In-plane motion

Here, we discuss the motion of a system of three identical nuclei in the vicinity of the D3/, configuration. The conventional coordinates for the in-plane motion are employed, as shown in Figure 5. The noraial coordinates Qx, Qy, Qz), the plane polar coordinates (p,(p,z), and the Cartesian displacement coordinates (xi,yhZi of the three nuclei (t = 1,2,3) are related by [20,94]... 

The widths of the narrow Lorentzians representing slow motions in the plane and perpendicular to the plane of the bilayer are compared in Ligures 11a and 11b, respectively. Lor the in-plane motion, the MD values for Q = 0.5 A agree well with the experimental results, but the increase with Q is significantly overestimated in the simulation compared to the experimental values. This suggests that the slower component of the in-plane motion in the simulation is too fast at short distances. On the other hand, the MD line widths for the slower component of the out-of-plane motion agree well with the experimental results at 30% hydration. As in the case of the LISL, the simulation predicts a slight anisotropy not seen in the experimental data. 

FIG. 2 Molecular orientation angles at liquid interfaces for rodlike molecules. The out-of-plane motion is a rotation away from the OZ axis, whereas the in-plane motion is performed with the OX, OY) plane. 

Simple shear (also known as planar Couette flow) is achieved when fluid is contained between two plane parallel plates in relative in-plane motion. If the velocity direction is taken to be x, one has x = y, all other xa 3 zero and... 

For liquid-phase sensing, both density and viscosity, as well as the nature of the acoustic mode, play a role in AW perturbations. For TSM and SH-APM devices, in-plane motion of the substrate surface entrains a thin layer of liquid through viscous coupling. Entraiiunent of a liquid layer by the sensor surface constitutes a mass load proportional to the product of thickness and density of the coupled liquid layer, giving rise to a velocity change. 

The most prominent features in NRVS spectra are the strong set of peaks in the middle portion of the spectrum, which are principally from the in-plane motion of iron. At this time, a complete general analysis ofthe in-plane modes is notpossible. However this is probably not a frnal state. A relationship between the frequencies of the in-plane modes, iron spin state, and coordination state can be reasonably expected and is qualitatively observed. The increasing database of NRVS measurements on oriented single crystals of iron porphyrins... 

A general valence force field for the in-plane motions of N2H2 has been determined from a total of 24 vibrational frequencies of HNNH, HNND, DNND, and the 15N-substituted counterparts.62 The Raman spectra of polycrystalline CH3N=NCH3 and CD3N=NCD3 have been examined at liquid-nitrogen temperatures and a force field has been computed.63... 

Figure 4.10 Vibrational modes of /3-sheets. Each mode is differentiated by different in-plane motions and out of plane deformations above (red arrow) or below (blue arrow) the plane of the illustration.

Dynamical properties of the commensurate and uniaxial incommensurate phases according to the model of Refs. 232, 340, and 342 could also be explored by the molecular dynamics technique used [203, 352]. It is found that in-plane and out-of-plane motions can be analyzed separately for ori-entationally ordered N2 on graphite [203]. The 40-ps simulations below the orientational ordering transition (see Ref. 342) show [203] that the amplitude of reorientation is small and the out-of-plane motion nearly harmonic in both phases, whereas the in-plane motion is more complex, because it is anhar-monic and collective. The out-of-plane motion in the disordered phases is still harmonic, but more strongly damped, and the in-plane dynamics cannot be analyzed any more in terms of a cumulant expansion. Thus, there is little qualitative difference between the reorientational motion observed in the commensurate and uniaxially compressed solids. Only the out-of-plane motion is slightly less damped in the uniaxial phase, and the fluctuations from the planar configuration are more pronounced. 

No cw-di-imide was detected when the discharge products of N2H4 were examined in the solid and matrix-isolated states by i.r. and Raman spectroscopy. By consideration of HNNH, HNND, and DNND the five in-plane vibrations of isolated rm/zj-HNNH were determined and a tentative assignment was made for the out-of-plane torsion mode. Ab initio MO calculations have been used to investigate the photochemical trans-cis isomerization of di-imide. An in-plane motion of the hydrogen atoms was preferred for the ground and (rr, w ) states whereas for the (n, ) states a twisting about the N—N bond was involved in the most favourable pathway. The results were seen as models for substituted derivatives. 

NMR spectrum of W(H2)(CO)3(PCy3)2 showing a distorted Pake-pattern, from which information on the H—separation and the chemical-shift anisotropy of the hydrogen atoms could be obtained. The temperature dependence indicated an in-plane motion of 16°. Similar results were also obtained for Mo, Mn, and Ru hydrogen complexes. 

A similar treatment can be applied to two-dimensional (2-D) problems. Deformations of the plate are classified into two motions. As illustrated in Fig. 8.12, one is in-plane motion where a crack surface is generated as the normal vector to the crack plane is vertical to the xs-axis and AE waves are detected at the edge of the plate. The other is out-of-plane motion where the crack surface is created parallel to the X1-X2 plane. 

In the case of in-plane motions, the xs-components in Fig. 8.12 of both the vector 1 and n are equal to zero. Then, the moment tensor in an isotropic solid becomes. 

For the two-dimensional soltution, in-plane motions of AE waves are treated. As a practical application, AE waves due to water leakage from a slit are detected and analyzed. The reliable solutions are selected by the post analysis. Because visualization of results is desirable, three-dimensional visualization procedure is developed by using VRML (Virtual Reality Modeling Language). 

Fig. 4 SERS spectra from A cetylpyridiniumbromide (C,.PyBr) and ce y nmethylamnionouinbromide(C,gTAB)on Agelectrode-surfaces ex situ roughening = -0.2V vs. SCE concentration 10" M in 0.11 1 excitation wavelength at 488 nm 10 mW integration time 1.5 s number of readings 60. pointed a band corresponding to a out of plane mode of the pyridine ring. pointed the bands due to in plane motions of the pyridine ring. The frequencies of the main CH-bands is depicted over both spectra...

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