Irregular case

In these irregular cases the negative sign applies in eq. (18) and... 

In some applications the interpretation of Bscan images may be difficult due to the roughness or irregularity of the surface opposite to the probe. In these cases, surface irregularities... 

Figure XVI-1 and the related discussion first appeared in 1960 [1], and since then a very useful mathematical approach to irregular surfaces has been applied to the matter of surface area measurement. Figure XVI-1 suggests that a coastline might appear similar under successive magnifications, and one now proceeds to assume that this similarity is exact. The result, as discussed in Section VII-4C and illustrated in Fig. VII-6, is a self-similar line, or in the present case, a self-similar surface. Equation VII-21 now applies and may be written in the form...

In this discussion, entropy factors have been ignored and in certain cases where the difference between lattice energy and hydration energy is small it is the entropy changes which determine whether a substance will or will not dissolve. Each case must be considered individually and the relevant data obtained (see Chapter 3), when irregular behaviour will often be found to have a logical explanation. 

This ideal case is rarely if ever encountered in practice in general there will be a distribution of particle sizes rather than a single size, and in addition there will usually be a range of particle shapes, many of them highly irregular. 

Conceptually, the problem of going from the time domain spectra in Figures 3.7(a)-3.9(a) to the frequency domain spectra in Figures 3.7(b)-3.9(b) is straightforward, at least in these cases because we knew the result before we started. Nevertheless, we can still visualize the breaking down of any time domain spectrum, however complex and irregular in appearance, into its component waves, each with its characteristic frequency and amplitude. Although we can visualize it, the process of Fourier transformation which actually carries it out is a mathematically complex operation. The mathematical principles will be discussed only briefly here. 

Zinc dust is smaller in particle size and spherical in shape, whereas zinc powder is coarser in size and irregular in shape. The particle size of zinc dust, important in some appHcations, is controUed by adjusting the rate of condensation. Rapid cooling produces fine dust, slower condensation coarse dust. In the case of zinc powder, changes in the atomization parameters can be employed to change particle size to some degree. The particle size distributions for commercial zinc powders range from 44 to 841 p.m (325—20 mesh). The purity of zinc powders is 98—99.6%. 

Figure 7.7 Svirface striations and shallow grooves on a carbon steel case coupling. Acid etched the metal along microstructural irregularities producing the grooves. Compare to Fig. 7.8. (Magnification 7.5x.)...

The cavitation damage in this spacer was due to vibrations from operation of the engine. The localized nature of the damage in this case is an illustration of a common feature of cavitation. Pits formed by initial cavitation damage become preferred sites for the development of subsequent cavitation bubble formation due to the jagged, irregular contours of the pit. This tends to localize and intensify the cavitation process, especially in later stages of pit development. 

Note that localized corrosion having the appearance illustrated in Figs. 12.18 through 12.20 could be associated with brief exposure to a strong acid. In this case, however, all available information indicated that the tubes had never been exposed to an acid of any type. Cavitation was caused by high-frequency vibration of the tubes. The vibration apparently induced a threshold cavitation intensity such that rough or irregular surfaces produced cavitation bubbles, and smooth internal surfaces did not. 

Figure 17.17 Longitudinally cut half-section. Note the severe wall thinning and the perforation of the wall on the left side. Compare it to the wall thickness on the right side. Also note the circumferential band of irregular metal loss just above the threads, near the bottom of the casing.

Proteins are usually separated into two distinct functional classes passive structural materials, which are built up from long fibers, and active components of cellular machinery in which the protein chains are arranged in small compact domains, as we have discussed in earlier chapters. In spite of their differences in structure and function, both these classes of proteins contain a helices and/or p sheets separated by regions of irregular structure. In most cases the fibrous proteins contain specific repetitive amino acid sequences that are necessary for their specific three-dimensional structure. 

Figure 2 Variations in the neutron scattering amplitude or scattering length as a function of the atomic weight. The irregularities arise from the superposition of resonance scattering on a slowly increasing potential scattering. For comparison the scattering amplitudes for X rays under two different conditions are shown. Unlike neutrons, the X-ray case exhibits a monotonic increase as a function of atomic weight.

Branching can to some extent reduce the ability to crystallise. The frequent, but irregular, presence of side groups will interfere with the ability to pack. Branched polyethylenes, such as are made by high-pressure processes, are less crystalline and of lower density than less branched structures prepared using metal oxide catalysts. In extreme cases crystallisation could be almost completely inhibited. (Crystallisation in high-pressure polyethylenes is restricted more by the frequent short branches rather than by the occasional long branch.)... 

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