Vertical Oscillations Research Articles

Generalization of the Faraday problem for the mechanical system «reservoir – liquid» in the presence of a vertical periodic (sawtooth) disturbance

The generalization of Faraday's classic problem about the parametric resonance of the free surface during vertical oscillations of the tank according to the periodic law of the modulus of the cosine is considered. Regions of stability and instability are designed, which are compared with similar results for the classical Faraday problem. The behavior of the system is considered on the basis of a nonlinear multimode model, which describes the combined movement of the tank and fluid under the influence of external force excitation or kinematic disturbance.

Influence of scalar field in massive particle motion in JNW spacetime

In this paper, we investigated the motion of massive particles in the presence of scalar and gravitational fields, particularly focusing on the Janis-Newman-Winicour (JNW) naked singularity solution. It is shown that the innermost stable circular orbit radius strongly depends on scalar coupling parameter. Additionally, we explored the radiation reaction effects on particle dynamics, incorporating a reaction term into the motion equations. Numerical simulations indicated minimal impact on particle trajectories from radiation reaction. We also examined the oscillatory motion of particles around compact objects in the JNW spacetime, focusing on radial and vertical oscillations. Our analysis indicated that the scalar field’s coupling parameter and the spacetime deformation parameter n significantly alter the fundamental frequencies of these oscillations. Furthermore, we studied quasiperiodic oscillations (QPOs) in x-ray binaries, using the relativistic precession model to analyze upper- and lower-frequency relationships. Our results indicated that increasing parameters (n and gs) shifts the frequency ratio of 3∶2 QPOs closer to the naked singularity, with n decreasing and gs increasing both frequencies. Finally, we analyzed QPO data from four selected x-ray binary systems using Markov chain Monte Carlo analysis to constrain JNW parameters. Our findings provided insights into the mass, coupling, and deformation parameter for each system, enhancing our understanding of compact object dynamics in strong gravitational fields. Published by the American Physical Society 2024

GAIT PATTERN INVESTIGATIONS OF BIONIC PIEZOELECTRIC ROBOT

The development of micro-robots based on bionic motion has garnered increasing attention with the advancement of bionic technology. These micro-robots can be employed in various tasks, such as military applications, disaster search and rescue, in vivo drug delivery, minimally invasive surgery, and tumor treatment. Robot joint motion is commonly achieved through actuators, which encompass motor, hydraulic, or pneumatic components that often carry excessive weight. To achieve the goal of miniaturizing robotic mechanisms, innovative actuators need to be developed. This study focuses on designing a four-limbed micro-robot that utilizes piezoelectric actuators. Automatic Dynamic Analysis of the Mechanical System is employed to investigate the kinematic aspects of the micro-robot’s motion, and finite element analysis is also used to obtain the resonant characteristics of the limbs actuated by piezoelectric bimorphs. The results indicate that the gait pattern of a piezoelectric robot changes according to the walking strategy and the robot dimension. The forward travel speed varies depending on the gait pattern, and adjustments in gait design can reduce the up/down oscillation and right/left offset. The robot’s travel speed increases with both trunk and limb length, although longer thigh and leg lengths might lead to greater offset and vertical oscillation. The resonant frequency and mode shapes change with the limb structure and affect the limb motion style. By adjusting the driving frequency of the bimorph actuators, the gait pattern can be manipulated. The information presented in this study contributes to a deeper understanding of micro-robot design.

