36 results on '"*VARIGNON'S theorem"'
Search Results
2. Current-driven non-linear magnetodynamics in exchange-biased spin valves.
- Author
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Heidi Seinige, Cheng Wang, and Maxim Tsoi
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SPIN valves , *MAGNETIC properties , *MAGNETIC fields , *MECHANICS (Physics) , *VARIGNON'S theorem - Abstract
This work investigates the excitation of parametric resonance in exchange-biased spin valves (EBSVs). Using a mechanical point contact, high density dc and microwave currents were injected into the EBSV sample. Observing the reflected microwave power and the small rectification voltage that develops across the contact allows detecting the current-driven magnetodynamics not only in the bulk sample but originating exclusively from the small contact region. In addition to ferromagnetic resonance (FMR), parametric resonance at twice the natural FMR frequency was observed. In contrast to FMR, this non-linear resonance was excited only in the vicinity of the point contact where current densities are high. Power-dependent measurements displayed a typical threshold-like behavior of parametric resonance and a broadening of the instability region with increasing power. Parametric resonance showed a linear shift as a function of applied dc bias which is consistent with the field-like spin-transfer torque induced by current on magnetic moments in EBSV. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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3. Micromagnetic model analysis of integrated single-pole-type head with tilted spin-torque oscillator for high-frequency microwave-assisted magnetic recording.
- Author
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Takuto Katayama, Yasushi Kanai, Kazuetsu Yoshida, Simon Greaves, and Hiroaki Muraoka
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VARIGNON'S theorem , *ROTATIONAL motion (Rigid dynamics) , *TORQUEMETERS , *OSCILLATIONS , *FORCED vibration (Mechanics) - Abstract
The spin-torque oscillator (STO) is the most important component in microwave-assisted magnetic recording. Some requirements for the STO are: large amplitude and stable oscillation, small injected current, and oscillation at a frequency that excites resonance in a recording medium. It is also necessary for the STO oscillation to closely follow the head coil current. In this paper, STOs were integrated into write heads and micromagnetic analyses carried out to obtain a write head structure with stable STO oscillation that could follow a high-frequency head coil current. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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4. LEARNING TO POSE PROBLEMS WITHIN DYNAMIC GEOMETRY ENVIRONMENTS: A SELF STUDY INVOLVING VARIGNON'S PROBLEM.
- Author
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Contreras, José N.
- Subjects
MATHEMATICS problems & exercises ,REASONING ,GEOMETRY education ,MATHEMATICAL proofs ,VARIGNON'S theorem - Abstract
This paper reports my second experience on my trajectory to learn how to pose mathematical problems within Dynamic Geometry Environments. I used The Geometer's Sketchpad and mathematical reasoning as tools to verify the plausibility and reasonability of each new problem situation. Using a problem-posing framework that I had developed during my first problem-posing experience within dynamic geometry environments, and subsequently refined and enriched with subsequent tasks, I was able to generate a diversity of problems by modifying the attributes of Varignon's problem. Among the problems generated were special problems, general problems, extended problems, further extended problems, converse problems, and proof problems. Examples of each of these types of problems are provided. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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5. The Principia's second law (as Newton understood it) from Galileo to Laplace.
- Author
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Pourciau, Bruce
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LAPLACE distribution , *VARIGNON'S theorem , *MACLAURIN'S series (Mathematics) - Abstract
Newton certainly regarded his second law of motion in the Principia as a fundamental axiom of mechanics. Yet the works that came after the Principia, the major treatises on the foundations of mechanics in the eighteenth century—by Varignon, Hermann, Euler, Maclaurin, d'Alembert, Euler (again), Lagrange, and Laplace—do not record, cite, discuss, or even mention the Principia's statement of the second law. Nevertheless, the present study shows that all of these scientists do in fact assume the principle that the Principia's second law asserts as a fundamental axiom in their mechanics. (For what that second law asserts, we rely on Newton's own testimony.) Some, like Varignon and Hermann, assume the axiom implicitly, apparently unaware that any assumption is being made, while others, like Maclaurin and Euler, assume the axiom explicitly, apparently unaware that the assertion assumed is the second law as Newton himself understood it. But in every case these scientists employ the principle asserted by the Principia's second law fundamentally, unaware that they should be citing Neutonus, Prin., Phil. Nat. Math., Lex II. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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6. Numerical analysis of thermally assisted spin-transfer torque magnetization reversal in synthetic ferrimagnetic free layers.
- Author
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Shen, J., Shi, M., Tanaka, T., and Matsuyama, K.
