Time as a Parameter

When used in the time-invariant mode (i.e., in equilibrium), it is a first-order chemical sensor that can yield qualitative and quantitative information based on the LSER paradigm about composition of the vapor mixtures (Fig. 10.13). By acquiring the data in the transient regime, it becomes a second-order sensor and in addition to the composition, information about diffusion coefficients in different polymers is obtained. This is then the added value. It is possible only because the model describing the capacitance change included diffusion. In spite of the complexity of the response function, a good discrimination and quantification has been obtained. 

Another example of a transient array is the set of microelectrodes on which cyclic voltammograms are recorded and a suitable pattern recognition technique is used to analyze it. Clearly, the boundaries of information acquisition can be greatly expanded by the inclusion of time and by careful analysis of the transient signals. 

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Let us assume that initially a particle at point x has the velocity v(x). After a time t it arrives at the point x + tv(x). We thus obtain a mapping of three-dimensional space onto itself (a point x corresponds to a point x + tv(x)) which depends on the time ( as a parameter. 

Price L. C. (1983) Geologic time as a parameter in organic metamorphism and vitrinite reflectance as an absolute paleogeothermometer. J. Petrol. Geol. 6, 5-38. 

The concentration profile expected for a system at one-half of the mass-transfer-limited current and for a concentration perturbation of 20 percent at the interface (see equation (11.44)) is presented in Figure 11.5 with dimensionless time as a parameter. At the higher frequency, the propagation of the disturbance away from... 

Figure 11.4 Oscillating concentration as a function of position with time as a parameter for a finite stagnant diffusion layer a) K=100 b) K=l.

Correlations proposed in the Bubble-Tray Design Manual4 may be used for the prediction of nG and n, for binary mixtures. These equations may be used to estimate the number of transfer units for multicomponent mixtures as shown by Graham et al.18 For the prediction of na, Eq. (2) on p. 27 of the Manual4 may be used for the prediction of n, the correlation given by Eq. (9) on p. 34 is available this correlation contains the liquid contact time as a parameter, which may be computed by use of Eq. (9) on p. 35 the liquid holdup may be estimated by use of Eq. (10) on p. 35. For sieve trays, which are not treated in the Manual,4 a correlation recommended by Gerster et al.15 has been presented by Smith.31... 

Another option in analysis kinetics of complex reactions is to separate activity from selectivity and to eliminate time as a parameter in the system of differential equations. 

Consider an operator A that contains the time as a parameter. We are interested in how the average value of the property A changes with time, and we have... 

The mutation frequency from five separate trials with 0.1 ml of 10% DMNA was 1.3 X 10" the lowest concentration giving a positive response was 20-50 mg/kg. When the MF after one injection of 10% DMNA was determined with time as a parameter, the maximal effect was noted at 120 min. Figure 2 is the dose-response curve found after a single oral administration of DMNA either in saline or ethanol. The organisms were recovered 180 min after treatment. 

From the data, there appears to be an ideal reaction time, between 0.1 and 2.1 h, where the toluene concentration is maximized. Using this insight, Sam carries out a series of additional experiments, attempting to isolate the exact reaction time that maximizes toluene concentration. In effect, her approach is to use reaction time as a parameter to find the maximum toluene concentration. 

I.e., depend on time (as a parameter) in such a way that the level of stress (or tension) decreases in time when the strain is held fixed, and each (of the possibly several) values of strain corresponding to a given fixed level of stress increases in time. 

The X dependence of this function has a form similar to g(x,w) shown in Fig. 6.2. In the present case the curves would be drawn for fixed values of time as a parameter. At small values of n(x,0 would show a sharply peaked form much like the shape of (x,mo). This curve would represent the spatial distribution of neutrons soon after their release from the source plane at x = 0. As t increases, the density function n(x,0 flattens much like the curves for Wi, U2, etc., of Fig. 6.2, indicating that as time progresses the neutrons wander farther from the source plane and tend to spread more evenly throughout the medium. One can also sketch from Eq. (6.32) a density-time function for given x analogous to the curve of Fig. 6.3. Such a curve would show how the density at a specified station would vary as the initial neutron burst passes by. In this case the interpretation of the curve would be as follows At short times after the burst, the neutrons have not yet had time to reach point x, and therefore the density would be low very long after the burst, the neutron density has fallen everywhere because of spreading out and absorption. Thus from the viewpoint of an observer at x, a pulse of neutrons passes sometime after the initial burst at the source. The time at which the maximum neutron density occurs at x is... 

During the spinning process, the polymer is subjected to an intense flow and to strong shear stresses, which can appreciably modify crystallization behaviour. The various studies available show an acceleration of crystallization under flow (Somani et al, 2000). During shear tests carried out before the isothermal crystallization of polypropylene, Lagasse and Maxwell (1976) highlighted the existence of a critical shear rate, beyond which the induction time decreases when the shear rate increases, the time before crystallization decreases under these conditions. However, certain studies (Vleeshouwers and Meijer, 1996) show that the use of the induction time as a parameter for the measurement of crystallization acceleration is not necessarily relevant. 

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