Rotation coefficients

The overall elements that contribute to the limiting of the PV factor are magnitude of pressure, speed of rotation, coefficient of friction of mating materials, lubrication, clearance between bearing and shaft, surrounding temperature, and surface finish, as well as hardness of the mating materials. Bearing wall thickness is also an element in the PV factor since it determines the heat dissipation. 

The constant A in Eq. (11) is here written a, the superscript D designates a disordered form, and a is the rotation coefficient for this conformation. Dispersions for polypeptides in helical form, H, fit the Moffitt equation,... 

In the last decade, a few approaches have been developed and applied in which the orbitals used in the CC calculation are optimized self-consistently with the energy. These include (a) the Brueckner CC (B-CC) methods in which the orbitals are chosen so that the T (single excitation) amplitudes vanish [107,108,110] and (b) the optimized-orbital CC (OO-CC) doubles approach in which the CCD energy is minimized [201,244]. Since the parameters used in these methods (orbital rotation coefficients and cluster amplitudes) are... 

Fig. 4.69. (a) Optical absorption and (b) magnetooptical rotation coefficients in YIG at 300 K, as a function of photon energy the broken lines correspond to the visible spectrum (Wemple et aL 1974). 

A number of ion substitutions produce a very high Faraday rotation coefficient in garnets namely, Pr and Nd (Wemple et ai, 1974), and Bi and Ce (Gomi, Satoh Abe, 1989). 

This spin-spin driven helium induced Zeeman relaxation is likely to be the dominant relaxation mechanism for molecules for which the spin-spin coefficient (kss) is larger than the spin-rotation coefficient (ysr). It is not clear from this qualitative model whether the additional 1 (jlb of magnetic moment gained in moving from E molecules to E states is worth the trouble. If the spin-spin driven Zeeman relaxation of E molecules is too strong, the trap lifetime will be substantially limited by inelastic collisions and not the trap depth. In 2003, a quantitative calculation was performed by Krems and colleagues that predicted a favorable Zeeman relaxation rate coefficient for imidogen (NH) with helium [35,36]. Furthermore, experiments... 

Computer simulation has also been used to study the solution properties of rigid-rod polymers (161,279,362). It has been foimd that the local structure and d5mamics of different rigid-rod polymers may be quite different but global motions in dilute and semidilute solutions are expected to be very similar (375). Based on the Broersma and Tirado-de la Torre relations, the translational and rotational coefficients, A and Dr, of rigid-rod polymers in dilute (or semidilute) solutions can be written in the forms... 

The rotation coefficients occurring in (74) have been recently worked out in a convenient polynomial form [61] involving the Euler angles Q = (a, P, y) [60]... 

Using the same procedure, the rotation coefficients for all atomic orbitals can readily be evaluated. For the p orbitals, these are given in Table 3, for the d orbitals in Table 4, and for... 

As can be seen from the last two terms in Eq. (3.3.24), the rotational energy level structure in each vibrational state resembles that for the vibrationless nonrigid rotator in Eq. (3.3.23). The rotational ladder in each vibration state begins (for / = 0) at the energy given by the first two, purely vibrational terms in Eq. (3.3.24). The rotational levels within each vibrational level follow a pattern similar to that described by Eq. (3.3.23), except that the rotational coefficients are now assigned their vibrationally dependent values B v) and D v). This overall vibration-rotation dependence is embodied in Eq. (3.3.27). 

The pressure dependence of the diffusion rotation coefficients Drot, calculated from Urot=l/(6Trot), is given by ... 

Fig. 7 (a) Dependence of the diffusion rotation coefficient on pressure, (b) Comparison of theoretical and experimental activation volumes of rotational diffusion. 

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