Toroids

An electron prisin , known as an analyser or monochromator, is created by tlie field between the plates of a capacitor. The plates may be planar, simple curved, spherical, or toroidal as shown in Figure Bl.6.2. The trajectory of an electron entering the gap between the plates is curved as the electron is attracted to the positively biased (iimer) plate and... 

Esselink K, Smit B and Hilbers P A J 1993 Efficient parallel implementation of molecular dynamics on a toroidal network. I. Parallelizing strategy J. Comput. Phys. 106 101-7... 

Tt provides unsupervised (Kohonen network) and supervised (counter-propagation network) learning techniques with planar and toroidal topology of the network. 

Figure 10.1-2. A four-fold toroidal KNM map for 1 293 compounds obtained by using ihe 15 input descriptors high" means compounds v ilh high solubiiity where log S is in the range -2.82 to 1.58 "middle" means compounds with medium solubility where log 5 is in the range -7.21 to -2.83 low means compounds with low solubility where log S is in the range -11.62 to -7.22.

Cyclodextrins are macrocyclic compounds comprised of D-glucose bonded through 1,4-a-linkages and produced enzymatically from starch. The greek letter which proceeds the name indicates the number of glucose units incorporated in the CD (eg, a = 6, /5 = 7, 7 = 8, etc). Cyclodextrins are toroidal shaped molecules with a relatively hydrophobic internal cavity (Fig. 6). The exterior is relatively hydrophilic because of the presence of the primary and secondary hydroxyls. The primary C-6 hydroxyls are free to rotate and can partially block the CD cavity from one end. The mouth of the opposite end of the CD cavity is encircled by the C-2 and C-3 secondary hydroxyls. The restricted conformational freedom and orientation of these secondary hydroxyls is thought to be responsible for the chiral recognition inherent in these molecules (77). 

Fig. 4. The effect of temperature for Mng 6 Zng 3 Fe Fe on (a) initial magnetic permeabiUty, )J., measured on a polycrystalline toroid appHed as a core for a coil driven by a low (B <0.1 mT) ampHtude, low (10 kHz) frequency sinusoidal signal and (b) magnetocrystalline anisotropy constant, measured on a monocrystalline sphere showing the anisotropy/compensation temperature Tq and the Curie temperature, T. To convert joules to calories, divide by...

Fig. 2. Cutaway view of a simple toroidal field configuration.

This deleterious effect can be obviated by introducing additional components of magnetic field, causing the field lines to circumscribe the toms without ever closing on themselves. The net magnetic field is then composed of a major, or toroidal, field component produced by the current cods, plus a smaller poloidal component which gives the desired twist to the lines. Particle drifts weaken or nullify the harmful electrical field and the plasma no longer tends to move to the wads. 

ATC Adiabatic Toroidal Compiessoi Princeton Plasma Physics Laboratory (PPPL), Princeton, N.J. 

The native form of chromatin in cells assumes a higher order stmcture called the 30-nm filament, which adopts a solenoidal stmcture where the 10-nm filament is arranged in a left-handed cod (Fig. 5). The negative supercoiling of the DNA is manifested by writhing the hehcal axis around the nucleosomes. Chromatin stmcture is an example of toroidal winding whereas eukaryotic chromosomes are linear, the chromatin stmctures, attached to a nuclear matrix, define separate closed-circular topological domains. 

Most schemes that have been proposed to propel starships involve plasmas. Schemes differ both in the selection of matter for propulsion and the way it is energi2ed for ejection. Some proposals involve onboard storage of mass to be ejected, as in modem rockets, and others consider acquisition of matter from space or the picking up of pellets, and their momentum, which are accelerated from within the solar system (184,185). Energy acquisition from earth-based lasers also has been considered, but most interstellar propulsion ideas involve nuclear fusion energy both magnetic, ie, mirror and toroidal, and inertial, ie, laser and ion-beam, fusion schemes have been considered (186—190). 

Commercial bellows elements are usually hght-gange [of the order of (0.05 to 0.10 in) thick] and are available in stainless and other alloy steels, copper, and other nonferrons materials. Multi-ply bellows, bellows with external reinforcing rings, and toroidal contour bellows are available for higher pressures. Since bellows elements are ordinarily rated for strain ranges which involve repetitive yielding, predictable... 

As the size or the pressure goes up, curvature on all surfaces becomes necessary. Tariks in this category, up to and including a pressure of 103.4 kPa (15 Ibf/in"), can be built according to API Standard 620. Shapes used are spheres, ellipsoids, toroidal structures, and circular cylinders with torispherical, elhpsoidal, or hemispherical heads. The ASME Pressure Vessel Code (Sec. TII of the ASME Boiler and Pressure Vessel Code), although not required below 103.4 kPa (15 Ibf/in"), is also useful for designing such tanks. 

Calculation of Tank Volume A tank may be a sin e geometrical element, such as a cylinder, a sphere, or an ellipsoid. It may also have a compound form, such as a c inder with hemispherical ends or a combination of a toroid and a sphere. To determine the volume, each geometrical element usually must be calculated separately. Calculations for a full tank are usually simple, but calculations for partially filled tanks may be complicated. 

Spheres, spheroids, and toroids use steel or concrete saddles or are suppoi ted by columns. Some may rest directly on soil. Horizontal cyhndrical tanks should have two rather than multiple saddles to avoid indeterminate load distribution. Small horizontal tanks are sometimes supported by legs. Most tanks must be designed to resist the reactions of the saddles or legs, and they may require reinforcing. Neglect of this can cause collapse. Tanks without stiffeners usually need to make contact with the saddles on at least 2.1 rad (120°) of their circumference. An elevated steel tank may have either a circle of steel columns or a large central steel standpipe. Concrete tanks usually have concrete columns. Tanks are often supported by buildings. 

For turbines at Reynolds numbers less than 100, toroidal stagnant zones exist above and below the turbine periphery. Interchange of hq-uid between these regions and the rest of the vessel is principally by molecular diffusion. 

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