Transverse spacing

FIG. 6-44 Friction factors vs. transverse spacing for single row of tubes. (From Boucher and Lapple, Gbem. Eng. Prog., 44,117 [1.94S].)... 

For the sake of simplification, let us regard a steady-state reaction with constant area for mass transport (A = constant) and let us use the Cartesian coordinate (p = — 1), in the following. Thus, Equation 14.2 can be obtained by rewriting of Equation 14.1, as follows (y is here the transverse space coordinate, perpendicular to the membrane interface) ... 

What fraction of the total volume of the fibril is occupied by the filaments is a controversial matter. Apart from the uncertainty as to how much of the transverse spacing of 115 A. is taken up by the filament and how much is interstitial space, there is no agreement as to the extent to which the fibril is filled by bundles of filaments at all. Draper and Hodge (1949) regard the fibril as a sort of tube of which only a thin wall contains the axially aligned filaments (c/. Pease and Baker, 1949). This view is based on the excellent electron optical transparency, which makes it possible to distinguish each individual filament even in relatively broad fibrils. Other authors assume either definitely (Rozsa et al., 1950) or tentatively (Hall et al., 1946 Hoffmann-Berling and Kausche, 1950) that the whole cross-section is occupied by filaments. 

Figure 1. (a) A random walk in d dimensions with 2 as the variable along the contour of the polymer i.e. giving the location of the monomers, (b) Directed polymer on a square lattice. A polymer as of (a) can be drawn in d -I-1 dimensions. This is like a path of a quantum particle in nonrelativistic quantum mechanics, (c) A situation where both the transverse space (r) and z are continuous, (d) The directed polymers on a hierarchical lattice. Three generations are shown for 4 bonds, (e) A general motif of 26 bonds. 

By definition, a directed polymer is defined in D dimensions out of which one direction is special that represents the sense of direction of the polymer. It is then useful to show that explicitly by writing D = d + 1 where d is the dimension of the transverse space. One may consider various possible models of the underlying space as shown in Fig. 1. 

The last attribute of tire electromagnetic field we need to discuss is wave polarization. The nature of tire transverse field is such tliat tire oscillating field disturbance (which is perjDendicular to tire propagation direction) has a particular orientation in space. The polarization of light is detennined by tire time evolution of tire direction of tire electric field... 

A special coil configuration is used to heat thin strips of metal that caimot be heated efficiently with a coil that encircles the load, as the strip thickness is small compared to the depth of penetration. The transverse flux induction coil is positioned on either side of a strip to produce a uniformly heated strip with good efficiency in a much smaller space than conventional radiant or convective strip heating furnaces (6). 

Fine, short, cracklike pits run transversely across the apex of many corrugations on the stainless sheets (Figs. 2.24 and 2.25). The corrosion sites originate at the apex of the corrugations at small circular discolorations, spaced apart exactly the peak-to-peak distance between corrugations. All cracklike pits are aligned in the same direction, regardless of their locations on the plate. 

We shall call an amplitude ( ), which satisfies Eq. (9-516), a transversal amplitude.20 We can summarize the above statements as follows in momentum space, a one-photon amplitude u(k) is defined on the forward light cone, i.e., for Jc2 = 0, k0 > 0, and satisfies the subsidiary... 

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