Frequency of Excitation

Dielectric spectroscopy techniques are promising for numerous applications that require non-invasive, non-destructive, non-contact, and real-time measurements. Non-invasive measurements with gas, liquid, solid, and mixed samples are possible on distance scales from nanometers to meters and a frequency of excitation from microhertz to terahertz. The main advantages of fringing electric field dielectric sensors include one-side access to material under test, convenience of application 

Hedvig, Dielectric Spectroscopy of Polymers, Wiley, New York, 1977. 

Bottcher, P. Bordewijk, Theory of Electric Polarization, Elsevier Scientific Publishing Company, Amsterdam, 

Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics Press, London, 1983. 

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This speed becomes critical when the frequency of excitation is equal to one of the natural frequencies of the system. In forced vibration, the system is a function of the frequencies. These frequencies can also be multiples of rotor speed excited by frequencies other than the speed frequency such as blade passing frequencies, gear mesh frequencies, and other component frequencies. Figure 5-20 shows that for forced vibration, the critical frequency remains constant at any shaft speed. The critical speeds occur at one-half, one, and two times the rotor speed. The effect of damping in forced vibration reduces the amplitude, but it does not affect the frequency at which this phenomenon occurs. 

Dependencies of luminescence bands (both fluorescence and phosphorescence), anisotropy of emission, and its lifetime on a frequency of excitation, when fluorescence is excited at the red edge of absorption spectrum. Panel a of Fig. 5 shows the fluorescence spectra at different excitations for the solutes with the 0-0 transitions close to vI vn, and vra frequencies. Spectral location of all shown fluorescence bands is different and stable in time of experiment and during lifetime of fluorescence (panel b)... 

Many other time parameters actually enter - if the molecule is conducting through a polaron type mechanism (that is, if the gap has become small enough that polarization changes in geometry actually occur as the electron is transmitted), then one worries about the time associated with polaron formation and polaron transport. Other times that could enter would include frequencies of excitation, if photo processes are being thought of, and various times associated with polaron theory. This is a poorly developed part of the area of molecular transport, but one that is conceptually important. 

Experimentally the sample is placed in a strong magnetic field and, rather than the frequency being scanned at a constant field strength to detect absorption of radiation, in practice the frequency of exciting radiation is kept constant and the magnetic field flux is varied. Both ESR and NMR spectroscopy have found widespread application in polymer studies and several excellent texts describing the techniques are available (1,17-19). 

To determine the dominant frequency of excitation, the near-fleld acoustic spectrum was obtained using a microphone. Typical near-fleld acoustic spectra for an excited jet and a natural jet are shown and compared in Fig. 29.5. When multiple peaks were observed in the spectrum, the peak with the highest spectral amplitude was denoted as the excitation frequency. By systematically varying the dimensions of the cavity, flow excitation occurred over a wide range of frequencies (4-40 kHz). Table 29.2 summarizes the normalized data. Initial tests were performed with semi-annular cavities to eliminate possible... 

The third rule of practical value concerns the intensity of fluorescence obtained and its variation with frequency of exciting light. The rate of emission of fluorescence is by definition equal to the rate of light absorption, measured in quanta, multiplied by the quantum efficiency of fluorescence, i.e.,... 

A diagram of the author s original spectrofluorimeter is shown in Figure 3. The light source, S, was either a 1 kw. compact source mercury vapor lamp, or for the measurement of fluorescence excitation spectra, a 375 w. xenon arc. The required frequency of exciting light was isolated by means of a Hilger 1)247 quartz prism monochromator, Mj, and... 

In early type stars, the bottom boundary penetrates into convective core (Osaki 1975). Accordingly, convective motion of eddies excites sound waves, as in the case of acoustic noise emmision from incompressible turbulence, shown by Lighthill (1978). Since the frequency of excited waves is higher than the Brunt-Vaisala frequency at the photosphere, the waves are not trapped, but running outward (cf. Unno et al 1979). 

Commercial LVDTs have a full range stroke from 0.1 to 80 mm with a sensitivity of about 25 to 1250 V/m depending upon the frequency of excitation and size of stroke. 

Suppose now that the energy difference between spin levels is evaluated for a particular nucleus in number of different compounds. It is found that this difference is very slightly (but, with good resolution, unmistakably) dependent on molecular environment. With the frequency of exciting radiation held constant, the protons in H2 absorb energy at a slightly different field strength than those in H20, and these, in turn,... 

Consider the following flow field over a flat plate that is excited simultaneously at the wall y = 0 and at the free stream y = Y) as shown in Fig.2.24, where Y is significantly larger than the boundary layer thickness. At the wall, a time-periodic blowing-suction device is placed at x = xq defined in a coordinate system fixed at the leading edge of the plate. The circular frequency of excitation of the wall device is lvq such that the transverse velocity oscillation at the wall is set up as. 

The RRE increases the intensity of some Raman-active vibrations by a factor of 10 -10. This effect occurs when the excitation-laser frequency is chosen in such a way that it crosses the frequencies of excited electronic states and resonates with... 

Now we turn to a discussion of the properties of excitons in layered molecular structures (1). First we consider the properties of excitations at the boundary of an anthracene crystal with the vacuum. Of course, this is a particular case of a boundary. However, this case has been investigated in many experiments and therefore can be considered as some kind of experimental confirmation of the approach we will use in our more general discussion. It can be considered now as well-established that the 2D exciton state - the lowest electronic excitation of the outermost monolayer of the anthracene crystal - is blue-shifted by 204 cm-1 with respect to the bottom of the exciton band in the bulk. Thus, the frequency of this electronic transition in the first monolayer lies between the bulk value of the exciton frequency and the frequency of excitation in an isolated molecule because the value of this molecular frequency in anthracene is blue-shifted by 2000 cm-1 with respect to the frequency of bulk excitation (see Fig. 9.1). 

A majority of work has been based on the assumption that the fluid motion is one-dimensional. With this simplification the governing equations are similar to those for an electrical transmission fine and for the long wavelength response of an elastic tube containing fluid. The equation for the pressure p in a tube with constant cross-sectional area A and with constant frequency of excitation is ... 

A few versions of CC theory have been developed for treating excited states. One such version, the equation-of-motion (EOM) CCSD, has given very good results for vertical excitation energies. Analytic gradients for the EOM-CCSD method are available, allowing calculation of geometries and vibrational frequencies of excited states. For details see R. J. Bartlett in Yarkony, Part II, Chapter 16, Section 9. 

Piezoelectric materials of thicknesses of 1 mm or more require applied voltages in excess of 100 V to reach maximum strain, depending on the frequency of excitation and the nature of the... 

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