Cubic geometrical model

P. J. Geometric modeling of the human torso using cubic Hermite elements. Annals of Biomedical Engineering 1997, 25 96— 111. 

The use of other geometrical models for the analytical treatment of the relation Y = f(5, d) does not markedly affect the form of Eqs. (20) and (22) but only alters the value of the factor in the numerator of Eq. (22) For the spherical model discussed above, this factor is tc = 3.14. For other models it may vary from 3.0 to 3.3. In contrast to the spherical model, other models involve greater discrepancies between the experimental and theoretical results. For example, when using a cubic model for PSB plastic foam having a volumetric weight of 90 + 0.5 kg/m, the discrepancy is 18% as compared with 9% in a spherical model. 

Such calculations, however, are based on crude geometrical models, and, so, cannot be considered to be rigorous. In fact, up to 88% of the positions of a primitive cubic lattice can be occupied, according to computer simulations, without the occurrence of ideal or perturbed chain bundles. So, space-filling problems do not hinder the dense packing of coiled molecules. 

A simple geometrical model consisting of spherical particles with a diameter a, arranged as a simple cubic pattern, as shown in Fig. 5.26a, is used to derive the sintering equations for the mechanism of grain boundary diffusion [70]. It is... 

Modeling Accuracy and Volumetric Properties The principal task addressed in this article is the shape fitting accuracy and the volumetric properties of the geometric models generated with the cubic interpolating curves and the bicubic surface patches with tension control. 

The geometric relaxation described in Section 12.3.1 occurs by redistributing the bond valence between the bonds until GII and BSI both have acceptable values, but in some cases this relaxation is restricted by symmetry. In the case of per-ovskite, the cubic symmetry of the archetypal ABO3 structure (Fig. 10.4) does not allow any of the bonds to relax unless the symmetry is lowered. Thus true cubic perovskites are rare since they can only exist if the A and B ions are exactly the right size. Most perovskites have a reduced symmetry that allows the bonds to relax. For compounds in which the A-O bonds are stretched, the relaxation takes the form of a rotation of the BOg octahedra and results in a reduction of the coordination number of A. The various relaxed structures based on different expected coordination numbers were modelled in Section 11.2.2.4. 

The first structural investigations of Prussian blue analogs date back to 1936 when Keggin and Miles (2) studied the X-ray powder patterns of iron cyanides. They found a luiit cell of the face-centered type and deduced a structural model from these geometrical data. This description, which will be briefly outlined below, has until recently been accepted by many authors (3, 39—44) for the discussion of the structural properties of cubic polynuclear cyanides Mfc[M (CN)e]i cHgO. In many cases the physically equivalent description has been used 3, 42,... 

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