Relative amplitude variation

The monitoring of membrane fouling with acoustic waves is one of the few non-invasive methods potentially applicable to commercial-scale modules. Nonetheless, amplitude measurements can only provide qualitative characterization (relative amplitude variations) of the cake formation process because of the lack of knowledge about the propagation mode of an acoustic wave in a deformable deposit. 

Most of the studies about the use of acoustic waves for fouling characterization gave qualitative information about the cake layer (relative amplitude variations) and concerned flat-sheet membranes. The originality of the method presented here [9] is to give the possibility of extracting qualitative information by using another characterization method in parallel. 

What is not commonly known outside the NMR community is the relative difficulty in making accurate relative density measurements by NMR/MRI compared, for example, with making velocity measurements by NMR/MRI. This is because density measurements rely on the signal strength, which can be affected by any number of factors. In contrast, the most common way to measure flow velocity by NMR/MRI is to use the phase of the NMR signal rather than the amplitude, which vastly reduces its sensitivity to amplitude variations. 

Cycled Feed. The qualitative interpretation of responses to steps and pulses is often possible, but the quantitative exploitation of the data requires the numerical integration of nonlinear differential equations incorporated into a program for the search for the best parameters. A sinusoidal variation of a feed component concentration around a steady state value can be analyzed by the well developed methods of linear analysis if the relative amplitudes of the responses are under about 0.1. The application of these ideas to a modulated molecular beam was developed by Jones et al. ( 7) in 1972. A number of simple sequences of linear steps produces frequency responses shown in Fig. 7 (7). Here e is the ratio of product to reactant amplitude, n is the sticking probability, w is the forcing frequency, and k is the desorption rate constant for the product. For the series process k- is the rate constant of the surface reaction, and for the branched process P is the fraction reacting through path 1 and desorbing with a rate constant k. This method has recently been applied to the decomposition of hydrazine on Ir(lll) by Merrill and Sawin (35). 

Figure 21.5 Response of linear system to external periodic perturbation (Eq. 21-12). Full lines show hypothetical steady-state (Eq. 21-19) dashed lines give system response (Eq. 21-18). The system rate constant k = 4.0 yr 1 corresponds to the behavior of PCE in Greifensee (Box 21.2). Curve A corresponds to an annual variation with relative amplitude Aj = 0.5, curve B to a variation with period of 4 years and A, = 1.

One of the first estimations of the number of photons that could be created from vacuum in a cavity whose boundary moves with nonrelativistic velocity have been performed by Rivlin [113], who considered the parametric amplification of the initial vacuum field oscillations in the framework of the classical approach. He estimated the number of created photons Jf (eooit)2, where e 8L/L is the relative amplitude of the variation of the distance between the... 

It should be noted that two signals, of equal amplitude, in phase, fed to the X and Y axes of a scope, give a 45-degree line on the scope. Any variation of relative amplitude shifts the angle of the line. 

Relative amplitude of the pressure variation in the absence of sorbent p-dichlorobenzene... 

Little Is known about the exact nature of these local motions or the relative amplitudes and frequencies of motions at specific sites. Resolution of these questions requires data that Is sufficiently accurate to differentiate the behavior at different sites, and to choose a model that appropriately describes the nature of these potentially complex motions. Despite low sensitivity at the natural abundance level, NMR methods are probably most useful In this regard. The chemical shift range for resonances Is large and shift dispersion due to local variations In environment Is modest. In practice this means that many DNA sites can be monitored, even though Intrinsic llnewldths are large compared to small molecule standards. In addition, the dominance of dipolar C-H coupling contributions to the relaxation of protonated carbons simplifies Interpretation of T. and NOE parameters. 

Most of the practical transmitters in use today are special variations on these canonical forms. Practical transmitters may perform the RF operations at some convenient lower RF frequency and then up-convert to the desired operating frequency. In the case of RF signals that contain no AM, frequency multipUers may be used to arrive at the operating frequency. Of course, power amplifiers are usually required to bring the output power level up to the specified value. If the RF signal contains no amplitude variations, class C ampMers (relatively high efficiency) may be used otherwise, class B amplifiers are used. 

Figure 9 Relative amplitude of variation of the viscosity upon irradiation at 365 nm as a function of the CD-EP/polymer ratio in (U) 225-0.9C12 azo 0.5%, (o)...

Figure 2.10 (A) Relative intensities in an INEPT spectrum presented as a variation of the Pascal triangle. (B) Signal phase and amplitudes of (a) quaternary, (b) CH (c) CH-2, and (d) CH5 carbons in a normal INEPT experiment.

The second possibility consists by assuming these variations to behave as a succession of steps whose amplitude is updated by measurements carried out off-line. If this method is indeed very simple, it proves practically impossible to implement in the most of the installed facilities because the variations are sometimes relatively sudden and unforeseen and the number of off-line essays to be realized may become too large to handle ... 

The amplitude of temperature fluctuations was controlled in a feedback loop by adjusting the relative phase between the primary and secondary forced air flows. A demonstration of the closed-loop performance is illustrated in Fig. 24.12. The controller converged on the optimum phase with a 1/e rise time of approximately 30 control steps (Fig. 24.12a). Figure 24.126 illustrates the difference between the power spectra with control off (i.e., neither primary nor secondary drivers) and control optimized. The response time necessary to reach the optimum phase was slowed by the large variations in the measured coherence (examples shown in Fig. 24.12a) which are attributed to the complex interactions between the inlet mode, the combustor modes, and the preferred mode of the jet. 

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