Transverse Motion Research Articles

On non-monotonic temperature dependence of linear contact probability in atomic chains

In this paper, we theoretically investigate the temperature T dependence of linear contact probability in atomic chains. In these chains, the transverse motion of the electrons is assumed to be confined in the harmonic oscillator confinement model. The intra-chain electron correlations are treated within both Hartree–Fock Approximation (HFA) and Random Phase Approximation (RPA). As artifact HFA correlation functions are used in the RPA perturbative calculations. Results are presented for numerically computed pair-correlation functions at different temperatures and electron densities. An enhanced singlet-state is observed in these chains at zero inter-electronic spacing which remains independent of T. At non zero inter-electronic spacing, shrinking of Pauli’s hole is observed with increasing T. Using the RPA, the short-range pair-correlation functions are found to be considerably modified at finite-T and contact probability shows non-monotonic dependence on T. Smearing of exchange-correlation hole is also observed above a critical value of T in the diffusion zone. We also estimate the strength of the coupling parameter up to what the RPA is capable of dealing with carrier correlations in atomic chains. This work may prove useful for density functional theory calculations as estimation of the exchange-correlation hole is imperative for exchange-correlation functionals.

Effect of Turbine Weight on the Seismic Response of a Wind Turbine-Monopile System Located in Liquefied Multilayer Soil

The core objectives of sustainable development are to develop access to renewable, sustainable, reliable, and cost-effective resources. Wind is an essential source of renewable energy, and monopile wind turbines are one method proposed for harnessing wind power. Offshore wind turbines can be vulnerable to earthquakes and liquefaction. This numerical study defined the effects of wind turbine weight on the seismic response of a wind turbine-monopile system located in liquefied multilayered soil with layer thicknesses of 5, 10, 15, and 20 m using four far-field records. OpenSees PL analysis indicated that if the liquefied sand had a lower density or a thickness of more than 10 m, then an increase in the earthquake acceleration beyond 0.4 g caused the pile to float like liquefied soil and to lose its vertical bearing capacity. Moreover, increasing the wind turbine power from 2 to 5 kW had no significant effect on the soil-structure interaction response. As the earthquake acceleration increased, the bending moment of the pile-column also increased as long as liquefaction did not occur and the pile-column deformation remained rotational-spatial in shape. As the acceleration and liquefaction increased and the pile began to float in response to its transverse motion, there was no significant difference in the pile-column displacement along the length, but there was a decrease in the pile-column bending moments. As this phenomenon increased and the pile continued to float, transformation of the pile increased the difference between the displacement of the pile-column along its length and further increased the bending moments. These results were derived from multiple correlation analysis, the bending moment relations, and lateral displacement of the pile-column of the wind turbine.

Study on dynamic characteristics of rotor-bearing system under pitching condition

In many cases, ships will encounter special conditions, such as bad sea conditions, and the effect of various disturbance factors, such as wind and waves, will cause low-frequency longitudinal and transverse rocking motion of ships. This would affect the rotor-bearing system of the power plant, which is directly attached to the hull of the ship, and would roll along with the hull in the same longitudinal and transverse motion. This will have a significant impact on the stability of the rotor bearing system of the ship power plant and the safety of the ship. In this paper, a rotor-bearing test rig is mounted on a multi-degree-of-freedom swing test rig simulating sea conditions. The multi-degree-of-freedom rocking test bed simulates sea conditions. The rotor-bearing test bed is equipped with an eddy current sensor and an acceleration sensor to obtain experimental data. The programmable loader is used to control the rotor speed so as to carry out the experiment process at different speeds. Finally, the dynamic characteristics of rotor-bearing system under swinging condition are obtained.

