Ideal Response

Thin-film ideal or Nemstian behavior is the starting point to explain the voltammetric behavior of polyelectrolyte-modified electrodes. This condition is fulfilled when (i) the timescale of the experiment is slower than the characteristic timescale for charge transport (fjD pp, with Ithe film thickness) in the film, that is all redox within the film are in electrochemical equibbrium at any time, (ii) the activity of redox sites is equal to their concentration and (iii) all couples have the same redox potential. For these conditions, anodic and cathodic current-potential waves are mirror images (zero peak splitting) and current is proportional to the scan rate [121]. Under this regime, there exists an analytical expression for the current-potential curve  

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Every accelerometer has a response curve of the type shown schematically in Figure 4-222. Instead of having an ideal linear response, a nonlinear response is generally obtained with a skewed acceleration for zero current, a scale factor error and a nonlinearity error. In addition, the skew and the errors vary with temperature. If the skew and all the errors are small or compensated in the accelerometer s electronic circuits, the signal read is an ideal response and can be used directly to calculate the borehole inclination. If not, modeling must be resorted to, i.e., making a correction with a computer, generally placed at the surface, to find the ideal response. This correction takes account of the skew,... 

Assume that the accelerometer has the ideal response shown in Figure 4-223, with a measurement range of 2 g (32.2 ft/s ). We want to measure 1 g, but the ambient vibration level is +3 g. In this case, the accelerometer s indications are shaved and the mean value obtained is not 1 g but 0.5 g. The maximum acceleration due to vibrations which are not filtered mechanically, plus the... 

True detector linearity is, in fact, a theoretical concept, and despite the claims by many manufacturers, LC detectors can only tend to exhibit this ideal response. As the linearity of the detector will determine the accuracy of the analysis, it is important to have some method for measuring detector linearity that can describe it in numerical terms. A method for linearity measurement was proposed by Scott and Fowlis (3), who assumed that for a nearly linear detector the response of the detector could be expressed by the following equation. 

Now we must specify the desired load response of the output. The ideal response would be to keep the output at zero, but this of course is not possible. The best that we could do would be to detect the error at the first sampling period and drive the process back to zero at the second sampling period. During the first sampling period, the system responds in an openloop manner to the load disturbance. So at t = Tj the output will be... 

Phil Kysor and I similarly developed a TRI to represent a subject s response to BZ. We combined changes in blood pressure (BP), heart rate (HR) and performance on Number Facility (NF), using a scale from 1- 9 for each variable. It helped us to compare responses to BZ given by various routes of administration. Eventually we could combine intravenous, intramuscular, oral, inhalation and percutaneous responses using the TRI as an indicator of relative effectiveness. Fig. 4 shows idealized response curves for various intensities of BZ response. 

Figure 4.6 Representation of the response surface of dependent variable y against design factor x and environmental factor z. x is the ideal response...

The ideal response value is represented by r, represents the mean response at a particular value of the product design factor (represented by the index x) calculated over the region of interest of the environmental factors (R ), so... 

The primary purpose of this filter is to add a delay to a pulse or data sequence. The use of the RC time constant allows this delay to be added to both the rising and the falling edge of the pulse. The ideal response... 

Constant Pattern Behavior In a real system the finite resistance to mass transfer and axial mixing in the column lead to departures from the idealized response predicted by equilibrium theory. In the case of a favorable isotherm the shock wave solution is replaced by a constant pattern solution. The concentration profile spreads in the initial region until a stable situation is reached in which the mass transferrate is the same at all points along the wave front and exactly matches the shock velocity. In this situation the fluid-phase and adsorbed-phase profiles become coincident. This represents a stable situation and the profile propagates without further change in shape—hence the term constant pattern. 

Figure 2.6 Idealized responses from the ganglion cells of the cat when stimulated with small spots of light. Some cells show an on-center surround response while others show an off-center surround response.

