Profile oscillations

Oscillations of the site density profiles develop at both sides of the liquid/Iiquid interface to a depth of 50 A, showing significant layering at the interface. The n-hexane and methanol density profiles oscillate in opposite phase to each other. Their period of about 20 A is three to four times longer than the size of the methanol and n-hexane molecules. This renders the oscillations as a collective, hydrostatic effect of a varying... 

The velocity profile across the tube lumen with pulsatile flow is not of the same parabolic form as that found in a steady laminar flow. The velocity profiles oscillate sinusoidally as discussed in detail by Hale et al. [44]. For example. Figure 8.26 shows the velocity profiles, at intervals of 15°, resulting from a simple sinusoidal pressure gradient (cos[mf]) during the half cycle (0°-180°) as for a simple harmonic motion, the second half is the same. 

At finite positive and negative charge densities on the electrode, the counterion density profiles often exhibit significantly higher maxima, i.e. there is an overshoot, and the derived potential actually shows oscillations itself close to the electrode surface at concentrations above about 1 M. 

A sine-shape has side lobes which impair the excitation of a distinct slice. Other pulse envelopes are therefore more commonly used. Ideally, one would like a rectangular excitation profile which results from a sine-shaped pulse with an infinite number of side lobes. In practice, a finite pulse duration is required and therefore the pulse has to be truncated, which causes oscillations in the excitation profile. Another frequently used pulse envelope is a Gaussian frmction ... 

In hydrodynamic voltammetry current is measured as a function of the potential applied to a solid working electrode. The same potential profiles used for polarography, such as a linear scan or a differential pulse, are used in hydrodynamic voltammetry. The resulting voltammograms are identical to those for polarography, except for the lack of current oscillations resulting from the growth of the mercury drops. Because hydrodynamic voltammetry is not limited to Hg electrodes, it is useful for the analysis of analytes that are reduced or oxidized at more positive potentials. 

The concentration profile is steeper for the MacCormack method than for the upstream derivatives, but oscillations can still be present. The flux-corrected transport method can be added to the MacCormack method. A solution is obtained both with the upstream algorithm and the MacCormack method and then they are combinea to add just enough diffusion to ehminate the oscillations without smoothing the solution too much. The algorithm is comphcated and lengthy but well worth the effort (Refs. 37, 107, and 270). 

Figure 3 A calculated reflectivity profile for a perdeuterated polystyrene film with a thickness of SO nm on a silicon substrate. The calculation was for a specimen where the interfaces between the specimen and air and the specimen and the substrate were sharp. This causes the reflectivity on average (shown by the dashed line) to decrease in proportion to k or 9. The separation distance between the minima of the oscillations diractly yields the thickness of the specimen, as shown.

The principal effect of the presence of a smooth wall, compared to a free surface, is the occurrence of a maximum in the density near the interface due to packing effects. The height of the first maximum in the density profile and the existence of additional maxima depend on the strength of the surface-water interactions. The thermodynamic state of the liquid in a slit pore, which has usually not been controlled in the simulations, also plays a role. If the two surfaces are too close to each other, the liquid responds by producing pronounced density oscillations. 

Fig. 5(a) contains the oxygen and hydrogen density profiles it demonstrates clearly the major differences between the water structure next to a metal surface and near a free or nonpolar surface (compare to Fig. 3). Due to the significant adsorption energy of water on transition metal surfaces (typically of the order of 20-50kJmoP see, e.g., [136]), strong density oscillations are observed next to the metal. Between three and four water layers have also been identified in most simulations near uncharged metal surfaces, depending on the model and on statistical accuracy. Beyond about...

A vibration is a periodic motion or one that repeats itself after a certain interval of time. This time interval is referred to as the period of the vibration, T. A plot, or profile, of a vibration is shown in Figure 43.1, which shows the period, T, and the maximum displacement or amplitude, X - The inverse of the period, j, is called the frequency, f, of the vibration, which can be expressed in units of cycles per second (cps) or Hertz (Hz). A harmonic function is the simplest type of periodic motion and is shown in Figure 43.2, which is the harmonic function for the small oscillations of a simple pendulum. Such a relationship can be expressed by the equation ... 

Figure 27. Layout of the cavity of the modeless oscillator. The acousto-optics frequency shifter prevents inlerrerenccs in the cavity, resulting in a bixuid coiiliu-uons spectral profile (Pique and Faiinotti, 2003).

Stelzer et al. [109] have studied the case of a nematic phase in the vicinity of a smooth solid wall. A distance-dependent potential was applied to favour alignment along the surface normal near the interface that is, a homeotropic anchoring force was applied. The liquid crystal was modelled with the GB(3.0, 5.0, 2, 1) potential and the simulations were run at temperatures and densities corresponding to the nematic phase. Away from the walls the molecules behave just as in the bulk. However, as the wall is approached, oscillations appear in the density profile indicating that a layered structure is induced by the interface, as we can see from the snapshot in Fig. 19. These layers are... 

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