S-shaped

For many reasons it may not be possible or desirable to drill a vertical well. There may be constraints because of the surface location. In the subsurface, multiple targets, the shape of the structure, faults, etc. may preclude a vertical well. Figure 3.14 shows some of the deviated we//trajectories freguently used in industry deviated with tangent to target, S-shaped and horizontal. 

In Fig. 2a, we compare the modulus of the normal component of the magnetic induction B (r) provided by the sensor and the one calculated by the model. Because of the excitation s shape, the magnetic induction B° (r) is rotation invariant. So, we only represent the field along a radii. It s obvious that the sensor does not give only the normal component B = but probably provides a combination, may be linear, of... 

In Section XVII-16C there is mention of S-shaped isotherms being obtained. That is, as pressure increased, the amount adsorbed increased, then decreased, then increased again. If this is equilibrium behavior, explain whether a violation of the second law of thermodynamics is implied. A sketch of such an isotherm is shown for nitrogen adsorbed on a microporous carbon (see Ref. 226). 

For T shaped curves, reminiscent of the p, isothemis that the van der Waals equation yields at temperatures below the critical (figure A2.5.6). As in the van der Waals case, the dashed and dotted portions represent metastable and unstable regions. For zero external field, there are two solutions, corresponding to two spontaneous magnetizations. In effect, these represent two phases and the horizontal line is a tie-line . Note, however, that unlike the fluid case, even as shown in q., form (figure A2.5.8). the symmetry causes all the tie-lines to lie on top of one another at 6 = 0 B = 0). 

Remember the units involved here For f they are length time for N, length and for t, time. Therefore the exponent is dimensionless, as required. The form of Eq. (4.24) is such that at small times the exponential equals unity and 6 = 0 at long times the exponential approaches zero and 0 = 1. In between, an S-shaped curve is predicted for the development of crystallinity with time. Experimentally, curves of this shape are indeed observed. We shall see presently, however, that this shape is also consistent with other mechanisms besides the one considered until now. 

The decrease in amorphous content follows an S-shaped curve. The corresponding curve for the growth of crystallinity would show a complementary but increasing plot. This aspect of the Avrami equation was noted in connection with the discussion of Eq. (4.24). 

If Fj = F2, with both values greater than unity, an S-shaped curve passing through the point (0.5, 0.5) would also result, but in this case reflected across the 45° line compared to item (3). 

Fig. 3. Typical nonionic amphiphile—oil—water—temperature phase diagram, illustrating (a) the S-shaped curve of T, M, and B compositions, (b) the lines of plait points, (c) the lower and upper critical end points (at and respectively), and (d) the lower and upper critical tielines.

Fig. 3. Passage of the adsorption wave through a stationary bed during the course of an adsorption cycle. The progressing S-shaped curves indicate the nonadsorbed vapor concentration by position in the bed at different time periods. represents the maximum permissible oudet concentration for release...

Volumetric heat generation increases with temperature as a single or multiple S-shaped curves, whereas surface heat removal increases linearly. The shapes of these heat-generation curves and the slopes of the heat-removal lines depend on reaction kinetics, activation energies, reactant concentrations, flow rates, and the initial temperatures of reactants and coolants (70). The intersections of the heat-generation curves and heat-removal lines represent possible steady-state operations called stationary states (Fig. 15). Multiple stationary states are possible. Control is introduced to estabHsh the desired steady-state operation, produce products at targeted rates, and provide safe start-up and shutdown. Control methods can affect overall performance by their way of adjusting temperature and concentration variations and upsets, and by the closeness to which critical variables are operated near their limits. 

The crystalliza tion resistance of vulcaniza tes can be measured by following hardness or compression set at low temperature over a period of time. The stress in a compression set test accelerates crystallization. Often the curve of compression set with time has an S shape, exhibiting a period of nucleation followed by rapid crystallization (Fig. 3). The mercaptan modified homopolymer, Du Pont Type W, is the fastest crystallizing, a sulfur modified homopolymer, GN, somewhat slower, and a sulfur modified low 2,3-dichlorobutadiene copolymer, GRT, and a mercaptan modified high dichlorobutadiene copolymer, WRT, are the slowest. The test is often mn near the temperature of maximum crystallization rate of —12° C (99). Crystallization is accelerated by polyester plasticizers and delayed with hydrocarbon oil plasticizers. Blending with hydrocarbon diene mbbers may retard crystallization and improve low temperature britdeness (100). 

