Time constant determination

Figure 9. Semi-log plot and relaxation time constant determination of data from Figure 8. The values of XI and X2 on the plot represent the points used to calculate the relaxation time constants.

The performance of the photomultiplier (representative of a very fast responding sensor even in terms of modern solid state devices) is shown in the lower curves and its performance is in complete contrast to that of the cadmium sulfide cell. The time constant, determined again from the slope of the log curve, was found to be only 40 milliseconds. Such a response time is generally acceptable for most GC and LC separations. Nevertheless in both fast GC and fast LC solutes can be eluted in less than 100 milliseconds in which case an... 

As noted above, step-scan FT-IR can provide a better time resolution than PA-IR spectroscopy for time-resolved studies, as well as full spectra at the desired resolution. On the other hand, its major limitation is that the phenomenon under study must be perfectly repeatable-information which often is not available before an experiment is carried out. Another problematic aspect to consider is that sufficient relaxation time must be allocated for the sample to return to its initial state between consecutive perturbations. Unfortunately, this parameter is also often not known a priori before the experiment is performed, and may risk artifacts appearing in the data. In contrast, a single perturbation is required in a PA-IR experiment to record the time-resolved data, eliminating the requirements of repeatability and an a priori knowledge of the relaxation time. PA-IR spectroscopy was used to assess directly the repeatability of the orientation/reorientation cycles for 5CB [27]. Table 13.1 shows the switch-on and switch-off time constants determined individually for a series of 300 consecutive reorientation cycles. As expected for this well-studied LC, the time constants did not evolve systematically as a function of the number of cycles. In this case, however, the repeatability was demonstrated experimentally and not only assumed, as is often necessary in step-scan studies. 

Weighting coefficients ao and ai might be related to the rate parameters of the surface chemical reaction. This relationship is not the subject of present study and will be analysed elsewhere. It is important to note that the time constants t in Equation (6) are proportional to the time constants determined by Equation (2). The fitting of the theory to the experiment was... 

Economics in process control, 3, 10-11, 15, 26, 532-34 Environmental regulations, 3 Equal-percentage valve, 254, 255 Equations of state, 57 Equilibria, 56, 78 chemical, 56 phase, 56-57, 71, 75, 78 Error criteria (see Time integral criteria) Euler s identities, 131-32, 149 Experimental modeling, 45, 656 frequency response techniques, 668 process identification, 657-62 time constant determination, 228, 232 Exponential function, 130 approximations, 215-16 Laplace transform, 130 z-transform, 592... 

Theoretical MRR based on equivalent electrical circuit model (Eq. (3.32)) is much more accurate compared to basic MRR model based on Eqn (3.21), as observed from Fig. 3.8. The experimental MRR is much less than the theoretical MRR based on Eqn (3.21). MRR based on equivalent electrical circuit model is perfectly valid over the whole range of frequency. At 2-MHz pulsed frequency, the experimental value of MRR is less than the theoretical MRR based on equivalent electrical circuit model by 4.7 pg and is less than theoretical basic MRR model by 54 pg. At a moderately low frequency of 0.217 MHz, the experimental value of MRR is less than the theoretical MRR based on basic MRR model by 90 pg, which is exceptionally high. This is due to the fact that the charging time constant determines the resolution of machining in low-frequency EMM. 

The characteristic time of the fluid is often taken to be the largest time constant describing the slowest molecular motions or else some mean time constant determined by linear viscoelasticity. The characteristic time may also be chosen as a time constant in a constitutive equation. The characteristic time for the flow is usually taken to... 

The form of the transmittance H(s) indicates that the time constant r is a decisive parameter for characterizing the inertial properties of the object (calorimeter). This also means that the value of the time constant determines the course of the output function, the character of which is approached more closely for either proportional or integrating objects. Simply, the values of r control the inertial, damping properties of the object. Different values of the function x(t), depending on the values of r, are responses to the same heat forcing (Fig. 2.13). 

Dielectric relaxation is somewhat limited in its application to the study of chemical processes because it reflects the reorientation of the dipole which occurs with a time constant determined by whole molecule motion rather than isomeric or chemical change. For chemical data to be obtained whole molecule motion has to be suppressed. 

The structural relaxation time T4 (the indices have been chosen for correspondence with previous results) decrease with rising concentration from 25 ms (70 mM) to 0.2 ms (300 mM) and the short time constant T3 decrease from 0.35 ms (70 mM) to 0.1 ms (250 mM). Therefore, they correspond well with the time constants determined hy dynamic electric hirefringence measurements. 

The time constant determines the personality of the response for a process or process element. 

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