Quasi-torque

In the FAFO picture, when the form of the HOs is fixed, the equilibrium condition for the hybridization tetrahedron can be written as the equilibrium condition for the orientation of the latter. Due to the angular character of the variables involved, the corresponding set of the energy derivatives with respect to the components can be thought to be a (quasi)torque (here the prefix quasi as previously refers to the fact that no rotation of any physical body is involved in its definition rather that of a fictitious hybridization tetrahedron). As one can check, each (m-th) bond, incident to the given atom A, contributes to the quasitorque the following increment ... 

These equilibrium conditions are completely analogous to the equilibrium conditions for a system of rigid bodies [42] which requires evanescence of all (quasi)torques. 

The additional pseudo- and quasi-torques yield the pseudo- and quasirotations of the hybridization tetrahedron on the boundary atom R, In the linear response approximation it corresponds to the treatment of the corresponding pseudo- and quasitorques by the matrix which is... 

Boltzmann distribution 13 change of average z projection 17 change per collision 18-19 correlation functions 12, 25-7, 28 calculation 14-15 correlation times quasi-free rotation 218 various molecules 69 and energy relaxation 164-6 impact theory 92 torque 18-19, 27... 

When a/l is small it is possible to obtain a general expression for the effect of boundaries on the quasi-static force and torque experienced by a trans-lating-rotating particle of arbitrary shape in a fluid which is otherwise at rest (B16, B20, C20). This relation takes the form... 

The characteristic scale of velocity variation (11.81) is equal to R. It means that for any region whose size is much smaller than R, the flow can be approximated as a quasi-planar flow in the meridian plane, formed by superposition of uniform flow and simple shear flow. The uniform flow induces the force Fs on the drop S2, while the shear flow produces torque Tj. At a sufficient distance from the drop S2 we have... 

Electroconvection in nematics is certainly a prominent paradigm for nonequilibrium pattern-forming instabilities in anisotropic systems. As mentioned in the introduction, the viscous torques induced by a flow field are decisive. The flow field is caused by an induced charge density p i when the director varies in space. The electric properties of nematics with their quite low electric conductivity 10 (fl m) ] are well described within the electric quasi-static approximation, i.e. by charge conservation and Pois-... 

When the equivalent mass, combined lateral stiflhess, etc., expressions above are substituted into these equations it is soon appreciated that many variables appear. Because of the inherent complexity it is difficult to determine the sensitivity of the lateral response to the influence of winding depth. Hence further simplification is adopted. The quasi-static lateral and rotational response to each of the aerodyncunic force, the Coriohs force and the head rope torque is now considered. In pursuing the qucisi-static response the inertia forces cue being ignored. 

Quasi static deflection (aero long side) Quasi-static rotation (head rope torque)... 

Now consider the quasi-static rotation of the conveyance in response to the head rope torque unbalance acting alone. The applied torque from the head ropes causes a rotation of the conveyance displacing both the guide ropes and to some extent the head ropes which develop an opposing reaction. The static equation of equilibrium to solve is t6 = M where M is the torque applied by the head ropes, 6 is the conveyance rotation and is t the torsional stiffness. To proceed consideration of the torsional stiffness is needed. Using the notation c = Va + -... 

Results for the quasi-static loads and lateral and rotational responses are shown in Table 3. Dynamic simulations for these shafts design have been run using the simulation technique described by Greenway et al (2000). The peak responses to lateral motion due to Coriolis and aerodynamic effects acting alone are given in the Table 3 as well as the peak rotations due to the head rope torque. 

Consideration of both quasi-static lateral motion of the conveyance and dynamic simulations of response due to either aerodynamic effects, Coriolis loads and rope torque effects show little sensitivity to shaft depth if tensioning ratios of around h/l= I are mcuntained. Deflections due to these forces are no worse for deep shafts as for shallow ones—other parameters being equal. 

Let both the helical axis and the electric field are parallel to the normal z of a cholesteric liquid crystal layer of thickness d and >0. In the case of a very weak field the elastic forces tend to preserve the original stack-like arrangement of the cholesteric quasi-layers as shown in Fig. 12.15a. On the contrary, in a very strong field, the dielectric torque causes the local directors to be parallel to the cell normal, as shown in Fig. 12.15c. At intermediate fields, due to competition of the elastic and electric forces an undulation pattern appears pictured in Fig. 12.15b. Such a structure has two wavevectors, one along the z-axis (nld) and the other along the arbitrary direction x within the xy-plane. The periodicity of the director pattern results in periodicity in the distribution of the refractive index. Hence, a diffraction grating forms. Let us find a threshold field for this instability. 

