Attenuation calculation

The first two quantities calculated from S(t, y) depended on measurements of times the second two depend on measurements of amplitudes. From the amplitude of the reflection from the top surface of the cell the impedance, and hence the density, can be found using eqns (8.58) and (8.59). The impedance is plotted in Fig. 9.4(c). Finally, knowing the thickness and the impedance of the cell, the attenuation can be deduced from the amplitude of the echo from the interface between the cell and the substrate the weaker this echo, the greater the attenuation. The attenuation calculated from (8.60), neglecting frequency dependence, is plotted in Fig. 9.4(d). It is also possible to calculate the frequency dependence of the attenuation using (8.70) (Daft et al. 1989). 

Fig. 9.13. Quantitative analysis of the contrast from a white spot lesion in human tooth enamel (i) micrograph, 370 MHz (ii) V(z) curves of selected points along the line in the micrograph (iii) Rayleigh velocity and attenuation calculated from V(z) measured at each of the points on the line in (i) (Peck et al. 1989).

The attenuation calculations for the design of the canal w ere based on the following factors ... 

In this report results of CCF calculations for two mentioned forms of pulses are presented. In these calculations the attenuating coefficient S is replaced by (I-factor of 0)... 

During the attenuation measurements. Transducer 1 was excited with a narrowband tone burst with center frequency 18 MHz, see Figure 1 for a schematic setup. The amplitude of the sound pressure was measured at Tranducer 2 by means of an amplitude peak detector. A reference amplitude, Are/, was measured outside the object as shown at the right hand side of Figure 1. The object was scanned in the j y-plane and for every position, (x, y), the attenuation, a x, y), was calculated as the quotient (in db) between the amplitude at Transducer 2, A[x, y), and Are/, i.e., a(x,y) = lOlogm Pulse echo measurements and preprocessing... 

Up to this point, we have calculated the linear response of the medium, a polarization oscillating at the frequency m of the applied field. This polarization produces its own radiation field that interferes with the applied optical field. Two familiar effects result a change in tlie speed of the light wave and its attenuation as it propagates. These properties may be related directly to the linear susceptibility The index of... 

This is the factor by which the echo magnetization is attenuated as a result of difhision. More elaborate calculations, which account for phase displacements due to difhision occurring during the application of the gradient pulses yield... 

Figure Bl.14.13. Derivation of the droplet size distribution in a cream layer of a decane/water emulsion from PGSE data. The inset shows the signal attenuation as a fiinction of the gradient strength for diflfiision weighting recorded at each position (top trace = bottom of cream). A Stokes-based velocity model (solid lines) was fitted to the experimental data (solid circles). The curious horizontal trace in the centre of the plot is due to partial volume filling at the water/cream interface. The droplet size distribution of the emulsion was calculated as a fiinction of height from these NMR data. The most intense narrowest distribution occurs at the base of the cream and the curves proceed logically up tlirough the cream in steps of 0.041 cm. It is concluded from these data that the biggest droplets are found at the top and the smallest at the bottom of tlie cream.

The underlying principle of the PEOE method is that the electronic polarization within the tr-bond skeleton as measured by the inductive effect is attenuated with each intervening o -bond. The electronic polarization within /r-bond systems as measured by the resonance or mesomeric effect, on the other hand, extends across an entire nr-system without any attenuation. The simple model of an electron in a box expresses this fact. Thus, in calculating the charge distribution in conjugated i -systems an approach different from the PEOE method has to be taken. 

The polarizability effect can be calculated by a simple attenuation model. 

Assume that a damping factor of 0.707 or greater is good and provides a -3dB attenuation at the corner frequency and does not produce noise due to ringing. Also assume that the input line impedance is 50 ohms since the regulatory agencies use an TISN test which make the line impedance equal this value. Calculate the values needed in the common-mode inductor and Y capacitors ... 

The substituent stabilization effects calculated for the methyl cation and the methyl anion refer to the gas phase, where no solvation effects are present, and therefore are substantially larger, in terms of eneigy, than would be the case in solution, where solvation contributes to stabilization and attenuates the substituent effects. 