Accretion tori around rotating neutron stars II. Oscillations and precessions

The four characteristic oscillation frequencies of accretion flows (in addition to the Keplerian orbital frequency) are often discussed in the context of the time variability of black hole and neutron star (NS) low-mass X-ray binaries (LMXBs). These four frequencies are the frequencies of the axisymmetric radial and vertical epicyclic oscillations, and the frequencies of non-axisymmetric oscillations corresponding to the periastron (radial) and Lense-Thirring (vertical) precessions. In this context, we investigated the effect of the quadrupole moment of a slowly rotating NS and provide complete formulae for calculating these oscillation and precession frequencies, as well as convenient approximations. Simple formulae corresponding to the geodesic limit of a slender torus (and test-particle motion) and the limit of a marginally overflowing torus (a torus exhibiting a critical cusp) are presented, and more general approximate formulae are included to allow calculations for arbitrarily thick tori. We provide the Wolfram Mathematica code used for our calculations together with the C++ and PYTHON codes for calculating the frequencies. Our formulae can be used for various calculations regarding the astrophysical signatures of the NS super-dense matter equation of state. For instance, we demonstrate that even for a given fixed number of free parameters, a model that accounts for fluid flow precession matches the frequencies of twin-peak quasiperiodic oscillations observed in NS LMXBs better than a model that uses geodesic precession.

Reliability Of Vertical Oscillation During Running Using Marker-less Motion Capture

Reliability Of Vertical Oscillation During Running Using Marker-less Motion Capture

Toward 3D magnetic force microscopy: Simultaneous torsional cantilever excitation to access a second, orthogonal stray field component

Magnetic force microscopy (MFM) is long established as a powerful tool for probing the local stray fields of magnetic nanostructures across a range of temperatures and applied stimuli. A major drawback of the technique, however, is that the detection of stray fields emanating from a sample’s surface rely on a uniaxial vertical cantilever oscillation, and thus are only sensitive to vertically oriented stray field components. The last two decades have shown an ever-increasing literature fascination for exotic topological windings where particular attention to in-plane magnetic moment rotation is highly valuable when identifying and understanding such systems. Here, we present a method of detecting in-plane magnetic stray field components, by utilizing a split-electrode excitation piezo that allows the simultaneous excitation of a cantilever at its fundamental flexural and torsional modes. This allows for the joint acquisition of traditional vertical mode images and a lateral MFM where the tip–cantilever system is only sensitive to stray fields acting perpendicular to the torsional axis of the cantilever.

QPOs and circular orbits around black holes in Chaplygin-like cold dark matter

Understanding the nature of dark energy in the universe is an actual issue in theoretical astrophysics and cosmology. One way to do it is by probing dark fluids with different equations of states (EoS). In the present work, we consider a Schwarzschild black hole (BH) surrounded by a dark fluid with a Chaplygin-like EoS as a generalized version of the Chaplygin EoS. We first investigate the effects of the dark fluid parameters on the horizon properties of the BH. The effective mass of the spacetime is calculated and analyzed under the dark fluid parameters. The scalar invariants of the BH spacetime are also calculated, and it is shown that the spacetime curvature increases as the dark fluid parameter increases. Next, we studied the circular motion of the test particle around the BH. As standard particle motion investigations, we analyze the effective potential of the particles for circular motion, specific energy, and angular corresponding to circular orbits with zero and nonvanishing values of the dark fluid intensity. In addition, we study the innermost stable circular orbits (ISCO). It is observed that there is an outermost stable circular orbit (OSCO) due to the presence of the dark fluid. It also shows that at a critical value of the dark fluid intensity parameter, ISCO and OSCO take the same radius. We calculate the frequency of Keplerian orbits and radial and vertical oscillations of the particles along stable circular orbits. We also applied orbital data from hotspots observed near Sgr A* to obtain upper and lower values for the EoS parameter. Finally, we investigate quasiperiodic oscillations and obtain the mass-to-EoS parameter relations for GRS J1915-105 and XTE 1550-564.

