Natural resonance frequency defined

One of the most accurate clocks in the world is located at the United States National Institute of Standards and Technology (NIST) in Boulder, Colorado. This cesium fountain atomic clock provides the official time for the United States. The dock is based on the natural resonance frequency of the cesium atom (9,192,631,770 Hz.), which defines the second. 

Table 2.1 is a compilation of nuclear characteristics of a number of nuclei important in studies involving carbon materials. Besides the values of /, it gives the natural abundance of each nuclide and the resonance frequency at a given applied magnetic field (corresponding to a 100-MHz NMR spectrometer), as defined in the next section. 

Relative activation enthalpies (Aif) in Table 2 were converted to o% kx k ) at 298 K, and were plotted against Hammett a constants. Here, we used enthalpies, because the size of the entropy and hence the free energy depend much on low frequencies, which are less reliable than higher frequencies, especially for compounds with weak interactions such as TS (8). The use of free energy (AG ) gave similar correlations with more scattered points. As for the Hammett o constant, we used dual-parameter o constants in the form of the Yukawa-Tsuno equation (LArSR equation) (9) as defined in eq 3. Here, the apparent a constant (aapp) has a variable resonance contribution parameter (r), which varies depending on the nature of the reaction examined for t-cumyl... 

We note that since Q involves the scattering coefficients, the radiation pressure force has resonance or near-resonance behavior. This first was observed and analyzed by Ashkin and Dziedzic (1977) in their study of microparticle levitation by radiation pressure. They made additional measurements (Ashkin and Dziedzic, 1981) of the laser power required to levitate a microdroplet, and Fig. 19 presents their data for a silicone droplet. The morphological resonance spectrum for the 180° backscattered light shows well-defined peaks at wavelengths corresponding to frequencies close to natural frequencies of the sphere. The laser power shows the same resonance structures in reverse, that is, when the scattered intensity is high the laser power required to levitate the droplet is low. 

This paper discusses the impact of wind action on natural-draft cooling towers. The structure of the wind load may be divided into a static, a quasistatic, and a resonant part. The effect of surface roughness of the shell and of wind profile on the static load is discussed. The quasistatic load may be described by the variance of the pressure fluctuations and their circumferential and meridional correlations. The high-frequency end of the pressure spectra and of the coherence functions are used for the analysis of the resonant response. It is shown that the resonant response is small even for very high towers, however, it increases linearly with wind velocity. Equivalent static loads may be defined using appropriate gust-response factors. These loads produce an approximation of the behavior of the structure and in general are accurate. 11 refs, cited. 

In terms of the structural features that are probed with various analytical methods, solid state nuclear magnetic resonance (SSNMR) may be looked upon as representing a middle ground between IR spectroscopy and X-ray powder diffraction methods. The former provides a measure of essentially molecular parameters, mainly the strengths of bonds as represented by characteristic frequencies, while the latter reflect the periodic nature of the structure of the solid. For polymorphs differences in molecular environment and/or molecular conformation may be reflected in changes in the IR spectrum. The differences in crystal structure that define a polymorphic system are clearly reflected in changes in the X-ray powder diffraction. Details on changes in molecular conformation or in molecular environment can only be determined from full crystal structure analyses as discussed in Section 4.4. 

As an alternative to the specific solutions that are available in ID NMR, the general approach adopted in 2D NMR is to apply a series of RF pulses to the sample such that there are two independent variable time intervals in the pulse sequence. One of these is the acquisition time, denoted by t, and the other is some incremental delay denoted /i. If an NMR FID is acquired for a period for each of a set of t values, the digital NMR signal intensity (S) will be a function of both t and giving a matrix of data S(ti, /i). If Fourier transformation is carried out with respect to both ti and tz a matrix of NMR intensity as a function of two frequencies will result. This is now a 2D NMR spectrum as it represents signal intensity as a function of two frequency axes. The delay ti and the actual nature of the pulse sequence will, as may be seen later, define exactly what the two frequency axes will represent. As a consequence of this process, there are two immediate benefits increased signal dispersion and hence less overlap, and if the experiment is conducted in certain ways, it is possible to evaluate connectivities between the various NMR resonances. On the other hand, the 2D approach usually requires increased experiment time and increased computer data storage requirements. 

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