Cross-frequency parameters

This says that due to the presence of the cross-frequency parameters P12 and P21 in (3.65), as well as the fact that A there exists no mirrorimages in respect... 

With the aid of the recurrence procedure described in the previous section, the <)) dependence of I2 incorporated in the interactive displacement parameters and Aj as well as in the cross-frequency parameters P21 been investigated. 

Note that the interactive displacement parameters are not quantities with physical significance. They merely represent the error incurred in making a crude approximation, assuming that all modes are parallel. Another remarkable feature of mode mixing is the dependence of the transition rate on the cross-frequency parameters (see Equation 4.71). (Note that in the parallel-mode approximation the transition rate depends solely upon and 3j, = per mode). Both of these findings are... 

The complexity introduced by the normal coordinate mixing (3.21) is considerable. Apart from the displacements kf] and kjj (referred to as the direct terms) and frequency parameters Pj and P2 of the individual modes, expressions 5.27-5.32 involve reciprocal displacements 2 well as cross-frequency parameters... 

Classical solutions to laminated shell buckling and vibration problems in the manner of Chapter 5 were obtained by Jones and Morgan [6-47]. Their results are presented as normalized buckling loads or fundamental natural frequency versus the Batdorf shell curvature parameter. They showed that, for antisymmetrically laminated cross-ply shells as for plates, the effect of coupling between bending and extension on buckling loads and vibration frequencies dies out rapidly as the number of layers... 

In the above numerical examples the held parameter F is taken to be the laser frequency and the nonadiabatic transition used is the Landau-Zener type of curve-crossing. The periodic chirping method, however, can actually be more... 

For general aspects on sonochemistry the reader is referred to references [174,180], and for cavitation to references [175,186]. Cordemans [187] has briefly reviewed the use of (ultra)sound in the chemical industry. Typical applications include thermally induced polymer cross-linking, dispersion of Ti02 pigments in paints, and stabilisation of emulsions. High power ultrasonic waves allow rapid in situ copolymerisation and compatibilisation of immiscible polymer melt blends. Roberts [170] has reviewed high-intensity ultrasonics, cavitation and relevant parameters (frequency, intensity,... 

The influence of bilinear cross terms of this type in force field caculations has been studied systematically only once so far (79). They are standard for vibrational-spectroscopic force field expressions (20), and accordingly vibrational frequencies depend considerably more sensitively on cross terms than e.g. conformational parameters. An example for the significant influence of cross terms also with respect to the latter is described in Section 6.1.3. 

Fig. 16.5 Cross sections through cross peaks taken from the HN(CO)CA derived experiments at the Hn frequency. The cross peaks in the dipole-dipole CCR experiment (a, c) are observed at the 13Ca frequency. Two spectra with different parameters are recorded [52]. The cross peaks are splitted by /caHa- The cross peaks in the two spectra are shifted relatively by Jnhho- The cross...

Fig. 18. The proton spin-lattice relaxation rate recorded as a function of the magnetic field strength plotted as the proton Larmor frequency for lysozyme samples. Dry ( ), hydrated to 8.9% ( ), 15.7% (O). 23.1% (A), and cross-linked in a gel ( ). The solid lines were computed from the theory. The solid lines are fits to the data using Eq. (4) with Rs given by Eq. (6). The two parameters adjusted are Rsl and b (97). The small peaks most apparent in the dry samples are caused by cross-relaxation to the peptide nitrogen spin (90,122).

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