Energy extraction and Keplerian fundamental frequencies in the Kalb–Ramond gravity

The nonminimal coupling of the nonzero vacuum expectation value of the self-interacting antisymmetric Kalb–Ramond field with gravity leads to a power-law hairy BH having a parameter s, which encompasses the Reissner-Nordström black hole (s=1). It is obtained the axially symmetric counterpart of this hairy solution, namely, the rotating Kalb–Ramond black hole, which encompasses, as special cases, Kerr (s=0) and Kerr–Newman (s=1) black holes. With rotating Kalb–Ramond black hole metric, we study its horizon structure and motion of the test particles in the near of the equatorial plane and we determine radial motion equations which governing t and ϕ. We also explore thatthe black hole mass increasing when falling many of mass-less particles are relative to the black hole mass. We consider how the Kalb–Ramond parameters depend on increasing its mass. Furthermore, we analyze the Keplerian frequency, as well as the vertical and horizontal oscillations of basic frequencies, using a graph-based approach. The frequency charts are contingent upon the Kalb–Ramond parameters s and Γ. By consulting certain sources, ones can investigate the distinctions between KR gravity and other models.

Constraints on Schwarzschild-like black hole from QPOs data

The search for compact astrophysical objects, such as black holes and wormholes, along with the testing of gravity theories, are crucial topics in relativistic astrophysics. In this context, theoretical and observational studies of quasi periodic oscillations (QPOs) detected in (micro)quasars prove useful for investigating their central object. We explore the massive particle motion around black hole in Schwarzschild-like spacetime and using the equation of motion, the dependence of innermost stable circular orbits (ISCO) on the parameter l was obtained. The frequencies of radial and vertical oscillations of particles around stable circular orbits have been studied and used to explain the mechanism of quasi periodic oscillations in the relativistic precession (RP) model. Using observational data from GRO J1655-40 and XTE J1550-564, we have determined a constraint on the parameter l in Schwarzschild-like spacetime through Monte-Carlo-Markovian-Chain (MCMC) analyses.

Updated Kinematics of the Radcliffe Wave: Nonsynchronous, Dipole-like Vertical Oscillations

The kinematic information of the Radcliffe wave (RW) is essential for determining its existence and gaining insights into its origin and evolution. In this work, we present an accurate measurement of the vertical velocity (V Z ) of the RW by incorporating the radial velocity (RV) measures through two methods, which is crucial but was neglected previously. First, the velocities are measured toward young stars, using their RV measurements from APOGEE-2 and proper motion measurements from Gaia DR3. Second, we combine RV measurements toward clouds with proper motion measurements of associated young stellar objects to determine the vertical velocities of the clouds. The results reveal that the oscillations in V Z are not synchronous with the vertical coordinate Z, which differs from the conclusions of previous studies. Instead, we find a 5 km s−1 kpc−1 gradient in V Z along the RW, exhibiting a dipole-like pattern. Consequently, the kinematic arrangement does not show a corresponding coherence with the spatial arrangement, bringing the RW model into question.

Metal-poor Stars in the MW Disk: Resonant Cooling of Vertical Oscillations of Halo Stars in Barred Galaxies

Using numerical simulations of a barred disk galaxy embedded in nonspinning and spinning dark matter (DM) halos, we present a novel mechanism of “cooling” the vertical oscillations of DM particles, which acquire disk kinematics. The underlying mechanism consists of resonant interactions between halo particles and the stellar bar, facilitated by a chaotic phase space of the system. The cooling mechanism acts both on dynamical and secular timescales, from ∼0.5 Gyr to a few Gyr. The stellar bar acts to absorb the kinetic energy of the vertical motions. Using a Milky Way (MW)–type stellar halo, we estimate the population of metal-poor disk stars trapped by the MW disk and analyze its kinematics. We find that the population of metal-poor MW disk stars with ∣z∣ ≲ 3 kpc detected by the Gaia DR3 and other surveys can have their origin in the stellar halo. The cooled population also migrates radially outwards by exchanging energy and angular momentum with the spinning bar, and prograde-moving stars have a different distribution from retrograde ones. Next, we calculated the ratio of the prograde-to-retrograde orbits of the cooled population and found that this ratio varies radially, with the fast-spinning stellar halo resulting in the shallower radial increase of this ratio outside of the corotation. The nonspinning stellar halo shows a monotonic increase of this ratio with radius outside the corotation. Together with the analyzed radial migration of these halo stars, the cooling phenomenon of halo metal-poor stars can explain their current disk population and has corollaries for the chemical evolution of disk galaxies in general.

