Profile equal-volume

Fig. 14-9 (a) The normalized intensity distribution for the fundamental mode on clad power-law profiles assuming V = 2.40S and unit total power, and (b) the corresponding intensity distribution assuming the equal volume profiles of Fig. 14-7 (b) with V= V = 2.405. 

The fundamental-mode inensity distribution is plotted in normalized form in Fig. 14-9(a), assuming K = 2. 5 for each profile. If we consider the equal volume profiles, then for each profile we use the value of K given by Eq. (14-45). The corresponding value of U follows from Eq. (14-33) and plots of the normalized intensity np S are given in Fig. 14-9(b). For q> I the intensity distribution is almost independent of profile shape. 

Values of this expression are compared with the exact values of in Table 15-3. There is negligible difierence except for the Gaussian profile (m = 0), so spot size is indeed neariy independent of profile shape when V=V This consistency check is a refinement of the approximation = 2.405 for all equal-volume profiles given in Table 15-2. 

The novel provision of side feeds promotes mixing between feed and crystallizing streams and increases solute concentration. This not only eliminates the need for equal volume (or residence time) of each crystallizer in the network but may also reduce the energy requirements for cooling the suspension. The magnitude of such reductions will depend, however, on the exact mixing profiles between the crystallizers. 

Figure 2.31 Characteristic temperature profiles in a counter-current micro heat exchanger for a very low (left), intermediate (middle) and very high (right) thermal conductivity of the wall material and equal volume flows inside the two channels, reproduced from [125],...

Dissolution was carried out with the paddle method according to USP XXI, using a Prolabo dissolution tester. The dissolution medium was 1000 ml of distilled water at 37 0.5°C and 50 rev min-1. At appropriate time intervals, 5 ml of sample was withdrawn and an equal volume of medium was added to maintain a constant volume. Sample were filtered, diluted with lithium carbonate solution as an internal standard, and analysed using a Dr Lange MD 70 flame photometer. Each dissolution profile is the average of six separate tablets. 

The goal of a pressure analysis of a chemical reaction is to construct the volume profile, which specifies at least the relative partial molar volumes of the reactants, products, and transition state. Figure 6.1 shows examples of several profiles. Note that the transition state may lie above, below, or in between the reactant and the product states and note that the difference between the forward and backward value of AV must be equal to AU. ... 

Figure 3 shows that the oxidation profile of the C6 alcohols mixture composed of equal volumes of C6 alcohols. 

Volume profiles have been determined for the aquation of [Co(en)2(NH3)X] ions (X = trans-C, trans-Br, cis-Br, ds-NOj). Values of AV and the reaction volume AV are summarized in Table 7.1. It is concluded that the entering H2O and the leaving group X participate almost equally in the transition state and that an I mechanism applies. 

The elution profile of proteins from the P-150 colunm was determined by densitometry of SDS-PAGE gels loaded with equal volumes from successive column fractions (Figure 3). The fractions which contained the most highly purified P subunit eluted from the column first, while the latter fractions contained a greater proportion of the 6, 9 and 35 kDa proteins. The fraction which had the maximum amount of P subunit indicated that the protein eluted from the colunm with an apparent molecular mass of about 180 kDa. If the a subunit were present in stoichiometry amounts to the p subunit, the similarity in the size of these proteins (57 versus 55 kDa) would require that the a subunit comprise about one third of the total protein rather than the small amount observed. Thus, the preparation probably exists in solution as an aggregate of about three copies of the p subunit. 

Figure 3 Human submandibular saliva. This gel shows the proteins in human submandibular saliva separated on a 4-12% Bis-Tris NuPAGE gel and stained with Coomassie Brilliant Blue R250. Samples 1, 2, and 3 are from three different subjects, in which the sample in track O is from a gland from which obstructive calculi had been removed 6 months previously and C is the contralateral normal control. Equal volumes of sample were applied to each track. On recovery from obstruction, the protein profile Is similar to the controls, but the increased band intensity results from a higher protein concentration. (Courtesy of Proctor GB and Osailan SM, Kings College, University of London.)...

Slurry reactors are usually equipped with stirrers, to prevent the solid particles from settling. Often propellers are employed in slurry reactors, but turbines can also be effective (see section 4.2.2, figure 4.1). The net action by gravity results in a solids concentration that gradually decreases with liquid height. The pumping action of the propeller transports equal volumes of liquid upward and downward however, the former contains more solids than the latter. In the steady state, the concentration profile is such that the difference of these upward and downward flows balances the flow of sinking particles. 

Figure 1.13 Pressure-volume profiles for formation of the reaction zone of an overdriven detonation in nitromethane with a 0.4 cm//iisec piston velocity until complete decomposition occurs at the piston, at which point the piston velocity is set equal to 0.3 cm/)usec.

Fig. 14-8 (a) The modal parameter 17 for the fundamental mode of the clad power-law profiles and (b) the upper limit on the range of singlemode operation given by the solid curve. The dashed curved is the analytic approximation of Eq. (14-45), and the solid curve is the equal volume curve for the profiles of Fig. 14-7 (b). 

The purpose of the equal volume concept is to normalize profiles with common values of n, and A in such a way as to separate effects which are dependent on profile shape from those which are almost independent of profile shape. To illustrate the idea we consider the profiles of the previous section. 

We have shown that clad power-law profiles of equal volume have a fundamental-mode intensity distribution and a maximum value Kg of the fiber... 

In Section 14-10, we introduced the concept of profile volume. We showed in the case of clad power-law profiles of equal volume that some properties, such as the range of single-mode operation and the fundamental-mode intensity distribution are insensitive to profile shape, whereas other properties, such as waveguide dispersion, depend critically on profile shape. Within the Gaussian approximation, we can demonstrate directly the insensitivity of the intensity distribution to profile shape. 

Consider a step-profile fiber of core index with a uniform density of nonuniformities of equal volume d index The factor C is given by the right side of Eq. (22-8), whence we deduce from Eqs. (22-11), Table 13-2, page 292, and the / = 0 integral and eigenvalue equation of Table 14-6, page 319, that the attenuation coefficient for the fundamental mode is... 

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