Conductivity Frequency

Frequency sweep studies in which G and G" are determined as a function of frequency (o)) at a fixed temperature. When properly conducted, frequency sweep tests provide data over a wide range of frequencies. However, if fundamental parameters are required, each test must be restricted to linear viscoelastic behavior. Figure 3-31... 

In this case the current density at any point in the medium depends on the distance from the source, and on the angle 9, that is, on geometric parameters only and it is directly proportional to the transmitter moment, conductivity, frequency and magnetic permeability. One can say that the actual distribution of the current density in a conducting medium could be described by Jq, if the effect of interaction between currents, that... 

Measurements in the only available substance have revealed well-aligned rolls in the whole conductive frequency range [30] similarly to case A (compare Fig. 11a with Fig. 4b), indeed with q J. n as predicted by the theory. The wavenumber scales as The calculations above provided a good quantitative agreement with experiments for both Udf) and qdf)-... 

Is there a preferential orientation of the mitotic poles of cell groups Is this linked with the electrical oscillations Are they in phase Is the orientation responsive to externally applied ac fields Care must be exercised here against making snap judgments and due regard must be taken of the inability of electric fields (ac or dc) to penetrate media effectively unless the conductivity-frequency interrelations are favorable. Only high-frequency fields can penetrate media of even low conductivity, for example. 

The conductivity increases at high frequency (>3 to 30 MHz, Debye-Falkenhagen effect). It takes approximately 0.1—1 ns to form an ionic atmosphere, and the time is dependent on the ion concentration. The literature is not clear as to the conductivity frequency dependence of electrolytes such as NaCl, but Cooper (1946) found no variations in the concentration range of 1—4 wt% and frequency range of 1—13 MHz. 

Figure 8.28 gives log G versus log G" plots for SI-Z at 80 °C, which were obtained by conducting frequency sweep experiments at every 30 min for the period of 8 h after the specimen had been quenched from 100 to 80 °C. In Figure 8.28 we observe... 

By increasing the probe diameter, we bring down tlie impedance point along the impedance curve with the same way as the electrical frequency or conductivity. We will describe only one type of probes, namely, the probe with ferritic circular section that we could qualify as punctual with an optimal sensibility. In order to satisfy these conditions, tests will be made to confirm these results by ... 

We showed that the impedance variation of low frequency probes is influenced by the coating depth. Consequently, the tempering increase and the surface processing decrease the permeability and the electrical conductivity. 

These equations are the coupled system of discrete equations that define the rigorous forward problem. Note that we can take advantage of the convolution form for indices (i — I) and (j — J). Then, by exciting the conductive media with a number N/ oi frequencies, one can obtain the multifrequency model. The kernels of the integral equations are described in [13] and [3j. 

The frequency correlation lowers environmental disturbances. The correlation provides an output proportional to the content of Aa at the reference signal fundamental frequency, the phase conelation gives the sign of Aa. Where the stress gradients are very steep in materials of high thermal conductivity being loaded at low frequencies, the SPATE signals are attenuated and a correction factor has to be introduced to take into account this effect. 

Measurements conducted on samples, made of other grades of steel have shown that the shift of frequency characferistics of the applied signal are closely connected with sizes of crystallite grains and may be applied for the determination of parameters of the material structure. 

Figure Al.3.30. Theoretical frequency-dependent conductivity for GaAs and CdTe liquids from ab initio molecular dynamics simulations [42].

Two major sources of ultrasound are employed, namely ultrasonic baths and ultrasonic immersion hom probes [79, 71]- The fonuer consists of fixed-frequency transducers beneath the exterior of the bath unit filled with water in which the electrochemical cell is then fixed. Alternatively, the metal bath is coated and directly employed as electrochemical cell, but m both cases the results strongly depend on the position and design of the set-up. The ultrasonic horn transducer, on the other hand, is a transducer provided with an electrically conducting tip (often Ti6A14V), which is inuuersed in a three-electrode thenuostatted cell to a depth of 1-2 cm directly facing the electrode surface. 

In the same section, we also see that the source of the appropriate analytic behavior of the wave function is outside its defining equation (the Schibdinger equation), and is in general the consequence of either some very basic consideration or of the way that experiments are conducted. The analytic behavior in question can be in the frequency or in the time domain and leads in either case to a Kramers-Kronig type of reciprocal relations. We propose that behind these relations there may be an equation of restriction, but while in the former case (where the variable is the frequency) the equation of resh iction expresses causality (no effect before cause), for the latter case (when the variable is the time), the restriction is in several instances the basic requirement of lower boundedness of energies in (no-relativistic) spectra [39,40]. In a previous work, it has been shown that analyticity plays further roles in these reciprocal relations, in that it ensures that time causality is not violated in the conjugate relations and that (ordinary) gauge invariance is observed [40]. 

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