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Basic Techniques for Capacitance and Impedance Measurements
Published in Jian V. Li, Giorgio Ferrari, Capacitance Spectroscopy of Semiconductors, 2018
Marco Carminati, Giorgio Ferrari
Impedance spectra can be displayed in two ways: in the Bode plot and in the Cole-Cole plot. As illustrated in Fig. 5.2, the Bode plot is composed of two separate plots: a log-log plot of the impedance magnitude as function of frequency (Fig. 5.2a) and a semi-log plot of the phase (Fig. 5.2b). The Cole-Cole is, instead, a single graph in the complex plane (where the sign of the imaginary axis is reversed, Fig. 5.2c). Each point corresponds to the apex of the impedance vector at a given frequency. As an example, in Fig. 5.2 the spectrum of a simple R||C impedance is shown. The magnitude is flat and equal to R up to the pole frequency (fp = 1/(2πRC)), above which it rolls off with a constant slope −20 dB/decade). Correspondingly, the phase starts from 0 (real resistance R at low frequency) and, after the pole, decreases reaching asymptotically −90° (the capacitor phase). The same spectrum has a semi-circular shape in the Cole-Cole complex plane. In DC (f = 0) the starting point is on the real axis at coordinate R (pure resistance). For increasing frequency the reactive component increases up to the maximum at the pole frequency. The use of the Bode plot is more common in the engineering community, while the Cole-Cole plot is mostly used in the electrochemistry and bio-sensing communities. From the point of view of information content, they are perfectly equivalent.
Analysis of well testing - well Pr2, Prušánky field
Published in Vladimir Litvinenko, Topical Issues of Rational Use of Natural Resources 2019, 2019
The outline of the study will be as follows: First of all, a brief insight to the underlying theory of pressure transient testing will be presented, followed by a summary of available information about geology, layer and fluid parameters. The study will also encompass distinct stages of analysing the data measured during the pressure build-up test, using the Weatherford’s PanSystem sw. This includes preparing pressure and rate data for analysis and using different graphs for data visualisation and interpretation such as type curves, log-log plot, semi-log plot, and test overview plot. Finally, simulation of the test behaviour using the interpreted reservoir and well parameters will be performed in order to check the validity of the interpretation.
Transient two-dimensional flow
Published in Mark Bakker, Vincent Post, Analytical Groundwater Modeling, 2022
In the example below, the top aquifer is unconfined so that the storage coefficient S0 represents the phreatic storage of the top aquifer. The head is computed and plotted in an observation well near the well (Figure 9.9). The head responds very quickly in the bottom aquifer, but it takes approximately one day before the head in the unconfined top aquifer starts to respond. The head in the bottom aquifer starts to go down again when the head in the top aquifer starts to go down. This delayed response of the water table can be seen especially well in a semi-log plot. For early times (in this case, for the first day), the head response is similar to a Hantush well, as the head in the top aquifer varies very little at early time.
The Rayleigh–Bénard convection in near-critical fluids: Influences of the specific heat ratio
Published in Numerical Heat Transfer, Part A: Applications, 2018
Yufeng Wei, Zhan-Chao Hu, Bin Chong, Jingyu Xu
In this section, we focus on the influences of γ during the convection-dominated stage. Figure 7 shows the evolution of average enstrophy Ω in the three cases. All of these curves start from an infinitesimal level. Exponential growths (representing by straight lines in the semi-log plot) are clearly seen from the curves, with different slopes for different cases. After the exponential growth, the flow enters a convection-dominated stage, featured by Ω fluctuating around a value denoted by Ωs. For different γ, Ωs is a constant value. These fluctuations are unavoidable because the turbulent convection is unsteady. Table 4 reports the slopes fitted from data in Figure 7, denoted by , at the exponential growth stage. It is shown that as γ is increased, the development of convection is decelerated. That is to say, driving a convection in the UBL is at the cost of slowing down the overall development of convection.