Settling velocity characteristics of inertial particles in turbulent and wave-induced environments

In the present study, a theoretical model is proposed to calculate the settling velocity of solid particles in turbulence generated by both oscillatory and nearly horizontal flow motions. In contrast to other previous models that typically compartmentalize two flow conditions in their studies, this study takes a more comprehensive approach by considering the combined effects of both conditions. Taking into account the influence of drag nonlinearity, virtual mass and Basset history forces, the new theoretical model is formulated. The proposed model is obtained by solving the particle motion in fluid flow under some reasonable assumptions. Accordingly, we obtain a new dimensionless term to better take into account the effect of turbulence anisotropy on the settling velocity and the role of the sediment damping coefficient. Application of this term for other conditions is discussed in the paper. The present model shows satisfactory agreement with a wide range of experimental and numerical data and with different flow conditions found in the existing literature. These data include homogeneous isotropic turbulence with high resolution direct numerical simulations (DNS), turbulent open channel and vertical oscillation.

Clustering Runners' Response to Different Midsole Stack Heights: A Field Study.

Advanced footwear technology featuring stack heights higher than 30 mm has been proven to improve running economy in elite and recreational runners. While it is understood that the physiological benefit is highly individual, the individual biomechanical response to different stack heights remains unclear. Thirty-one runners performed running trials with three different shoe conditions of 25 mm, 35 mm, and 45 mm stack height on an outdoor running course wearing a STRYD sensor. The STRYD running variables for each participant were normalized to the 25 mm shoe condition and used to cluster participants into three distinct groups. Each cluster showed unique running patterns, with leg spring stiffness and vertical oscillation contributing most to the variance. No significant differences were found between clusters in terms of body height, body weight, leg length, and running speed. This study indicates that runners change running patterns individually when running with footwear featuring different stack heights. Clustering these patterns can help understand subgroups of runners and potentially support running shoe recommendations.

Effects of the increase of longitudinal bending stiffness of advanced footwear technology on 3,000m performance, pacing strategy, and biomechanics

This study aimed to analyse the effects of shoes with increased longitudinal bending stiffness (LBS) on 3,000 m performance, pacing strategy, heart rate, and biomechanics in trained runners. Twelve male trained runners performed a 3,000 m time trial test in an experimental shoe with a carbon fibre plate to increase the LBS (LBS-increased) and a Control shoe (without carbon fibre plate). Running performance (total time), pacing, heart rate, and biomechanical variables were registered and analysed for each 1000 m split. An individual analysis of the responders was performed based on the smallest worthwhile change. The 3,000 m time trial performance improved by 0.74% (585.83 ± 33.39 vs. 590.17 ± 34.35 s, p < 0.001, large d = 0.829) in the LBS-increased condition compared to the Control condition with a high inter-individual variability. There were no significant differences for the split effect (p = 0.898, small ηp2 = 0.021). The performance improvement was accompanied by an increase in step length (p < 0.001, large ηp2 = 0.717) throughout the time trial test and an increase of flight time in the split 1 and 2 (p < 0.05, moderate d = 0.793, 0.686, respectively) and vertical oscillation in the split 2 and 3 (p < 0.05, moderate d = 0.727, 0.652). However, the heart rate remained unchanged between conditions. The increase of LBS in footwear can improve 3,000 m performance without causing changes in the pacing strategy. Small modifications in running kinematics accompanied the improvements in running performance but without changes in heart rate. Moreover, LBS-increased did not affect all runners equally highlighting the need for further understanding of individual responses.

