Symmetry Force Research Articles

Decoding the phonon transport of structural lubrication at silicon/silicon interface

Although the friction characteristics under different contact conditions have been extensively studied, the mechanism of phonon transport at the structural lubrication interface is not extremely clear. In this paper, we firstly promulgate that there is a 90°-symmetry of friction force depending on rotation angle at Si/Si interface, which is independent of normal load and temperature. It is further found that the interfacial temperature difference under incommensurate contacts is much larger than that in commensurate cases, which can be attributed to the larger interfacial thermal resistance (ITR). The lower ITR brings greater energy dissipation in commensurate sliding, and the reason for that is more effective energy dissipation channels between the friction surfaces, making it easier for the excited phonons at the washboard frequency and its harmonics to transfer through the interface. Nevertheless, the vibrational frequencies of the interfacial atoms between the tip and substrate during the friction process do not match in incommensurate cases, and there is no effective energy transfer channel, thus presenting the higher ITR and lower friction. Eventually, the number of excited phonons on contact surfaces reveals the amount of frictional energy dissipation in different contact states.

Effects of prolonged brisk walking induced lower limb muscle fatigue on the changes of gait parameters in older adults

BackgroundLower extremity muscle fatigue affects gait stability and increases the probability of injuries in the elderly. Research questionHow does prolonged walking-induced fatigue affect lower limb muscle activity, plantar pressure distribution, and tripping risk? MethodsEighteen elderly adults walked fast on a treadmill for 60 minutes at a fixed speed. The plantar pressure was measured with an in-shoe monitoring system, eight lower limb muscles were monitored using surface electromyography, and foot movements were tracked by a motion capture analysis system. The above data and participants’ subjective fatigue level feedback were collected every 5 minutes. Statistical analysis used the Friedman one-way repeated measures analysis of variance by ranks test followed by Wilcoxon signed-ranks test with Benjamini-Hochberg stepwise correction. ResultsThe subjective reported fatigue on the Borg scale increased gradually from 1 to 6 (p = 0.001) during the 60 minutes, while the EMG amplitude of vastus medialis significant decreased (p = 0.013). The results of plantar pressure demonstrated that the distribution of load and impulse shifted medially in both the heel and arch regions while shifted laterally in both the toes and metatarsal regions. The significantly increased contact area supports this shift at the medial arch (p = 0.036, increased by 6.94%, the 60th minute vs. the baseline). The symmetry of medial-lateral plantar force increased at the toes, metatarsal, and arch regions. The significantly increased parameters also include the swing time and contact time. The minimum foot clearance was reduced, increasing tripping probability, not significantly, though. SignificanceThis study facilitates a better understanding of changes in lower limb muscle activity and gait parameters during prolonged fast walking. Besides, this study has good guiding significance for developing smart devices based on plantar force, inertial measurement units, and EMG sensors to monitor changes in muscle activation in real-time and prevent tripping.

Generation of a net flow due to fixed oblique beam structures in the nucleate boiling region

Effective utilization of unused heat below 200 °C is essential for a sustainable society. In this study, we propose a thermally driven water pump using fixed oblique beam structures with bubbles in the nucleate boiling region (approximately, 100–130 °C). Here, the oblique beam structure breaks the symmetry of the bubble force, and thus, they provide a net flow. Specifically, by using six fixed oblique beams along a circular fluidic channel, we observed a net flow of an average flow velocity of ∼40 mm/s and an average volume flow rate of ∼10 000 mm3/s (∼0.01 l/s) at the superheat of ∼22 K. Our findings should contribute to the effective use of unused heat such as factory waste heat and environmental energy.

