Sense of rotation

In the early 1960s efforts were made in the United States to operate vane motors and reciprocating motors with compressed air. The vane motors experienced some limited test success but were not competitive in the market of that day [84]. Out of these development efforts evolved the reciprocating (compressed) air hammers that have been quite successful and are operated extensively in the mining industry and have some limited application in the oil and gas industry [85]. The air hammer is not a motor in the true sense of rotating equipment. The reciprocating action of the air hammer provides a percussion effect on the drill bit, the rotation of the bit to new rock face location is carried out by the conventional rotation of the drill string. 

Each energy level (n 0) is doubly degenerate since the energy depends on n2 and therefore is independent of the sense of rotation. The quantum number n = 0 is no longer forbidden as in the linear case since the boundary conditions (0) = 4> L) = 0 no longer apply. In the cyclic case n = 0 implies infinite A, i.e. ifio = constant, and Eo = 0. 

Fig. 22 a, b. Orientation of the effective field B H and sense of rotation of the circularly polarized driving field for indue- m -.1 tion of nuclear transitions. S = 1/2, s 2... 

S) atoms. In both cases, the reference system does not change the three-dimensional arrangement of the groups around the chiral center. For example, if the sense of rotation had been chosen by convention to go from the small to the large atom (Schemes 11c and d), the corresponding symbols would have been reversed, but the absolute configuration of the molecule would have remained the same. 

Fig. 2. Evolution of twist angle around the P-bond (grey) and I-bond (black) after photoexcitation of the neutral form of GFP chromophore in the gas phase (left panel) and solvated by 150 water molecules (right panel). Solid lines are population-weighted averages over die trajectory basis functions. Dashed lines represent the twist angles for the individual trajectory basis functions. The sense of rotation for the two torsions is defined such that HT motion corresponds to both angles moving towards more negative values.

By definition chirality involves a preferred sense of rotation in a three-dimensional space. Therefore, it can only be affected by a modification of the nonscalar fields appearing in the rate equations. For a reaction-diffusion system [equations (1)] these fields are descriptive of a vector irreversible process, namely, the diffusion flux J of constituent k in the medium. According to irreversible thermodynamics, the driving force conjugate to diffusion is... 

To confirm the above conjectures we have performed a numerical simulation of equation (29) on the Brusselator model chemical reaction.46 The results are shown in Fig. 7. We start with an initial condition corresponding to a clockwise wave. Under the effect of the counterclockwise field this wave is deformed and eventually its sense of rotation is reversed. In other words, the system shows a clear-cut preference for one chirality. As a matter of fact we are witnessing an entrainment phenomenon of a new kind, whereby not only the frequency but also the sense of rotation of the system are adjusted to those of the external field. More complex situations, including chaotic behavior, are likely to arise when the resonance condition w = fl, is not satisfied, but we do not address ourselves to this problem here. 

Fig. 7. Numerical simulation of equation (29) for the Brusselator model on a ring. At t = 0 a clockwise wave propagates along the ring at t = 4.49 the effect of the counterclockwise external field deforms this wave appreciably after a while the sense of rotation is reversed and for t > 22.49 one obtains a stable wave solution in the counterclockwise direction. The period of both the external field and of the linearized solution of the unperturbed system is 4.28 time units.

Upon complexation with a lanthanide ion, these complexes may form square antiprism or twisted square antiprism (TS APR) structures with a vacant coordination site in the cap position, which is assumed to be occupied by a solvent molecule. Just as in the chelated complexes described previously, two distinct types of chiral stereochemistry are present. In analogy with OC-6 species, the sense of rotation of the pendant arms is denoted as A or A depending upon if the arms rotate clockwise (A) or counterclockwise (A) as one proceeds down the direction of the C4 axis. There is also chirality (or helicity) associated with the nonplanar 12-membered ring. If one looks along the skew-line connecting the coordinated nitrogens, the carbon atoms... 

Fig. 10.17 The counter- and co-rotating thin-flight, open C-shaped channels used in the three-dimensional FEM study of Katziguara et al. (32). The two-screw configurations are identical except for the sense of rotation. [Reprinted by permission from T. Katziguara, Y. Nagashima, Y. Nakano, and K. Funatsu, A Numerical Study of TSEs by 3-D Flow Analysis - Development of Analysis Technique and Evaluation of Mixing Performance for Full Flight Screws, Polym. Eng. Sci., 36, 2142 (1996).]...

As in the definition of rotations for the backbone, the sense of rotation is such that a right-handed rotation about any side-chain bond, looking in the direction of numbering, is taken to be positive. The choice of zero angle of rotation is such that the planar eclipsed (cis) conformation is denoted by Xj — 0 (Fig. 4). For the C —bond, the N—C and the —Cy bonds are used to define the angle xi In branched chains, Branch 1 is always used to define the angle of rotation. 

Fresnel proved that linearly polarized light is actually the resultant of two coherent circular components of opposite sense of rotation. 

With the hypothesis that allene-olefin cycloadditions and methylenecyclobutane rearrangements have a common intermediate comes the prediction that common stereochemical modes for the various rotations involved will prevail. The cycloaddition model outlined above involves disrotatory ring closure with the same sense of rotation about C(4)C(5) and C(5)C(2). For the methylenecyclobutane rearrangement, the same stereochemistry is anticipated for the reverse reaction. 

The angular wave number m may be either a positive or a negative integer depending on the sense of rotation of harmonic angular waves. 

In this expression, the cross products between cosine and sine functions, which depend on the sense of rotations introduce the cog-wheel effects between... 

Berson, J. A. Nelson, G. L. Steric prohibition of the inversion pathway. Test of the orbital symmetry prediction of the sense of rotation in thermal suprafacial 1,3-sigmatropic rearrangements, 7. Am. Chem. Soc. 1970, 92,1096-1097. 

In order to find the character of the representation of rotational motions and librations, the transformation properties of an axial vector (Fig. 2.1-lb) have to be taken into account. This vector is defined not only by its length and orientation, but also by a definite sense of rotation inherent to it. For linear molecules with only two degrees of rotational freedom, the Xr R) values for Cj and a depend on the orientation of the molecular axis to the symmetry elements. All values of XriR) tire also included in Table 2.7-1. 

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