Wilson plot

Wilms tumor Wilson model Wilson plots Wilson s disease Wilson s equation... 

If (U is plotted against 1/m0 8 a straight line, known as a Wilson plot, is obtained with a slope of l/ and an intercept equal to the value of the constant. For a clean tube R, should be nil, and hence h0 can be found from the value of the intercept, as xw/kw will generally be small for a metal tube, hi may also be obtained at a given velocity from the difference between 1 jU at that velocity and the intercept. 

Substituting the observed passage into Eq. (20-60) and rearranging yields Eq. (20-61). A plot of the LHS versus J data yields the mass-transfer coefficient from the slope, similar to the Wilson plot for heat transfer-coefficient determination ... 

Since the central beam is spread out over a disk, its intensity will lie within the dynamic range of the same detector used to detect the Bragg beams. Hence it can be recorded and used for normalization, so that absolute intensity measurements may be made, and the unsatisfactory Wilson plot method is not needed. 

The Wilson plot is shown in Figure 4.At first sight all seems well except that the overall temperature factor is B=327 57a. This is clearly unlikely, but is a common feature when carrying out normalisation with such a sparse data set. To overcome the problem, a temperature factor of B=0.0A is imposed on the data. 

Checking the data quality is strongly recommended inspection of the Wilson plot and data reduction statistics is very useful in judging the extent of the resolution to which the data can realistically be used. Pathologically bad data, for example those from a split crystal, twinned data, systematically incomplete data, low resolution overloads will always make model building and refinement hard if not impossible. 

Thus for a given reaction mass, the heat transfer coefficient of the internal film can be influenced by the stirrer speed and its diameter. The value of the equipment constant (z) can be calculated using the geometric characteristics of the reactor. The value of material constant for heat transfer (y) can either be calculated from the physical properties of the reactor contents-as far as they are known-or measured by the method of the Wilson plot in a reaction calorimeter [4, 5]. This parameter is independent of the geometry or size of the reactor. Thus, it can be determined at laboratory scale and used at industrial scale. The Wilson plot determines the overall heat transfer coefficient as a function of the agitator revolution speed in a reaction calorimeter ... 

The Wilson plot (Figure 9.15) verifies the correlation in Equation 9.18, that is, if the measures fit on a straight line, a validation is built into the method. The... 

Figure 9.15 Wilson plot obtained for toluene in a reaction calorimeter, 1 /U as a function of the stirrer speed to power -2/3. The reference stirrer speed n0 is taken as 1 s. ...

A 2.5 m3 stainless steel stirred tank reactor is to be used for a reaction with a batch volume of 2 m3 performed at 65 °C. The heat transfer coefficient of the reaction mass is determined in a reaction calorimeter by the Wilson plot as y = 1600Wnr2KA The reactor is equipped with an anchor stirrer operated at 45 rpm. Water, used as a coolant, enters the jacket at 13 °C. With a contents volume of 2 m3, the heat exchange area is 4.6 m2. The internal diameter of the reactor is 1.6 m. The stirrer diameter is 1.53 m. A cooling experiment was carried out in the temperature range around 70 °C, with the vessel containing 2000 kg water. The results are represented in Figure 9.16. 

A plot of 1/kobs vs. 1/[R] will be linear if the reaction obeys Equation 9. From the extrapolated intercepts and slope of such a Kitz-Wilson plot one readily can obtain values for k2 and KR. Figure 3 shows a theoretical Kitz-Wilson plot that indicates the values of slope and intercepts from which k2 and KR can be calculated. 

Figure 3. Kitz-Wilson plot for verifying affinity-labeling mechanism.

This effect can be reduced if affinity-labeling kinetic data are analyzed by other types of linear plots used by enzyme kineticists. Two which appear to be useful improvements over the Kitz-Wilson plot are analogs of the Eadie-Hofstee and the Eisenthal-Comish-Bowden plots (20,21). 

The effects of L on the appearance of the Kitz-Wilson plot is exactly analogous to the effect of an enzyme competitive inhibitor on a Line-weaver-Burk plot. 

Kl. Figure 3 compares Kitz-Wilson plots obtained plus and minus L. Of course the effects of L on affinity-labeling kinetics could also be analyzed quantitatively by Eadie-Hofstee or direct linear-type plots. 

To calculate equation (14) correctly, the structure factor magnitudes must be expressed on the absolute scale, that is, relative to the scattering factor of a single electron under the same conditions. In practice, the observed //, and hence Fhki obs values are on an arbitrary scale, depending on the crystal size, primary beam flux, photon-multiplying effect of the counter, and so on, which are in practice impossible to estimate. The scale factor K, required to bring Fhki obs to the absolute scale, can be found by means of a so-called Wilson plot, 2i gives also the overall temperature factor B (see below) of the stmcture... 

Two Wilson plots are shown in Figure 7.22, one for a small molecule and the other for a macromolecule. In these plots the average values of F[hkl) are compared in narrow ranges of sin 0/A to the values that can be calculated for a random arrangement of the same atoms in the same unit cell (that is, S/J). A plot of the natural logarithm of the... 

FIGURE 7.22. Two Wilson plots, (a) Diffraction data for a small structure, sodium citrate, (b) Diffraction data for macromolecule, D-xylose isomerase. Note that all the data for the macromolecule in (b) are within the value of sin0/A for the first point for the small structure in (a). (Courtesy H. L. Carrell)... 

Structure amplitudes are put on an absolute scale by a Wilson plot, which gives an overall scale factor and temperature factor. 

FIGURE 9.3. Numerical values for the calculated electron density (a) at grid points, and (b) a two-dimensional plot, showing how contours are drawn in two dimensions. The level of contours (in electrons per cubic A) can be calculated if the volume of each three-dimensional grid block is known in A , and the absolute scale is know for the electron density (from the Wilson plot initially, and then from the subsequent lecist-squares refinement). 

This predicted intensity falloff was observed experimentally by W. H. Bragg. He studied rock salt at two temperatures, 15 and 37°C, and found that the intensities of Bragg reflections, particularly those at high 20-values, were smaller at the higher temperature. This effect was described in Chapter 7, where it was shown that the falloff in intensity as a function of scattering angle (20) is routinely used to obtain an average B value for the entire crystal structure by way of a Wilson plot. ... 

The magnitudes of these displacements may interest the reader. If iliso, found from a Wilson plot (Figure 7.14, Chapter 7), is 4 A, then U = (w ) is about 0.05 and the root-mean-square amplitude is... 

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