Forward Modeling of Simulated Transverse Oscillations in Coronal Loops and the Influence of Background Emission

Abstract We simulate transverse oscillations in radiatively cooling coronal loops and forward-model their spectroscopic and imaging signatures, paying attention to the influence of background emission. The transverse oscillations are driven at one footpoint by a periodic velocity driver. A standing kink wave is subsequently formed and the loop cross section is deformed due to the Kelvin–Helmholtz instability, resulting in energy dissipation and heating at small scales. Besides the transverse motions, a long-period longitudinal flow is also generated due to the ponderomotive force induced slow wave. We then transform the simulated straight loop to a semi-torus loop and forward-model their spectrometer and imaging emissions, mimicking observations of Hinode/EIS and SDO/AIA. We find that the oscillation amplitudes of the intensity are different at different slit positions, but are roughly the same in different spectral lines or channels. X-t diagrams of both the Doppler velocity and the Doppler width show periodic signals. We also find that the background emission dramatically decreases the Doppler velocity, making the estimated kinetic energy two orders of magnitude smaller than the real value. Our results show that background subtraction can help recover the real oscillation velocity. These results are helpful for further understanding transverse oscillations in coronal loops and their observational signatures. However, they cast doubt on the spectroscopically estimated energy content of transverse waves using the Doppler velocity.

The Nature of High-frequency Oscillations Associated with Short-lived Spicule-type Events

Abstract We investigate high-resolution spectroscopic and imaging observations from the CRisp Imaging SpectroPolarimeter (CRISP) instrument to study the dynamics of chromospheric spicule-type events. It is widely accepted that chromospheric fine structures are waveguides for several types of magnetohydrodynamic (MHD) oscillations, which can transport energy from the lower to upper layers of the Sun. We provide a statistical study of 30 high-frequency waves associated with spicule-type events. These high-frequency oscillations have two components of transverse motions: the plane-of-sky (POS) motion and the line-of-sight (LOS) motion. We focus on single isolated spicules and track the POS using time–distance analysis and in the LOS direction using Doppler information. We use moment analysis to find the relation between the two motions. The composition of these two motions suggests that the wave has a helical structure. The oscillations do not have phase differences between points along the structure. This may be the result of the oscillation being a standing mode, or that propagation is mostly in the perpendicular direction. There is evidence of fast magnetoacoustic wave fronts propagating across these structures. To conclude, we hypothesize that the compression and rarefaction of passing magnetoacoustic waves may influence the appearance of spicule-type events, not only by contributing to moving them in and out of the wing of the spectral line but also through the creation of density enhancements and an increase in opacity in the Hα line.

Steady-state ballistic thermal transport associated with transversal motions in a damped graphene lattice subjected to a point heat source

In the paper we deal with ballistic heat transport in a graphene lattice subjected to a point heat source. It is assumed that a graphene sheet is suspended under tension in a viscous gas. We use the model of a harmonic polyatomic (more exactly diatomic) lattice performing out-of-plane motions. The dynamics of the lattice is described by an infinite system of stochastic ordinary differential equations with white noise in the right-hand side, which models the point heat source. On the base of the previous analytical unsteady analysis an analytical formula in continuum approximation is suggested, which allows one to describe a steady-state kinetic temperature distribution in the graphene lattice in continuum approximation. The obtained solution is in a good agreement with numerical results obtained for the discrete system everywhere excepting a neighbourhood of six singular rays with the origin at the heat source location. The continuum solution becomes singular at these rays, unlike the discrete one, which appears to be localized in a certain sense along the rays. The factors, which cause such a directional localization and the mismatch between the continuum and discrete solutions are discussed. We expect that the suggested formula is applicable for various damped polyatomic lattices where all particles have equal masses in the case of universal for all particles external viscosity.

