Constant Relative Speed Research Articles

Research of the movement of a material particle on the internal surface of a vertical cylinder that performs planetary motion

Planetary motion of a cylinder is understood as its motion when it is in two rotational motions at the same time: it rotates around its own vertical axis with a constant angular velocity, and the cylinder axis itself rotates with a constant angular velocity around a vertical fixed axis. The movement of the particle will be complex and will consist of its relative movement along the inner surface of the cylinder and the translational movement of the cylinder itself. Such a drive scheme is used in cylindrical sieves for sorting seeds of agricultural crops. Problems on the complex motion of a particle can be successfully solved using the trihedron and Frenet's formulas. The purpose of the study is to establish the complex movement of a material particle along the inner surface of a cylindrical sieve using a trihedron and Frenet's formulas at the same and different angular velocities of transfer and relative rotation of the sieve. A characteristic feature of the application of the trihedron and Frenet formulas is that the independent variable in them is not time t, as is generally accepted in problems of kinematics and dynamics of a point, but the length of the arc s of the directional curve (in our case, a circle of radius R), so the relationship was established the connection between rotational movements through this parameter. The system of differential equations is integrated by numerical methods. An exact analytical solution was found in the case when the motion of the particle stabilizes and its speed becomes constant. The obtained results were visualized. Some regularities of the relative and absolute motion of a particle in a cylindrical sieve were established when the angular velocity of rotation of the cylinder around its own axis is zero and is not equal to zero. In the first case, it was found that the particle on the surface of the cylinder occupies a position at which it is as far as possible from the axis of rotation of the cylinder around a vertical line and then it moves down the plane of the cylinder uniformly accelerated, uniformly or uniformly decelerated until it "sticks" depending on the value angular velocity. In the second case, the particle behaves similarly: it remains at the maximum distance after the motion is stabilized. At the same time, it slides along the surface of the cylinder with a constant relative speed along a helical line. The direction of the rise of the helical line changes to the opposite when the direction of the angular velocity of the cylinder changes. Such movement is possible in a certain range of angular velocities of the particle and the cylinder. As the angular velocity of the particle increases, there comes a moment when it cannot maintain the described state of sliding and begins to move along the surface of the cylinder with stops and is prone to "sticking". This state occurs sooner when the angular velocities of the particle and the cylinder have the same direction, and later when they are directed in opposite directions.

The Feature Extraction through Wavelet Coefficients of Metal Friction Noise for Adhesive and Abrasive Wear Monitoring

Friction between metals is a physical phenomenon that occurs in manufacturing machine tools. This annoying noise implies unnecessary metal contact and deterioration of a mechanical system. In this study, for the monitoring of the friction between two metal surfaces, the acoustic signature was extracted by applying the wavelet transform method to the noise measured from the change in contact force for each state of adhesive and abrasive wear. Experiments were conducted with a constant relative speed between the contacting metal surfaces. For the adhesive wear, the peak signal-to-noise ratio (PSNR) calculated by the wavelet transformation increases with the increasing contact pressure. Opposite trends were observed for the abrasive wear. The proposed index formed a group within a specific range. This ratio exhibited a strong relationship with the wear characteristics and the surface condition. From the proposed index calculated by the wavelet coefficients, the continuous monitoring of the wear influence on the failure of the machine movement operations is achieved by the sound radiation from the contacting surfaces.

On the thermodynamic foundations of the complementary relationship of evaporation

The simultaneous thermodynamic pathways (i.e., isenthalps) of the air at the measurement height and at the vegetated land surface under isobaric and adiabatic wetting/drying cycles of the environment make it possible to define the actual evaporation rate with the help of three (one measured and two derived) vapor pressure (and corresponding temperature) terms. From the first-order approximation about the constancy of the relative average speed which the two isenthalps are travelled at during drying out of the environment, a non-dimensional, linear form of the complementary relationship (CR) of evaporation naturally emerges, but now expressed by vapor pressures (and temperatures, respectively). Without an artificially low Priestley-Taylor parameter value this linear CR would overestimate the evaporation rates because the surface warms faster than the constant relative speed assumption permits. With the appropriate estimation of the wet-surface temperature and employment of realistic boundary conditions, the latter leading to a nonlinear CR, land evaporation rates can be estimated fairly accurately with minimal input variables (air temperature, humidity, wind speed and net surface radiation) and without any information of land surface properties. Not only actual but three potential evaporation rates can also be defined by linking the temperature/vapor pressure coordinates of the air and the surface isenthalps, thus reproducing certain existing formulations of the CR as well as re-creating an existing hybrid (containing, both non-dimensional vapor pressure and evaporation terms) version of it.