Current-Induced Magnetic Skyrmions with Controllable Polarities in the Helical Phase

We report the current-induced creation of magnetic skyrmions in a chiral magnet FeGe nanostructure by using in situ Lorentz transmission electron microscopy. We show that magnetic skyrmions with controllable polarity can be transferred from the helical ground state simply by controlling the direction of the current flow at zero magnetic fields. The force analysis and symmetry consideration, backed up by micromagnetic simulations, well explain the experimental results, where magnetic skyrmions are created because of the edge instability of the helical state in the presence of spin-transfer torque. The on-demand generation of skyrmions and control of their polarity by electric current without the need for a magnetic field will enable novel purely electric-controlled skyrmion devices.

Quadriceps strength symmetry predicts vertical ground reaction force symmetry during running in patients who have undergone ACL reconstruction

ObjectiveTo determine whether quadriceps strength symmetry can predict peak vertical ground reaction force (vGRF) running force symmetry in patients who have undergone ACL reconstruction (ACLR). We also sought to determine a cutoff for quadriceps strength symmetry to identify patients at risk for vGRF running asymmetry. DesignRetrospective cross-sectional. SettingClinical facility. MethodsBilateral quadriceps strength and vGRF data during running were obtained from 79 patients 26–30 weeks post ACLR. Linear regression was used to determine if quadriceps strength symmetry predicted peak vGRF running force symmetry. Classification and regression tree (CART) analysis was used to determine the cutoff value for quadriceps strength symmetry to identify patients at risk for vGRF running asymmetry. ResultsIncreased quadriceps strength symmetry predicted increased vGRF running symmetry (R2 = 0.20). CART analysis revealed that patients with quadriceps strength symmetry less than or equal to 88% were at highest risk for vGRF running asymmetry (R2 = 26%). ConclusionGreater quadriceps strength symmetry is predictive of greater vGRF running force symmetry in patients who have undergone ACLR. This finding highlights the need for clinicians to consider the degree of quadriceps strength symmetry before initiating a return to running program.

Reduction of risk factors for ACL Re-injuries using an innovative biofeedback approach: A phase I randomized clinical trial

ObjectivesDetermine the safety and initial efficacy of a novel biofeedback intervention to improve landing mechanics in patients following anterior cruciate ligament reconstruction (ACLR). MethodsForty patients post-ACLR (age: 16.9 ± 2.0 years) were randomly allocated to a biofeedback intervention or an attention control group. Patients in the biofeedback group completed 12 sessions over six-weeks that included bilateral unweighted squats with visual and tactile biofeedback. Patients in the control group completed a six-week educational program. Lower extremity mechanics were collected during a bilateral stop jump at baseline, six-weeks, and 12-weeks post-intervention. Linear mixed-effects models adjusted for sex and graft type determined the main effects of and interactions between group and time. ResultsNo group by time interaction existed for peak knee extension moment symmetry. A group by time interaction existed for peak vertical ground reaction force symmetry (p = 0.012), where patients in the biofeedback group had greater improvements in symmetry between baseline and post-intervention that were not maintained through the retention assessments. ConclusionThis novel biofeedback program did not reduce risk factors for second ACL injuries. Future work could develop and test multidisciplinary interventions for reducing second ACL injury risk factors. Clinicaltrials.gov identifier(NCT03273673)

Equivariant bifurcation, quadratic equivariants, and symmetry breaking for the standard representation of S k

Motivated by questions originating from the study of a class of shallow student-teacher neural networks, methods are developed for the analysis of spurious minima in classes of gradient equivariant dynamics related to neural networks. In the symmetric case, methods depend on the generic equivariant bifurcation theory of irreducible representations of the symmetric group on k symbols, S k ; in particular, the standard representation of S k . It is shown that spurious minima (non-global local minima) do not arise from spontaneous symmetry breaking but rather through a complex deformation of the landscape geometry that can be encoded by a generic S k -equivariant bifurcation. We describe minimal models for forced symmetry breaking that give a lower bound on the dynamic complexity involved in the creation of spurious minima when there is no symmetry. Results on generic bifurcation when there are quadratic equivariants are also proved; this work extends and clarifies results of Ihrig & Golubitsky and Chossat, Lauterbach & Melbourne on the instability of solutions when there are quadratic equivariants.

