Toroidal network

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... 

Key Words—Carbon nanotubes, vapor-grown carbon fibers, high-resolution transmission electron microscope, graphite structure, nanotube growth mechanism, toroidal network. 

HEMI-TOROIDAL NETWORKS IN PYROLYTIC CARBON NANOTUBES... 

Hemi-toroidal networks in pyrolytic carbon nanotubes... 

In this way the adjacency of such a toroidal network can conveniently be represented as a planar rectangular polycyclic structure with opposite sides marked as being identical, i.e., in a labeling, the set of vertices along one side is the same, and in the same sequence, as those of the opposite side (or of a cyclic permutation of them). For toroidal polyhexes this is equivalent to the diagrammatic approach discussed elsewhere. Klein ° uses the Xtxmparity in discussing which identifications are possible. 

Figure 15. Two topologically in-equivaleni embeddings for the construction of graphically equivalent toroidal networks.

Forster S, Hermsdorf N, Leube W, Schnablegger H, Regenbrecht M, Akari S (1999) Fusion of charged block copolymer micelles into toroid networks. J Phys Chem B 103 6657-6668... 

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

Although toroids are the most common morphology in DNA condensation, different manipulations can produce various morphologies, including rods, spherical globules and fibrous networks (Bloomfield, 1998 ... 

Kohonen networks can be arranged in toroidal shape that is, both ends of each plane are connected to each other so that the complete map forms a torns. Conse-qnently, each neuron has the same number of neighbors, and a central nenron at the edge of the plane influences neurons at the other end of plane (Fignre 4.14). 

Once class or properties are available in the training set, the training parameters can be selected net dimension and number of epochs, the learn radius and learn rate, and the initialization parameters. Neurons can be arranged in a rectangular or quadratic network, as well as in a toroidal mode that is, the left and right side as well as the upper and lower sides of the topological map are connected to a closed toroidal plane. 

Another striking experimental feature is that the attractions do not appear to lead to macroscopic phase separation. In this sense, the counterion-mediated attraction between the chains appears to have a different character from ordinary attractions that lead simply to phase separation at sufficiently high concentrations. Instead, the chains tend to form dense bundles of a fairly well-defined thickness [8,11]. The precise morphology of the bundles appears to depend sensitively on the persistence length of the polyelectrolyte, the chain length, and the concentration. In the case of dilute DNA, the bundles tend to be toroidal or rod-shaped. Other stiff polyelectrolytes tend to form rodlike bundles or networks of bundles. In each case, however, there is a well-defined cross-sectional thickness for the bundles. We will concentrate on the question of why there is a characteristic cross-sectional bundle diameter, rather than on the specific morphology of the bundles. 

For more specific cases where the surface network has a simple uniform pattern of rings, we specify the surface type and refer, for example, to a toroidal polyhex (also called a toroidal hexagonal system by John and Walther ) or a toroidal azulenoid, and so on. Others " -prefer to speak more generally of torusenes or toroidal forms of carbon or of graphitic carbon or graphite. 

The closed but boundless network of hexagons embedded as an all-hexagon toroidal polyhex can be represented by an infinite planar lattice, on which the set of hexagons forms a parallelogram which repeats itself endlessly in two dimensions (i.e., it is doubly periodic). Figure 14 shows an example of a torus with nine hexagons (A-I). 

The most widely used coaxial line is a standard APC 7 corresponding to toroidal samples of external diameter 7 mm. This geometry permits measurements from 100 KHz to 18 GHz on small samples, depending on the type of network analyser which is used. The problem is the measurement of heterogeneous materials [115,116] (for example short-fibre loaded materials), or anisotropic materials (for example, when fibres are oriented in one direction of the plane, such as magnetic... 

---