Signaling problem

Figure 2.21 The solution of the signal problem at the indicated Reynolds numbers, for the same circular frequency. Note that the local solution components in all the cases are the same.

For this case, the Bromwich contours have to be traced simultaneously in both the a— and the u>— plane. The choice of Bromwich contour in the u>— plane is not difficult, because in choosing it, one has to satisfy the causality requirement. However, the choice of Bromwich contour in the wave number plane remains as difficult as before for the signal problem. 

Figure 2.23 Comparison of solutions obtained by full receptivity analysis (solid line) and signal problem analysis (dotted line)- at the indicated heights.

Presented time accurate solution can be termed appropriately as the correct receptivity solution, as compared to its idealization in the signal problem. Later on, the results of this solution process is considered to look at the cases of spatially stable systems , those actually admit spatio-temporally growing wave-fronts-as given in Sengupta et al. (2006, 2006a). What is apparent for all spatially unstable cases is that there are no differences between the signal problem and the actual time-dependent problem-as two solutions shown in Fig. 2.23 match up to a certain distance-with the streamwise distance over which the match is seen stretches with time. 

Both the type of receptivity analyses (signal problem and full time dependent problem) provide the local solution in the neighbourhood of the exciter, but a forerunner- preceding the asjmiptotic solution is present only for the full time analysis. For spatially unstable system one cannot see a clear demarcation line between the asymptotic solution from the forerunner-with one merging smoothly into the other. 

Other combinations may reveal trends in particrrlar sitrrations. Productivity measures plotted over time can show trends in utilization of the energy resource relative to a baseline that can signal problems or show progress in energy reduction. 

A high degree of worker involvement is important in a JIT facility. The workers initiate many actions such as turning on andon lights when there are problems. These lights are used by workers to signal problems. 

The regeneration air exhaust temperature can signal problems in the dryer. For instance, if the exhaust temperature climbs almost immediately to a level approaching the regeneration inlet temperature of 425°F, it indicates that there is no adsorbed moisture in the desiccant. This condition will result if... 

Smart Materials. Smart materials are materials that react in ways appropriate to the stimulus or situation they encounter. Combining smart materials with nanoscale materials would, for example, enable scientists to create drugs that would respond when encountering specific viruses or diseases. They could also be used to signal problems with other systems, like nuclear power generators or pollution levels. 

Since the saturation Si (x,t) (following Whitham s solution to the signaling problem) is a step function in the x direction whose hump moves at the shock velocity, the pressure gradient in Equation 11-35 takes on either of two constant values, depending on whether Sj equals or S locally. Thus, on either... 

As discussed, we can expect shockwaves and steep saturation discontinuities to form in time, depending on the exact form and values of our fractional flow functions and initial conditions. We will assume that the particular functions do lead to piston-like shock formation very close to the borehole. The shock boundary value problem just stated can be solved in closed form, and, in fact, is the petroleum engineering analogue of the classic nonlinear signaling problem (Pt -I- c(p) Px = 0, p = po for X > 0, t = 0, and p = g(t) for t > 0, x = 0) discussed in the wave mechanics book of Whitham (1974). 

Sn. As a result, all three are relatively easy to study, except where long relaxation times or the null signal problem make for difficulties. Therefore, the relevant NMR literature is extensive. In the three years 1978-80, Si, Sn, and Pb proved to be the 7th, 18th, and 26th most popular nuclei, respectively, for chemical NMR studies, with at least 85, 28, and 9 publications, respectively (including solid state studies). There seems to have been only one publication (6) involving Ge (measured via the INDOR technique) in the same period, and there do not appear to have been any in 1981. 

Based on the small-signal response of RuOj capacitors, it is possible to estimate their performance, assuming that no large-signal problems arise (such as concentration polarization). In Fig. 18, aregion of expected performance is shown for devices based on RuOj. The calculation included measured pore resistance (based on the data in Ref. 74) and the weight of all materials except for the package. A factor of 2 - 3 reduction... 

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