Phototropic Aggregation and Light-Guided Long-Distance Collective Transport of Colloidal Particles.

Phoretic swarming and collective transport of colloidal particles in response to environmental stimuli have attracted tremendous interest in a variety of fields. In this work, we investigate the light-actuated motion, aggregation, and light-guided long-distance mass transport of silica microspheres in simple spiropyran solutions under the illumination of UV spot sources. The phototactic motion is confirmed by the dependence of swarming on the illumination intensity and spiropyran concentrations, ON-OFF switching tests, pattern-masked UV sources, etc. The aggregates formed via swarming of silica spheres can chase after a moving UV source, however, relying on a critical speed of the UV source. Only when the UV source speed is below the critical value, the aggregates follow the UV spot at a constant relative speed to the light spot. Analysis on the shape of silica microsphere currents indicates that continuous illumination of the UV spot source and resultant chemical gradients are important for the formation of steady microsphere currents. Light-guided aggregation and long-distance mass transport are interesting for targeted delivery and remote-controlled enrichment of environmental hazards.

A formulation of unifiable multi-commodity kinematic wave model with relative speed ratios

Observations suggest that the First-In-First-Out (FIFO) principle is usually violated on multi-lane roads. Jin (2017) formulated and solved unifiable multi-commodity kinematic wave models, when different commodities have the same contributions to overall traffic congestion (unifiable) but may travel at different speeds (non-FIFO). However, the construction of unifiable multi-commodity fundamental diagrams and the assumption of concave or convex commodity flow proportion functions are purely mathematical and lack behavioral explanations. Thus the existing formulation is only of pure mathematical and theoretical interests and too complicated for real-world calibration, validation, or applications.In this study, we present a new formulation of unifiable multi-commodity kinematic wave models to address the aforementioned limitations. We first introduce a new variable for the relative speed ratios of different commodities and particularly discuss constant relative speed ratios. The relative speed ratios are physically, behaviorally, and economically meaningful since they characterize drivers’ relative aggressiveness, values of times, and other features. We then present unifiable multi-commodity fundamental diagrams based on the relative speed ratios, which can be used to derive the mathematical generating functions in Jin (2017). Then we show that non-FIFO multi-commodity kinematic wave model is a system of non-strictly hyperbolic conservation laws and solve the Riemann problem for a two-commodity system with constant relative speed ratios, in which the commodity flow proportion function is either concave or convex. We also present an empirical evidence for the existence of unifiable multi-commodity fundamental diagrams with constant relative speed ratios, which help to demonstrate the advantage of the new formulation. In summary, the new formulation is as general as the original formulation, but physically more meaningful, theoretically easier to solve, and empirically simpler to calibrate. Finally we conclude the study with discussions on potential future applications.

Effect of progressive horizontal resistive force on the comfortable walking speed of individuals post-stroke.

BackgroundIndividuals post-stroke select slow comfortable walking speeds (CWS) and the major factors used to select their CWS is unknown.ObjectiveTo determine the extent to which slow CWS post-stroke is achieved through matching a relative force output or targeting a particular walking speed.MethodsTen neurologically nonimpaired individuals and fourteen chronic stroke survivors with hemiplegia were recruited. Participants were instructed to “walk at the speed that feels most comfortable” on a treadmill against 12 progressively increasing horizontal resistive force levels applied at the pelvis using a robotic system that allowed participant to self-select their walking speed. We compared slope coefficients of the simple linear regressions between the observed normalized force vs. normalized speed relationship in each group to a slope of -1.0 (i.e. ideal slope for a constant relative force output) and 0.0 (i.e. ideal slope for a constant relative speed). We also compared slope coefficients between groups.ResultsThe slope coefficients were significantly greater than -1.0 (p < 0.001 for both) and significantly less than 0 (p < 0.001 for both). However, compared with nonimpaired individuals, people post-stroke were less able to maintain their walking speed (p = 0.003).ConclusionsThe results of this study provide evidence for a complex interaction between the regulation of relative force output and intention to move at a particular speed in the selection of the CWS for individuals post-stroke. This would suggest that therapeutic interventions should not only focus on task specific lower-limb strengthening exercises (e.g. walking against resistance), but should also focus on increasing the range of speeds at which people can safely walk.

