Geometric model entities

A shape object is described as a form feature entity. It is related to geometric model entities in its representation. 

Figure 8-17 shows types of coincidence relationships between real and reference geometric model entities. They are concentricity (Figure 8-17a), point-on-line (Figure 8-17b), coaxiality (Figures 8-16a, 8-17c), and coplanarity (Figure 8-17d). Points coincide as centers of spheres SPj and SP2 in the case of two concentric spheres. The center of sphere SP lies on the line Lj. Ring shaped parts Rj and R2 have the same axis. Surface PI2 lies in the plane of Plj.

Wire frames with unified topology and geometry use the same entities as solid models but without face and surface definitions. Note that these wire frames are not the same representations as the wire frames in the early era of geometric modeling. When a wireframe model defines a shape unambiguously, a surface or solid model can be replaced by the simple wire frame for economical modeling. If necessary, a verified wire frame can be completed into a surface or solid. 

Material properties are examples of properties which may be assigned to CAD geometric models. In order to allow geometric models to be defined independently from the relevant material properties in various application areas, the property is material of is not included in the geometric entity, but is implemented as a property associated to geometric entities. 

Linear transformations may be applied to all entities which represent geometrical models and elementary geometric information ... 

ENTITY GEOMETRIC MODEL = CLASS( WIREFRAME MODEL(DIM),... 

The GEOMETRIC MODEL is a class representing entities according to the geometric modeling techniques WIREFRAME MODEL (two-dimensional and three-dimensional) SURFACE MODEL, and SOLID MODEL. 

On the other hand, hi- or multi-metallic supported systems have been attracting considerable interest in research into heterogeneous catalysis as a possible way to modulate the catalytic properties of the individual monometalUc counterparts [12, 13]. These catalysts usually show new catalytic properties that are ascribed to geometric and/or electronic effects between the metalUc components. Of special interest is the preparation of supported bimetallic catalysts using metal carbonyls as precursors, since the milder conditions used, when compared with conventional methods, can render catalysts with homogeneous bimetallic entities of a size and composition not usually achieved when conventional salts are employed as precursors. The use of these catalysts as models can lead to elucidation of the relationships between the structure and catalytic behavior of bimetalUc catalysts. 

Geometric and electronic properties are obviously mutually interdependent. These also influence, and are influenced by, the interaction of chemical entities with their environment (e.g., solvent). A number of molecular properties which are accessible by experiment result from, or are markedly influenced by, interactions with the environment (e.g., solvation, ionisation, partitioning, reactivity). For these reasons, the concept of chemical structure must be extended to include interaction with the environment. Table 1 summarizes the above discussion and may help broaden the intuitive grasp of the concept of chemical structure. Table 1 is also useful in that it allows a delineation of the matters to be discussed in this chapter. As indicated by the title, we will consider molecules at the geometric levels of modellization, either as rigid (configurational aspects) or as flexible geometric objects (conformational aspects). Broader conceptual levels (electronic features, interaction with the environment) lie outside the scope of this chapter and will be considered only occasionally. 

In the third simulation example, we carried out an analysis of some of the aspects that characterize the case of the mass transfer of species through a membrane which is composed of two layers (the separative and the support layers) with the same thickness but with different diffusion coefficients of each entity or species. To answer this new problem the early model has been modified as follows (i) the term corresponding to the source has been eliminated (u) different conditions for bottom and top surfaces have been used for example, at the bottom surface, the dimensionless concentration of species is considered to present a unitary value while it is zero at the top surface (iii) a new initial condition is used in accordance with this case of mass transport through a two-layer membrane (iv) the values of the four thermal diffusion coefficients from the original model are replaced by the mass diffusion coefficients of each entity for both membrane layers (v) the model is extended in order to respond correctly to the high value of the geometric parameter 1/L. 

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