Is the quality of occlusal contacts comparable after aligner and fixed orthodontic therapy? A non-randomized cohort comparison using computerized occlusal analysis during 6 months of retention

ABSTRACT Objective Less than ideal contacts have been reported following aligner therapy, but it is considered a transitory problem, spontaneously resolving with the phenomenon of settling. Methods: Thirty-nine orthodontic patients (14 treated with aligners; 25 with fixed appliances) were evaluated with a digital occlusal analysis system (T-scan™10), assessing Maximum Intercuspation contact simultaneity, symmetry, and relative force distribution at treatment completion and after 3 and 6 months. Results No significant differences in occlusal contact quality were found between groups at treatment completion or follow-up. The center of force moved posteriorly and remained stable after 3 months but was located more anteriorly in females (p = 0.01). One-third of patients (both groups combined) had marked contact force asymmetry even after 6 months’ retention. Conclusion: Occlusal contacts were comparable at completion of treatment with aligners or brackets and after 3–6 months of retention. Settling did not improve marked asymmetry in all patients.

Effects of step frequency during running on the magnitude and symmetry of ground reaction forces in individuals with a transfemoral amputation

BackgroundIndividuals with unilateral transfemoral amputation are prone to developing health conditions such as knee osteoarthritis, caused by additional loading on the intact limb. Such individuals who can run again may be at higher risk due to higher ground reaction forces (GRFs) as well as asymmetric gait patterns. The two aims of this study were to investigate manipulating step frequency as a method to reduce GRFs and its effect on asymmetric gait patterns in individuals with unilateral transfemoral amputation while running.MethodsThis is a cross-sectional study. Nine experienced track and field athletes with unilateral transfemoral amputation were recruited for this study. After calculation of each participant’s preferred step frequency, each individual ran on an instrumented treadmill for 20 s at nine different metronome frequencies ranging from − 20% to + 20% of the preferred frequency in increments of 5% with the help of a metronome. From the data collected, spatiotemporal parameters, three components of peak GRFs, and the components of GRF impulses were computed. The asymmetry ratio of all parameters was also calculated. Statistical analyses of all data were conducted with appropriate tools based on normality analysis to investigate the main effects of step frequency. For parameters with significant main effects, linear regression analyses were further conducted for each limb.ResultsSignificant main effects of step frequency were found in multiple parameters (P < 0.01). Both peak GRF and GRF impulse parameters that demonstrated significant main effects tended towards decreasing magnitude with increasing step frequency. Peak vertical GRF in particular demonstrated the most symmetric values between the limbs from − 5% to 0% metronome frequency. All parameters that demonstrated significant effects in asymmetry ratio became more asymmetric with increasing step frequency.ConclusionsFor runners with a unilateral transfemoral amputation, increasing step frequency is a viable method to decrease the magnitude of GRFs. However, with the increase of step frequency, further asymmetry in gait is observed. The relationships between step frequency, GRFs, and the asymmetry ratio in gait may provide insight into the training of runners with unilateral transfemoral amputation for the prevention of injury.

Iskušenja vremena i odgovornost historičara / Trials of Time and Responsibility of Historians

The break-up of Yugoslavia and the period of transition more generally have resulted in differential profiling of Balkan historians, in how they approach certain processes in the past, work on the darker aspects of history, changing perspectives, degrees of awareness and of education, as well as standards in current and future work. This politicisation of their approach to and tendentious formulation of issues has entailed the imposition of a forced symmetry when dealing with already sensitive themes. It raises general questions about the responsibility of the historian, while at the same time bringing to light the set of preconditions that informs the action and effectiveness of historians and entire institutions at the local level. Historians have been facing the challenge of fragmentation for some time and it is reflected not just in the results of their historiographical work, but also directly in generations of their students.