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TORQUE control , *VARIGNON'S theorem , *TORQUE , *MAGNETIC anisotropy , *MAGNETIC moments - Abstract
The spin transfer torque magnetization reversal of synthetic ferrimagnetic free layers under pulsed temperature rise was numerically studied by solving the Landau-Lifshitz-Gilbert equation, taking into account the stochastic random fields, the temperature dependence of magnetic parameters, and the spin torque terms. The anti-parallel magnetization configuration was retained at the elevated temperature, due to interlayer dipole coupling. A significant thermal assistance effect, resulting in a 40% reduction in the switching current, was demonstrated during a nanosecond pulsed temperature rise up to 77% of the Curie temperature. [ABSTRACT FROM AUTHOR]
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- 2015
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7. Large amplitude oscillation of magnetization in spin-torque oscillator stabilized by field-like torque.
- Author
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Tomohiro Taniguchi, Sumito Tsunegi, Hitoshi Kubota, and Hiroshi Imamura
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AMPLITUDE modulation , *TORQUE control , *VARIGNON'S theorem , *PARAMETRIC oscillators , *KINEMATICS - Abstract
Oscillation frequency of spin torque oscillator with a perpendicularly magnetized free layer and an in-plane magnetized pinned layer is theoretically investigated by taking into account the field-like torque. It is shown that the field-like torque plays an important role in finding the balance between the energy supplied by the spin torque and the dissipation due to the damping, which results in a steady precession. The validity of the developed theory is confirmed by performing numerical simulations based on the Landau-Lifshitz-Gilbert equation. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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8. METHOD FOR DETERMINING HIGH-SPEED VEHICLE CONTACT FORCES OF THE GROUND TRANSPORT.
- Author
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Pivnyak, G. G., Sakhno, V. P., Kravets, V. V., and Bas, K. M.
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TRANSPORT vehicles ,RELIABILITY in engineering ,CLASSICAL mechanics ,ENGINEERING mathematics ,ANALYTICAL solutions ,HIGH speed trains - Abstract
Copyright of Scientific Bulletin of National Mining University is the property of National Mining University, State Higher Educational Institution and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2019
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9. Reconfigurable workspace and torque capacity of a compliant ankle rehabilitation robot (CARR).
- Author
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Zhang, Mingming, Cao, Jinghui, Zhu, Guoli, Miao, Qing, Zeng, Xiangfeng, and Xie, Sheng Q.
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DEGREES of freedom , *VARIGNON'S theorem , *TORQUE control , *MECHANICAL properties of condensed matter , *ROTATIONAL motion (Rigid dynamics) - Abstract
The novelty of this paper is the adjustable workspace and torque capacity of a compliant ankle rehabilitation robot (CARR). The robot has three rotational degrees of freedom (DOFs) redundantly actuated by four compliant actuators. It suffers from conflicting workspace and actuation torque due to the use of a parallel mechanism and compliant actuators. To address this issue, also considering physical constraints imposed by human users, the CARR is designed with reconfigurability to make a trade-off between workspace and torque capacity for meeting different training requirements. Theoretical analysis indicates that varying kinematic and dynamic performance of the robot can be achieved by reconfiguring the layout of the actuators. Experiments with/without load also demonstrate the validity of the reconfigurable robotic design for practical applications. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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10. Wheel slip control with torque blending using linear and nonlinear model predictive control.
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Basrah, M. Sofian, Siampis, Efstathios, Velenis, Efstathios, Cao, Dongpu, and Longo, Stefano
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HYBRID electric vehicle design & construction , *NONLINEAR statistical models , *PREDICTIVE control systems , *TORQUE control , *VARIGNON'S theorem , *ROTATIONAL motion (Rigid dynamics) , *MATHEMATICAL models - Abstract
Modern hybrid electric vehicles employ electric braking to recuperate energy during deceleration. However, currently anti-lock braking system (ABS) functionality is delivered solely by friction brakes. Hence regenerative braking is typically deactivated at a low deceleration threshold in case high slip develops at the wheels and ABS activation is required. If blending of friction and electric braking can be achieved during ABS events, there would be no need to impose conservative thresholds for deactivation of regenerative braking and the recuperation capacity of the vehicle would increase significantly. In addition, electric actuators are typically significantly faster responding and would deliver better control of wheel slip than friction brakes. In this work we present a control strategy for ABS on a fully electric vehicle with each wheel independently driven by an electric machine and friction brake independently applied at each wheel. In particular we develop linear and nonlinear model predictive control strategies for optimal performance and enforcement of critical control and state constraints. The capability for real-time implementation of these controllers is assessed and their performance is validated in high fidelity simulation. [ABSTRACT FROM PUBLISHER]
- Published
- 2017
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11. Nonlinear current resonance in a spin-torque diode with planar magnetization.
- Author
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Kulagin, N. E., Skirdkov, P. N., Popkov, A. F., Zvezdin, K. A., and Lobachev, A. V.
