Branch orientation

FIGURE7-1 Schematic of flow in daughter brandies of bifurcation model for steady inspiratory flow with flat profile in parent bran<. Velocity profiles in plane of bifurcation (—) and in normal plane (—) are indicated in right branch. Orientation of secondary flows and position of laminar boundary layer are shown in left branch. Redrawn wifo permisnon from Bdl. ... 

The dimensionless drag coefficient cd (in meteorological practice the usual factor of 1/2 is omitted) is treated as isotropic and includes the influence of leaf and branch orientation, since the quantity a is the one-sided plant area density (m2/m3), not the cross-section exposed to the wind. Here, U is the scalar wind speed, while ui is the velocity vector in the -direction. 

A branched alkyl group such as isopropyl exhibits a greater preference for the equato rial orientation than does methyl... 

Reaction (5.W) is interesting inasmuch as either the AA or BB monomer must be present to produce crosslinking. Polymerization of AB with only Aj- (or Bf) introduces a single branch point, but no more, since all chain ends are mis-oriented for further incorporation of branch points. Including the AA or BB molecule reverses this. The bb unit which accomplishes this in reaction (5.W) is underscored. 

All polymer molecules have unique features of one sort or another at the level of individual repeat units. Occasional head-to-head or tail-to-tail orientations, random branching, and the distinctiveness of chain ends are all examples of such details. In this chapter we shall focus attention on two other situations which introduce variation in structure into polymers at the level of the repeat unit the presence of two different monomers or the regulation of configuration of successive repeat units. In the former case copolymers are produced, and in the latter polymers with differences in tacticity. Although the products are quite different materials, their microstructure can be discussed in very similar terms. Hence it is convenient to discuss the two topics in the same chapter. 

Mechanical Properties. The principal mechanical properties are Hsted in Table 1. The features of HDPE that have the strongest influence on its mechanical behavior are molecular weight, MWD, orientation, morphology, and the degree of branching, which determines resin crystallinity and density. 

Syn- and anti-orientations are possible and there is evidence that the anti-orientation does not favor orbital overlap such an orientation is favored with larger branched-chain substituents. A C-nmr study found that the TT-electron density on the vinyl P-carbon is lower as the reactivity of the monomer increases (20). Methyl vinyl ether exists almost entirely ia the syn-stmcture, a favorable orbital overlap situation, and MVE for this reason is less reactive to both polymerization and hydrolysis (21). 

The unit was shut down, drained, and visually examined. Numerous branched cracks of the type shown in Fig. 9.21 were observed. Cracks were oriented longitudinally. 

Microstructural examinations revealed that branched cracks originated at shallow pit sites on the external surface. The pits, which may have formed during idle periods from differential oxygen concentration cells formed beneath deposits, acted as stress concentrators. The transverse (circumferential) crack orientation and the localization of cracks along just one side of the tube revealed that bending of the tube was responsible for the stresses involved. 

Pinhole perforations were discovered in the walls of chiller condenser tubes of an air-conditioning system. Close laboratory examination of the internal surfaces of affected tubes revealed distinct patches of small pits (Fig. 12.18) and pit sites aligned along longitudinal mandrel marks and fine scratches (Fig. 12.19). In some locations, transversely oriented pit sites that were aligned with the locations of the fins on the external surface branched off the primary longitudinal pit alignment (Fig. 12.20). 

MW and MWD are very significant parameters in determining the end use performance of polymers. However, difficulty arises in ascertaining the structural properties relationship, especially for the crystalline polymers, due to the interdependent variables, i.e., crystallinity, orientation, crystal structure, processing conditions, etc., which are influenced by MW and MWD of the material. The presence of chain branches and their distribution in PE cause further complications in establishing this correlation. 

Following the operating principle of the most commonly used universal joint, the input shaft and the output shaft both terminate in yokes that are oriented in mutually perpendicular planes. The branches of each yoke are pinned to a cross connector so that each yoke can pivot about its beam of the cross. This mechanism was employed in the sixteenth century by Italian mathematician Geronimo Cardano, who used it to maintain a shipboard compass in a horizontal plane, regardless of the movement of the ship. Consequently it is often called a Cardan joint. 

Fundamental research in pyrotechnics is published in the US in Combustion and Flame by the Combustion Institute, and in the UK in Combustion Science and Technology and in Fuel . Germany has the new, journal, Propellants and Explosives (German Chemical Society), which is the successor to the discontinued Explosivstoffe . A necessary caveat is that these journals are strongly oriented toward combustion or propulsion so that only rarely do they yield pyrotechnic information. Likewise, the various publications of the learned societies contain much data on thermodynamics, spectroscopy, and instrumental analysis which are useful in the study of pyrotechnics. In the USSR the situation is somewhat better as Physics of Combustion and Explosion (Fizika Gorenia i Vzryva) of the Siberian Branch Academy of Sciences USSR is exclusively oriented toward subjects of interest, as several scientific institutes are primarily devoted to research in pyrotechnics. The same authors do publish also, however, in the journals of the Academy of Science USSR (of which there are several) as well as in the corresponding journals of the academies of the various republics, so that the impression is created of a high level of activity... 

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

The envelope of the Stark structure of the rotator in a constant orienting field, calculated quantum-mechanically in [17], roughly reproduces the shape of the triplet (Fig. 0.5(c)). The appearance of the Q-branch in the linear rotator spectrum indicates that the axis is partially fixed, i.e. some molecules perform librations of small amplitude around the field. Only molecules with high enough rotational energy overcome the barrier created by the field. They rotate with the frequencies observed in the... 

Let us demonstrate that the tendency to narrowing never manifests itself before the whole spectrum collapses, i.e. that the broadening of its central part is monotonic until Eq. (6.13) becomes valid. Let us consider quantity x j, denoting the orientational relaxation time at ( = 2. If rovibrational interaction is taken into account when calculating Kf(t) it is necessary to make the definition of xg/ given in Chapter 2 more precise. Collapse of the Q-branch rotational structure at T = I/ojqXj 1 shifts the centre of the whole spectrum to frequency cog. It must be eliminated by the definition... 

In other words, the following description of the orientational relaxation spectrum is valid at such pressures when the Q-branch has already collapsed and starts to broaden. 

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