Fragment concepts

The isolobal fragment concept can be extended to include charged species, ligands other than CO, and organometallic fragments not based on octahedral geometries. Some ways of extending the isolobal parallels are summarized as follows ... 

The concept of concentric environment has been introduced by Dubois in the DARC system as an alternative to the traditional fragment concept. The radius of perception was two, i.e., the first and the second neighbours of the atom in question were taken into account. Features used for characterisation were the type of the atom, the type of its bonds and the number of neighbours. To limit the number of fragments only the environment of tertiary and quaternary atoms have been used for structure descriptions in the DARC system. 

This basic LFER approach has later been extended to the more general concept of fragmentation. Molecules are dissected into substructures and each substructure is seen to contribute a constant inaement to the free-energy based property. The promise of strict linearity does not hold true in most cases, so corrections have to be applied in the majority of methods based on a fragmentation approach. Correction terms are often related to long range interactions such as resonance or steric effects. 

However, one of the most successfiil approaches to systematically encoding substructures for NMR spectrum prediction was introduced quite some time ago by Bremser [9]. He used the so-called HOSE (Hierarchical Organization of Spherical Environments) code to describe structures. As mentioned above, the chemical shift value of a carbon atom is basically influenced by the chemical environment of the atom. The HOSE code describes the environment of an atom in several virtual spheres - see Figure 10.2-1. It uses spherical layers (or levels) around the atom to define the chemical environment. The first layer is defined by all the atoms that are one bond away from the central atom, the second layer includes the atoms within the two-bond distance, and so on. This idea can be described as an atom center fragment (ACF) concept, which has been addressed by several other authors in different approaches [19-21]. 

An acceptable reconciliation of inherent flaw and fracture energy concepts has not been achieved and provides an area of current study. The two theoretical concepts will be discussed, and several applications in fragment-size prediction will be described. We will make comparisons between the two fragmentation approaches and attempt to identify some conditions which determine when one or the other method applies. 

Comparison of Inherent Flaws and Energy Concepts in Dynamic Fragmentation... 

A reasonable estimate of the number of flaws needed to sustain an equilibrium value of A can be made based on the concepts introduced earlier in this section. To achieve a nominal fragment size of d, the number of activated flaws per unit volume should be of order d From the equilibrium... 

Up to this point we have addressed primarily the flaw structure and energy concepts in stress-wave loaded solids governing the creation of new fracture surface area (or the mean fragment size) in catastrophic fragmentation events. It remains to consider a concept which is frequently the end concern in impulsive fracture applications, namely, the distribution in sizes of the particles produced in the dynamic fragmentation event. 

Theoretical efforts a step beyond simply fitting standard statistical curves to fragment size distribution data have involved applications of geometric statistical concepts, i.e., the random partitioning of lines, areas, or volumes into the most probable distribution of sizes. The one-dimensional problem is reasonably straightforward and has been discussed by numerous authors... 

Although progress in continuum and computer modeling of dynamic fracture and fragmentation is encouraging, it is apparent that further advancements are needed. Many of the emerging physical and statistical concepts, some of which have been discussed in the present chapter, are not yet included in these... 

Finally the concepts of fragment size, and fracture number or frequency statistics, need to be included within the framework of continuum and computational modeling of dynamic fracture and fragmentation. This challenging area of research has the potential for addressing many needs related to dynamic fragmentation. 

The general maintenance system is fragmented and can be classified into many maintenance concepts. The following are five P s of maintenance for major power plants, petro-chemical corporations, and other process type industries leading to the ultimate maintenance system ... 

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