Synergistic effect of memory-size-microstructure on thermoelastic damping of a micro-plate

The design of high-performance micro-mechanical resonators requires sufficiently accurate analysis of their thermoelastic damping. In this paper, a micro-resonator is modeled as a thin rectangular plate in vibration, and its thermoelastic damping is characterized in terms of the inverse quality factor Q−1. The Kirchhoff plate theory containing the memory, nonlocal, and size effects is presented, where the memory effect of heat flow is described by a convolution integral for time, its nonlocal effect is captured by the Guyer–Krumhansl model for space and the size effect for microstructures is characterized by Hadjesfandiari and Dargush’s consistent couple stress theory. The temperature field related to the deflection is solved first, and the governing equation of the transverse motion of a vibrating plate is obtained later. Two methods including the complex frequency approach and energy dissipation approach are employed to derive the analytical expression for the inverse quality factor. Emphasis is focused on the synergistic effect of non-locality, memory, and microstructure on the thermoelastic dissipation in micro-plates. Additionally, the influences of boundary conditions, vibration modes, and structural dimension on the thermoelastic damping are also analyzed. The temperature dependence of the thermoelastic damping is predicted and anelastic internal friction is elucidated.

Numerical analysis of hydrodynamics influenced by a deformed bed due to a near-bank vegetation patch

Abstract This study uses a 2D hydro-morphological model to analyze hydrodynamics over flat and deformed beds with a near-bank vegetation patch. By varying the patch density, the generalized results show that the hydrodynamics over deformed beds differs a lot from those over flat beds. It is found that the deformed bed topography leads to an apparent decrease in longitudinal velocity and bed shear stress in the open region and longitudinal surface gradient for the entire vegetated reach. However, the transverse flow motion and transverse surface gradient in the region of the leading edge and trailing edge is enhanced or maintained, suggesting the strengthening of secondary flow motion. Interestingly, the deformed bed topography tends to alleviate the horizontal shear caused by the junction-interface horizontal coherent vortices, indicating that the turbulence-induced flow mixing is highly inhibited as the bed is deformed. The interior flow adjustment through the patch for the deformed bed requires a shorter distance, La, which is related to the vegetative drag length, (Cda)−1, with a logarithmic formula (La = 0.4ln[(Cda)−1] + b, with b = 3.83 and 4.03 for the deformed and flat beds). The sloping bed topographic effect in the open region accelerating the flow may account for the quick flow adjustment.

Geometrically exact dynamics of cantilevered pipes conveying fluid

In this paper, the global dynamics of a hanging fluid conveying cantilevered pipe with a concentrated mass attached at the free end is investigated. The problem is of interest not only for engineering applications, but also because it displays interesting and often surprising dynamical behaviour. The widely used nonlinear models based on the transverse motion of the pipe are not able to accurately capture the dynamical behaviour of the system at very high flow velocities. Thus, a high-dimensional geometrically-exact model is developed for the first time, utilising Hamilton’s principle together with the Galerkin modal decomposition technique. Extensive numerical simulations are conducted to investigate the influence of key system parameters. It is shown that at sufficiently high flow velocities past the first instability (Hopf bifurcation), the system undergoes multiple bifurcations with extremely large oscillation amplitudes and rotations, beyond the validity of third-order nonlinear models proposed to-date. In the presence of an additional tip mass, quasi-periodic and chaotic motions are observed; additionally, it is shown that for such cases an exact model is absolutely essential for capturing the pipe dynamics even at relatively small flow velocities beyond the first instability.

Research on Decoupled Optimal Control of Straight-Line Driving Stability of Electric Vehicles Driven by Four-Wheel Hub Motors

The optimal control strategy for the decoupling of drive torque is proposed for the problems of runaway and driving stability in straight-line driving of electric vehicles driven by four-wheel hub motors. The strategy uses a hierarchical control logic, with the upper control logic layer being responsible for additional transverse moment calculation and driving anti-slip control; the middle control logic layer is responsible for the spatial motion decoupling for the underlying coordinated distribution of the four-wheel drive torque, on the basis of which the drive anti-skid control of a wheel motor-driven electric vehicle that takes into account the transverse motion of the whole vehicle is realized; the lower control logic layer is responsible for the optimal distribution of the driving torque of the vehicle speed following control. Based on the vehicle dynamics software Carsim2019.0 and MATLAB/Simulink, a simulation model of a four-wheel hub motor-driven electric vehicle control system was built and simulated under typical operating conditions such as high coefficient of adhesion, low coefficient of adhesion and opposing road surfaces. The research shows that the wheel motor drive has the ability to control the stability of the whole vehicle with large intensity that the conventional half-axle drive does not have. Using the proposed joint decoupling control of the transverse pendulum motion and slip rate as well as the optimal distribution of the drive force with speed following, the transverse pendulum angular speed and slip rate can be effectively controlled with the premise of ensuring the vehicle speed, thus greatly improving the straight-line driving stability of the vehicle.