Equiauxetic Hinged Archimedean Tilings

There is increasing interest in two-dimensional and quasi-two-dimensional materials and metamaterials for applications in chemistry, physics and engineering. Some of these applications are driven by the possible auxetic properties of such materials. Auxetic frameworks expand along one direction when subjected to a perpendicular stretching force. An equiauxetic framework has a unique mechanism of expansion (an equiauxetic mode) where the symmetry forces a Poisson’s ratio of −1. Hinged tilings offer opportunities for the design of auxetic and equiauxetic frameworks in 2D, and generic auxetic behaviour can often be detected using a symmetry extension of the scalar counting rule for mobility of periodic body-bar systems. Hinged frameworks based on Archimedean tilings of the plane are considered here. It is known that the regular hexagonal tiling, {63}, leads to an equiauxetic framework for both single-link and double-link connections between the tiles. For single-link connections, three Archimedean tilings considered as hinged body-bar frameworks are found here to be equiauxetic: these are {3.122}, {4.6.12}, and {4.82}. For double-link connections, three Archimedean tilings considered as hinged body-bar frameworks are found to be equiauxetic: these are {34.6}, {32.4.3.4}, and {3.6.3.6}.

Cellular Self-Structuring and Turbulent Behaviors in Atmospheric Laminar Channels

Assimilating the atmosphere with multifractal entities, nonlinear behaviors in the framework of scale relativity theory regarding its hydrodynamic functionality are established at various scale resolutions. From this perspective, revealing a “hidden” symmetry of the specific multifractal force with the SL(2,R) group leads to synchronization of atmospheric entities on the basis of operational procedures (differential and integral Riemann-type geometries, harmonic mappings from Euclidian to hyperbolic space, variational principles, and others) that imply cellular self-structuring, laminar channels and singularities as turbulence generators. These behaviors can then be assimilated and compared with recent discoveries regarding laminar channels found in atmospheric turbulence through lidar data processing.

Double proton transfer in hydrated formic acid dimer: Interplay of spatial symmetry and solvent-generated force on reactivity.

The double proton transfer (DPT) reaction in the hydrated formic acid dimer (FAD) is investigated at molecular-level detail. For this, a global and reactive machine learned (ML) potential energy surface (PES) is developed to run extensive (more than 100 ns) mixed ML/MM molecular dynamics (MD) simulations in explicit molecular mechanics (MM) solvent at MP2-quality for the solute. Simulations with fixed – as in a conventional empirical force field – and conformationally fluctuating – as available from the ML-based PES – charge models for FAD show a significant impact on the competition between DPT and dissociation of FAD into two formic acid monomers. With increasing temperature the barrier height for DPT in solution changes by about 10% (∼1 kcal mol−1) between 300 K and 600 K. The rate for DPT is largest, ∼1 ns−1, at 350 K and decreases for higher temperatures due to destabilisation and increased probability for dissociation of FAD. The water solvent is found to promote the first proton transfer by exerting a favourable solvent-induced Coulomb force along the O–H⋯O hydrogen bond whereas the second proton transfer is significantly controlled by the O–O separation and other conformational degrees of freedom. Double proton transfer in hydrated FAD is found to involve a subtle interplay and balance between structural and electrostatic factors.

Force production and symmetry in water fitness exercises: a gender comparison

Force production and symmetry in water fitness exercises: a gender comparison

Experimental investigation of the angular symmetry of optical force in a solid dielectric

The textbook-accepted formulation of electromagnetic force was proposed by Lorentz in the 19th century, but its validity has been challenged due to incompatibility with the special relativity and momentum conservation. The Einstein–Laub formulation, which can reconcile those conflicts, was suggested as an alternative to the Lorentz formulation. However, intense debates on the exact force are still going on due to lack of experimental evidence. Here, we report the first experimental investigation of angular symmetry of optical force inside a solid dielectric, aiming to distinguish the two formulations. The experiments surprisingly show that the optical force exerted by a Gaussian beam has components with the angular mode numbers of both 2 and 0, which cannot be explained solely by the Lorentz or the Einstein–Laub formulation. Instead, we found that a modified Helmholtz theory by combining the Lorentz force with additional electrostrictive force can explain our experimental results. Our results represent a fundamental leap forward in determining the correct force formulation and will update the working principles of many applications involving electromagnetic forces.

