Ring spirality

A versatile enumeration technique for fullerene cages was developed by Fowler and Manolopoulos [96,97,308]. They represent fullerenes by a ring spiral as fullerenes can be peeled like an orange—each face, after the first, borders its immediate predecessor, so a single continuous spiral is created. Some exceptional cases are, however, possible [302] like a tetrahedral fullerene with 380 atoms. 

All four equations have been used to count and construct fullerenes within the respective symmetry classes, and the tetrahedral construction in particular was central to the identification of a counterexample to the ring-spiral conjecture. The Gold-berg/Coxeter construction is demonstrably complete, though as the symmetry is lowered the number of parameters needed to specify the net increases and the removal of redundant codes becomes more difficult Nets for several further groups have been devised and the coding of threefold cylinders has been worked out in Exeter. As most fullerenes have no symmetry at all, the method does not offer a practical solution for horizontal enumeration of all fullerenes at given n. 

Vol. 51, P. Hansen, P. W. Fowler, and M. Zheng, Eds., American Mathematical Society, Providence, Rhode Island 2000, pp. 175-188. A Generalized Ring Spiral Algorithm for Coding Fullerenes and Other Cubic Polyhedra. 

Flow probes Doppler Electromagnetic Ultrasonic Isolated tissue preparations Arterial (rings, spiral strips, perfused) Veins (intacl/denuded endothelium)... 

Ring spiral distribution - Central borehole for internal air exchange - Ring-shaped melt distribution - Axial boreholes... 

Accretion disk A flattened ring of gas surrounding a normal star or compact object. Gas in the ring spirals onto the central object, which increases the mass of the accreting object and may generate X-rays via the conversion of gravitational potential energy to heat. 

Figure C3.6.8 (a) A growing ring of excitation in an excitable FitzHugh-Nagumo medium, (b) A spiral wave in tlie same system.

Amorphous or "plastic" sulfur is obtained by fast cooling of the crystalline form. X-ray studies indicate that amorphous sulfur may have a helical structure with eight atoms per spiral. Crystalline sulfur seems to be made of rings, each containing eight sulfur atoms, which fit together to give a normal X-ray pattern. 

For Raschig rings, Berl saddles, and spiral tile ... 

Application of Packing Coils and spirals are cut to form closed or nearly closed rings in the stuffing box. Clearance between ends should be sufficient to allow for fitting and possible expansion due to increased temperature or hquid absorption of the packiug while in operation. 

The spiral-wound type furnished with a sohd metallic ring on the outside to hmit gasket compression provides protection against blowout when used with raised facing. 

The small-spiral-large-sbaft type (Fig. ll-60b) is inserted in a solids-product line as pipe banks are in a fluid line, solely as a heat-transfer device. It features a thin burden ring carried at a high rotative speed and subjected to two-sided conductance to yield an estimated heat-transfer coefficient of 285 W/(m °C) [50 Btu/(h fU °F)], thereby ranking thermally next to the sheU-fluidizer type. This device for powdered solids is comparable with the Votator ol the fluid field. 

Rubber (straight) To 600 See Gasket Materials for properties. Mainly used for ring-type seals, although some types are available as spiral packings. 

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