Toroidal structure

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. 

Fig. 8. The lip of PCNTs with continuous hollow core (a) and the cone-like shape (b) (T indicates the toroidal structure shown in detail in Fig. 11).

In Fig. 1 lb are depicted sets of molecular graphics images of flattened toroidal structures which are... 

Fig. 11. The sealed lip of a PCNT heat treated at 2800°C with a toroidal structure (T) and, (b) molecular graphics images of archetypal flattened toroidal model at different orientations and the corresponding simulated TEM images.

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

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.

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

We showed the possible existence of various forms of helically coiled and toroidal structures based on energetic and thermodynamic stability considerations. Though the formation process of these structures is not the subject of this work, the variety of patterns in the outer and inner surface of the structures indicates that there exist many different forms of stable cage carbon structures[10-19]. The molecules in a onedimensional chain, or a two-dimensional plane, or a three-dimensional supermolecule are possible extended structures of tori with rich applications. 

During the course of the study on the simplest archetypal twin-walled structures in PCNT material described here, the observation of lijima et al.[5 on related multi-walled hemi-toroidal structures in ACNTs appeared. It will be most interesting to probe the differences in the formation process involved. 

There are two levels of self-assembly in the formation of tetra-, penta-and hexa-nuclear products from the poly-bipyridyls (L) 20 and 21 and iron(II) salts FeCl2, FeBr2 or FeS04 - the products are anion-dependent. The coordination of three bpy units, from different ligand molecules, to the Fe2+ centers produces a helical structure interaction of these helical strands with anions results in further molecular organization to form the final toroidal product. The discussion draws parallels between the helical and toroidal structures here and secondary and tertiary structure in biological systems (482). Thermodynamic and kinetic intermediates have been characterized in the self-assembly of a di-iron triple stranded helicate with bis(2,2/-bipyridyl) ligands (483). 

Kajava, a. V. What curves alpha-solenoids Fvidence for an alpha-helical toroid structure of Rpnl and Rpn2 proteins of the 26 S proteasome. J Biol Chem 2002, 277, 49791-8. 

Figure 6 displays the Poincare maps for all experiments. Note that even the projections in canonical planes (see Figure 5) seem ordered in layers. That is, a toroidal structure can be seen form the Poincare surface. That is, small amplitude oscillations were detected in time series (see Figures 3 and 4) for all experiments. The t3rpical behavior of aperiodic (possibly chaotic) oscillations can be confirmed is one takes a look at the corresponding Poincare section... 

The weakly immunogenic protamine sulfate USP (1) condenses DNA to form a toroid structure of super-coiled DNA about 50 nm in diameter (2). The DNA in this form or in the preformed LPDI complex cannot be displaced from the protamine by polycations such as spermidine and histones or by other nucleic acids like genomic DNA (2). DNA in this toroid structure is transcriptionally inactive and this conformation allows for protection of DNA from enzymatic degradation by nucleases and other environmental assaults such as mechanical stress (1,2). After the liposome surrounds the toroid, the resulting homogenous LPDI nanoparticles are slightly less than... 

The detailed structure of the radioactive cloud after stabilization has occurred (within 10 minutes) has not been studied extensively. Figure 2 shows some relative radiation intensity data obtained by rockets following the Zuni explosion (3.5-megatons, coral island surface). The data pertain to the situation 15 minutes after the explosion. The evidences of a toroidal structure are still marked. Note that the bulk of the radioactivity is in the core of the cloud and that the distribution, either horizontally or vertically, is far from uniform. The aircraft samples on Zuni were collected at 41 kft., well below the core of concentration as found at 15 minutes. Since only the lower fringes of the nuclear cloud were penetrated, analyses probably do not represent fairly the nuclear cloud as it existed at the time of sampling. 

The toroidal structure of PCNA has distinct front and back faces that might provide a variety of sites for interaction with other proteins. The loop region between the twin domains of each monomer is a highly immunogenic exposed site that is important for interaction with other proteins. Such functional protein partners are thought to be crucial in regulating the role of PCNA in replication and repair. The aforementioned symmetry could define the directionality of PCNA movement as it slides along DNA. 

Rotaxanes may appear to have no equivalents in biology but some of the most important proteins possess the same structural motif. For example, exo- and endonucleases have a toroidal structure through which DNA passes in a sequential manner and can also be considered as rotaxanes, or at least pseudorotaxanes. 

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