Equations (8-23) and (8-24) can be multiphed together to give the final transfer function relating changes in ho to changes in as shown in Fig. 8-13. This is an example of a second-order transfer function. This transfer function has a gain R Ro and two time constants, R A and RoAo. For two equal tanks, a step change in fi produces the S-shaped response in level in the second tank shown in Fig. 8-14. 

The use of the Monte Carlo method in project appraisal was illustrated by Holland et al. [F. A. Holland, F. A. Watson, and J. K. Wilkinson, Chem. Eng., 81, 76-79 (Feb. 4, 1974)]. The cumulative-probability cui-ves of (DCFRR) and (NPV) can never be more accurate than the opinions on which they are based, and comparable accuracy can be obtained by the use of S-shaped cui ves with relatively small computational effort. 

S-Shaped Curves K. D. Tocher (The Ait of Simulation, rev. ed., English Universities Press, London, 1967) presented a comprehen-... 

In all such S-shaped curves the range of x is from —oo to so that... 

Powder Insulation A method of reahzing some of the benefits of multiple floating shields without incurring the difficulties of awkward structural complexities is to use evacuated powder insulation. The penalty incurred in the use of this type of insulation, however, is a tenfold reduction in the overall thermal effectiveness of the insulation system over that obtained for multilayer insulation. In applications where this is not a serious factor, such as LNG storage facihties, and investment cost is of major concern, even unevacuated powder-insulation systems have found useful apphcations. The variation in apparent mean thermal conductivity of several powders as a function of interstitial gas pressure is shown in the familiar S-shaped curves of Fig. 11-121. ... 

No industrially significant reaction has 3 > 0,3 (or with y = 20, and D/a = 1, 5 > 5) and only above this value are the interesting S-shaped curves possible. Of the three values of T, the effectiveness at one value of the Thiele modulus < >, the middle one is an artificial, non-existent solution. The two other values for T show the possibility of discontinuity inside the pellet. While this is possible, it is very unlikely to occur. 

The S -shaped flexible elements were required to keep the stiffness and stresses low, due to the relatively heavy rotor weight as evident by the finite element stress analysis shown in Figure 6-30. The wire EDM teehnology allows the produetion of sueh a damper deviee, whieh ean be easily designed with an offset to eompensate for the defleetion due to rotor weight. 

Assuming that the CESTR is operating at steady state, the rate of heat generation must equal the rate of heat removal from the reaetor. Plotting Qg as a funetion of T for fixed values of the other variables, an S-shaped eurve is obtained as shown in Eigure 6-19. 

For a known reactor and kinetics, and at a given feed temperature Tq, the intersection of the energy balance line with the S-shaped mass... 

If, on the other hand, a vapor cloud s explosive potential is the starting point for, say, advanced design of blast-resistant structures, TNT blast may be a less than satisfactory model. In such cases, the blast wave s shape and positive-phase duration must be considered important parameters, so the use of a more realistic blast model may be required. A fuel-air charge blast model developed through the multienergy concept, as suggested by Van den Berg (1985), results in a more realistic representation of a vapor cloud explosion blast. 

After a fragment has attained a certain initial velocity, the forces acting upon it during flight are those of gravity and fluid dynamics. Fluid-dynamic forces are subdivided into drag and lift components. The effects of these forces depend on the fragment s shape and direction of motion relative to the wind. 

Figure 6-9 shows Fhs and Fs plotted against pH, according to Eqs. (6-61) and (6-62), for a weak acid of p/c = 4.0. Because of their appearance such curves are called S-shaped or sigmoid curves. 

Just how fast can proteins move in a biological membrane Many membrane proteins can move laterally across a membrane at a rate of a few microns per minute. On the other hand, some integral membrane proteins are much more restricted in their lateral movement, with diffusion rates of about 10 nm/sec or even slower. These latter proteins are often found to be anchored to the cytoskeleton (Chapter 17), a complex latticelike structure that maintains the cell s shape and assists in the controlled movement of various substances through the ceil. 

Another selectivity question arises when molecules contain multiple reactive sites. If the relevant frontier orbital is delocalized over all of these sites, then the orbital s energy is useless as a guide to site selectivity . In this case, only the orbital s shape is important. 

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