Stability of Running Stride Biomechanical Parameters during Half-Marathon Race

This study explores the stability of biomechanical parameters of the running stride of male trained athletes during a half-marathon competition. Using a field-based descriptive design, eight male athletes from a local training group were monitored throughout an official half-marathon race under identical conditions, assessing biomechanical parameters including ground contact time (GCT), leg spring stiffness (LSS), vertical oscillation (VO), and stride length (SL) recorded via the Stryd Summit Power Meter. A repeated measures analysis of variance (RM ANOVA) was conducted to detect significant changes in biomechanical parameters as the race progressed. Results demonstrated minimal changes in all parameters, with no significant differences observed for GCT (F = 0.96, p = 0.38), VO (F = 0.23, p = 0.87), and SL (F = 1.07, p = 0.35), and a small (η2 = 0.004) yet statistically significant difference in LSS (F = 5.52, p = 0.03) between the first and second segments, indicating that athletes were able to maintain stable biomechanical parameters throughout the race. The conclusion highlights the need for personalized training programs tailored to the unique biomechanical adaptations and demands of endurance running.

Assessing Trail Running Biomechanics: A Comparative Analysis of the Reliability of StrydTM and GARMINRP Wearable Devices.

This study investigated biomechanical assessments in trail running, comparing two wearable devices-Stryd Power Meter and GARMINRP. With the growing popularity of trail running and the complexities of varied terrains, there is a heightened interest in understanding metabolic pathways, biomechanics, and performance factors. The research aimed to assess the inter- and intra-device agreement for biomechanics under ecological conditions, focusing on power, speed, cadence, vertical oscillation, and contact time. The participants engaged in trail running sessions while wearing two Stryd and two Garmin devices. The intra-device reliability demonstrated high consistency for both GARMINRP and StrydTM, with strong correlations and minimal variability. However, distinctions emerged in inter-device agreement, particularly in power and contact time uphill, and vertical oscillation downhill, suggesting potential variations between GARMINRP and StrydTM measurements for specific running metrics. The study underscores that caution should be taken in interpreting device data, highlighting the importance of measuring with the same device, considering contextual and individual factors, and acknowledging the limited research under real-world trail conditions. While the small sample size and participant variations were limitations, the strength of this study lies in conducting this investigation under ecological conditions, significantly contributing to the field of biomechanical measurements in trail running.

Probing the eccentricity in protostellar discs: Modelling kinematics and morphologies

Context. Protostellar discs are mostly modelled as circular structures of gas and dust orbiting a protostar. However, a number of physical mechanisms, for example, the presence of a (sub)stellar companion or initial axial asymmetry, can cause the gas and dust orbital motion to become eccentric. Theoretical studies have revealed that, when present, disc eccentricity is expected to occur with predictable profiles that can be long-lasting and potentially observable in protostellar systems. Aims. We construct an analytical model predicting the typical features of the kinematics and morphology of eccentric protostellar discs, with the final goal of characterising the observational appearance of eccentricity in discs. Methods. We validate the model using a numerical simulation of a circumbinary disc (where the binary makes the disc eccentric). We finally post-process the simulation with Monte Carlo radiative transfer to study how eccentric features would appear through the ‘eyes’ of ALMA. Results. Besides the motion of the material on eccentric Keplerian orbits in the disc orbital plane, the most characteristic eccentric feature emerging from the analytical model is strong vertical motion with a typical anti-symmetric pattern (with respect to the disc line of pericentres). A circumbinary disc with a ≈ 40 au eccentric cavity (ecav = 0.2), carved by an abin = 15 au binary, placed at a distance d = 130 pc, is expected to host in its upper emission surface vertical oscillations up to vz ~ 400 m s−1 close to the cavity edge, that is to say, well within ALMA spectral and spatial resolution capabilities. A residual spiral pattern in the vertical velocity Δvz ~ 150 m s−1 of the simulation cannot be captured by the theoretical model, we speculate it to be possibly linked to the presence of a companion in the system.

