric applied mechanical forcing is primarily balanced by a change in wave force. This provides an explanation for the recently identified compensation between resolved and parameterized waves in driving modeled trends in the Brewer–Dobson circulation.

Equatorial superrotation in Held and Suarez like flows with weak equator‐to‐pole surface temperature gradient

Equatorial superrotation under zonally symmetric thermal forcing is investigated in a set‐up close to that of the classic Held and Suarez set‐up. In contrast to the behaviour in the classic set‐up, a transition to equatorial superrotation occurs when the equator‐to‐pole surface equilibrium entropy gradient is weakened. Two factors contribute to this transition: (i) the reduction of breaking Rossby waves from the midlatitudes that decelerate the equatorial flow and (ii) the presence of barotropic instability in the equatorial region, providing stirring to accelerate the equatorial flow. In the latter, Kelvin waves excited by instability near the Equator generate and maintain the superrotation. However, the superrotation is unphysically enhanced if simulations are underresolved and/or overdissipated. On leave from Queen Mary University of London.

Mixing enhancement by degenerate modes in electrically actuated sessile droplets

The dependence of oscillation dynamics of a sessile droplet on the actuation parameters (voltage and frequency) in AC electrowetting which leads to the manifestation of non-axisymmetric oscillation patterns were investigated through experiments and theoretical modeling. The symmetrical nature of the electrowetting force leads to a circular three phase contact line for low actuation voltages. At higher actuation voltages, despite of symmetrical actuation force the contact line showed a transition from axisymmetric to non-axisymmetric oscillations. We found a good match between the experimentally determined region in the actuation parameter space where non-axisymmetric modes are dominant and the theoretically modeled parametric instability region derived from the Mathieu equation. The results showed that these non-axisymmetric modes are degenerate sectoral modes defined by the spherical harmonic functions. In contrast to axisymmetric oscillations, for non-axisymmetric oscillations the variation of contact angle and base radius remained in-phase between successive resonant modes. Finally, mixing by these parametric oscillations was investigated and the best mixing time was approximately 2% of the diffusive mixing time.

Punching behaviour of RC flat slabs under reversed horizontal cyclic loading

The aim of this work is to study the behaviour of reinforced concrete flat slab structures under combined vertical and horizontal cyclic loading. A total of five specimens were cast and tested: a control specimen was punched without eccentricity, one specimen was tested under constant vertical loading and monotonically increased eccentricity until failure and the remaining three were tested under constant vertical load, at different shear ratios, and cyclic horizontal loading with increasing horizontal drift ratios. All slabs were similar, measuring 4.25×1.85×0.15m3. The reinforced concrete slab specimens were connected to two steel half columns by 0.25×0.25m2 rigid steel plates, prestressed against the slab using steel bolts, to ensure monolithic behaviour. The cyclic tests were performed using an innovative test setup that allows bending moment redistribution, line of inflection mobility, assures equal vertical displacements at the North-South borders and symmetrical shear forces. Results show that cyclic horizontal actions are very harmful to the slab–column connection, resulting in low horizontal drifts and energy dissipation.

Greater Medial Compartment Forces During Total Knee Arthroplasty Associated With Improved Patient Satisfaction and Ability to Navigate Stairs

BackgroundThe purpose of this study was to determine if postoperative patient satisfaction, subjective outcomes, and functional force testing differed between those with symmetric or asymmetric intraoperative mediolateral (ML) compressive forces. We hypothesized that the threshold would be similar to the previously reported valued of 15 lbf and that a significantly greater proportion of those with more symmetrical medial and lateral compressive forces would be satisfied with their total knee arthroplasty. MethodsA commercially available instrumented trial tibial liner was used to measure ML compressive force differences with the knee at 0°, 20°, and 90°. Patient satisfaction and Knee Society Scores were compared between patients with ML asymmetries above and below the calculated optimal threshold. ResultsSurprisingly, lower ML asymmetries in extension were associated with a greater risk of being dissatisfied. Of the 50 total knee arthroplasties, 6 of 23 (26%) with ML force asymmetries <10 lbf were dissatisfied compared with 0 of 27 with ML asymmetries >10 lbf (P = .01). Greater asymmetry was associated with significantly greater gains in EQ-5D scores (P = .05) and pain scores (P = .03) and greater pain relief (P = .006) and reduced impact forces when navigating stairs (P = .05). ConclusionContrary to our hypotheses, the results of this study support the concept that recreating greater forces in the medial compartment much like that of the native knee may yield improved patient-reported outcomes and increased patient satisfaction. The current results further suggest that recreating greater medial compartment forces may have the greatest affect on more demanding activities such as navigating stairs.

