Local frequency

As the wetting front advances at speed U, the solid undergoes a strain cycle at a variety of frequencies, /, the local frequency depending on the distance of the element of solid from the contact line at the moment under consideration. The solid the furthest from the contact line, yet still perturbed by the presence of the three-phase line, is at a distance of ca. to and thus feels a strain cycle at frequency [//to. At the other extreme, near the lower cutoff at x = 8, the frequency is ca. [7/8. The latter frequency will be dominant, since it is in the direct vicinity of the three-phase line that the solid is strained the most. As a consequence, and using Eq. (10), we can define the rate at which work is being done as ... 

Masselon, C. Tolmechev, A. V. Anderson, G. A. Harkewicz, R. Smith, R. D. Mass measurement errors caused by local frequency perturbations in FTICR mass spectrometry. J. Am. Soc. Mass Spectrom. 2002,13, 99-107. 

In analogy to the time frequency, /, the spatial concentration behaviour may be characterized by the local frequency, focal = 1 /liocai- In Fig. 2.6, four types of spatial concentration functions are shown. These types and combinations of them can characterize all the variations of concentration in analytical practice both in one- and more-dimensional cases. 

There must be some spatial autocorrelation in the image, that means that the local frequency have to be low or medium according to Fig. 2.6b,c (in contrast, in cases of zero- and high local frequencies, see Fig. 2.6a,d, there is no autocorrelation). 

The study of dynamics of a real polymer chain of finite length and containing some conformational defects represents a very difficult task. Due to the lack of symmetry and selection mles, the number of vibrational modes is enormous. In this case, instead of calculating the frequency of each mode, it is more convenient to determine the density of vibrational modes, that is, the number of frequencies that occur in a given spectral interval. The density diagram matches, apart from an intensity factor, the experimental spectmm. Conformational defects can produce resonance frequencies when the proper frequency of the defect is resonating with those of the perfect lattice (the ideal chain), or quasi-localized frequencies when the vibrational mode of the defect cannot be transmitted by the lattice. The number and distribution of the defects may be such... 

Employing the probabilistic model developed by Tsutsui and Miyauchi (14), the following expression is derived for the local frequency distribution of bubble length (17). 

When applied to a particular case, N is chosen using the prescription introduced by Davis and Gray. For example, in Hel2 the frequency of the van der Waals bond is 26.4cm and the diatom vibrational state with v = 20 has a local frequency r(v) = 93.81 cm, implying that 4 < A < oo. 

This is the case of most molecules. There are, however, certain molecules in which the inversion barrier is so low that the vibrational wave functions cannot be considered as localized. Frequencies of the transitions between symmetrically equivalent configurations A and B are then high enough for the splitting of energy levels due to the tunneling to be detected experimentally. 

Figure 10. The potential F in the presence of lich the motion of the Brownian particle takes place. The right well is (xmsideted. The dashed curve expresses the harnuniic e q>anaon of the potential V around x a. The r ions 0 < x < a and a.< x

In turn. How does such a resonance occurring in the vicinity of first-rank saddles affect the associated local frequencies d)t(J) One might anticipate naively that, if the system is not in the quasiregular regime where all or almost of all the actions are good approximate invariants, the invariants of all coj(J) are spoiled, including that of the reactive mode F, since 6)p (j) depends not only on the invariant Jp but also on the other J . Now, let us look into di i(J) at second order ... 

C. C. Martens, M. J. Davis, and G. S. Ezra, Chem. Phys. Lett., 142, 519 (1987). Local Frequency Analysis of Chaotic Morion in Multidimensional Systems Energy Transport and Bottlenecks in Planar OCS. 

C. Gonnet and B. Torresani, Signal Process., 37, 389-404 (1994). Local Frequency Analysis... 

Keywords Laser Doppler Vibrometer, Ambient vibration, Forced vibration. Local frequency, Global frequency. Local mode. Global mode... 

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