Microscale Friction Behaviour of Single Crystal Si (111) When Rubbed with Diamond Spherical and Conical Styli

An experimental study is described of the friction behaviour of samples of single crystal Si (111) when they were rubbed with diamond spherical (radius of 0.18 mm) and conical styli of included angles of 120° and 136°. Several techniques were used including (1) a reciprocating friction machine, (2) Raman spectroscopy and (3) environmental scanning electron microscopy. Friction force was measured for a constant relative speed of 0.22 mm s−1 between the rubbing stylus and the substrate. The normal load on the stylus was varied in the range 100–500 mN. In the case of the spherical stylus, the coefficient of friction was in the range 0.03–0.08, whereas for the conical styli, it was up to ten times higher, but it varied with the number of friction cycles. Raman spectroscopy revealed that in all cases, structural phase transitions of the silicon had occurred in the friction tracks and both amorphous silicon and Si-III phases were found. Environmental scanning electron microscope showed no debris in the friction tracks produced by the spherical stylus, whereas a considerable amount of debris was found within the friction tracks produced by the conical styli. This debris has been shown to be responsible for the gradual decrease in the coefficient of friction with increasing number of friction cycles. Calculations of the frictional heating between the spherical stylus and the Si (111) substrate have shown that only a negligible interfacial temperature rise would occur. It has been suggested that, in the absence of ploughing, the coefficient of friction between the spherical stylus and the Si (111) substrate is controlled by the adhesion between the two surfaces, whereas the very initial coefficient of friction between the conical styli and the Si (111) substrate is controlled by the ploughing process.

In-line quality control of moving objects by means of spectral-domain OCT

In-line quality control of intermediate and final products is essential in various industries. This may imply determining the thickness of a foil or evaluating the homogeneity of coating applied to a pharmaceutical tablet. Such a qualitative and quantitative monitoring in a depth-resolved manner can be accomplished using optical coherence tomography (OCT). In-line quality control based on OCT requires additional consideration of motion effects for the system design as well as for data interpretation. This study focuses on transverse motion effects that can arise in spectral-domain (SD-) OCT systems. The impact of a transverse movement is analyzed for a constant relative speed difference up to 0.7m/s between sample and sensor head. In particular, transverse motion is affecting OCT system properties such as the beam displacement (distance between adjacent A-scans) and transverse resolution. These properties were evaluated theoretically and experimentally for OCT images of a resolution target and pharmaceutical film-coated tablets. Both theoretical and experimental analyses highlight the shift of the transverse resolution limiting factor from the optics to the beam displacement above a relative speed difference between sensor head and sample of 0.42m/s (for the presented SD-OCT setup). Speeds above 0.4m/s are often demanded when monitoring industrial processes, such as a coating process when producing film-coated tablets. This emphasizes the importance of a fast data acquisition when using OCT as in-line quality control tool.

Resonant control of cold-atom transport through two optical lattices with a constant relative speed

We show theoretically that the dynamics of cold atoms in the lowest energy band of a stationary optical lattice can be transformed and controlled by a second, weaker, periodic potential moving at a constant speed along the axis of the stationary lattice. The atom trajectories exhibit complex behavior, which depends sensitively on the amplitude and speed of the propagating lattice. When the speed and amplitude of the moving potential are low, the atoms are dragged through the static lattice and perform drifting orbits with frequencies an order of magnitude higher than that corresponding to the moving potential. Increasing either the speed or amplitude of the moving lattice induces Bloch-like oscillations within the energy band of the static lattice, which exhibit complex resonances at critical values of the system parameters. In some cases, a very small change in these parameters can reverse the atom's direction of motion. In order to understand these dynamics we present an analytical model, which describes the key features of the atom transport and also accurately predicts the positions of the resonant features in the atom's phase space. The abrupt controllable transitions between dynamical regimes, and the associated set of resonances, provide a mechanism for transporting atoms between precise locations in a lattice: as required for using cold atoms to simulate condensed matter or as a stepping stone to quantum information processing. The system also provides a direct quantum simulator of acoustic waves propagating through semiconductor nanostructures in sound analogs of the optical laser (SASER).