Hummingbirds control turning velocity using body orientation and turning radius using asymmetrical wingbeat kinematics.

Turning in flight requires reorientation of force, which birds, bats and insects accomplish either by shifting body position and total force in concert or by using left-right asymmetries in wingbeat kinematics. Although both mechanisms have been observed in multiple species, it is currently unknown how each is used to control changes in trajectory. We addressed this problem by measuring body and wingbeat kinematics as hummingbirds tracked a revolving feeder, and estimating aerodynamic forces using a quasi-steady model. During arcing turns, hummingbirds symmetrically banked the stroke plane of both wings, and the body, into turns, supporting a body-dependent mechanism. However, several wingbeat asymmetries were present during turning, including a higher and flatter outer wingtip path and a lower more deviated inner wingtip path. A quasi-steady analysis of arcing turns performed with different trajectories revealed that changes in radius were associated with asymmetrical kinematics and forces, and changes in velocity were associated with symmetrical kinematics and forces. Collectively, our results indicate that both body-dependent and -independent force orientation mechanisms are available to hummingbirds, and that these kinematic strategies are used to meet the separate aerodynamic challenges posed by changes in velocity and turning radius.

Can increasing albedo of existing ship wakes reduce climate change?

AbstractSolar radiation management schemes could potentially alleviate the impacts of global warming. One such scheme could be to brighten the surface of the ocean by increasing the albedo and areal extent of bubbles in the wakes of existing shipping. Here we show that ship wake bubble lifetimes would need to be extended from minutes to days, requiring the addition of surfactant, for ship wake area to be increased enough to have a significant forcing. We use a global climate model to simulate brightening the wakes of existing shipping by increasing wake albedo by 0.2 and increasing wake lifetime by ×1440. This yields a global mean radiative forcing of −0.9 ± 0.6 Wm−2 (−1.8 ± 0.9 Wm−2 in the Northern Hemisphere) and a 0.5°C reduction of global mean surface temperature with greater cooling over land and in the Northern Hemisphere, partially offsetting greenhouse gas warming. Tropical precipitation shifts southward but remains within current variability. The hemispheric forcing asymmetry of this scheme is due to the asymmetry in the distribution of existing shipping. If wake lifetime could reach ~3 months, the global mean radiative forcing could potentially reach −3 Wm−2. Increasing wake area through increasing bubble lifetime could result in a greater temperature reduction, but regional precipitation would likely deviate further from current climatology as suggested by results from our uniform ocean albedo simulation. Alternatively, additional ships specifically for the purpose of geoengineering could be used to produce a larger and more hemispherically symmetrical forcing.

A numerical study of macro-mesoscopic mechanical properties of gangue backfill under biaxial compression

Based on the Particle Flow Code (PFC2D) program, we set up gangue backfill models with different gangue contents and bond strength, and studied the stress–strain behaviours, the pattern of shear band and force chains, motion and fragmentation of particles under biaxial compression. The results show that when the bond strength or contents of gangue are high, the peak strength is high and the phenomena of post-peak softening and fluctuation are obvious. When gangue contents are low, the shape of the shear band is symmetrical and most strong force chains transfer in soil particles. With an increase in gangue content, the shape of the shear band becomes irregular and the majority of strong force chains turn to transfer in gangue particles gradually, most of which distribute along the axial direction. When the gangue content is higher than 50%, the interconnectivity of strong force chains decreases gradually; at the same time, the strong force chains become tilted and the stability of the system tends to decrease. With an increase in external loading, the coordination numbers of the system increase at first and then decrease and the main pattern of force chains changes into columnar from annular. However, after the forming of the advantageous shear band, the force chains external to the shear band maintain their columnar shape while the inner ones bend obviously. As a result, annular force chains form.

