Tori structures

In low temperature states like this, a kinetic effect would also be important for the generation of multiple tori structures. (See [32] for more details.)... 

On the other hand, if the peripheral gold atoms have a ring or torus structure for [AujeLje i]B+, the number of valence electrons for a filled shell should be 12 + 4. The complexes [Au8L7]2+ (100 valence electrons) and [Au9L8]3+ (112 valence electrons) fall into this class.663,685... 

Torus Structure formed by the translation of a circle through space along a path defined by a second circle whose plane is orthogonal to that of the first circle. 

Here, the topological nature of the tori will be discussed briefly. Figure 1 shows the five possible prototypes of toroidal forms that are considered to be related to fullerenes. These structures are classified by the ratios of the inner and outer diameters r, and r, and the height of the torus, h. (Note that is larger than / ,) As depicted in Fig. 1, if r, = r, and h r, and h = — r,) then the toroidal forms are of type... 

Fig. 2. Optimized toroidal structures of Dunlap s tori (a) torus C540 and (b) torus 05, pentagons and heptagons are shaded.

The relaxed structures of the various (rotational) symmetric toroidal forms were obtained by steepest decent molecular-dynamics simulations[15]. For the elongated tori derived from torus C240, the seven-fold rotational symmetry is found to be the most stable. Either five-fold or six-fold rotational symmetry is the most stable for the toroidal forms derived from tori Cjyo and C540, respectively (see Fig. 5). 

Fig. 4. Optimized toroidal structures (a) torus and (b) torus C24o Pentagons and heptagons are shaded. The diameters of the tube of the stable torus determined by optimization using molecular dynamics with Stillinger-Weber poiemial[211, is 8.8 A. The diameter of the hole is 7.8 A, which is quite close to the diameter of fullerence Qy.

Elongated tori. The experiments, at the present time, suggest that the torus of type (D) with parallel fringes at a separation of 3.7 A, such as C240, is likely to exist. Thus, the type (C) structures having height of 3.7 A could exist. See Fig. 6. 

Fig. 8. Optimized shallow toroidal structures the subscripts indicate the number of the carbon atoms in the torus pentagons and heptagons are shaded.

The properties of optimized helical structures, which were derived from torus C54D and Cs7a, >yps (A), (proposed by Dunlap) and torus C ,o> Dpe (B), (proposed by us) by molecular dynamics were compared. (see Figs. 9 (a) and 10). (Although the torus Cs7f, is thermodynamically stable, helix 57 was found to be thermodynamically unstable 14]. Hereafter, we use helix C to denote a helix consisting of one torus (C ) in one pitch. 

From elongated tori, such as type (C), type (D), and type (E), helical structures are derived. For example, from the type (C) elongated torus of mentioned in 3.2.2, helix C756 (/t = 6, /t2 = 3, L = 1) and... 

As seen in the previous section, if two identical knees of the (L,0)-(L, L ) family are connected together symmetrically with respect to a connecting plane, and if this connecting process is continued while maintaining the knees in a common plane, the structure obtained will close to a torus which will be completed after 10 fractional turns (Figs 7 and 9), However, if a rotational bond shift is introduced... 

MKI The Mark I containment consists of two separate structures (volumes) connected by a series of l.irae pipes One volume, the dry well, houses the reactor vessel and primary system components. The other i oUmic is a torus, called the wetwell, containing a large amount of water used for pressure suppression and as, i heai sink. The Brunswick units use a reinforced concrete structure with a steel liner. All other M,uk 1 cnni.un ments are free-standing steel structures, The Mark I containments are inerted during plant oper.mon i. prevent hydrogen combustion. 

The pneumatic tire has the geometry of a thin-wallcd toroidal shell. It consists of as many as fifty different materials, including natural rubber and a variety ot synthetic elastomers, plus carbon black of various types, tire cord, bead wire, and many chemical compounding ingredients, such as sulfur and zinc oxide. These constituent materials are combined in different proportions to form the key components of the composite tire structure. The compliant tread of a passenger car tire, for example, provides road grip the sidewall protects the internal cords from curb abrasion in turn, the cords, prestressed by inflation pressure, reinforce the rubber matrix and carry the majority of applied loads finally, the two circumferential bundles of bead wire anchor the pressnrized torus securely to the rim of the wheel. 

FIGURE 16.44 The structure of a molecular magnet. The nano-size molecular torus contains 84 manganese atoms and is approximately 4 nm in diameter. The manganese atoms are bonded to groups of carbon atoms in the form of acetate ions, water molecules, and chlorine atoms. In this molecule the manganese atoms act as terromagnets. 

SCHEME 9.6 A macrocyclic oligosaccharide cyclodextrin forming a torus-shaped structure of cyclodextrin with rigid lipophilic cavities. (Adapted from Polyakov, N.E., Free Rad. Biol. Med., 36, 872, 2004. With permission.)... 

Examination of flame-etched surfaces revealed only scattered torus-shaped ring and moat structures, 100-200m in diameter. These features probably result from differential resistance of anthraxolite and rare impurities to oxidation. 

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