Wicking of a liquid bridge connected to a moving porous surface

AbstractWe study the coupled problem of a liquid bridge connected to a porous surface and an impermeable surface, where the gap between the surfaces is an externally controlled function of time. The relative motion between the surfaces influences the pressure distribution and geometry of the liquid bridge, thus affecting the shape of liquid penetration into the porous material. Utilizing the lubrication approximation and Darcy’s phenomenological law, we obtain an implicit integral relation between the relative motion between the surfaces and the shape of liquid penetration. A method to control the shape of liquid penetration is suggested and illustrated for the case of conical penetration shapes with an arbitrary cone opening angle. We obtain explicit analytic expressions for the case of constant relative speed of the surfaces as well as for the relative motion between the surfaces required to create conical penetration shapes. Our theoretical results are compared with experiments and reasonable agreement between the analytical and experimental data is observed.

Homotopy symmetry in the multiply connected twin paradox of special relativity

In a multiply connected space, the two twins of the special relativity twin paradox move with constant relative speed and meet a second time without acceleration. The twins' situations appear to be symmetrical despite the need for one to be younger due to time dilation. Here, the suggestion that the apparent symmetry is broken by homotopy classes of the twins' worldlines is reexamined using space-time diagrams. It is found that each twin finds her own spatial path to have zero winding index and that of the other twin to have unity winding index, i.e. the twins' worldlines' relative homotopy classes are symmetrical. Although the twins' apparent symmetry is in fact broken by the need for the non-favoured twin to non-simultaneously identify spatial domain boundaries, the non-favoured twin {\em cannot} detect her disfavoured state if she only measures the homotopy classes of the two twins' projected worldlines, contrary to what was previously suggested. We also note that for the non-favoured twin, the fundamental domain can be chosen by identifying time boundaries (with a spatial offset) instead of space boundaries (with a temporal offset).

Z-pinch Vlasov-fluid equilibria including sheared-axial flow

New solutions are presented to the equilibrium Vlasov-fluid equations in Z-pinch geometry that include the effect of sheared axial ion flow. These are different to previous Vlasov-fluid equilibria in that the ion distribution function shows an axial temperature anisotropy. Examples of three new classes of equilibria are calculated, these being the anisotropic-parabolic (constant current density) and Bennett (constant relative speed) profiles and a set of profiles resulting from assuming that the ion fluid velocity is given by (b1+rp) for b1=−0.5 and p&gt;1.

Transition probabilities of atomic systems between moving walls.

The transition probabilities of a quantum system introduced between parallel conducting walls approaching or receding from each other with arbitrary constant relative speed are evaluated in the dipole approximation. The interaction with the vacuum fluctuations of the quantum electromagnetic field inside the box induces modifications in the spontaneous emission probabilities. While the transition probabilities in free space are recovered in the ultrarelativistic limit, an enhancement or inhibition of the spontaneous emission in the nonrelativistic limit is expected according to the dipole moment orientation of the detector. These results are discussed in the context of photon generation by the moving walls. \textcopyright{} 1996 The American Physical Society.

On hydrodynamic boundary conditions for microstructural fluids

Various types of boundary conditions used when investigating microrotation are analysed. A boundary condition for studying microstructural fluid flows, which depends on experimental parameters, is suggested. To illustrate the result, expressions are derived for the velocity and microrotation of a micropolar fluid between two coaxial cylinders with a constant relative speed of rotation.

Tunneling between Two Moving Wells in the Adiabatic Approximation

A solution in the adiabatic approximation of the Born-Oppenheimer type to Schrödinger's time-dependent equation in one dimension for a model three-body system is presented. The model problem for this system is a particle of mass m interacting with two attractive square wells that are receding at constant relative speed. Graphs of the time development of the probability distribution for the tunneling particle are presented for various initial conditions. The series of graphical solutions is useful as a visual aid in understanding the time development of a simplified three-body problem and the results of the model problem are used as a basis for understanding a nuclear reaction leading to three bodies in the final state.

Thyratron Control of D-C Motors

This paper describes the characteristics of new thyratron circuits which have been developed for the control of direct current motors. By means of these circuits it is possible to hold constant motor speed, constant armature voltage, or constant relative speed between two systems. It is also possible to hold constant either an alternating or direct current voltage which is dependent on the speed or position of the armature of a direct current motor.

Thyratron control of D-C motors

This paper describes the characteristics of new thyratron circuits which have been developed for the control of direct current motors. By means of these circuits it is possible to hold constant motor speed, constant armature voltage, or constant relative speed between two systems. It is also possible to hold constant either an alternating or direct current voltage which is dependent on the speed or position of the armature of a direct current motor.