Design - intersection

The method discussed in this chapter allows, in principle, the detection of all conical intersections connecting the ground with the excited state. Assuming that photochemical products are mainly formed through conical intersections, it therefore provides a means to design selection rules for photochemisby. 

Having two consecutive states j and () + 1), the two form the conical intersection to be designated as Cj as shown in Figure 4, where Nj conical intersection are presented. 

In case of three conical intersections or more, a contour that surrounds Cj and Cj. but not the in-between conical intersections will be designated as F j. Thus, for example, Fi surrounds Cj and C3 but not C2 (see Fig. 5d). 

Figure 12, Results for the C2H molecule as calculated along a circle surrounding Che 2 A -3 A conical intersection, The conical intersection is located on the C2v line at a distance of 1,813 A from the CC axis, where ri (=CC distance) 1.2515 A. The center of the circle is located at the point of the conical intersection and defined in terms of a radius < . Shown are the non-adiabatic coupling matrix elements tcp((p ) and the adiabatic-to-diabatic transformation angles y((p i ) as calculated for (ii) and (b) where q = 0.2 A (c) and (d) where q = 0.3 A (e) and (/) where q = 0.4 A. Also shown are the positions of the two close-by (3,4) conical intersections (designated as X34).

It should be noted that a log-log plot condenses the data considerably and that the transition between a first-power and a 3.4-power dependence occurs over a modest range rather than at a precise cutoff. Nevertheless, the transition is read from the intersection of two lines and is identified as occurring at a degree of polymerization or molecular weight designated n, or, respectively. 

Liquid helium-4 can exist in two different liquid phases liquid helium I, the normal liquid, and liquid helium II, the superfluid, since under certain conditions the latter fluid ac4s as if it had no viscosity. The phase transition between the two hquid phases is identified as the lambda line and where this transition intersects the vapor-pressure curve is designated as the lambda point. Thus, there is no triple point for this fluia as for other fluids. In fact, sohd helium can only exist under a pressure of 2.5 MPa or more. 

Once the design recovery for an absorber has been established, the operating curve can be constructed by first locating the point X9, y2 ou the diagram. The intersection of the horizontal hue corresponding to the inlet gas composition yi with the equilibrium curve y° = F x)... 

Crystallizers with Fines Removal In Example 3, the product was from a forced-circulation crystallizer of the MSMPR type. In many cases, the product produced by such machines is too small for commercial use therefore, a separation baffle is added within the crystallizer to permit the removal of unwanted fine crystalline material from the magma, thereby controlling the population density in the machine so as to produce a coarser ciystal product. When this is done, the product sample plots on a graph of In n versus L as shown in hne P, Fig. 18-62. The line of steepest ope, line F, represents the particle-size distribution of the fine material, and samples which show this distribution can be taken from the liquid leaving the fines-separation baffle. The product crystals have a slope of lower value, and typically there should be little or no material present smaller than Lj, the size which the baffle is designed to separate. The effective nucleation rate for the product material is the intersection of the extension of line P to zero size. 

Locating now in their respec tive scales on Nomograph 4 the design factor (from Nomograph 3) and the calculated equivalent lengm, draw an extended straight line to intersect the pivot line in the center. Now connect this point in the pivot line with the solids-ratio scale (from Nomograph 2), and read the system ressure loss. 

It is possible for some materials to produce an FFplot having no intersection with the j/curve. This inmcates that a different hopper-bin design is needed or that the material cannot be made to flow. Figure 21-23 shows FF cuiwes for several materials. 

Upon developing the. system eurve, the pump eurve will always intersect the. system curve, it doesn t matter about the pump design. We ll. see this later in Chapter 8. 

For each q and q risk value and the Severity Rating (S), a level of design acceptability is determined from where these values intersect on the Conformability Map. The symbols, relating to the levels of design acceptability, are then placed in the nodes of the Conformability Matrix for each variability risk which the failure mode is directly dependent on for the failure to occur. Once the level of design acceptability has been determined, it can then be written on the Conformability Matrix in the Comments section. Cpi values predicted or comments for suppliers can be added too, although predicted Cp values can also be written in the variability risks results table. 

Reading the intersection of 3.45 vs. 2.08 shows that for either weep point curve, the weep point is well below the ralues for operation, so this design not near the weep point... 

Figure 12-143 shows the individual static pressure curve Pf and total pressure curve Pff If pressure losses between the two fans are neglected (and they should he very low for good design), the combined total pressure curve is twice the value of curve Pft, 2 Pff The new operating static pressure also should be twice the individual total pressure value minus the velocity pressure, 2 p — p for identical fans, the new operating static pressure is equal to 2 p + Pf. The operation of the series fans will be along the system resistance curve, and the resultant point of operation will be at the intersection of the system curve with the curve for (2 pa — Pfv). 

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