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MAGNETIZATION , *FORCED vibration (Mechanics) , *RESONANT states , *VARIGNON'S theorem , *MAGNETOSTRICTION , *MAGNETIC anisotropy - Abstract
The microwave sensitivity of a spin diode consisting of a tunnel junction with two magnetic electrodes is investigated. The specific feature of the magnetic tunnel structure under consideration is a skew of the electrode magnetizations in the plane of the layers, arising due to exchange interaction with the adjacent antiferromagnetic layers with different superparamagnetic blocking temperatures. Within the framework of the macrospin model the stability analysis of the stationary magnetization states is carried out as a function of the electric current and the skew angle between the magnetizations of the magnetic layers on the angle-current plane, taking into account the effect of spin torque transfer. For the obtained stationary states, variations of the resonant response to an ac current of microwave range and volt-watt sensitivity of the spin diode far away from and near the critical bias-current lines of the transition to self-oscillations are determined. It is shown that with increasing the bias current upon the approach to the critical point, hysteresis of the frequency branches of resonant response appears, induced by the nonlinear microwave modulation of torque. This effect is different from the foldover-effect under the condition of initial Lorentzian character of the ferromagnetic resonance with a constant linewidth. Furthermore, micromagnetic simulation of the diode sensitivity for similar magnetic parameters is carried out. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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12. EFFECT OF SOIL TEXTURE ON BULK DENSITY, PTO TORQUE, PULVERIZATION INDEX AND SOIL HARDNESS DURING TILLAGE WITH SPADING MACHINE.
- Author
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Dhiman, Mankaran, Dogra, Ritu, and Dogra, Baldev
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TORQUE control ,VARIGNON'S theorem ,FREE precession ,PROPERTIES of matter ,DENSITOMETERS - Abstract
Afield study was conducted to investigate the effect of texture of two types of soil (SI: sandy loam and S2: silty clay loam) as independent parameters on selected soil physical properties namely, bulk density, soil strength (hardness), pulverization index (weighted mean clod diameter) and PTO torque, using the spading machine (SM) Model 175.50 series. The sandy loam soil texture (SI) registered higher bulk density, lower soil strength, lower pulverization index than the silty clay loam soil texture (S2). The PTO torque was lower in sandy loam soil (SI) than silty clay loam soil (S2). The study has generated data on the effect of soil texture on soil physical conditions during tillage with spading machine. This will help in further improvement or modification of the machine to suit the regional conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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13. Cyclic quadrilaterals corresponding to a given Varignon parallelogram.
- Author
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POP, OVIDIU T., KISS, SÁNDOR NAGYDOBAI, and MINCULETE, NICUŞOR
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VARIGNON'S theorem , *QUADRILATERALS , *PARALLELOGRAMS - Abstract
In this paper, we will study the cyclic quadrilaterals that have as a Varignon parallelogram any given parallelogram. [ABSTRACT FROM AUTHOR]
- Published
- 2016
14. Maximum Reachable Torque, Power and Speed for Five-Phase SPM Machine With Low Armature Reaction.
- Author
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Scuiller, Franck, Zahr, Hussein, and Semail, Eric
- Subjects
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ELECTRIC potential , *STANDARD deviations , *ARMATURES , *TORQUE control , *VARIGNON'S theorem - Abstract
In this paper, the study of the torque and power versus speed characteristics for a family of five-phase surface-mounted permanent magnet machine is carried out. With considering hypotheses [linear magnetic modeling, only first and third harmonic terms in the back electromotive force (EMF) and current spectrums], an optimization problem that aims to maximize the torque for given maximum peak voltage and root mean square (RMS) current is formulated: the optimal torque sharing among the two virtual machines (the two dq-axis subspaces) that represent the real five-phase machine is thus calculated for any mechanical speed. For an inverter and a dc voltage sized with only considering the first harmonic of back EMF and current, the problem is solved with changing the virtual machine back EMFs and inductances ratios. With the introduction of the maximum torque/speed point, maximum power/speed point, and maximum reachable speed, it can be shown that, if the inductance ratio is large enough for given Volt–Ampere rating, the machine can produce higher torque without reducing its speed range, thus meaning that the capability of the inverter to work is improved with the use of the third harmonic. This property is all the truer as the base armature reaction is large. A particular five-phase machine is sized and numerically analyzed to check this property. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
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15. Diameter dependence of emission power in MgO-based nano-pillar spin-torque oscillators.
