Frequency indirect method

In principle, the velocities c and ti can be determined by taking a series of pictures at a very high frequency of the flow through a transparent plastic tube. Because of the particle size distribution, each particle moves at a different velocity, and this makes this method difficult to apply in practice. We have therefore used an indirect method, where we have measured the pressure losses of pneumatic conveying for two mixture ratios and then fit the parameters so that Eq, (14.126) coincides as accurately as possible with measured pressure losses. 

According to the International Union of Pure and Applied Chemistry (IUPAC O)) the turnover frequency of a catalytic reac tion is defined as the number of molecules reacting per active site in unit time. The term active sites is applied to those sites for adsorption which are effective sites for a particular heterogeneous catalytic reaction. Because it is often impossible to measure the amount of active sites, some indirect method is needed to express the rate data in terms of turnover frequencies In some cases a realistic measure of the number of active sites may be the number of molecules of some compound that can be adsorbed on the catalyst. This measure is frequently used in the literature of the Fischer-Tropsch synthesis, where the amount of adsorption sites is determined by carbon monoxide adsorption on the reduced catalyst. However, it is questionable whether the number of adsorption sites on the reduced catalyst is really an indication of the number of sites on the catalyst active during the synthesis, because the metallic phase of the Fischer-Tropsch catalysts is often carbided or oxidized during the process. 

Another indirect method for the estimation of Gibbs elasticity modulus is based on the determination of the surface dilatation modulus E in experiments in which the surfaces of the surfactant solutions undergo small amplitude deformations of oscillatory nature [100-102], It is shown [100, see also Chapter 7] that the concentration dependence of a Gibbs elasticity modulus at constant film thickness should be nearly the same as the concentration dependence of (twice) the surface elastic modulus E when film thickness and frequency are related by... 

In the calculation of total pressure and vapor composition from boiling point data using the indirect method, the greatest source of error lies in the liquid-phase composition. We have attempted to characterize the frequency distribution of the error in the calculated vapor composition by the standard statistical methods and this has given a satisfactory result for the methanol- vater system saturated with sodium chloride when the following estimates of the standard deviation were used x, 0.003 y, 0.006 T, 0.1° C and tt, 2 mm Hg. This work indicates that in the design of future experiments more data points are required and, for each variable, a reliable estimate of the standard deviation is highly desirable. 

The derivation of the elastic constant tensor to be used in RUS is an indirect iterative procedure. Provided the sample dimensions, density and elastic constants are known, the spectrum of resonant frequencies can be easily calculated. The inverse problem viz. calculating the elastic constants from a measured spectrum of mechanical resonances) has no known solution, however. For the indirect method, a starting resonant frequency spectrum, 7 (n = 1,2, ), can be calculated by elastic constants estimated from theory or from literature data for similar materials in addition to the known sample dimension and density. The difference between the calculated and measured resonance frequency spectrum, 7 (n = 1,2, ), is identified by a figure-of-merit function,... 

All coalescence frequency work reported in the literature with the exception of that of two groups of investigators has used indirect means of obtaining an average coalescence frequency for the entire mixing vessel. The indirect methods can be divided into two categories chemical and physical. 

For smaller particles, an indirect method is required to measure the particle velocity. The easiest is phase amplitude light scattering. An alternating electric field with a frequency of a few Hertz is applied. The phase shift of scattered light is dependant on the applied electric field and is proportional to the mobility of particles causing the scattering. 

Moreover, it is remarkable that at least four bands in the photoelectron spectrum exhibit vibrational fine structure. Thus, the ion possesses as many stable excited states. Only one of them, the first one is due to ionization from a n-orbital. (This makes the fine structure observed in both the photoelectron and electronic spectra of ethane less surprising.) Vy, U2. and V3 are Raman active, but v is both Raman and infrared inactive and its frequency had to be determined by indirect methods (ref. 96). 

The indirect methods for the determination of anions by on-line precipitation using A AS are shown in Table 7.1. It can be seen that methods with a dissolution step generally have much lower sampling frequencies than those without dissolution. One has to remember, however, that the filters have to be cleaned periodically if the precipitates are not dissolved within each cycle. Therefore, the differences in real sample throughputs will not be that significant if the time for the off-line cleaning of filters is taken into account. 

Alternative to the direct detection of specific modes, indirect methods that take advantage of combination modes can be applied. Combination modes, which arise from addition or subtraction of two frequencies, appear in IR spectra, though generally with low intensity. By analyzing the combinations of masked vibrations with OH stretching vibrations, it is possible to deduce the positions of the masked vibrations (through knowledge ofv(OH)). 

Various experimental methods have been developed for investigating the magnetoelastic properties of thin films. Indirect methods are based on the stress dependence of any magnetic properties, e.g., susceptibility or resonance frequency, while the most common direct method was introduced as early as 1976 by Klokholm (1976, 1977) who observed the deflection of the end of a bimorph when subjected to a magnetic field. 

A somewhat indirect method for measuring characteristic impedance at low frequencies is used in the acoustic streaming device of Thurston, in which the liquid is pumped back and forth through parallel capillaries. It is appropriate for liquids of very low viscosity in a continuous frequency range from 10 to 300 Hz. 

Quasielastic neutron scattering (QENS) is a rather indirect method with many limitations. It makes use of the small ( quasielastic ) energy shift that neutrons experience in any scattering by a moving particle, say by the diffusive translations of protons on a molecule. Mathematically, the normalized scattered neutron intensity as a function of kinetic neutron energy E (or frequency (o=2nElh) is related to the time Fourier transform of the dynamic pair-distribution function G(r, i) of the sample material [6, 32]. Hence in Pick s approxima-... 

Besides direct methods of detection, indirect NQR detection methods have also been developed. As a rule, they are used at low frequencies or in cases when the concentration of quadrupolar nuclei is not high, i.e. when the sensitivity of the direct methods is not sufficient. For most experiments, when using these methods, a constant magnetic field is needed. To apply these methods, it is necessary for the sample to have two spin systems connected by dipole-dipole interactions. Indirect methods can be conventionally divided into double-resonance techniques and the cross-relaxation spectroscopy method. 

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