Catastrophe set

Fig. 3.4. A two-dimensional cross-section of the structure diagram for an ABC system. The full lines, denoting the catastrophe set, partition nuclear configuration space into its structural regions. The structure associated with each region is indicated by a representative molecular graph. The two broken lines indicate two possible reaction mechanisms for changing the structure A-B-C into the structure B-C-A.

As discussed above and illustrated in Fig. 3.4, the partitioning of nuclear configuration space obtained as a result of the definition of molecular structure leads to the concept of a structure diagram. The space R is partitioned into a finite number of structural regions with their boundaries, as defined by the catastrophe set, denoting the configurations of unstable structures. This information constitutes a system s structure diagram, a... 

Some of the eigenvalues may equal zero. The set of parameters (like the intemuclear distance) at which det g =0 (corresponding to an eigenvalue equal to 0) is called the catastrophe set. Calculations have shown that when the two nuclei separate, the rope elongates and suddenly, at a certain intemuclear distance, it breaks down (this Thus, the catastrophe theory of Rend... 

B3LYP functional (p. 700) catastrophe set (p. 672) correlation hole (p. 697) critical (stationary) points (p. 669)... 

During the initial pressurization at launch, if the primary 0-ring experiences blow-by, there is only going to be so much blowing because it will seal in its seat. The joint is still going to seal and you are not going to have a catastrophic set of circumstances occur. 

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