Topological characterization

Techniques that have been used to measure the prepreg surface roughness were mentioned in Section 7.2.1 and include direct measurement with a micrometer and photo-micrographs of the prepreg cross section. Li and Loos [22,23] showed that a surface topology characterization machine (Talysurf 4) can be used to measure the waviness or roughness of the resin rich... 

On the other hand, we should mention that, at the level of classical mechanics, periodic-orbit analysis provides a topological characterization of the system in terms of a symbolic dynamics, which appears as a common feature for a given class of systems. 

The basic assumption of our treatment is that polymer structures are topologically characterized by rod-like segments that are packed together to form representative domains. The concept allows us to generate structures of very different shapes with the aid of a unique formalism. The utility of this approach will be discussed with representative examples. 

Table 12.3 Topological characterization of C3v C60H18 Fullerene derivatives. Sites with same bim belong to the same topologically class S with multiplicity l. In CW)H x(tt) the six hydrogen atoms... 

Table 12.5 CmII.)ri(T) fullerane topological characterization. W = 24738 M = 11 B = 126 by summing vertex connectivity bn we get B value twice. Sites with same bjm belong to a topologically equivalent class with multiplicity l. NMR theoretical spectrum then has five equally intense 13C-NMR experimental lines and three equally intense II-NMR peaks as experimentally reported (graph shows distribution of equivalent sites)...

Table 12.10 C60H36 fullerane topological characterization for each isomer topological invariants W, p and NMR theoretical spectrum are given, being l multiplicity of resonance lines. Highly symmetric Th molecule, in bold, has low W, p values...

Morona, R., van den Bosch, L., Manning, P. Molecular, genetic, and topological characterization of O-antigen chain length regulation in Shigella flexneri. J Bacteriol 177 (1995) 1059-1068. 

We call such a sequence a topological sequence of families of density domains or, since each family DDj(aj) represents a formal molecular body DD(aj) at the density level a=aj, a topological sequence of molecular bodies. Below we shall discuss several examples as illustrations of the DD approach. The techniques of actual topological characterization will be described in the following chapters. 

As an example, in Figure 5.13 a topological characterization of five stages in a folding process of a molecular backbone (represented by a space curve) is shown. 

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