- Author
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Bochong Wang, Hitoshi Kubota, Kay Yakushiji, Shingo Tamaru, Hiroko Arai, Hiroshi Imamura, Akio Fukushima, and Shinji Yuasa
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EMISSION control , *ELECTRIC oscillators , *CRYSTAL oscillators , *VARIGNON'S theorem , *TORQUE control - Abstract
The dependence on diameter of the emission power in MgO-based nano-pillar spin torque oscillators (STOs) was systematically investigated. A maximum emission power of over 2.5 μW was obtained around 300 nm in diameter, which is the largest reported to date among the out-of-plane precession STOs. By analyzing physical quantities, precession cone angle of the free-layer magnetization was evaluated. In the diameter range below 300 nm, the increase in power was mainly due to the increase of the injected current. The power decrease above 300 nm is possibly attributed to the decrease in the averaged precession cone angle, suggesting spatial phase difference of magnetization precession. This study provides the method for estimating the optimum STO diameter, which is of great importance in practical use. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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16. Development of a gearbox test rig with non-torque loading capacity.
- Author
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Nam, Ju Seok, Park, Young Jun, Jo, Seung Je, Kim, Heung Sub, and Shim, Sung Bo
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GEARBOXES , *FREE precession , *TORQUE control , *VARIGNON'S theorem , *TORQUE - Abstract
We developed a gearbox test rig having non-torque loading capacity and applicable to up to 75 kW (100 hp) class gearboxes. The test rig is electrical back-to-back type with an input motor and output dynamometer, which control rotational speed and torque of gearboxes. Five hydraulic cylinders are used to apply the 5 degrees of freedom static and dynamic non-torque loads: The axial loading capacity is 300 kN, and the vertical and lateral loading capacities are 50 kN, respectively. The test rig is applicable to various drive train systems by using some modular components, and durability and performance tests are all possible. The test rig can faithfully reproduce the operating conditions required for gearbox test, including design complex loads and rotational speed; thus, it can be used for the gearbox test of various fields. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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17. Generalized fluctuation theorems for classical systems.
- Author
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Agarwal, G. S. and Dattagupta, Sushanta
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CYCLOTRONS , *ANALYTICAL mechanics , *MULTIBODY systems , *NONLINEAR mechanics , *VARIGNON'S theorem - Abstract
The fluctuation theorem has a very special place in the study of nonequilibrium dynamics of physical systems. The form in which it is used most extensively is the Gallavoti-Cohen fluctuation theorem which is in terms of the distribution of the work p(W)/p(-W) = exp(αW). We derive the general form of the fluctuation theorems for an arbitrary multidimensional Gaussian Markov process. Interestingly, the parameter a is by no means universal, hitherto taken for granted in the case of linear Gaussian processes. As a matter of fact, conditions under which ex does become a universal parameter 1 /KT are found to be rather restrictive. As an application we consider fluctuation theorems for classical cyclotron motion of an electron in a parabolic potential. The motion of the electron is described by four coupled Langevin equations and thus is nontrivial. The generalized theorems are equally valid for nonequilibrium steady states and could be especially important in the presence of anisotropic diffusion. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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18. Torque data on non-isothermal rarefied Cylindrical Couette flow.
- Author
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Akhlaghi, Hassan and Javadi, Khodayar
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TORQUE control , *COUETTE flow , *ROTATING fluid , *LAMINAR flow , *VARIGNON'S theorem - Abstract
The torque exerted on the walls of a micro cylindrical Couette gas flow is studied using Direct Simulation Monte Carlo (DSMC) method and analytical solutions. An analytical solution for temperature filed under specified wall heat flux condition is proposed using a previously introduced power-law (PL) wall-scaling approach. The results of cylindrical Couette flow under specified wall heat flux condition are compared with those of isothermal flow. The effects of rarefaction, compressibility, tangential momentum accommodation coefficient (TMAC) and gas-surface heat exchange on the torque values are investigated for slip to free molecular flow regimes. The results indicate that the torque coefficient has a maximum value at the transitional flow regime for TMAC values less than unity. Lower TMAC values and higher Knudsen numbers lead to reduction and deviation of torque magnitudes from those of continuum limit. Thermal simulations of cylindrical Couette flow show that heating and cooling have significant effects on the torque values. Velocity profiles and normalized torque values demonstrate mixed increasing/decreasing behavior under heating/cooling processes for rarefied gas flow. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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19. Resistive torque in permanent magnet couplings operating through a conductive wall.
- Author
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Rezek Matsumoto, Thomas and Chabu, Ivan
- Subjects
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TORQUE control , *PERMANENT magnets , *MAGNETIC coupling , *EDDY currents (Electric) , *VARIGNON'S theorem - Abstract
Purpose The purpose of this paper is to propose an analytical approach to determine the resistive torque caused by a conductive wall between the rotors of axial permanent magnet couplings. In this configuration, relative motion between the coupling rotors and the wall generates a resistive torque that is a consequence of the induced eddy currents in this barrier. Therefore, such induced resistive torque implies a reduction in the permanent magnet coupling performance, that is, its torque transmission capacity.Design/methodology/approach The developed resistive torque analytical formulation was based on eddy-current brakes of previous studies. To validate the proposed method, tests were conducted in a prototype and results were compared with analytical ones.Findings The analytical method showed a good correlation with the experiment data. Furthermore, a major degradation of the coupling capability to transmit torque was found because of the conductive wall presence, enhancing the importance of predicting such phenomenon when designing these devices.Originality/value A novel direct assessment of the resistive torque while in motion is presented in this paper. These measurements were of great importance to accurately compare the analytical and experimental data. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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20. Numerical investigation of contact stress between rotor and stator in a two-lead progressing cavity pump.