Parameter constraints on traversable wormholes within beyond Horndeski theories through quasiperiodic oscillations

compact astrophysical objects such as black holes and wormholes, as well as testing gravity theories, are important issues in relativistic astrophysics. In this sense, theoretical and observational studies of quasiperiodic oscillations (QPOs) observed in (micro)quasars become helpful in exploring their central object, which can be a black hole or a wormhole. In the present work, we study the throat properties of traversable wormholes beyond Horndeski theory. Also, we investigate the circular motion of test particles orbiting the wormhole. We analyze the test particle’s effective potential and angular momentum for circular orbits. Frequencies of radial and vertical oscillations of the particles around stable circular orbits have also been studied and applied in explaining the quasiperiodic oscillations mechanism in the relativistic precession (RP) model. Finally, we obtain constraint values for the parameters of beyond Horndeski gravity and the mass of the wormhole candidates using QPOs observed in the microquasars GRO J1655-40, GRS 1915+105 &amp; XTE J1550-564 and at the center of Milky Way galaxy through Monte-Carlo-Markovian-chain (MCMC) analyses. Published by the American Physical Society 2024

Three-dimensional Effects on Gap-Resonances in Twin-Hull Vessels in Time-Harmonic Vertical Oscillations

Three-dimensional effects induced by dimensional ratios on the gap resonances happening in twin hull vessels oscillating in forced vertical motion have been analyzed. They can lead to relevant consequences, such as the amplification of the inner radiated waves or the generation of standing waves in between the demi-hulls, that can have a direct effect on the operating profile of the vessel. The response of twin hull vessels in waves can be strongly affected by these resonant phenomena. Also, some of these behaviors can be exploited in the framework of wave energy conversion systems. The present analysis is carried out by using an open-source, linear, Boundary Element Method (BEM), based on the Green function approach. Mathematical backgrounds of the added mass and damping coefficients computation for a floating body under harmonic vertical oscillation are provided as well as details of the numerical discretization used in the BEM. A panel mesh sensitivity study is carried out and the numerical prediction is validated by comparison against available experimental data, another CFD solution obtained by a high-fidelity viscous solver based on the open-source libraries Open-FOAM and approximate analytic formulations. The effect of the beam ratio and the length-to-beam ratio on the resonant phenomena has been analyzed. This has been achieved by systematic variations of the geometric dimensions of the hull, focusing on the trends of the hydrodynamic coefficients, the amplitude of the radiated waves, and the location of the resonant frequencies over the analyzed range.

Are Gait Patterns during In-Lab Running Representative of Gait Patterns during Real-World Training? An Experimental Study.

Biomechanical assessments of running typically take place inside motion capture laboratories. However, it is unclear whether data from these in-lab gait assessments are representative of gait during real-world running. This study sought to test how well real-world gait patterns are represented by in-lab gait data in two cohorts of runners equipped with consumer-grade wearable sensors measuring speed, step length, vertical oscillation, stance time, and leg stiffness. Cohort 1 (N = 49) completed an in-lab treadmill run plus five real-world runs of self-selected distances on self-selected courses. Cohort 2 (N = 19) completed a 2.4 km outdoor run on a known course plus five real-world runs of self-selected distances on self-selected courses. The degree to which in-lab gait reflected real-world gait was quantified using univariate overlap and multivariate depth overlap statistics, both for all real-world running and for real-world running on flat, straight segments only. When comparing in-lab and real-world data from the same subject, univariate overlap ranged from 65.7% (leg stiffness) to 95.2% (speed). When considering all gait metrics together, only 32.5% of real-world data were well-represented by in-lab data from the same subject. Pooling in-lab gait data across multiple subjects led to greater distributional overlap between in-lab and real-world data (depth overlap 89.3-90.3%) due to the broader variability in gait seen across (as opposed to within) subjects. Stratifying real-world running to only include flat, straight segments did not meaningfully increase the overlap between in-lab and real-world running (changes of <1%). Individual gait patterns during real-world running, as characterized by consumer-grade wearable sensors, are not well-represented by the same runner's in-lab data. Researchers and clinicians should consider "borrowing" information from a pool of many runners to predict individual gait behavior when using biomechanical data to make clinical or sports performance decisions.