Three-Dimensional Finite Element Modeling of Blast Wave Transmission From the External Ear to a Spiral Cochlea.

Blast-induced injuries affect the health of veterans, in which the auditory system is often damaged, and blast-induced auditory damage to the cochlea is difficult to quantify. A recent study modeled blast overpressure (BOP) transmission throughout the ear utilizing a straight, two-chambered cochlea, but the spiral cochlea's response to blast exposure has yet to be investigated. In this study, we utilized a human ear finite element (FE) model with a spiraled, two-chambered cochlea to simulate the response of the anatomical structural cochlea to BOP exposure. The FE model included an ear canal, middle ear, and two and half turns of two-chambered cochlea and simulated a BOP from the ear canal entrance to the spiral cochlea in a transient analysis utilizing fluid-structure interfaces. The model's middle ear was validated with experimental pressure measurements from the outer and middle ear of human temporal bones. The results showed high stapes footplate (SFP) displacements up to 28.5 μm resulting in high intracochlear pressures and basilar membrane (BM) displacements up to 43.2 μm from a BOP input of 30.7 kPa. The cochlea's spiral shape caused asymmetric pressure distributions as high as 4 kPa across the cochlea's width and higher BM transverse motion than that observed in a similar straight cochlea model. The developed spiral cochlea model provides an advancement from the straight cochlea model to increase the understanding of cochlear mechanics during blast and progresses toward a model able to predict potential hearing loss after blast.

Effect of grain boundaries on elastic shock wave in graphene

Effect of grain boundaries (GBs) on elastic shock wave in graphene is investigated by molecular dynamics simulations. Bicrystal graphenes with symmetrical GB are shocked along directions perpendicular and parallel to GB. For perpendicular shock loadings, double elastic shock waves emerge in form of quasilongitudinal (QL) and quasitransverse (QT) waves, since the loading direction is neither zigzag nor armchair. GB attenuates the QL wave and gives rise to new QT waves propagating into grains. Transverse particle motion in the elastic shocks can induce small lattice rotations and different oriented regions, whose number increases upon the passage of waves through GB. Upon shock loadings along GB, transverse particle motions of opposite direction generate in the two grains, and change the pressure distribution right behind wavefront, and then result in deviation of shock wave from planar loading or “V” shaped wavefront turning at GB. The above phenomena are attributed to the turn of grain orientation at GB and transverse particle motions induced by lattice symmetry reduction upon shock compression.

Large amplitude vibrations of imperfect porous-hyperelastic beams via a modified strain energy

In this paper, the porous-hyperelastic properties of soft materials are obtained experimentally and a general model for a combination of porosity (of functional type) and hyperelasticity using the Mooney-Rivlin strain energy density is obtained. Porous-hyperelastic samples are fabricated using thermoplastics with different porosities by varying the infill rate of 3D-printing. Following the available standards, the stress-strain behaviour for different samples are obtained and a general model for hyperelastic closed-cell porosity is presented. After obtaining model's characteristics from the experimental testings, a general beam formulation is presented for hyperelastic beams with functional porosity through the length. Both the axial and transverse motions are considered in the model of hyperelastic beams in the framework of the Mooney-Rivlin material model and Hamilton's principle. A geometrical imperfection of the beam is also considered in the formulation. The nonlinear forced vibrations of the imperfect porous-hyperelastic beam are studied by simultaneously solving the axial and transverse nonlinear coupled equations using a dynamic equilibrium technique. It is shown that having a uniform and functional porosity has a significant effect in changing the nonlinear frequency response of the system. Geometrical imperfection leads to a significant coupling between the axial and transverse coordinates when the porosity varies functionally through the length which shows the importance of considering both motions while analysing such structures. The results are useful for better understanding the effects of imperfections in studying the mechanics of soft structures and can be useful in designing soft robotics and artificial organs.