- Author
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Pan, Long and Tan, Jinzhu
- Subjects
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NATIVE element minerals , *FLUID pressure , *ROTATIONAL motion (Rigid dynamics) , *VARIGNON'S theorem , *TORQUEMETERS - Abstract
The contact stress between rotor and stator in a progressing cavity pump (PCP) is critical to seal performance and service lifetime of the PCP. In this paper, an approach to predict the contact stress and friction behavior in PCPs is proposed. The approach is based on the results from the finite element analysis (FEA) and Stribeck-type curve. A three-dimensional finite element model for the contact stress between the rotor and the stator within a two-lead PCP is successfully established. The fluid pressure, the eccentric force and the laden torque are applied to the model. And the finite element analysis is conducted to investigate the contact stress between the rotor and the stator in the two-lead PCP. The simulated results show that the contact stress in the spiral seal lines (SPSLs) is always high compared to that in warping seal lines (WSLs) at the identical relative position, and the contact stress increases along seals from the first seal line to the last one. The maximum contact stress of the PCP appearing in every seal line is off-center. It is found that the serious wear and/or damage for the progressing cavity pump during operating always occurs on the paths which are off-center of the spiral seal lines. The results are validated against the actual phenomenon which appeared in oilfields from open literatures. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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21. Humanoid robot upper body motion generation using B-spline-based functions.
- Author
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Ruchanurucks, M.
- Subjects
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HUMANOID robots , *UNCANNY valley theory , *MECHANICS (Physics) , *VARIGNON'S theorem , *MECHANICAL properties of condensed matter - Abstract
This paper aims to represent a human's upper body motion using a humanoid robot. As a robot has different physical limitations than a human, we present a method that can filter the trajectories to meet the limitations. The filtering can be used directly and also can be used as a constraint for optimization. It will be shown to be applicable both offline and online. Many physical attributes, namely angle, collision, velocity, and dynamic torque, are represented as B-spline explicit functions. The B-spline coefficients are then calculated to limit the physical attributes. This explicit method can guarantee that many limits are met. Hence, it is better than many methods that only reduce such physical attributes using objective functions. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
22. THE PLAYGROUND.
- Subjects
MATHEMATICAL formulas ,POLYGONS ,RADIUS (Geometry) ,PARALLELOGRAMS ,VARIGNON'S theorem ,MATHEMATICAL models - Abstract
The article presents sandbox problem in various mathematical equations. Mathematical problems include the equation of polygons, the equation on how to solve the radius of a small circle, and the equation on how to to construct a parallelogram called the Varignon parallelogram. It also mentions the carousel solution which is to find the divisor a number of perfect square.
- Published
- 2015
- Full Text
- View/download PDF
23. Spin-transfer torque and electric current in helical edge states in quantum spin Hall devices.
- Author
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Meng, Qinglei, Vishveshwara, Smitha, and Hughes, Taylor L.
- Subjects
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TORQUEMETERS , *VARIGNON'S theorem , *MECHANICS (Physics) , *ELECTRIC current measurement , *ELECTRIC fields - Abstract
We study the dynamics of a quantum spin Hall edge coupled to a magnet with its own dynamics. Using spin-transfer-torque principles, we analyze the interplay between spin currents in the edge state and dynamics of the axis of the magnet, and draw parallels with circuit analogies. As a highlighting feature, we show that while coupling to a magnet typically renders the edge state insulating by opening a gap, in the presence of a small potential bias, spin-transfer torque can restore perfect conductance by transferring angular momentum to the magnet. In the presence of interactions within the edge state, we employ a Luttinger liquid treatment to show that the edge, when subject to a small voltage bias, tends toform a unique dynamic rotating spin wave state that naturally couples into the dynamics of the magnet. We briefly discuss realistic physical parameters and constraints for observing this interplay between quantum spin Hall and spin-transfer torque physics. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
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24. Torque magnetometry of an amorphous-alumina/strontium-titanate interface.
- Author
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Tomarken, S. L., Young, A. F., Lee, S. W., Gordon, R. G., and Ashoori, R. C.