Pedal force asymmetries and performance during a 20-km cycling time trial

It is unclear if applying larger or more symmetrical pedal forces leads to better performance in cycling. The aims of this study were to assess the relationship between pedal force production and performance in a cycling time trial and to evaluate the relationship between asymmetries in pedal force production and performance. Fifteen competitive cyclists/triathletes performed a 20 km cycling time trial on a cycle trainer while bilateral forces applied to the pedals were recorded along with total time. Total forces applied to the pedals were computed and converted into dominant and non-dominant forces using a leg preference inventory. Pedal force asymmetries ranged from 43% (in favour of the dominant limb) to 34% (in favour of the non-dominant limb). The relationship between total pedal force (averaged from both pedals) and performance time was small (r=-.32, effect size=.66) as well as the association between the asymmetry indices and performance time (r=.01, effect size=.06). In conclusion, applying large forces on the pedals and balancing pedal force application between the dominant and non-dominant limbs did not lead to better performance in this cycling time trial.

A Dynamic Axially Symmetric Goal and its Extended Solution for a Fixed Rigid Circular Multi-layer Plate

The subject matter of the article is a fixed circular multi-layer plate and its reaction to the axially symmetrical force (direct stress) affecting its front face. The force itself is an arbitrary time and radial coordinate function. The authors apply the method of finite integral transformation (based on the theory of electroelasticity in a three-dimentional model) to develop a new closed solution. The improvement of this new solution lies in the fact that boundary conditions for cylinder and front faces of a multi-layer plate here are completely fulfilled when compared with the data obtained in previous research. The achieved ratio design allows to further analyze this multi-layer plate fluctuations frequency content as well as to analyze changing characteristics of its stress-strain behaviour and their dependence on different layers stress-strain properties.

Numerical study on river bar response to spatial variations of channel width

ABSTRACT Managing river bar formation in alluvial channels remains a challenging issue related to the need to free intakes, improve navigation and optimise river restoration works. This work studies the effects of locally varying the channel width on bar formation to see whether channel widening and narrowing could be feasible bar control measures. The investigation focuses on steady (hybrid) bars, the most common type of bars in lowland rivers. Several numerical experiments are performed using a two-dimensional physics-based finite-difference code. Model simplifications include capacity-limited sediment transport, uniform grain size and constant discharge. Previous tests on field and experimental data show that the simulations of the relevant processes are realistic. The results indicate that the formation of steady alternate bars downstream of lateral structures occurs at a distance that depends on the local width reduction and that narrowing the channel for a distance of 10 times the original width appears sufficient to locally suppress alternate bars. A symmetric inflow forces the formation of symmetric bed topography, as for instance a flat bed or central bars. Similarly, an asymmetric inflow forces asymmetric bed topography, as alternate bars. Upstream flow asymmetries disrupt the symmetry of central bars leading to a compound bed configuration characterised by a dominant wandering channel, a common feature in wide lowland rivers. Central and alternate bars are found to coexist even if bar stability theories predict the development of alternate bars only. These results are promising and raise fundamental questions, but need experimental and field confirmation.

Increased visual information gain improves bimanual force coordination

Bimanual force control requiring asymmetrical forces between limbs is more challenging than bimanual force control when the limbs produce symmetrical forces. Previous studies investigated visual information gains between 8 and 80pixels/N to facilitate asymmetrical force control. Given that previous studies limited visual information gain to 80pixels/N, the current experiment expanded the range by increasing visual information gains (8, 80, 256, and 512pixels/N). A second manipulation involved three task constraint coefficients imposed on bimanual force control: (a) left-biased, (b) right-biased, and (c) equal-biased. Analyses of 15 right-handed adult volunteers revealed a decrease in bimanual force variability and more negative correlation coefficient with increased visual information gain in the equal biased condition. Significant reductions in bimanual force variability were found between 8 and 80pixels/N. In contrast, significant improvements in coordination patterns between hands continued up to 256pixels/N. These novel findings demonstrate that bimanual force coordination was more sensitive to an increase in visual information gains (>80pixels/N) than bimanual force variability.

