Cylinders array

Ruland, W. Smarsly, B. 2005. SAXS of self-assembled nanocomposite films with oriented two-dimensional cylinder arrays An advanced method of evaluation. J. Appl. Cryst. 38 78-86. 

The SAXS intensity profile is a product of the cylinder form-factor for the individual pores and a two-dimensional structure factor for the disordered array of parallel channels. The general intensity profile for an assembly of parallel pores oriented at an angle to the incident beam is very complex, and no general analytic expression for the intensity distribution for any orientation of a defined cylinder array has yet been derived. Consequently, a full analytical interpretation of the data is not yet possible. Quantitative data can best conveniently be extracted by studying radial summations of the two-dimensional SAXS data, summing the intensity values around the ring [15]. 

White, B.L., and Nepf, H.M. (2003) Scalar transport in random cylinder arrays at moderate Reynolds number, J. Fluid Mech. 487, 43-79. 

Slab Cylinder-Array Experimental Data, Grover Tuck, Harold E. Clark (Dow-Colo)... 

The detection of Hquid crystal is based primarily on anisotropic optical properties. This means that a sample of this phase looks radiant when viewed against a light source placed between crossed polarizers. An isotropic solution is black under such conditions (Fig. 12). Optical microscopy may also detect the Hquid crystal in an emulsion. The Hquid crystal is conspicuous from its radiance in polarized light (Fig. 13). The stmcture of the Hquid crystalline phase is also most easily identified by optical microscopy. Lamellar Hquid crystals have a pattern of oil streaks and Maltese crosses (Fig. 14a), whereas ones with hexagonal arrays of cylinders give a different optical pattern (Fig. 14b). 

Fig. 14. A sample of a lamellar liquid crystal between crosses polarized in an optical microscope gives a pattern of "oily streaks" and Maltese crosses (a) while the Hquid crystal consisting of an array of cylinders shows the characteristic sectional pattern (b).

A variation on the exact soiutions is the so-caiied seif-consistent modei that is explained in simpiest engineering terms by Whitney and Riiey [3-12]. Their modei has a singie hollow fiber embedded in a concentric cylinder of matrix material as in Figure 3-26. That is, only one inclusion is considered. The volume fraction of the inclusion in the composite cylinder is the same as that of the entire body of fibers in the composite material. Such an assumption is not entirely valid because the matrix material might tend to coat the fibers imperfectiy and hence ieave voids. Note that there is no association of this model with any particular array of fibers. Also recognize the similarity between this model and the concentric-cylinder model of Hashin and Rosen [3-8]. Other more complex self-consistent models include those by Hill [3-13] and Hermans [3-14] which are discussed by Chamis and Sendeckyj [3-5]. Whitney extended his model to transversely isotropic fibers [3-15] and to twisted fibers [3-16]. 

Another important parallel /3-array is the eight-stranded parallel j8-barrel, exemplified in the structures of triose phosphate isomerase and pyruvate kinase (Figure 6.30). Each /3-strand in the barrel is flanked by an antiparallel a-helix. The a-helices thus form a larger cylinder of parallel helices concentric with the /3-barrel. Both cylinders thus formed have a right-handed twist. Another parallel /3-structure consists of an internal twisted wall of parallel or mixed /3-sheet protected on both sides by helices or other substructures. This structure is called the doubly wound parallel j8-sbeet because the structure can be... 

FIGURE 10.37 Gap Juoctioos consist of hexameric arrays of cylindrical protein subunits in the plasma membrane. The subunit cylinders are tilted with respect to the axis running through the center of the gap Junction. A gap Junction between cells is formed when two hexameric arrays of subunits in separate cells contact each other and form a pore through which cellular contents may pass. Gap Junctions close by means of a twisting, sliding motion in which the subunits decrease their tilt with respect to the central axis. Closure of the gap Junction is Ca -dependent. 

Milton, GW McPhedran, RC McKenzie, DR, Transport Properties of Arrays of Intersecting Cylinders, Applied Physics 25, 23, 1981. 

Perrins, WT McKenzie, DR McPhedran, RC, Transport Properties of Regular Arrays of Cylinders, Proceedings of the Royal Society of London Series A 369, 207, 1979. 

Tomadakis, MM Sotirchos, SV, Transport Properties of Random Arrays of Freely Overlapping Cylinders with Various Orientation Distributions, Journal of Chemical Physics 98, 616, 1993. 

Some virus particles have their protein subunits symmetrically packed in a helical array, forming hollow cylinders. The tobacco mosaic virus (TMV) is the classic example. X-ray diffraction data and electron micrographs have revealed that 16 subunits per turn of the helix project from a central axial hole that runs the length of the particle. The nucleic acid does not lie in this hole, but is embedded into ridges on the inside of each subunit and describes its own helix from one end of the particle to the other. 

The reactors are cylindrical in shape and can carry up to 30 mg of resin. Polymer sieves at the top and bottom of the cylinders serve for liquid feed and withdrawal. The array of reactors is attached to a capillary system allowing feed to either columns or rows. This distribution system is said to provide uniform charges to the various reactors. A specific detail of the reaction system is that mixing is achieved by pneumatic actuation using a fluoropolymer membrane (Figure 4.36). 

Measurements on arrays of horizontal cylinders were reported by Smith and Wragg (SI5a). 

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