Measurements inverse proportions

For this kind of case, a modification of the dilution method is being developed. Instead of using an external fixed-geometry measurement chamber, a suitable part of the process, e.g. a stretch of pipe, is used. A radiation detector is mounted on the outside of the pipe, and a tracer emitting sufficiently hard gamma radiation is used. As sufficient mixing can be achieved by injecting upstream the separator the radiation level found will be strictly proportional to the concentration and thus inversely proportional to the true flow rate. 

The time-dependent structure factor S k,t), which is proportional to the intensity I k,t) measured in an elastic scattering experiment, is a measure of the strength of the spatial correlations in the ordering system with wavenumber k at time t. It exliibits a peak whose position is inversely proportional to the average domain size. As the system phase separates (orders) the peak moves towards increasingly smaller wavenumbers (see figure A3.3.3. 

For example, when the activity is determined by counting 10,000 radioactive particles, the relative standard deviation is 1%. The analytical sensitivity of a radiochemical method is inversely proportional to the standard deviation of the measured ac-... 

The principle of the Rockwed hardness test is that the depth of the indentation between a minor and a major load appHed through an indenter is inversely proportional to the hardness number. Using a minor load to set the indenter helps to reduce backlash in the measuring system. 

The concentration [MB] constantly experiences tiny fluctuations, the duration of which can determine linewidths. It is also possible to adopt a traditional kinetic viewpoint and measure the time course of such spontaneous fluctuations directly by monitoring the time-varying concentration in an extremely small sample (6). Spontaneous fluctuations obey exactly the same kinetics of return to equiUbrium that describe relaxation of a macroscopic perturbation. Normally, fluctuations are so small they are ignored. The relative ampHtude of a fluctuation is inversely proportional to the square root of the number of AB entities being observed. Consequently, fluctuations are important when concentrations are small or, more usehiUy, when volumes are tiny. 

The uncertainty principle, according to which either the position of a confined microscopic particle or its momentum, but not both, can be precisely measured, requires an increase in the carrier energy. In quantum wells having abmpt barriers (square wells) the carrier energy increases in inverse proportion to its effective mass (the mass of a carrier in a semiconductor is not the same as that of the free carrier) and the square of the well width. The confined carriers are allowed only a few discrete energy levels (confined states), each described by a quantum number, as is illustrated in Eigure 5. Stimulated emission is allowed to occur only as transitions between the confined electron and hole states described by the same quantum number. 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

The mass transport influence is easy to diagnose experimentally. One measures the rate at various values of the Thiele modulus the modulus is easily changed by variation of R, the particle size. Cmshing and sieving the particles provide catalyst samples for the experiments. If the rate is independent of the particle size, the effectiveness factor is unity for all of them. If the rate is inversely proportional to particle size, the effectiveness factor is less than unity and

experimental points allow triangulation on the curve of Figure 10 and estimation of Tj and ( ). It is also possible to estimate the effective diffusion coefficient and thereby to estimate Tj and ( ) from a single measurement of the rate (48). 

The film thickness of epitaxial and highly textured thin films can be measured with XRD. Close to the usual or primary difftaction peaks there are secondary or subsidiary maxima in the difftacted intensity (see Figure 6), which are due to the finite film thickness. The film thickness is inversely proportional to the spacing between these maxima and is easily calculated. X-ray reflectivity is another accurate method for measuring a film s thickness. 

Thus, the variance of the peak is inversely proportional to the number of theoretical plates in the column. Consequently, the greater the value of (n), the more narrow the peak, and the more efficiently has the column constrained peak dispersion. As a result, the number of theoretical plates in a column has been given the term Column Efficiency. From the above equations, a fairly simple procedure for measuring the efficiency of any column can be derived. 

Analytical information taken from a chromatogram has almost exclusively involved either retention data (retention times, capacity factors, etc.) for peak identification or peak heights and peak areas for quantitative assessment. The width of the peak has been rarely used for analytical purposes, except occasionally to obtain approximate values for peak areas. Nevertheless, as seen from the Rate Theory, the peak width is inversely proportional to the solute diffusivity which, in turn, is a function of the solute molecular weight. It follows that for high molecular weight materials, particularly those that cannot be volatalized in the ionization source of a mass spectrometer, peak width measurement offers an approximate source of molecular weight data for very intractable solutes. 

The area form factor [176] can be considered as a measure of the gluing efficient surface area based on the volume and is inversely proportional to the thickness of the particles F/V = 2jd = 2x sj 1. 

It is conventional to define (for the case being considered) the weight of a measurement yi to be inversely proportional to the variance of y that is. 

A measure of variability of the estimate can be gained from the standard error but it can be seen from Equations 11.4 and 11.5 that the magnitude of the standard error is inversely proportional to n (i.e., the larger the sample size the smaller will be the standard error). Therefore, without... 

In the hrst case, the degree of self coherence depends on the spectral characteristics of the source. The coherence time Tc represents the time scale over which a held remains correlated this hme is inversely proportional to the spectral bandwidth Au) of the detected light. A more quantitative dehnition of quasi-monochromatic conditions is based on the coherence time all relevant delays within the interferometer should be much shorter than the coherence length CTc. A practical way to measure temporal coherence is to use a Michel-son interferometer. As we shall see, in the second case the spatial coherence depends on the apparent extent of a source. 

An alternative method for inferring accumulation rate relies on assuming that the rain of cosmogenic nuclides such as °Be onto the ice sheet surface is known. Then high accumulation rate dilutes the cosmogenic nuclide so its concentration as measured in the ice core is inversely proportional to accumulation rate. 

Depth of EB penetration The depth of penetration of energetic electrons into a material at normal angle of incidence is directly proportional to the energy of the electrons and inversely proportional to the density of the material [49,50]. The depth is expressed as a product of penetration distance and the density of the material (i.e., 1 g/cm = 1 cm X 1 g/cm ). The radiation energy and thus the type of electron accelerator to be used are dependent on the required penetration depth, the density of the irradiated material, and the chosen irradiation system. If one measures the density (d) in gram per cubic centimeter (g/cm ) and the layer thickness (T) in millimeter (mm), one can determine the radiation energy ( ) necessary for optimal homogeneity from [40] ... 

One performs so many repeat measurements at each concentration point that standard deviations can be reasonably calculated, e.g., as in validation work the statistical weights w, are then taken to be inversely proportional to the local variance. The proportionality constant k is estimated from the data. 

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