Regulatory Guide 1.145 provides corrections to the sigmas to correct for the c ffects of wind meander at low windspeed - much the same effect as achieved in the CRACIT code. Figure 8.3-1, taken from this guide, shows how the horizontal dispersion coefficient varies with distance from the source. To calculate x/Q (the fractional attenuation) use formula (8.3-1) for a particular distance from the plant, say 1 km. 

The proportion of ionized and unionized forms of a chemical compound can be readily calculated according to the above equation. It can be easily seen that pK is also a pH value at which 50% of the compound exists in ionized form. The ionization of weak acids increases as the pH increases, whereas the ionization of weak bases increases when the pH decreases. As the proportion of an ionized chemical increases, the diffusion of the chemical through the biological membranes is greatly impaired, and this attenuates toxicokinetic processes. For example, the common drug acetosalicylic acid (aspirin), a weak acid, is readily absorbed from the stomach because most of its dose is in an unionized form at the acidic pH of the stomach. 

This equation gives higher transmissivity values than those calculated with methods described earlier. Presumably, Lihou and Maund s transmissivity is to be used for conditions of low relative humidity, in which dust particles (haze) are the main cause of attenuation. A conservative approach is to assume = 1. 

The solid-flame model, presented in Section 3.5.2, is more realistic than the point-source model. It addresses the fireball s dimensions, its surface-emissive power, atmospheric attenuation, and view factor. The latter factor includes the object s orientation relative to the fireball and its distance from the fireball s center. This section provides information on emissive power for use in calculations beyond that presented in Section 3.5.2. Furthermore, view factors applicable to fireballs are discussed in more detail. 

Estimate the radiation received at a receptor. With an attenuation factor of 1, the radiation received by a vertical receptor at a distance X from the tank can be calculated from ... 

The attenuation of the pressure waves increases with depth and with the mud pressure wave velocity. More attenuation is observed with oil-base muds, which are mostly used in deep or very deep holes, and can be calculated with the mud and pipe characteristics [108] according to the equations... 

The above equations are useful for calculating distance-attenuation effects. 

The absorption problems for other detectors may be considered under three headings (1) attenuation along the beam path, (2) attenuation by the detector window, (3) absorption by the detecting medium. The results of absorption calculations (1.9) in Table 2 1 show the importance of these problems and suggest ways of dealing with them. 

In a recent study of the transport of coarse solids in a horizontal pipeline of 38 mrrt diameter, pressure drop, as a function not only of mixture velocity (determined by an electromagnetic flowmeter) but also of in-line concentration of solids and liquid velocity. The solids concentration was determined using a y-ray absorption technique, which depends on the difference in the attenuation of y-rays by solid and liquid. The liquid velocity was determined by a sail injection method,1"1 in which a pulse of salt solution was injected into the flowing mixture, and the time taken for the pulse to travel between two electrode pairs a fixed distance apart was measured, It was then possible, using equation 5.17, to calculate the relative velocity of the liquid to the solids. This relative velocity was found to increase with particle size and to be of the same order as the terminal falling velocity of the particles in the liquid. 

Why should calculations of evidently converge more slowly than those for b, and both more slowly than cross-section calculations It seems likely that this is a consequence of the very different interference structure of these three terms and their different phase dependence— particularly the slower convergence of the sin(ri — riy /) terms in the b expression (see Section III.C). When phase differences are small, as they will be for higher (. waves that are partly attenuated in the molecular core region by centrifugal barriers, the rapidly varying sine term will lend them a disproportionate influence on the final... 

Unfortunately, experimental difficulties precluded measurements closer to threshold, and the B-spline calculation also does not properly span this near threshold region down to the onset [57]. However, the general trend rising above 5 eV is for the dichroism to become attenuated, easily rationalized as the ejected photoelectron displaying less sensitivity to the chiral molecular potential as it acquires more energy. 

Figure 1 shows AES data for the oxidized titanium surface before and after deposition of 30 X of platinum with the substrate held at 130 K. The platinum thickness was calculated from the attenuation of the oxygen AES signal assuming layered growth of the metal. From the spectra It Is clear that the platinum was sufficient to completely attenuate the underlaying features of the titanium oxide. 

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