But how to force the system relax to a particular state selected by an experimentalist Berreman and Heffner [20] suggested to exploit the backflow ejfect discussed in Section. 11.2.6. We know that, upon relaxation of the director from the field-ON quasi-homeotropic state (barrier state B) to a field-OFF state, a flow appears within the cell. The direction of the flow depends on the curvature of the director field, which is more pronounced near the electrodes. Moreover it has the opposite sign at the top and bottom electrodes, see the molecules distribution in state B in Fig. 12.17. Due to this, the close-to-electrode flows create a strong torque exerted on the director mostly in the middle of the cell that holds the director to be more or less parallel to the boundaries in favour of the n = 2) initial state in Fig. 12.17. 

As the excitation energy is increased, vibrational levels above the barrier are populated and the excited state becomes quasi-bound. The earhest Rydberg tagging studies showed that the NH2 product was highly excited rotationally but had little vibrational excitation. This was attributed to the excitation out-of-plane vibrational motion in the excited state, which transforms into NH2 rotation as the H atom departs. Thus, the bending motion in the A state results in a torque, which flips the NH2 radical, causing it to rotate about its u-axis (i.e. perpendicular to the C3 axis in the planar configuration) as the H atom recoils. 

This is also the blocked force of the main mode of the actuator at resonance. So, it is an important parameter for several applications for example, in both quasi-static and resonant motors it strongly influences the maximum force/torque of the motors. 

Following a principle used in piezoelectric ultrasonic motors [60], T. Aku-ta [61] has built the first magnetostrictive friction motor. This stator is made of pairs of orthogonal actuators excited with sinusoidal 90° phase-shift currents, which produce an elliptical vibration. The modeling of such magnetostrictive stators [42] has shown that in quasi-static operation a good elliptical motion is produced. It has also been shown that there are many coupled modes, but none of them provides a satisfactory elliptical motion. Therefore, unlike piezoelectric motors, this motor cannot operate at resonance. As a consequence and in relation to the previous analysis of power (Fig. 6.34), the efficiency is comparatively weak. Its other characteristics are a speed of 40°/s and a torque of 1.8 Nm [62]. 

The slope of the moment-angle curve, quasi-stiffness , varied at different sub-phases and also at different speeds. It has already been proposed that ankle-foot system can be modeled as a spring and torque generator and the spring stiffness should change at different sub-phases of walking [3, 8, 9-11]. However, based on our study, the quasi-stiffness is a function of walking speed. 

Franck, A. J. P., Quasi-Infinite Stiff Transducer for Measuring Torque and Normal Force, presented at conference on New Techniques in Experimental Rheology, University of Reading, U.K., September 1985a. Manuscript available from Rheometrics, Inc., Piscataway, NJ. 

Two kinds of dielectric responses due to the permanent and induced dipole moments are expected in the dilute solution of the conducting polymers. If carries move along a polymer chain even more slowly than the rotation of the chain, the inhomogeneous distribution of the carriers yields the permanent (or quasi-permanent) dipole moment on the polymer chain. Thus, the electric polarizability arises from the orientation of the permanent dipole moment towards the direction of the external field. On the other hand, if the carriers move much faster than the rotation, the external electric field induces the electric polarizability and exerts a different type of torque on the polymer chain. These two different responses can be clearly distinguished by FEBS [149]. 

For design and selection purposes, the mechanical analysis of lead screws usually is limited to the factors affecting their static or quasi-static performance, such as efficiency, driving torque requirements, and load capacity [33-35]. There are... 

At the quasi-stable point no action is needed to correct an increase in speed because the negative torque will slow the Brayton unit back to the quasi-stable operating point. However, if the speed decreases, the total electrical load must be reduced below the net Brayton unit work at the reduced speed. This is done by decreasing the electrical work removed by the PLR. The net Brayton unit work will now be positive, resulting in a positive torque on the Brayton unit shaft and increasing Brayton unit speed. The PLR load must be increased again as the Brayton unit approaches the quasi-stable point, in a similar manner the PLR can be used to operate the Brayton unit at the unstable point. Because the PLR is an electrical system and can respond much faster than the mechanical Brayton unit system, it is possible to operate at the quasi-stable and unstable points. 

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