Parabolic taper

The crown profile dictates the type of formation for which the bit is best suited. They include the round, parabolic, tapered and flat crown used in hard to extremely hard formations, medium to hard formations, soft formations and for fracturing formations or sidetracks and for kick-offs, respectively. 

Fig. 5-5 Step-profile tapers, showing (a) a slowly-varying taper illuminated by a diffuse source and (b) a parabolic taper illuminated by an on-axis beam.

For an on-axis beam Og = 0, in which case Eqs. (5-58) and (5-59b) show that the minimum length parabolic taper is longer than the corresponding linear taper by a factor (po + p)/(Po — p) provided the taper angle is small and the fiber is weakly guiding. 

To ensure the integrity and stability of compounds used in HTS assays and to maximize the number of HTS screens, which can be performed with microgram quantities of compounds, all research sites at Roche use prealiquoted compound samples that are delivered to the HTS labs in sealed, ready-to-use sample plates . The sample plates contain aliquots of frozen millimolar compound solutions in water-free DMSO, 1 aL per well, corresponding to a small liquid droplet of approximately 1 mm diameter. The sample plate is a standardized, low-cost 384-well plate made from polypropylene with a tapered or parabolic well bottom forming a cavity for the small aliquot. This sample distribution concept for the HTS compound library is based on the following rationale ... 

The solids distribution profile may tend to be parabolic with thicker cakes near the bottom of the basket, tapering down toward the top, since the G-field is perpendicular to the force of gravity. This is especially true with fast-sedimenting solids that will settle toward the basket bottom before the slurry is fully accelerated by the basket. The coarser solids can settle toward the basket bottom, while the finer solids deposit preferentially toward the top. This can result in uneven filtration resistance in the cake, affecting the wash pattern and efficiency of the wash. In cases where this is a concern, a rotating feed cone may be better for even distribution, or a horizontal peeler centrifuge may be better suited to the application. 

Typically, a parabolic dish is fed from a horn as shown in Fig. 2.16, top, resulting in a tapered aperture distribution with an aperture efficiency r] < 1. This will produce a transmitting pattern with lower sidelobes, which might be highly desirable for many applications. However, as discussed in the previous section, it will also... 

Fig. 2.16 A parabolic antenna has a tapered aperture distribution and will therefore scatter more in the forward scattering direction than it absorbs. Thus, it is not an MSA even in the relaxed sense.

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