Effects of walking speed on magnitude and symmetry of ground reaction forces in individuals with transfemoral prosthesis

Individuals with unilateral transfemoral amputation (uTFA) walk asymmetrically. Investigating gait symmetry in ground reaction force (GRF) is critical because asymmetric loading on the residual limb can result in injury. The aim of this study was to investigate the GRF of individuals with uTFA by systematically controlling their walking at eight speeds(2.0–5.5 km/h with increments of 0.5 km/h) on a treadmill. Forty-eight individuals participated in this study, which included 24 individuals with uTFA (K3 and K4) and 24 individuals without amputation. GRFs (anteroposterior, mediolateral, and vertical) of the prosthetic and intact limb steps were collected for the individuals with uTFA and those of the right limb were collected for the control group. Peak force values of the GRF components, temporal parameters, impulses, and their asymmetry ratios were investigated and statistically analyzed. With an increasing walking speed, the magnitude of GRF changed gradually; individuals with uTFA exhibited increased GRF asymmetry in the vertical and mediolateral components, while that of the anteroposterior component remained constant. uTFA individuals typically maintained a constant asymmetry ratio in the mediolateral and anteroposterior (braking and propulsive) GRF impulses across a wide range of walking speeds. This result suggests that individuals with uTFA may cope with various walking speeds by maintaining symmetric mediolateral and anteroposterior impulses. The data provided in this study can serve as normative data for the GRF and its symmetry across a range of walking speeds in individuals with uTFA.

Analyzing the motion of a mass sliding on a sphere with friction

A well-known problem in classical mechanics that is often presented for pedagogical purposes involves a small mass that slides without friction under a gravitational force on the surface of a sphere. Commonly, students are asked to find the angular position where a mass with no azimuthal motion leaves the spherical surface, and this question is easily within the reach of most intermediate physics students. However, a complete solution for more general motion of the mass on the spherical surface (including friction) may be suitable for many advanced undergraduates. Without friction, the problem including azimuthal motion is really an inverted version of an ideal spherical pendulum. This problem is also useful for extending discussion in classical mechanics to more sophisticated topics beyond solving Newton's laws of motion, such as the importance of conservation laws and constants of motion as they relate to symmetry, conservative versus dissipative forces, and the role of constraints.

Establishing Normative Values for Inter-Limb Kinetic Symmetry During Landing in Uninjured Adolescent Athletes.

BackgroundAssessment of inter-limb kinetic symmetry during landing could provide valuable insights when working with athletes who have undergone anterior cruciate ligament reconstruction. However, it is difficult to determine if the asymmetry exhibited by an injured athlete is excessive or within a range that is similar to uninjured athletes, until normative values are established.PurposeThe purpose of this study was to establish normative values for inter-limb impact force symmetry in uninjured adolescent athletes. In addition, an example is provided of how these normative values could be used to identify athletes who exhibit atypically high levels of asymmetry following anterior cruciate ligament reconstruction.Study DesignCross-sectional studyMethodsOne hundred and thirty-six uninjured athletes completed drop vertical jumps and countermovement jumps while force plates recorded ground reaction forces. Symmetry indices captured inter-limb symmetry in impact forces during landing for both tasks. These symmetry indices were also combined to create an index that captured symmetry across both tasks. Normative values were established using the uninjured athletes’ data. Eleven athletes who had undergone anterior cruciate ligament reconstruction and been cleared to return to landing and jumping performed the same tasks and their data were compared to the results for the uninjured group.ResultsMeasures of central tendency, variability, percentiles, and outliers were calculated/identified based on the uninjured athletes’ symmetry indices. Six of the 11 injured athletes exhibited atypically high symmetry index values.ConclusionThe normative values established as part of this study may serve as a basis for identifying athletes who exhibit atypically high levels of inter-limb impact force asymmetry during jumping tasks following anterior cruciate ligament reconstruction.Level of Evidence3b