- Subjects
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TORQUE , *STRONTIUM titanate , *KINEMATICS , *AMORPHOUS alloys , *VARIGNON'S theorem , *ALUMINUM oxide - Abstract
We report torque magnetometry measurements of an oxide heterostructure consisting of an amorphous Al2O3 thin film grown on a crystalline SrTiO3 substrate (a-AO/STO) by atomic layer deposition. We find a torque response that resembles previous studies of crystalline LaA103/SrTi03 (LAO/STO) heterointerfaces, consistent with strongly anisotropic magnetic ordering in the plane of the interface. Unlike crystalline LAO, amorphous Al2O3 is nonpolar, indicating that planar magnetism at an oxide interface is possible without the strong internal electric fields generated within the polarization catastrophe model. We discuss our results in the context of current theoretical efforts to explain magnetism in crystalline LAO/STO. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
25. Pose and Solve Varignon Converse Problems.
- Author
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Contreras, José N.
- Subjects
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VARIGNON'S theorem , *MATHEMATICS , *QUADRILATERALS , *ANALYTICAL mechanics , *POLYGONS , *STUDENTS - Abstract
The article offers information on the use of Geometer's Sketchpad (GSP) which inspires students regarding the midpoints of the sides of a quadrilateral. The reformulation of Varignon's theorem as an open-ended problem is stated. It discusses some of the converse problems and proofs and conjectures that the students generated in using GSP in investigating some special cases of the Varignon problem.
- Published
- 2014
26. THE PLAYGROUND.
- Author
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WAITE, MATT
- Subjects
MATHEMATICAL formulas ,POLYGONS ,RADIUS (Geometry) ,PARALLELOGRAMS ,VARIGNON'S theorem ,MATHEMATICAL models - Abstract
The article presents sandbox problem in various mathematical equations. Mathematical problems include the equation of polygons, the equation on how to solve the circumference of a teething ring, and the equation on how to construct a parallelogram called the Varignon parallelogram. It also mentions the carousel solution which is to find the divisor a number of perfect square.
- Published
- 2014
- Full Text
- View/download PDF
27. Sensorless Inverter-Fed Compressor Drive System Using Back- EMF Estimator with PIDNN Torque Observer.
- Author
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Lin, Faa‐Jeng, Hung, Ying‐Chih, Chen, Jia‐Ming, and Kao, Zi‐Yin
- Subjects
FREE precession ,TORQUEMETERS ,HUMAN body ,TORQUE ,KINEMATICS ,VARIGNON'S theorem - Abstract
A saliency back- EMF estimator with a proportional-integral-derivative neural network ( PIDNN) torque observer is proposed in this study to improve the speed estimating performance of a sensorless interior permanent magnet synchronous motor ( IPMSM) drive system for an inverter-fed compressor. The PIDNN torque observer is proposed to replace the conventional proportional-integral-derivative ( PID) torque observer in a saliency back- EMF estimator to improve the estimating performance of the rotor flux angle and speed. The proposed sensorless control scheme use square-wave type voltage injection method as the start-up strategy to achieve sinusoidal starting. When the motor speed gradually increases to a preset speed, the sensorless drive will switch to the conventional saliency back- EMF estimator using the PID observer or the proposed saliency back- EMF estimator using the PIDNN observer for medium and high speed control. The theories of the proposed saliency back- EMF rotor flux angle and speed estimation method are introduced in detail. Moreover, the network structure, the online learning algorithms and the convergence analyses of the PIDNN are discussed. Furthermore, a DSP-based control system is developed to implement the sensorless inverter-fed compressor drive system. Finally, some experimental results are given to verify the feasibility of the proposed estimator. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
28. Anthropometric Robotic Hand for Pressurized Glove Torque Measurement.
- Author
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Roberts, Dustyn P., Poon, Jack, Patrick, Daniella, and Kim, Joo H.
- Subjects
VARIGNON'S theorem ,FREE precession ,HUMAN anatomy ,ROBOTICS equipment ,COMPLICATIONS of prosthesis - Abstract
While robotic hands have been developed for tasks such as manipulation and grasping, their potential as tools for evaluation of engineered products - particularly compliant structures that are not easily modeled - has not been broadly studied. In this research, a low-cost anthropometric robotic hand is introduced that is designed to characterize glove stiffness in a pressurized environment. The interaction with the compliant pressurized glove provides unique performance requirements and design constraints. The anthropometric robotic hand was designed to mimic the human hand in a configuration corresponding to the neutral position in zero gravity, including the transverse arch, longitudinal arch, and oblique flexion of the rays. The resulting robotic hand also allows for realistic donning and doffing of the prototype glove, its pressurization, and torque testing of individual joints. Solid modeling and 3D printing enabled the rapid design iterations necessary to work successfully with the compliant pressure garment. An instrumentation and data processing method was used to calculate the required actuator torque at each finger's knuckle joint. The performance of the robotic hand was experimentally demonstrated with a prototype spacesuit glove at different levels of pressure, followed by a statistical repeatability analysis. The reliable measurement method validated the pressure-induced stiffening. The resulting robotic design and testing method provide an objective and systematic way of evaluating the performance of compliant gloves. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
