Distortion oscillatory

Some typical oscillatory records are shown in Fig. 4.6. For conditions close to the Hopf bifurcation points the excursions are almost sinusoidal, but this simple shape becomes distorted as the oscillations grow. For all cases shown in Fig. 4.6, the oscillations will last indefinitely as we have ignored the effects of reactant consumption by holding /i constant. We can use these computations to construct the full envelope of the limit cycle in /r-a-0 phase space, which will have a similar form to that shown in Fig. 2.7 for the previous autocatalytic model. As in that chapter, we can think of the time-dependent... 

A crucial aspect of our approach is based on the idea that segmental rotation is activated thermally as the simplest mode of collective motions. This kind of first order distortion substantiated by oscillatory or diffusive segmental rotation is possible in a crystal lattice as well. This must not necessarily affect the ideal periodic structure but can be discussed in terms of the molecular structure factor. 

Small oscillatory torsions of molecular units within the segment produce a de-localization of the electronic density according to the Debye-Waller effect . In a very distorted structure as in the melt its smooth intensity distribution is not affected to a measurable extent. Rotational isomers, on the other hand, induce remarkable changes of the ru involved. Moreover, it is easily shown that the Boltzmann weighting factor of the molecular conformation ensemble also has a substantia] influence on the ru. It is strictly not possible to calculate the... 

Fretting corrosion is a combined wear and corrosion process in which material is removed from contacting surfaces when motion between the surfaces is restricted to very small amplitude oscillations (often, the relative movement is barely discernible ranging from a few tens of nanometers to a few tens of micrometers). Fretting occurs where low-amplitude oscillatory motion in the tangential direction takes place between contacting surfaces, which are nominally at rest. (Waterhouse) It is necessary that the load be sufficient to produce a distortion of surfaces. This is a common occurrence, since most machinery is subjected to vibration, both in transit and in operation. Figure 6.41 shows a typical example. Pressed-on wheels can often fret at the shaft/wheel hole interface.31... 

We have presented a thorough description and discussion about the molecular origin of the second kind (b) - bamboo like extrudate distortion - in the preceding Sect. 8. The present section is devoted to a specific illustration of the molecular origin of the type (a) distortion, i.e., sharkskin, which occurs in a range of stress/rate below the oscillatory flow or stick-slip transition, as indicated in Fig. 1. The next section will provide a brief discussion of the origin of the type (c), often spiral-like distortion. The macroscopic nature of the type (c) distortion was first discussed at least over 20 years ago [75]. Note that when the type (c) spiral distortion occurs on very fine length scales on the extrudate it can be and has sometimes been mistaken as sharkskin. 

Figure 2a shows contours of (/>5(p) at R v 2.35 bohr, which is close to the equilibrium geometry. Orbital (j>s now takes the form of a distorted H(ls) function which extends over the boron centre, but which makes relatively little use of the boron basis functions. Accordingly, much of the oscillatory structure disappears from the p-space electron density. 

Two especially important variants of REMPI (Johnson, et al., 1975) spectroscopy are ionization-dip (Cooper, et al., 1981) and Zero Electron Kinetic Energy (ZEKE) (Miiller-Dethlefs and Schlag, 1991 Merkt, 1997 Signorell and Merkt, 1999) photoelectron spectroscopy. Ionization-dip REMPI spectroscopy is especially useful when one wants to record free<—bound spectra from a single, selectable v, J level. Without such v, J selection, most of the oscillatory structure in a free<—bound spectrum will be washed out. One potential problem with some ionization-dip schemes is that, if the ionization transition originates from the initial level of the free<—bound transition being studied, there is a possibility that the observed linewidths will be distorted by power broadening (especially when the free final state is a weakly predissociated state with linewidth < lcm-1). 

Sharp cutoff filters should be avoided in biopotential measurements where the bioelectric waveform shape is of interest Filtering can greatly distort waveforms where waveform frequencies are near the filter breakpoints. Phase and amplitude distoitions are more severe with higher-order sharp-cutoff filters. Filters such as the Elliptic and the Tchebyscheff exhibit drastic phase distortion that can seriously distort bioelectric waveforms. Worse still for biopotential measurements, these filters have a tendency to ring or overshoot in an oscillatory way with transient events. The result can be addition of features in the bioelectric waveform that are not really present in the raw signal, time delays of parts of the waveforms, and inversion of phase of the waveform peaks. Figure 17.34 shows that the sharp cutoff of a fifth-order elliptical filter applied to an ECG waveform produces a dramatically distorted waveform shape. 

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