Scheme I. Concept of a two-terminal microsensor showing two possible idealized responses to a species L which binds to the indicator molecule M. A) The linear sweep voltammograms reveal a difference between the current peaks for oxidizing the reference molecule, R, and M or M-L. The position of the current peak along the potential axis, V, is variable and depends on the concentration of L. B) The linear sweep voltammograms reveal a decrease in amplitude for the current peak assigned to M and proportional growth of a new current peak assigned to M-L.

Beacause of the imperfections in mechanical and electrical devices, true linearity is a hypothetical concept and practical detectors can only approach this ideal response. It is therefore important that the analyst has some measure of linearity that is specified in numerical terms so that comparisons can be made between detectors and the proximity of the detector to true linearity understood. Fowlis and Scott [4] proposed a method of measuring detector linearity. They assumed that for a closely linear detector the response could be described by the... 

The deviation of the practical device from the ideal response depends on the ratio d/w. We will perform an analysis of Eq. (93) that will allow us to estimate the bandwidth of the PTR. In particular, we will investigate the influence of phase and amplitude errors on the achievable level of performance. A high Q resonator will probably be the bandwidth-limiting component in a practical resonator. Nevertheless, it is an important... 

The impedance response of electrodes rarely show the ideal response expected for single electrochemical reactions. The impedance response typically reflects a distribution of reactivity that is commonly represented in equivalent electrical circuits as a constant phase element (CPE). ° For a blocking electrode, the impedance can be expressed in terms of a CPE as... 

Describe in one or two sentences the ideal response from your readers. What would you like them to do or know after reading about your topic ... 

The complex convolution integral is reduced to a simple product and it is obvious that an excitation at a frequency f only results in a response at the same frequency. If, as in the case of gas—surface studies, the overall response is determined by a number of processes, then the one of interest may be extracted by deconvolution techniques, which are particularly simple in the frequency domain [53]. In particular, attenuation and phase shift of the signal produced by the flight time of molecules from the modulator to the detector and any non-ideal response of the detector may be taken into account [55]. 

Based on this requirement, one obtains the correlation shown in Table 22-4 between the interpellet Damkohler number and the critical value of the mass transfer Peclet number for ideal response. For interpellet Damkohler numbers between 100 and 500 [i.e., 100 < (1 interpellet) ( A, intrapeIlet) A, interpellet — ... 

The idea is easiest understood graphically in a case with 2 variables Fig. 1 depicts an ideal response surface the yield of a batch reactor with respect to the batch length in minutes and the reactor temperature in °C. The model is ideal in the sense that the response values are free from experimental error. We can see that first the simplex expands because the surface around the starting simplex is quite planar. Once the chain of simplexes attains the ridge going approximately from right, some of the simplexes are contracted, i.e. they shrink considerably. You can easily see, how a reflection would worsen the response (this is depicted as an arrow in the upper left panel). Once the chain finds the direction of the ridge. 

In operation the ideal response from the TDR signal will show a flat response at the impedance value of the Une. Comers, breaks, deviations in impedance due to stress, and their distance from the signal source should all recognizable features. Figure 4-3 illustrates a possible TDR response with several different kinds of seal anomalies. 

Fig. 5.26 (a) The ideal response of T, as a function of T for a pair of protons 0.1 nm apart. The numbers in parentheses denote the values of o>a/ ln) in megahertz, (b) The T relaxation times for the ( ) methylene and (O) methine carbon atoms of isotactic propylene, ((a) Reproduced from Nuclear Magnetic Resonance in Solid Polymers by V. J. McBrierty and K. J. Packer. Cambridge University Press, 1993 (b) reproduced by permission of IBM Technical Journals.)... 

If h(t) is the "ideal" response of a linear system to an impulse (i.e., an infinitely short pulse) excitation, and e(t) is an actual excitation waveform, then the observed response of the system is the convolution of h(t) with e(t) according to Equation 31. In general, the shape of the "ideal" response h(t) to an impulse excitation will not be obvious from the shape of the observed response f(t). 

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