29. Reducing the motor power losses of a four-wheel drive, fully electric vehicle via wheel torque allocation.
- Author
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Pennycott, Andrew, De Novellis, Leonardo, Sabbatini, Alessio, Gruber, Patrick, and Sorniotti, Aldo
- Subjects
TORQUE ,MECHANICS (Physics) ,ELECTRIC vehicles ,MOTOR vehicles ,VARIGNON'S theorem - Abstract
Individually controlled electric motors provide opportunities for enhancing the handling characteristics and the energy efficiency of fully electric vehicles. Online power loss minimisation schemes based on the electric motor efficiency data may, however, be impractical for real-time implementation owing to the heavy computational demand. In this paper, the optimal wheel torque distribution for minimal power losses from the electric motor drives is evaluated in an offline optimisation procedure and then approximated using a simple function for online control allocation. The wheel torque allocation scheme is evaluated via a simulation approach incorporating straight-ahead driving at a constant speed, a ramp manoeuvre and a sequence of step steer manoeuvres. The energy-efficient wheel torque allocation scheme provides motor power loss reductions and yields savings in the total power utilisation compared with a simpler method in which the torques are evenly distributed across the four wheels. The method does not rely on complex online optimisation and can be applied on real electric vehicles in order to improve the efficiency and thus to reduce power consumption during different manoeuvres. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
30. Opća svojstva konveksnog četverokuta
- Author
-
Žužul, Marija, Krnić, Mario, and Bombardelli, Mea
- Subjects
Ptolomejev teorem ,Euler’s theorem ,PRIRODNE ZNANOSTI. Matematika ,Varignon’s theorem ,četverokut ,teorem o kosinusu ,Eulerov teorem ,quadrilateral ,NATURAL SCIENCES. Mathematics ,cosine theorem ,Ptolemy’s theorem ,Varignonov teorem - Abstract
Na početku rada prisjećamo se osnovne podjele četverokuta, temeljnih pojmova i činjenica potrebnih za ostatak rada. U drugom poglavlju bavimo se Eulerovim teoremom koji je poopćenje relacije paralelograma, dajemo formulu za površinu općeg konveksnog četverokuta i proširenje Teorema o kosinusu. Dajemo i poopćenje dobro poznatog Ptolomejevog teorema. U trećem poglavlju definiramo težište i težišnice četverokuta, dajemo iskaz i dokaz Varignonovog teorema i njegove posljedice, te se bavimo drugim osobitim točkama u četverokutu. At the beginning of the paper, we recall the basic classification of the quadrilateral, the basic concepts and facts needed for the rest of the paper. In the second chapter we deal with the Euler’s theorem which is a generalization of the relation of parallelograms, we give a formula for the surface of a general convex quadrilateral and an extension of the cosine theorem. We also give a generalization of the well-known Ptolemy’s theorem. In the third chapter, we define the centroids and the medians of the quadrilateral, give a statement and proof of Varignon’s theorem and its consequences, and deal with other significant points in the quadrilateral.
- Published
- 2019
31. Nonlinear dynamics of an optomechanical system with a coherent mechanical pump: Second-order sideband generation.
- Author
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Hiroyuki Suzuki, Brown, Eric, and Sterling, Ray
- Subjects
- *
ANALYTICAL mechanics , *STATISTICAL mechanics , *CONTINUUM mechanics , *VARIGNON'S theorem , *THERMODYNAMICS - Abstract
Second-order sideband generation in a coherent-mechanical pumped optomechanical system is discussed, and the features of the coherent mechanical pump induced enhancement of second-order sideband generation are identified. We show that the coherent mechanical pump induced enhancement of second-order sideband generation exhibits an essential difference between the case of a weak control field and a strong control field. In the weak control field case, the efficiency of second-order sideband generation increases as the amplitude of the mechanical pump increases. In the strong control field case, the effect of optomechanically induced transparency occurs and increasing the amplitude of the mechanical pump does not always bring an enhancement of second-order sideband generation. The phase-dependent effect of the second-order sideband generation with a coherent mechanical pump is also discussed, and it is shown that the phase difference ∅ plays an important role in the process of second-order sideband generation. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
32. Using Varignon’s Theorem to show concurrency of coplanar forces in equilibrium
- Author
-
Ker Liang Goh
- Subjects
Mathematical logic ,Varignon's theorem ,Science instruction ,Concurrency ,05 social sciences ,050301 education ,General Physics and Astronomy ,01 natural sciences ,Object (philosophy) ,Action (physics) ,Coincidence ,Education ,Classical mechanics ,0103 physical sciences ,Point (geometry) ,010306 general physics ,0503 education - Abstract
If a body is in equilibrium under the action of three non-parallel coplanar forces, the forces must be concurrent (Muncaster 1993 A Level Physics 4th edn (Cheltenham: Nelson Thornes) p 44, 45, 49; Goh 2018 Phys. Teach. 56 384). It is easy to show that they are concurrent when the forces meet at a point in the body (Muncaster 1993 A Level Physics 4th edn (Cheltenham: Nelson Thornes) p 44, 45, 49). However, in a situation that is easily found in common physics problems, the point of coincidence of the three lines of forces lie outside the object. It is our intention in this paper to illustrate to students how Varignon's Theorem could be used to show that the forces must meet at a point even if the point lies outside the object when the three forces are in equilibrium.