On the Shape of Nucleons at High Energies

A scenario of the evolution of the shape of nucleons with increasing energy is described in the framework of an extended parton model, which consistently takes into account the transverse motion of the partons. At the energy E up to LHC, the nucleons have the form of a spheroid which expands as lnE in the transverse directions and grows linearly in E in the longitudinal direction. With a further increase in the energy, a mode of correlated behavior of the partons is established, which stops the longitudinal growth. Simultaneously, the expansion in the transverse directions changes to lnE, and a hollow mostly free of partons is formed inside the nucleons along the central axis in the direction of their motion. Numerical estimates of the corresponding parameters are obtained.

Design and control of an ultrasonic surface haptic device for longitudinal and transverse mode comparison

The design and closed loop control of a device able to produce both longitudinal mode and transverse mode vibration, at about the same resonance frequency (60 kHz) are presented in this article. The structure uses an array of piezo-ceramics. A dynamic analysis is performed on the obtained modes, and their dynamic lumped parameters are identified. A closed loop control is performed to maintain the desired vibration amplitude in the presence of a finger. Longitudinal and transverse motion cartographies show that the objective of achieving and controlling pure modes independently has been achieved. Using this device, tribological, psychophysical and energetic analyses are carried out. The analyses show that in terms of friction measurements and perception, both modes produce equivalent results. In terms of active power losses, an advantage of the longitudinal mode over the transverse mode is observed due to the interaction with the finger.

Closed form solutions of cross flows of Casson fluid over a stretching surface

The boundary layer flow for the Casson fluid generated by a stretching sheet with cross flows is studied. In this paper we analyzed three different cases of cross flow with streamwise flow. The cross flow in the first case, is generated due to uniform transverse free stream while the stretching surface is at rest. In second case the cross flow is caused by the motion of stretching surface with uniform transverse velocity and the cross flow in third case deals with the transverse shearing motion of the stretching surface. In all the case, possible one parameter solutions appear namely material parameter. The similarity solution for the present model is obtained from the Weidman solution by using some proper transformation. The velocity profiles and the wall shearing parameters for all type of flows are displayed in graphical form. It is depicted that Casson fluid material parameter β causes reduction in stream wise flow, uniform transverse plate motion and transverse shearing motion. Moreover, it is found that the magnitude of longitudinal wall shear stress parameter is greater than or equal to transverse wall shear stress for β.