Assessing the effects of gait asymmetry: Using a split-belt treadmill walking protocol to change step length and peak knee joint contact force symmetry

Asymmetrical gait may affect important outcomes such as knee joint contact force (KJCF). A split-belt treadmill (SBTM) can be used to provoke changes in step length symmetry (SLsym) and may produce a similar response in KJCF symmetry (KJCFsym) between limbs. The purpose of this study was to explore the utility of employing a SBTM walking paradigm to alter KJCF and KJCFsym and to determine if changes in SLsym coincided with changes in KJCFsym. Twenty healthy individuals performed a standardized SBTM protocol, where baseline and post-adaptation conditions had tied belt speeds of 0.5 m/s and the split-adaptation condition used a 3:1 belt speed ratio. OpenSim techniques were used to produce normalized, averaged stance phase peak KJCF during baseline walking, early- and late-adaptation, and post-adaptation. SLsym and KJCFsym values were determined. Comparisons were made for symmetry values between early- and late-adaptation and between baseline and post-adaptation. SLsym and KJCFsym did not respond in the same manner during the walking conditions. While step lengths (SL) were asymmetric during early adaptation but become more symmetric by late adaptation (p < 0.01), KJCF was symmetric throughout adaptation. Conversely, SL and KJCF exhibited similar responses during the baseline and post-adaptation conditions, with symmetry at baseline and asymmetry during post-adaptation (p < 0.01). In the post-adaptation condition, higher peak forces were demonstrated on the limb taking a shorter step. Results suggest a SBTM program may alter KJCF and KJCFsym between limbs. Furthermore, a comparison between baseline and post-adaptation may be more appropriate for evaluating the relationship between SL and KJCF.

Characteristics of landing impact in athletes who have not returned to sports at the pre-injury competition level after anterior cruciate ligament reconstruction

BackgroundMost patients with anterior cruciate ligament (ACL) injury undergo ACL reconstruction (ACLR) with the expectation of being able to return to sport (RTS) at the same level of the competition as before the injury. The magnitude and asymmetry of landing impact are important post-ACLR functional variables related to increased ACL strain and poor athletic performance. However, the association between the RTS status and landing impact in post-ACLR patients is unknown. ObjectiveTo investigate the association between RTS status and landing impact during single-leg landing in post-ACLR patients. MethodsForty-four patients after primary, unilateral ACLR participated in this study. They had already participated in sports post-ACLR. Questionnaires were used to assess whether the participants achieved the same competitive level of RTS as before the injury. The magnitude and symmetry of the peak vertical ground reaction force (pVGRF) were collected and analysed during single-leg jump landings. Additionally, knee functions (range of motion, laxity, effusion, strength, and single-leg hop distance) were measured. ResultsA total of 28 (64%) patients reported RTS at their pre-injury competition levels. The no-RTS group had a lower pVGRF magnitude on the operated side than the yes-RTS group (P = .019). The no-RTS group had a higher rate of pVGRF asymmetry (50%) than the yes-RTS group (18%) (P = .040). Logistic regression analysis revealed that pVGRF magnitude and asymmetry were significantly associated with the RTS status. Logistic regression analysis adjusted for knee function revealed that the pVGRF magnitude was significantly associated with the RTS status. ConclusionIn patients who are unable to RTS at their pre-injury competition level after ACLR, the pVGRF is lower and more likely to be asymmetrical than in those able to RTS at their pre-injury competition level.