- Published
- 2018
33. Proof Without Words: Varignon’s Theorem
- Author
-
Alik Palatnik
- Subjects
Discrete mathematics ,Varignon's theorem ,Quadrilateral ,General Mathematics ,010102 general mathematics ,05 social sciences ,Diagonal ,050301 education ,Computer Science::Computational Geometry ,01 natural sciences ,Midpoint ,Education ,Combinatorics ,Proof without words ,Computer Science::Graphics ,Mathematics::Metric Geometry ,0101 mathematics ,0503 education ,Analytic proof ,Mathematics - Abstract
We present a visual proof of Vairgnon’s theorem by partitioning the Varignon parallelogram using a midpoint of the quadrilateral diagonal.
- Published
- 2017
34. Varignon's Theorem for Octahedra and Cross-Polytopes
- Author
-
John Pesek
- Subjects
Combinatorics ,Varignon's theorem ,Parallelepiped ,Quadrilateral ,General Mathematics ,Orthodiagonal quadrilateral ,Polytope ,Equidiagonal quadrilateral ,Parallelogram ,Midpoint ,Mathematics - Abstract
Varignon's theorem states that the midpoints of a quadrilateral form the vertices of a parallelogram (figure 1). From a historical point of view this simple theorem is noteworthy in that no one seemed to have been aware of it until Varignon discovered it in the 1700s [7]. It occurred to us that since an octahedron can be considered to be a 3-dimensional generalization of a quadrilateral and that since a midpoint can be considered as the centroid of the endpoints of a segment, it might be that the centroids of the faces of an octahedron form the vertices of a parallelepiped (figure 4). In this note, we show this and extend the result to cross-poly topes of all dimensions. We also observe that the results remain true if weights are attached to the vertices (Figure 5). At the time this article was submitted, we were not able to find the 3-dimensional
- Published
- 2009
35. Using Varignon’s Theorem to show concurrency of coplanar forces in equilibrium.
- Author
-
Ker Liang Goh
- Subjects
- *
CONCURRENT force , *EQUILIBRIUM , *VARIGNON'S theorem - Abstract
If a body is in equilibrium under the action of three non-parallel coplanar forces, the forces must be concurrent (Muncaster 1993 A Level Physics 4th edn (Cheltenham: Nelson Thornes) p 44, 45, 49; Goh 2018 Phys. Teach. 56 384). It is easy to show that they are concurrent when the forces meet at a point in the body (Muncaster 1993 A Level Physics 4th edn (Cheltenham: Nelson Thornes) p 44, 45, 49). However, in a situation that is easily found in common physics problems, the point of coincidence of the three lines of forces lie outside the object. It is our intention in this paper to illustrate to students how Varignon’s Theorem could be used to show that the forces must meet at a point even if the point lies outside the object when the three forces are in equilibrium. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
36. Investigating Primary School Mathematics Teachers’ Deductive Reasoning Ability through Varignon’s Theorem
- Author
-
Al Jupri
- Subjects
Varignon's theorem ,History ,Deductive reasoning ,Primary education ,Context (language use) ,Computer Science Applications ,Education ,Test (assessment) ,Wonder ,Exploratory survey ,ComputingMilieux_COMPUTERSANDEDUCATION ,Mathematics education ,Van Hiele model ,Mathematics - Abstract
The responsibility to promote the growth of deductive reasoning ability of school students through learning mathematics is in the hand of mathematics teachers and particularly primary school mathematics teachers. However, how we can make sure whether teachers are able to do so. To investigate this issue, we conducted a three-step of an exploratory survey study. First, we designed tasks from the Varignon's theorem. Second, we administered an individual written test involving twenty master students of primary education program, in which they are prospective of and primary school mathematics teachers. Finally, we address the results in the light of Van Hiele theory. The results showed that participated students lack of deductive reasoning ability in the context of geometry. For further research, we wonder whether the designed tasks are also applicable to assess student deductive reasoning ability if the students have acquired appropriate teaching.
- Published
- 2017
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