Trunk Kinematics Using Musculoskeletal Modeling During Range Of Motion Tasks

A spine model can be used to predict post-spinal fusion motion needed to perform physical activities in individuals with scoliosis. Full body lumbar spine (FBLS) model (Raabi and Chaudhari, 2016) allows for modeling lumbar spine and pelvis movement and was validated for jogging. However, like other existing adult spine models, FBLS model does not allow for a motion providing thoracic spine. PURPOSE: To adapt the FBLS model for simulating thoracic, lumbar and pelvis motion during trunk rotation in all 3 planes of motion. METHODS: Since T12-L1 in FBLS model is designed as a dependent joint (axial rotation analogous to L5-S1), the constraints between torso and lumbar spine were removed and modified to allow 3 degrees of freedom for T12-L1. Model ROM were adjusted to match for expected ranges of the test tasks. Inverse kinematics (IK) were calculated for the adjusted model. Range of motion (ROM; max-min) at T12-L1 and L5-S1 joints from FBLS were compared to the 3D motion capture data of 3 healthy adults during maximal flexion-extension, lateral bending, and axial rotation tasks. RESULTS: Experimental data calculated for axial rotation for T12-L1 and L5-S1, respectively were 64.4 ± 3.8° and 30.0 ± 7.2° of flexion-extension, 40.8° ± 4° and 10.9° ± 4.7° of lateral bending, and 29.7° ± 3.6° and 13.9° ± 1.1°. While IK from FBLS were 2.4° ± 0.1 and 16.3° ± 2.0 of flexion-extension, 7.9° ± 0.7 and 1.5° ± 0.4° of lateral bending, and 32.7° ± 0.6° and 12.9° ± 4° of axial rotation for T12-L1 and L5-S1, respectively. T12-L1 joint motion from OpenSim and human data movement patterns did not corroborate in sagittal and frontal planes where a disconnection between thoracic and lumbar segments was noted. Subsequently, experimental data was significantly greater than IK for sagittal (mean difference: 96.3% and 45.7%) and frontal planes (80.6% and 86.2%) from FBLS and matched best for transverse plane (10.1% and 7.2%) for T12-L1 and L5-S1, respectively. CONCLUSION: The existing FBLS model shows reasonable promise to be adapted for ROM tasks in transverse plane motion but not for sagittal and frontal planes to model trunk motions greater than those expected in jogging.

Dynamics and stability of imperfect flexible cylinders in axial flow

This paper aims to study theoretically the effects of geometric and support imperfections on the static equilibrium and linear dynamical behaviour of a flexible cylinder in confined axial flow. The support imperfection is modelled via translational and rotational springs at the upstream end of the cylinder while the geometric imperfection is represented by an initially inclined configuration with respect to the fluid flow. The static equilibrium equation is obtained from the principle of virtual work while the equation describing the dynamics of the system around the equilibrium position is obtained using the extended Hamilton’s principle. A central finite difference method and the Galerkin scheme are employed to spatially discretize the static equilibrium equation and dynamic equation of transverse motions, respectively. Numerical results are obtained to show the effects of support and geometric imperfections on the critical flow velocities of the system with various parameters. It is shown that, in general, cylinders with the upstream support imperfection may lose stability at a lower flow velocity compared to the perfectly supported cylinders. It is also shown that the geometric imperfection may have a considerable effect on the dynamic stability of very slender cylinders and those terminated with a perfectly streamlined end-piece.

Stochastic Technical Stability Test of a Passenger Railroad Car Crossing a Turnout

This article presents a definition of stochastic technical stability that was applied to test a mathematical model of a passenger railroad car crossing a turnout with the speed exceeding 160 km/h. Stability defined in this way allows testing of Lyapunov’s stability with disturbances from the track and for a nonlinear system. The STS test of a nonlinear mathematical model of a passenger car was carried out by perturbing the motion of the mathematical model with irregularities originating from the track gauge change and wheelset motion in the direction transverse to the track axis. The main aim of this paper was to determine the influence of various factors and technical conditions on the assessment of the stability of various means of transport. The analysis presented can be used to assess the dynamics of electric vehicles, whose mechanical parameters differ from those of combustion vehicles at present. The area of stable motion in the Lyapunov sense was defined using the STS method. Simulations were performed to determine the trajectory of the wheelset transverse motion. The probability of finding the wheelset in the stable motion area in relation to the rail for a single-point contact was determined. In practice, this is a one-point contact of the wheel with the rail. Conclusions from the conducted research are presented.

Couette Resistance Due to a Sliding Plate Over a Plate With Stripes of Nonhomogeneous Slip

Abstract Couette flow with nonhomogeneous partial-slip stripes on one plate is studied. Drag and flowrate are found by an efficient eigenfunction expansion and point match method. Longitudinal motion (parallel to the stripes) experiences lower drag than transverse motion. As the gap width between the two plates approaches zero, the drag increases to a finite value if the stripes have partial slip, as comparison to the infinite value for no slip. Analysis of the region near the junction of a perfect stick-slip boundary shows a weak stress singularity while there is no singularity for partial slip junctions.