Distortion definition

C. J. Lemerande. (1998). Harmonic Distortion Definitions and Countermeasures, Part 2. 

By analogy with Eq. (3.1), we seek a description for the relationship between stress and strain. The former is the shearing force per unit area, which we symbolize as as in Chap. 2. For shear strain we use the symbol y it is the rate of change of 7 that is involved in the definition of viscosity in Eq. (2.2). As in the analysis of tensile deformation, we write the strain AL/L, but this time AL is in the direction of the force, while L is at right angles to it. These quantities are shown in Fig. 3.6. It is convenient to describe the sample deformation in terms of the angle 6, also shown in Fig. 3.6. For distortion which is independent of time we continue to consider only the equilibrium behavior-stress and strain are proportional with proportionality constant G ... 

Martensitic phase transformations are discussed for the last hundred years without loss of actuality. A concise definition of these structural phase transformations has been given by G.B. Olson stating that martensite is a diffusionless, lattice distortive, shear dominant transformation by nucleation and growth . In this work we present ab initio zero temperature calculations for two model systems, FeaNi and CuZn close in concentration to the martensitic region. Iron-nickel is a typical representative of the ferrous alloys with fee bet transition whereas the copper-zink alloy undergoes a transformation from the open to close packed structure. ... 

A snap can be characterized by the geometry of its spring component. The most common snaps are the cantilever type, the hollow-cylinder type (as in the lids of pill bottles) and the distortion type (Fig. 4-15). These snaps include those in any shape that is deformed or deflected to pass over interference. The shapes of the mating parts in a hollow cylinder snap is the same, but the shapes of the mating parts in a distortion snap are different, by definition. These classifications are rather nominal, because the cantilever category is used loosely to include any leaf-spring components, and the cylinder type is used also to include noncircular section tubes. 

The annular flow pattern discussed above shows a definite connection with burn-out, and enables a simple burn-out mechanism to be set forth. There are many other flow patterns referred to in the literature, however, and we will consider here what can be said about any connection they may have with burn-out. It does not follow that there must be a connection, as a flow pattern is essentially a description of the bulk conditions in a channel and depends upon the none-too-reliable results of visual observation, which is often impeded by optical distortion. Thus, although gross conditions may appear to change and one pattern give way to another, the hydrodynamic state prevailing close to the heated surface may remain practically unaffected and the burn-out mechanisms unaltered. 

Tor the purpose of this brief account we will provide only a notional definition of optical aberrations. In an optical system, the angular coordinates of incident rays are transformed according to sequential applications of Descarte s law from one optical surface to the next. Aberrations are essentially the non-linear terms of the transformation, the angular coordinates of emerging rays not being strictly proportional to those of the incident ones -thereby generating distorted and/or blurred images. 

A definitive identification of the proteins in each peak is not possible, however, the elution times of the peaks at 13-14 min. and 15 min. are close to the times which would be expected for gamma-globulins and albumins, two of the principal classes of serum proteins. These data also indicate the loading capacity of this column with serum. More than 14 mg. of undiluted serum was injected before evidence of overloading in the form of band broadening and peak distortion was observed. 

Various other interactions have been considered as the driving force for spin-state transitions such as the Jahn-Teller coupling between the d electrons and a local distortion [73], the coupling between the metal ion and an intramolecular distortion [74, 75, 76] or the coupling between the d electrons and the lattice strain [77, 78]. At present, based on the available experimental evidence, the contribution of these interactions cannot be definitely assessed. Moreover, all these models are mathematically rather ambitious and do not show the intuitively simple structure inherent in the effect of a variation of molecular volume considered here. Their discussion has to be deferred to a more specialized study. 

Trying to determine which column is ideal for a specific analysis can be difficult with over 1000 different columns on the market [74]. A proper choice implies a definition of parameters such as column material, stationary phase (polarity), i.d., film thickness and column length. Guides to column selection are available [74,75]. The most important consideration is the stationary phase. When selecting an i.d., sample concentration and instrumentation must be considered. If the concentration of the sample exceeds the column s capacity, then loss of resolution, poor reproducibility and peak distortion will result. Film thickness has a direct effect on retention and the elution temperature for each sample compound. Longer columns provide more resolving probe, increase analysis times and cost. 

This property is readily established from the definition of Fourier transform and convolution. In scattering theory this theorem is the basis of methods for the separation of (particle) size from distortions (Stokes [27], Warren-Averbach [28,29] lattice distortion, Ruland [30-34] misorientation of anisotropic structural entities) of the scattering pattern. 

It is worth to be noted that these definitions of first- and second-order distortions according to Warren-Averbach are model-free. From a linear or a quadratic increase of peak breadths it can neither be concluded in reverse that strain broadening, nor that paracrystalline disorder were detected. 

The coverage of the survey has though been deliberately restricted to those sandwich systems in which the pseudo-axial structure is definitely established or is strongly indicated by the available evidence, and species in which extensive distortion from this geometry is likely have thus been excluded. Consequently this has had the effect of largely limiting the coverage to the metallocenes and bisarene compounds of the 3d series since in the 4c and... 

Another, very notable, case where the two definitions are in conflict is that of het-eroannular cisoid dienes. As we have mentioned, this was just the class of molecules that stimulated the introduction of the AAR. Here, in order to have the correct results one should refer the chirality of the axial substituent to the individual double bonds (olefin-picture), as depicted in Figure 6 and in the upper parts of Figure 7(b) and (c). The case of heteroannular dienes is anyway peculiar, because in these compounds the chromophore is unusually distorted. This case is treated in the following section. 

The model shown in Scheme 2 indicates that a change in the formal oxidation state of the metal is not necessarily required during the catalytic reaction. This raises a fundamental question. Does the metal ion have to possess specific redox properties in order to be an efficient catalyst A definite answer to this question cannot be given. Nevertheless, catalytic autoxidation reactions have been reported almost exclusively with metal ions which are susceptible to redox reactions under ambient conditions. This is a strong indication that intramolecular electron transfer occurs within the MS"+ and/or MS-O2 precursor complexes. Partial oxidation or reduction of the metal center obviously alters the electronic structure of the substrate and/or dioxygen. In a few cases, direct spectroscopic or other evidence was reported to prove such an internal charge transfer process. This electronic distortion is most likely necessary to activate the substrate and/or dioxygen before the actual electron transfer takes place. For a few systems where deviations from this pattern were found, the presence of trace amounts of catalytically active impurities are suspected to be the cause. In other words, the catalytic effect is due to the impurity and not to the bulk metal ion in these cases. 

One way of getting rid of distortions and basis set dependence could be that one switches to the formalism developed by Bader [12] according to which the three-dimensional physical space can be partitioned into domains belonging to individual atoms (called atomic basins). In the definition of bond order and valence indices according to this scheme, the summation over atomic orbitals will be replaced by integration over atomic domains [13]. This topological scheme can be called physical space analysis. Table 22.3 shows some examples of bond order indices obtained with this method. Experience shows that the bond order indices obtained via Hilbert space and physical space analysis are reasonably close, and also that the basis set dependence is not removed by the physical space analysis. 

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