Electromechanical buckling of functionally graded electrostatic nanobridges using strain gradient theory

Electromechanical buckling (EMB) of beam-type nanoelectromechanical systems (NEMSs) is investigated based on modified strain gradient theory. The system is modeled as a clamped-guided nanobeam which is under compressive or tensile axial loads as well as the effect of nonlinear electrostatic and van der Waals symmetric transverse forces. In addition, the beam is considered to be made of axially and transverse functionally graded materials. Here, FGM is Poly-SiGe, of which the general properties change gradually from silicon to germanium based on a simple power-law method. Considering the Euler–Bernoulli beam theory and using the principle of minimum potential energy, the governing equations and corresponding boundary conditions are established. After validation of results, the effects of power law index, variation of size effect parameters, length-thickness ratio and the distance between the two fixed and movable electrodes on the buckling response of the system are discussed.

Regime Transitions of Cross-Equatorial Hadley Circulations with Zonally Asymmetric Thermal Forcings

Abstract Observed nonlinearities in the seasonal evolution of monsoons have been previously explained using theories for Hadley circulations driven by zonally symmetric thermal forcings, even though monsoonal forcings deviate strongly from the assumption of zonal symmetry. Here, an idealized model of a dry, three-dimensional atmosphere is used to compare the response to zonally symmetric and asymmetric off-equatorial thermal forcings. For symmetric forcings, the zonal-mean, cross-equatorial mass flux increases more rapidly with the amplitude of the forcing once the forcing becomes strong enough to reduce the upper-tropospheric absolute vorticity to near zero, consistent with previous studies of the transition to angular momentum–conserving flow. For zonally asymmetric forcings, the zonal-mean cross-equatorial flow exhibits a similar dependence on forcing strength and a similar reduction of the zonal-mean upper-level vorticity, but asymmetric forcings also produce strong zonal overturnings with subsidence west of the heating, as in the well-known linear response to off-equatorial heatings. The mass flux in these zonal overturnings increases linearly with forcing strength until its rate of increase tapers off for the strongest forcings; the total upward mass flux (i.e., the zonal-mean plus zonally asymmetric components) increases linearly with the strength of zonally asymmetric forcings and exhibits no abrupt or nonlinear dependence on forcing amplitude. These results indicate the importance of considering the zonally asymmetric part of the divergent response to off-equatorial forcings and suggest that theories based on zonally symmetric forcings need further examination before they can be assumed to describe observed monsoons.

Classical solvability of the stationary free boundary problem describing the interface formation between two immiscible fluids

Stationary free boundary problems related to the formation of the interface between two immiscible fluids are investigated. The corresponding models were introduced originally by Shikhmurzaev to remove singularities arising in contact-line problems. We consider two models which are derived under different assumptions for the structure of the interfacial layer, and prove the existence of rotationally symmetric solutions in Holder spaces for a sufficiently small rotationally symmetric external force.

Sun-stirred Kraken Mare: Circulation in Titan’s seas induced by solar heating and methane precipitation

Density-driven circulation in Titan’s seas forced by solar heating and methane evaporation/precipitation is simulated by an ocean circulation model. If the sea is transparent to sunlight, solar heating can induce anti-clockwise gyres near the sea surface and clockwise gyres near the sea bottom. The gyres are in geostrophic balance between the radially symmetric pressure gradient force and Coriolis force. If instead the sea is turbid and most sunlight is absorbed near the sea surface, the sea gets stratified in warm seasons and the circulation remains weak. Precipitation causes compositional stratification of the sea to an extent that the sea surface temperature can be lower than the sea interior temperature without causing a convective overturning. Non-uniform precipitation can also generate a latitudinal gradient in the methane mole fraction and density, which drives a meridional overturning with equatorward currents near the sea surface and poleward currents near the sea bottom. However, gyres are more ubiquitous than meridional overturning.