Radial mode

When samphng from moving belt conveyors, the cutter operates in a radial mode with the belt surrace contoured at the point of samphng by idlers, fixing radial curvature to the outer radius of the cutter. Clearance is minimized between outer edges of cutter blades and belt surface by cutter-shaft adjustment in the drive-clamping bracket. 

Fig. 10. Unpolarized Raman spectra (T = 300 K) for solid Ceo, KaCeo, RbsCeo, NaeCeo, KaCco, RbeCeo and CseCeo [92, 93], The tangential and radial modes of Ag symmetry are identified, as are the features associated with the Si substrates. From the insensitivity of these spectra to crystal structure and specific alkali metal dopant, it is concluded that the interactions between the Cao molecules are weak, as are also the interactions between the Cao anions and the alkali metal cations.

Fig. 6.9. Two-dimensional numerical simulations are depicted for the Sandia Momma Bear fixture. Pressure contours within one-half the powder compact are shown at various times. The principal feature shown is the development of a radial-mode loading due to the low shock impedance of the powder (after Graham [87G03]).

Fig. 8.33 Calculated sensitivity in bulk index sensing for different radial mode numbers with the same azimuthal number m 700...

The Bragg confinement mechanism allows great flexibility in engineering the radial mode profile. For example, it is possible to design a resonator in which the light is confined within a defect composed of low refractive index material or even air. By contrast, this would be impossible in the case of conventional TIR-based resonators. Such configuration is useful for sensing applications as discussed later. 

Figure 2.4 Schematic diagram of an ICP torch. The sample is carried into the torch by the carrier argon gas, and is ignited by radio-frequency heating from the RF coils. The tangential argon flow lifts the flame from the burner, preventing melting. The position of the detector in axial or radial mode is shown. (From Pollard et al., 2007 Fig. 3-3, by permission of Cambridge University Press.)...

One of the consequences of this is that improvements in the cold drawing of metal tubing can be achieved when the die to be used is subjected to radial ultrasonic vibrations. There are several advantages obtained from drawing round products through a die ultrasonically vibrating in a radial mode, these include ... 

Fig. 13.21 shows another example of oscillatory burning of an RDX-AP composite propellant containing 0.40% A1 particles. The combustion pressure chosen for the burning was 4.5 MPa. The DC component trace indicates that the onset of the instability is 0.31 s after ignition, and that the instability lasts for 0.67 s. The pressure instability then suddenly ceases and the pressure returns to the designed pressure of 4.5 MPa. Close examination of the anomalous bandpass-filtered pressure traces reveals that the excited frequencies in the circular port are between 10 kHz and 30 kHz. The AC components below 10 kHz and above 30 kHz are not excited, as shown in Fig. 13.21. The frequency spectrum of the observed combustion instability is shown in Fig. 13.22. Here, the calculated frequency of the standing waves in the rocket motor is shown as a function of the inner diameter of the port and frequency. The sonic speed is assumed to be 1000 m s and I = 0.25 m. The most excited frequency is 25 kHz, followed by 18 kHz and 32 kHz. When the observed frequencies are compared with the calculated acoustic frequencies shown in Fig. 13.23, the dominant frequency is seen to be that of the first radial mode, with possible inclusion of the second and third tangential modes. The increased DC pressure between 0.31 s and 0.67 s is considered to be caused by a velocity-coupled oscillatory combustion. Such a velocity-coupled oscillation tends to induce erosive burning along the port surface. The maximum amplitude of the AC component pressure is 3.67 MPa between 20 kHz and 30 kHz. - ...

As a generalization of these observations it follows that vibrations in a central field i.e. around a special central point) are of two types, radial modes and angular modes. Laplace s equation separates into angular and radial components, of which the angular part accounts in full for the normal angular modes of vibration. Radial modes are better described by the related radial function that separates out from a Helmholtz equation. It is noted that the one-dimensional oscillator has no angular modes. 

A more common geometry is a thin disc of diameter d electroded over both faces and poled in a direction perpendicular to the faces. The resonance on which attention is focused is that of a radial mode, excited through the piezoelectric effect across the thickness of the disc. In this case the route from the resonant frequencies to the coefficients d and g is the same as in the case of the rod, although the expressions are more complex. 

We report on the influence of a short-wave laser radiation on the properties of SWCNTs. This effect is confirmed by considerable increase of the intensities of 2vq and 2vd harmonics and of low-frequency radial mode Vr in their Raman spectra under increase of the energy of exciting photons. While the G-band intensity remains almost the same, the intensity of the 2vd band increases 1.7 times under excitation with 476.5 nm in comparison with 514.5 nm. Excitation with the 476.5 nm laser beam also leads to increase of the side bands in the fine structure of the Vd mode as well as Vd+Vg and Vg+Vrbm harmonics. We demonstrate that... 

Another device for automated development is the chamber constructed by Tyihak [4], in which the adsorbent layer is placed between two plates and the mobile phase flows under increased applied pressure. It can be operated in the linear or radial mode. Another automated device is the UMRC (Ultra Micro Rotation Chromatograph), where the eluent is delivered to the center of a rotating TLC plate [5]. A simple device was constructed by Delvorde and Postaire [6] in which the liquid is pumped out (by vacuum) which causes the flow of the mobile phase and decreases the vapor pressure. 

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