Ramp wave

The simple wave produced by impacting vitreous silica has approximately the form of a linear ramp of velocity. When this ramp wave is used to load another elastic solid placed in contact with the vitreous silica, a measurement... 

The most distinctive aspect of the shock work is the determination of higher-order piezoelectric constants. The values determined for the constants are, by far, the most accurate available for quartz and lithium niobate, again due to the direct nature of the measurements. Unfortunately it has not been possible to determine the full set of constants. Given the expense and destructive nature of the shock experiment, it is unlikely that a full set of higher-order piezoelectric constants can be determined. A less expensive investigation of higher-order constants could be conducted with the ramp wave or acceleration wave loading experiment described in the chapter. 

For several types of time function, such as pulse, step, ramp, wave changes, the Laplace transformations are shown in Table 5.1. The time functions belonging to a particular Laplace transform are given in Table 5.2. 

Assuming that the cyclic waveform used in the previous section was sinusoidal then the effect of using a square wave is to reduce, at any frequency, the level of stress amplitude at which thermal softening failures start to occur. This is because there is a greater energy dissipation per cycle when a square wave is used. If a ramp waveform is applied, then there is less energy dissipation per cycle and so higher stresses are possible before thermal runaway occurs. 

Fig. 2.17. Fused quartz is known to have an anomalous softening with stress or pressure in both static and shock loading. The time-resolved wave profile measured with a VISAR system shows the typical low pressure ramp followed by a shock at higher pressure. The release to zero pressure is with a shock, in agreement with the shape of the pressure-volume curve (after Setchell [88S01]).

To examine the response of PVDF to a higher pressure, ramp-type loading, an experimental arrangement with a ceramic Pyroceram similar to that of the fused quartz loading was employed. In this case, the loading wave transmitted through the Pyroceram is only approximately known and a simultaneous measurement must be carried out of the wave transmitted through the pyroceram and the response of the PVDF. 

The basis of all control Icd-potcntial techniques is the measurement of the current response to an applied potential. There exist a multihide of potential excitations, including a ramp, potential steps, pulse trains, a sine wave, and various combinations thereof. The present chapter reviews those techniques that are widely used. 

Some other less important types of AC polarography may also be considered as sinusoidal ac techniques, as their theoretical treatment can be based on signals from a complex Fourier function in this context we confine ourselves to mentioning sawtooth or triangular wave48 superimposed on the dc ramp. Square-wave polarography is also of that type, but in view of its greater importance we shall treat it separately. 

In connection with the square-wave technique, mention can be made of high-frequency polarography, also called radiofrequency polarography and developed by Barker53, in which a sinusoidal radio-frequency cu, (100kHz to 6.4 MHz) square-wave modulated at co2 (225 Hz) is superimposed on to the dc potential ramp as the wave form includes (apart from additional higher... 

Waves I and II in Figure 2.81(b) are due to the formation of Cu(I) and Cu(II) surface oxides. Subsequent reduction of these films occurs during the cathodic sweep to give waves III and IV. The points A to D represent the potentials at which reflectivity data were collected during the voltammetric scan. The potential was ramped at lOmV/s until one of these potentials was reached, at which the scan was stopped for the duration of the data acquisition. The spectrum collected at A represents the condition of the electrode surface... 

For this purpose, perfluorooctanesulfonyl-tagged benzaldehydes were reacted with 1.1 equivalents of a 2-aminopyridine (or 2-aminopyrazine), 1.2 equivalents of an isonitrile, and a catalytic amount of scandium(III) triflate [Sc(OTf)3] under micro-wave irradiation in a mixture of dichloromethane and methanol (Scheme 7.85). A ramp time of 2 min was employed to achieve the pre-set temperature, and then the reaction mixture was maintained at the final temperature for a further 10 min. The fluorous tag constitutes a multifunctional tool in this reaction, protecting the phenol in the condensation step, being the phase tag for purification, and serving as an acti-... 

