Broad frequency

A novel optimization approach based on the Newton-Kantorovich iterative scheme applied to the Riccati equation describing the reflection from the inhomogeneous half-space was proposed recently [7]. The method works well with complicated highly contrasted dielectric profiles and retains stability with respect to the noise in the input data. However, this algorithm like others needs the measurement data to be given in a broad frequency band. In this work, the method is improved to be valid for the input data obtained in an essentially restricted frequency band, i.e. when both low and high frequency data are not available. This... 

An alternative perspective is as follows. A 5-frmction pulse in time has an infinitely broad frequency range. Thus, the pulse promotes transitions to all the excited-state vibrational eigenstates having good overlap (Franck-Condon factors) with the initial vibrational state. The pulse, by virtue of its coherence, in fact prepares a coherent superposition of all these excited-state vibrational eigenstates. From the earlier sections, we know that each of these eigenstates evolves with a different time-dependent phase factor, leading to coherent spatial translation of the wavepacket. 

Electrochemical impedance spectroscopy (EIS) in a sufficiently broad frequency range is a method well suited for the determination of equilibrium and kinetic parameters (faradaic or nonfaradaic) at a given applied potential.268,269 EIS has been used to study polycrystalline Au, Cd, Ag, Bi, Sb, and other electrodes.152249 270-273... 

From a theoretical perspective, the object that is initially created in the excited state is a coherent superposition of all the wavefunctions encompassed by the broad frequency spread of the laser. Because the laser pulse is so short in comparison with the characteristic nuclear dynamical time scales of the motion, each excited wavefunction is prepared with a definite phase relation with respect to all the others in the superposition. It is this initial coherence and its rate of dissipation which determine all spectroscopic and collisional properties of the molecule as it evolves over a femtosecond time scale. For IBr, the nascent superposition state, or wavepacket, spreads and executes either periodic vibrational motion as it oscillates between the inner and outer turning points of the bound potential, or dissociates to form separated atoms, as indicated by the trajectories shown in Figure 1.3. 

Figure 9.7. Noise content of a fiberoptic oxygen sensor signal (a) in the time and (b) in the frequency domains. Time domain signals require broad frequency bandwidths. Frequency domain signals require very limited-frequency bandwidths. Noise is reduced by band limiting the signal, an advantage of frequency domain methods.

We showed in the preceding section that for solids with strong vibrational bands the position of features in absorption spectra can be shifted appreciably in going from the bulk to particulate states. Metallic particles can deviate even more markedly from the behavior of the bulk parent material they can have absorption features over broad frequency regions where none appear in the bulk. For a simple metal—one that is well described by the Drude formula... 

The index n is a small integer, n = 0, 1,. .. Because of the nearly exponential fall-off of typical spectral functions, these integrals do exist. An evaluation of spectral moments is possible if good measurements over a sufficiently broad frequency band exist. (We note that units of spectral moments specified elsewhere sometimes differ from those implied here, mainly because angular frequency, a)nda), is often substituted for frequency in wavenumbers, v" dv.)... 

In order to gain a direct experimental approach to probe the internal conversion of P, LIOAS was further developed to afford time-resolved measurements. For this purpose / -polyvinylidene difluoride foil was introduced [81] as a broad-frequency band piezoelectric detector—instead of the previously used ceramic transducers—which permitted for the first time the... 

Stretching frequencies characteristic of the most important types of bonds found in organic molecules are given in Table 9-2. You will notice that the absorption band for each bond type is described by its position within a more or less broad frequency range and. by its shape (broad, sharp) and intensity (strong, medium, weak). 

Figure 15.6 shows the influence of pressure on the dielectric response of pmn [14], The broad frequency-dependent peaks and the frequency dispersion in both s and e" are the characteristic signatures of the rl state. It is seen that pressure shifts the peaks to lower temperatures and suppresses e and e" in the high temperature phase. The suppression of e"(T) is mostly due to the suppression of e T) as e"(T) = e (T) tan<5(T), where tan <5 represents the dielectric loss. These pressure effects are characteristic of ABO3 rls and are well understood [14],... 

The dilatational rheology of the poly(vinylacetate) monolayer onto an aqueous subphase has been studied between 1°C and 25°C by Monroy et al. [59], These authors have used the combination of several techniques. By this way, the exploration of a broad frequency range was possible. The relaxation experiments have shown multiexponential decay curves, whose complexity increases with decreasing the temperature. A regularization technique has been used to obtain the relaxation spectra from the relaxation curves and the dilatational viscoelastic parameters have been calculated from the spectra. The shapes of the relaxation spectra agree with the predictions of the theoretical model proposed by Noskov [100],... 

Johnson noise arises because the random thermal motion of electrons in an isolated resistor produces random fluctuations in voltage between its ends, covering a broad frequency band. It can be shown that... 

Broadband Dielectric Spectroscopy provides a direct experimental access to the molecular relaxations of polymers over a broad frequency and temperature range. It is also especially suitable for the investigation of thin polymer films, because it does not suffer sensitivity loses with decreasing sample amount. This technique does require a special sample preparation for thin films, because of the need to have metal electrodes and good electrical contacts at both interfaces. Spin-coating, one of the most commonly employed methods for the preparation of... 

As mentioned previously, the complex dielectric permittivity (g>) can be measured by DS in the extremely broad frequency range 10-6-1012 Hz (see Fig. 1). However, no single technique can characterize materials over all frequencies. Each frequency band and loss regime requires a different method. In addition to the intrinsic properties of dielectrics, their aggregate state, and dielectric permittivity and losses, the extrinsic quantities of the measurement tools must be taken into account. In this respect, most dielectric measurement methods and sample cells fall into three broad classes [3,4,91] ... 

In the series realization, consecutive segments of the reflected signal on an increasing time scale are registered and linked into a combined time scale. The combined response is then transformed using a running Laplace transform to produce the broad frequency spectra [112]. 

In solid state cross polarization the spin lock is obtained with a long, high power pulse, but for HOHAHA such a single, unmodulated pulse is not effective. Instead, the pulse cycle MLEV-16, as described in Section 9.6, or a variant with an additional pulse, MLEV-17, covers a sufficiently broad frequency range, much as in the broadband decoupling methods we discussed in Section 9.6. 

Figure 8 is a plot of the HOI data obtained with the DMTA. The data clearly overlap due to the relatively broad frequency range of operation of this device. The G data contains very little scatter, but there is moderate scatter in the loss factor data. 

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