After tq is passed, the second step starts by scanning the potential from Ed to a potential when all the deposited metals are re-oxidized (the reverse of reaction 25). The oxidation current recorded as a function of potential is the anodic stripping voltammogram (ASV). A typical ASY of three metals (Cd, Pb, and Cu) deposited on a mercury film electrode is shown in Fig. 18b.12b. The sensitivity of ASY can be improved by increasing the deposition time and by using the pulse technique to record the oxidation current. ASV in Fig. 18b. 12b was obtained by using the square wave voltammetry. In most cases a simple linear or step ramp is sufficient to measure sub-ppm level of metals in aqueous solution. The peak current of a linear scan ASV performed on a thin mercury film electrode is given by... 

The performance of the temperature controller was measured in the tracking mode. Figure 6.18 shows a graph, where the temperature of one of the three microhotplates is kept at a constant temperature of 300 °C, the temperature of the second microhotplate is modulated using a sine wave of 10 mHz, while rectangular temperature steps of 150 °C, 200 °C, 250 °C, 300 °C, and 350 °C have been appHed to the third microhotplate. Temperature measurements on one of the hotplate that has been operated at constant temperature in the stabihzation mode showed a variation of less than 1 °C, even though the temperature of the neighboring hotplates was, at the same time, modulated dynamically (sine wave, ramp, steps). This is a consequence of the individual hotplate temperature control, without which thermal crosstalk between the hotplates would have been clearly detectable. The power dissipation of the chip is approximately 190 mW, when all three hotplates are simultaneously heated to 350 °C. In the power-down mode, the power consumption is reduced to 8.5 mW. 

Figure D-4. Compression by the formation of three oblique shock waves with three ramps.

Fig. D-5 shows an external compression air-intake designed for optimized use at Mach number 2.0. Fig. D-6 shows a set of computed airflows of an external compression air-intake designed for use at Mach number 2.0 (a) critical flow, (b) sub-critical flow, and (c) supercritical flow. The pressures at the bottom wall and the upper wall along the duct flow are also shown. Two oblique shock waves formed at two ramps are seen at the tip of the upper surface of the duct at the critical flow shown in Fig. D-6 (a). The reflected oblique shock wave forms a normal shock wave at the bottom wall of the throat of the internal duct. The pressure becomes 0.65 MPa, which is the designed pressure. In the case of the subcritical flow shown in Fig. D-6 (b), the shock-wave angle is increased and the pressure downstream of the duct becomes 0.54 MPa. However, some of the airflow behind the obhque shock wave is spilled over towards the external airflow. Thus, the total airflow rate becomes 68% of the designed airflow rate. In the case of the supercritical flow shown in Fig. D-6 (c), the shock-wave angle is decreased and the pressure downstream of the duct becomes 0.15 MPa, at which the flow velocity is stiU supersonic.

Many of the experimental parameters for normal-pulse polarography are the same as with differential-pulse polarography. Differential-pulse polarography is a technique that uses a series of discrete potential steps rather than a linear potential ramp to optimize specific applications (130). Unlike normal-pulse polarography, each potential step has the same amplitude, whereas the return potential after each pulse is slightly negative of the potential prior to the step. In this manner, the total waveform applied to the dropping mercury electrode is very much like a combination of a linear ramp with a superimposed square wave. 

Square wave voltammetry achieves increased sensitivity and a derivative peak shape by applying a square wave superimposed on a staircase voltage ramp. With each cathodic pulse, there is a rush of analyte to be reduced at the electrode surface. During the anodic pulse, reduced analyte is reoxidized. The voltammogram is the difference between the cathodic and the anodic currents. Square wave voltammetry permits fast, real-time measurements not possible with other electrochemical methods. 

With the advent of digital implementation of electroanalytical experiments came the technique called staircase cyclic voltammetry, wherein the triangular wave is approximated by a series of small potential steps. The reason for such an approximation is partly due to the impossibility of digitally generating a pure ramp and more importantly to the realization that substantial improvements accrue from sampling the current at the end of each step, where double-layer charging has decayed away. If the steps are small, the data will fit theory based on pure ramps quite well. 

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